High Power Fiber Lasers

High Power Fiber Lasers
High Power Fiber Lasers

High Power Fiber Lasers:A Review Michalis N.Zervas and Christophe A.Codemard

(Invited Paper)

Abstract—In this paper,we summarize the fundamental proper-ties and review the latest developments in high power?ber lasers. The review is focused primarily on the most common?ber laser con?gurations and the associated cladding pumping issues.Spe-cial attention is placed on pump combination techniques and the parameters that affect the brightness enhancement observed in single-mode and multimode high power?ber lasers.The review includes the major limitations imposed by?ber nonlinearities and other parasitic effects,such as optical damage,transverse modal in-stabilities and photodarkening.Finally,the paper summarizes the power evolution in continuous-wave and pulsed ytterbium-doped ?ber lasers and their impact on industrial applications.

Index Terms—Beam quality,brightness,cladding-pumping,?ber ampli?ers,?ber lasers,high power,holmium-doped,indus-trial lasers,material processing,modal instabilities,optical dam-age,optical?bers,optical?ber nonlinearities,optical pulses,pho-todarkening,pump combiners,thulium-doped,transverse mode instabilities,ytterbium-doped.

I.I NTRODUCTION

F IBER lasers[1],[2]were proposed and studied as a promis-

ing laser con?guration soon after the discovery and?rst laser demonstration by Maiman[3].Ever since lasers have played central role in the fast developing?eld of Photonics, which in turn has revolutionized existing,as well as,enabled entire new scienti?c and industrial sectors[4].

Lasers exploit the quantum effect of stimulated emission to generate light and share a number of common features,such as an active medium to provide gain,an optical cavity to enhance and control the optical?eld and a pumping source to provide the energy[5].However,the details of these features play an im-portant role in differentiating the laser performance,the power scaling capabilities,stability,footprint and cost.Different gas-?lled tubes,crystal rods and discs have been traditionally used as active media,incorporated in various bulk-optic cavities.Fiber lasers are the latest entry in the solid-state laser technology arena[6],fast increasing their penetration in all sectors of in-dustrial,medical and directed energy application space[7]. There are a number of features that differentiate?ber lasers from the other existing laser technologies and give them su-

Manuscript received January20,2014;revised March29,2014;accepted April23,2014.Date of publication April30,2014;date of current version June 2,2014.The work was partially supported by the EPSRC Center for Innovative Manufacturing in Photonics,University of Southampton.

M.N.Zervas is with the Optoelectronics Research Center,University of Southampton,Southampton,SO171BJ,U.K.,and also with SPI Lasers, Southampton,SO302QU,U.K.(e-mail:mnz@https://www.360docs.net/doc/907866321.html,).

C.A.Codemard is with SPI Lasers,Southampton,SO302QU,U.K.(e-mail: christophe.codemard@https://www.360docs.net/doc/907866321.html,).

Color versions of one or more of the?gures in this paper are available online at https://www.360docs.net/doc/907866321.html,.

Digital Object Identi?er10.1109/JSTQE.2014.2321279perior overall performance.Due to large surface-to-volume ra-tio,?ber lasers provide better thermal management and total elimination of thermal lensing,which plagues solid-state crys-tal counterparts.The well controlled spatial distribution of the signal,provided by the continuous guidance,results in supe-rior beam quality and stability,while small quantum defect, as well as,low cavity and transmission losses result in record wall-plug ef?ciencies.Also,?ber lasers show turn-key opera-tion and small foot print.Their unique properties,in particular the output power stability and unparalleled beam quality at high output powers,have increased their market penetration and have enabled a number of new applications[7].

The amorphous nature of glass host in the?ber core produces inhomogeneously broadened active-ion emission and absorp-tion spectra,which are wider than they would be in crystals[8], [9].This enables?ber lasers to be widely tuned and work ef-?ciently from continuous-wave(CW)operation to ultra-short optical pulses.They show high gain,which enables master-oscillator power ampli?er(MOPA)and cascaded ampli?er con-?gurations and makes them suitable for average power scaling. However,the small saturation energy,associated with the rel-atively small—compared to solid-state rod counterparts—?ber core diameter compromises the energy storage capabilities and high energy operation.

Over the last decade,the performance advances in?ber lasers have been spectacular making?ber lasers a success-ful,fast increasing commercial business currently worth over $800M/year,with compound annual growth rate of about 13%—the highest among the different laser technologies[7]. Key for the power scaling of high power?ber(YDF)lasers are the developments in major technologies,such as high-quality passive and active?bers,high-power passive?ber components, including,beam combiners,?ber Bragg gratings(FBG),isola-tors,cladding mode strippers and end caps,and bright diode laser pump modules.

The expansion of the high-power?ber laser?eld has been already captured in a number of excellent reviews and book monographs available in the literature[6],[10]–[14].The fast observed pace though warrants frequent reviews of the latest de-velopments.This paper summarizes the fundamental properties and reviews the latest developments in high power?ber lasers, which so far have been the most commercially successful.The review is focused primarily on the most commonly used?ber laser con?gurations and the issues related to cladding pumping, the preferred technique for power scaling.Special attention is given on pump combination techniques and the parameters that affect the brightness enhancement observed in high power?ber lasers.The review also includes the major limitations imposed by?ber nonlinearities and other parasitic effects,such as opti-cal damage and photodarkening and gives a brief account of

1077-260X?2014IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.

See https://www.360docs.net/doc/907866321.html,/publications standards/publications/rights/index.html for more information.

Fig.1.Cladding-pumped?ber laser con?gurations(a)hybrid end-pumped (b)all-?ber end-pumped and(c)all?ber intra-pumped.

transverse mode instabilities(TMI).The paper summarizes the power evolution in continuous-wave and pulsed ytterbium-doped?ber lasers and their impact on material processing and other industrial applications.It concludes with the future prospects in the?eld of high power?ber lasers.

II.F UNDAMENTALS

A.Fiber Laser Cavity Con?gurations

The gain in?ber lasers is provided by?bers of various types with cores doped with active rare-earth ions,such as ytterbium, erbium,thulium,or holmium.Typically the cavity is formed either by bulk mirrors placed on either?ber end,or FBGs[15] written directly into the?ber core[16].The pumping is achieved by combining laser diodes(single emitters,bars or stacks)and launching either in the core or cladding of the?ber.

1)Most Common Fiber Laser Con?gurations:A number of different con?gurations have been used for?ber laser demon-strations,depending on the active?ber and availability in pump-ing technology.

The most commonly used?ber laser con?gurations are shown in Fig.1(a)–(c).Fig.1(a)shows a hybrid end-pumped arrange-ment with the active?ber placed inside an optical cavity formed by two bulk mirrors,a high re?ector(HR)with R>99%and a lower re?ectivity output coupler.The pump is launched through the?ber ends with appropriately placed dichroic mirrors(DM) that transmit the signal and re?ect the pump wavelengths or vice versa.

Fig.1(b)shows an all-?ber end-pumped con?guration,where the bulk-optic mirrors are replaced by intra-core FBGs and the combined pumps are launched through the FBGs.This con?g-uration puts extra stress on the FBGs as they are subjected to strong pump and signal powers and special care should be taken to protect them.Finally,Fig.1(c)shows an all-?ber

con?gura-Fig.2.Schematic of cladding pumping principle of operation.

tion with intra-cavity pump launching,which alleviates some of these issues.

High power hybrid?ber laser con?gurations require careful bulk-optic mirror alignment and special?ber-end facet prepa-ration[17],[18]to avoid unwanted backre?ections,as well as, avoid surface damage.Such con?gurations are primarily more suitable for high power lab demonstrations[19]–[21]or low average power laser systems.However,the overall robustness of the laser can be improved if mirrors are butt-coupled or di-rectly deposited onto the?ber facet[22].Such approaches are more suitable for multimode(MM)operation.All?ber con?g-urations,on the other hand,are preferable if all the bene?ts of the?ber technology are to be harnessed,and such systems are suitable for service-free,reliable industrial systems[23]–[30]. FBGs are usually written in single-mode(SM)?bers,which in addition to wavelength can also determine the output beam modality.

B.Cladding Pumping

In his seminal paper[1]E.Snitzer states that“the major dis-advantage(of the?ber laser)is that of getting the pump power into the?ber.However,it should be possible to overcome this dif?culty with proper design of the?ber and the illuminating optics.”Subsequently in1988E.Snitzer proposes an elegant so-lution to this problem in the form of cladding pumping[31],[32] which has proven to be the most powerful enabling technique for power scaling?ber lasers.

In cladding pumping schemes(see Fig.2),instead of launch-ing into the highly restrictive—in terms of size and numerical aperture(NA)—active core,high-power low-brightness pump light is launched into the much larger,in size and numerical aperture,cladding.As the pump light rays propagate down the highly multimoded?ber cladding they cross and get absorbed gradually by the active core.However,the generated light is ef?-ciently trapped inside the much smaller size and lower NA core, and as a result the cladding-pumped ampli?er or laser output is much brighter and intense.In this respect,cladding-pumped ?ber lasers are extremely ef?cient brightness converters(see Appendix A for de?nitions).

From the de?nition of brightness(see Appendix A),the max-imum pump power that can be launched into a circular?ber cladding is given by

P in p=B p

πr2cl

πNA2cl

=

1

2

B pλ2p N p.(1) The launched power is proportional to the brightness of the pump source(B p),the square of the cladding radius(r cl),

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW

0904123

Fig.3.Modal space for multimode step-index ?bers.Region I (II)shows the group of modes overlapping (non-overlapping)with the doped core.

and numerical aperture (NA cl ).Alternatively,the maximum launched pump power is proportional to the number of supported pump modes N p =V 2

cl 2,where V cl is the cladding V-number.Therefore,power scaling in ?ber lasers relies on the develop-ment of high brightness pump modules (see Section B.3)),and ?bers with high cladding NA and large cladding area.However,the launched pump power cannot be increased inde?nitely due to limitations imposed by the practically achievable NA,the onset of nonlinear effects and optical damage (see Section III).The overall cladding-pumped ?ber laser and ampli?er length depends on the pump absorption coef?cient (αC P ),which scales as αC P =ηS αco (A co /A cl ),where αco is the small-signal

pump absorption when launched into the core,and A co =πr 2

co is the doped core area.ηS is a coef?cient,which de?nes the ef-fectiveness of modal absorption of the various mode scrambling techniques.ηS =1implies that all cladding modes are excited equally,overlap equally with the doped core and are absorbed uniformly.This can only be achieved by a cladding shape that fully scrambles the propagating modes [33].In the case of a straight circular ?ber with centered core,this assumption ap-plies to all LP 0n modes,which correspond to meridional rays,and only to a small fraction of the LP m n (m 0)modes,cor-responding to skew rays.The majority of the LP m n (m =0)modes miss the doped core entirely.For a straight ?ber with circular cladding the fraction of modes,which overlap with the doped core and are effectively absorbed,is approximated by ηS ≈(πr co )/(2r cl )[34].

Fig.3shows the power overlap with the doped core in the cladding modal space,in the case of a ?ber with r co =3μm,r cl =65μm,and NA cl =0.46.It is shown that the majority of the overlapping modes (region I)have ~10%of their power within the doped core,independently of their order.The steep transition between regions I and II is de?ned by the higher order modes whose internal caustic coincides with the active core perimeter [34].

In order to improve the overall pump absorption,a number of ?ber designs have been proposed which break the cladding’s rotational symmetry and increase the fraction of cladding modes overlap with the active core.Equivalently,we can consider

that

Fig.4.Cladding-pumped ?ber cross-sections.

these improved designs “scatter”skew rays towards the active core [35]–[42].

Fig.4shows a number of commonly used cladding-pumped ?ber cross-sections.The pump NA is de?ned by the choice of the outer cladding material.Typically,these ?bers use ?uorinated polymer outer cladding giving NAs of ~0.46.In this case,at high power operation special cooling arrangements are required to avoid excess heating of the polymer.Cooling requirements are relaxed considerably if low index ?uorosilicate glass is used as the inner cladding.Unfortunately,although such glass–glass in-terface has superior power and thermal handling capabilities,the obtained NAs with current technologies are rather low (~0.22–0.26),reducing the amount of pump power that can be launched.In this case,large diameter coiling is required to avoid excessive pump bend-induced loss.Also,compatibility with standard high power TFB fused combiners would also be compromised.

To overcome these problems,novel jacketed-air clad (JAC)?ber designs [Fig.4(d)]have been developed,which rely on a row of cylindrically arranged air holes to provide effectively a glass/air interface with NAs >0.8[43],[44].Such JAC ?bers can also be used to reduce the cladding diameters considerably,increase the pumping rate and enable ef?cient 3-level operation,e.g.,at 980nm [45].

The choice of the cladding perturbation should be consider judiciously in order to maximize mode scrambling,while avoid-ing excess scattering loss [46].It was found,for example,that for the same material compositions,the effective NA of rect-angular ?bers is smaller than that of circular ?bers and the pump light propagation loss in rectangular inner-cladding ?bers [Fig.4(c)]is larger [47].Boron-doped stress elements can be incorporated into the inner cladding to maintain polarization.In the case of cladding pumped hi-bi ?bers,the low refractive index of the borosilicate stress-applying elements ensures that pump light will not be trapped in these elements,and their presence along with the applied stresses scrambles helical modes/skew rays within the inner cladding [48],[49].From the various inner-cladding shapes,shown in Fig.4,the ones with multiple truncations,e.g.Fig.4(f)and (g),are shown to be more ef?cient in mode scrambling [38].

In most practical cases,breaking the cladding cross-section rotational symmetry alone is not enough to absorb effectively the launched pump power over the entire ?ber length and over all wavelengths.In order to increase the pump absorption close to its limiting value,given by the core over cladding area ratio,the modes should be continuously mixed over the entire length,

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER

2014

Fig.5.Effect of longitudinal mode mixing and wavelength on pump absorp-tion,in Yb 3+-doped alumina-silicate ?ber lasers [34].

which is achieved by properly perturbing the ?ber along its length [50],[51],using periodic/quasi-periodic ?ber bending [52],[53]or ?ber tapering [54].

Fig.5plots the increase in pump absorption of a cladding-pumped ?ber as a function of length for different wavelengths,with and without mode mixing.In this case the mode mixing is achieved by periodic ?ber bending.It is shown that in the case without mode mixing,the pump absorption at both wave-lengths is small and saturates quickly with ?ber length.In this

case,pumping at 976nm,the Yb 3+

absorption peak,offers no signi?cant advantage over 940nm.This results in an effective absorption spectrum deformation and can be observed irrespec-tive of the pumping scheme (discussed in Section II)[34].Mode mixing,increases the pump absorption considerably and restores to large extent the absorption (in dB)linearity with length.How-ever,at the 976nm absorption peak the absorption still saturates with length,demonstrating that wavelengths with higher absorp-tion require stronger mode mixing.Nonlinear pump absorption affects the signal evolution and overall ef?ciency in ?ber laser cavities [55].More importantly,though,for ?xed overall pump absorption it results in highly non-uniform heat generation along the ?ber length,with most of the heat generated over short length at the launching side.Cladding pumping has also been imple-mented for power scaling in planar waveguide lasers [56]–[58].1)Brightness Enhancement in Cladding-Pumped Lasers:It has already been mentioned that cladding pumping combined with high output beam quality,in addition to power scaling,provides extraordinary brightness enhancement.The brightness enhancement factor is given by

ηB =B out s B in p =ηoo λp λs 2V 2cl 2V 2co 2

≈η?oo N cl

N co (2)where B out s

and B in

p are the brightness of the output signal and input pump (see Appendix A),respectively.ηoo =P out s P in

p

is the optical-to-optical power conversion ef?ciency,where P out

s and P in

p are the output signal and input pump powers,respec-tively.N cl (N co )is the total number of cladding (core)modes (including degenerate spatial orientations and orthogonal po-larizations).The maximum brightness enhancement factor is simply proportional to the ratio of the cladding pump mode

to

Fig.6Brightness enhancement factor for different cladding radii and NAs and single-mode signal output (λp =945nm and ηo ?o =75%)

.

Fig.7.Main cladding-pumping schemes for (a)–(c)end-pumping,and (d)–(f)side-pumping.

signal core mode numbers.In the case of single mode core,N co =2.

Fig.6plots the brightness enhancement factor in single-mode,cladding-pumped ?ber lasers and ampli?ers as a function of the cladding radius for different cladding NAs and λp =945nm and optical-to-optical ef?ciency of 75%.For commonly used ?bers with cladding radius between 65and 250μm and NA larger than 0.4the expected brightness enhancement factor lies between 103and 104.

2)Cladding-Pumping Schemes:Over the years,a number of different cladding pumping schemes have been proposed in pursue for higher ?ber laser output power.These schemes can be broadly classi?ed into two main categories of end-pumping and side-pumping.Fig.7(a)–(c)shows schematically the main end-pumping techniques used to-date,while Fig.7(d)–(f)shows the most prevalent side-pumping techniques.

Fig.7(a)shows free-space geometric combination of pump modules [59],while Fig.7(b)shows a scheme based on TFBs [60],[61].The number of combined free space or ?ber-coupled pump modules depends on the cladding diameter and NA and is

restricted by the ′e

tendue conservation principle (see Appendix A).Fig.7(c)shows an end-pumping scheme where the pump modules are wavelength multiplexed,using a series of bulk-optic

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW

0904123

Fig.8.Pump combination modules for cladding pumping. wavelength-division-multiplexing(WDM)couplers[20].In ge-ometric combination schemes[see Fig.7(a)and(b)],the bright-ness of the combined pump module is usually lower than the brightness of the contributing pump modules.It is equal in the lossless case.In contrast,in wavelength-multiplexed schemes [see Fig.7(c)],since multiple aligned beams are superimposed, the brightness of the pumping module is actually increased.It should be mentioned that,in this case,the spectral brightness (see Appendix A)of the module is reduced.This though is not a major handicap given that most dopants in silica?bers show large absorption bandwidths.

In the aforementionedend-pumping schemes the signal beam is usually intertwined with the pump-combiner optics.In high power laser systems,the overlap of strong pump and signal beams increases the risk of bulk optics and?ber end-face fail-ures.In the case of the?ber tapered bundle,special care should be taken to minimize signal losses in the taper region.

Fig.7(d)shows a side-pumping scheme based on total internal re?ection taking place in a V-groove milled in the cladding[62]. Such an invasive approach,although employed in low pow-ers[63],it is very dif?cult to be scaled to the currently achieved kilowatt levels.Fig.7(e)shows a side-pumping scheme con-sisting of an angle-polished[64],[65]or tapered[66]pump ?ber attached to or fused into the cladding of the signal?ber. The angle-polished?ber approach pump scheme is found not only to launch light into the cladding but also to leak out,which leads to ef?ciency loss and compromises the laser integrity[67]. Fig.7(f)shows a side-pumping scheme based on a multi-?ber assembly in optical contact surrounded and held together by a common low-index polymer cladding,applied the usual way during the drawing(trade name GTWave)[68],[69].Remov-ing part of the polymer over-cladding frees the individual?ber members,which then can be accessed independently.Such?ber assembly provides multiple ports for pump power to be injected into the cladding and be absorbed by the core of the optically coupled signal?ber.A variant of this scheme uses multiple bare pump and signal?bers held together by an external heat-shrunk tube[70].In the side-pumping schemes,the signal path is kept separate from the pump injection paths.This simpli?es the op-tical design and enhances the overall laser robustness.Finally, the side-pumping scheme,based on evanescently-coupled?bers [Fig.7(f)],has the additional advantage of distributing the pump

power more uniformly along the?ber length,resulting in better

heat management[71].

3)Pump Combination Schemes for Cladding Pumping: High-brightness,high-power pumping modules are key com-

ponents for the development of robust,high-power?ber lasers.

Pump brightness is a commodity that should always be spared

and used wisely.Once it has been compromised,it cannot be re-

covered by passive means.Single broad-area emitters launched

into MM?bers(typically105/125μm,and0.22NA)reduce to ~1/100of their initial brightness.After fast axis collimation, this is primarily due to the large mismatch between the rect-

angular shape of the diode emitting aperture and the receiving

circular?ber.This mismatch is even more pronounced in the

case of diode bars.

In order to fully utilize the brightness of pump?bers,a num-

ber of different techniques have been developed to re-organize

and aggregate the outputs of high power single-diode emitters,

as well as,minimize the in-between“dead”space of diode bars

or stacks and turn them into high brightness modules suitable

for cladding-pumping high power?ber lasers.The pump com-

bination in most of the cases is achieved in two stages.It in-

volves a relatively low count combined single-emitter diodes,or

diode mini-bars(stage#1),feeding into a tapered multi-?ber

bundle(stage#2).These can then be used for either end-or

side-coupling into the active?ber cladding,using one of the

schemes presented in Fig.7.

The brightness of a combined multiple-pump module can

in some cases exceed the brightness of the individual pump

elements[72].This can be achieved if mutual coherence is es-

tablished across the pump lasers and the output of the entire

source behaves as a single spatial supermode.The resulting

brightness can in this case be equal to the sum of the individual

laser brightness.Another way to increase the brightness of the

combined module is to use pump lasers with different eigen-

properties,such as wavelength or polarization.Passive optical

elements such as diffraction gratings or polarizing beam split-

ters,respectively,can be used to multiplex several beams[72].

In the case of wavelength combination,the spectral brightness

is reduced and these modules can only be used with active ions

with broad absorption spectra,such as Yb3+around940nm.

High brightness laser pump sub-modules capable of cou-

pling over100W of optical power into a105μm,0.15NA

?ber at976nm have been demonstrated with NA<0.13and

an electrical to optical ef?ciency>40%[73].The pump sub-

module brightness is~0.21W/(μm2sr).Such sub-modules

have been spliced to a7:1fused?ber combiner,providing

500W coupled into a220μm,0.22NA?bers.The resulting

combined pump module brightness reduces to~0.086W/(μm2

sr).Commercially available pump modules using TFBs and ge-

ometrically combined single,large-area emitters can provide

140W in106.5μm,0.22NA?bers.The resulting brightness is

0.1W/(μm2sr)[74].Also,wavelength-beam-combined pump

modules,using diode stacks,have been demonstrated,which

provide200W at91Xnm in200μm/0.22NA?bers[75].

The resulting brightness is0.04W/(μm2sr),less than half to

what has been achieved with geometrically combined single

emitters.Seven such modules were then combined with a7:1

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER2014

tapered fused?ber bundle to provide~1.5kW pump power in 400μm diameter?ber.

Most of the measured pump insertion loss in combined mod-ules is due to the brightness loss across the tapered?ber com-biner.Therefore,designs closer to the brightness limit are con-siderably more sensitive to variations of the input power distri-bution as a function of NA[76]By proper design and optical loss minimization in both directions,TFBs with kW-level power handling capabilities are possible[75],[77],[78].A number of different pump modules,using different combination tech-niques,have been developed.The choice of diode type(e.g., single emitter or bar size)and optimum arrangement(i.e.,num-ber of emitters and input NA)is?nally in?uenced by the result-ing wall-plug ef?ciency,life-time,manufacturability and?nal cost.These considerations favour large area,single emitters and small-size diode bars.

In addition to MM TFBs,used extensively to combine MM pumps,there have been demonstrations of SM-to-MM TFBs.Up to three hundred0.12NA,9μm-core and125μm-clad single mode?bers can be combined into a single output multi-mode ?ber with0.15NA,105μm-core and125μm-clad diameter[79]. The SM-to-MM TFBs can be used to combine the outputs of high power SM?ber lasers into a scaled-up MM output beams for industrial applications.It can also be used to combine short wavelength,SM?ber lasers for cladding in-band(or tandem) pumping[80]of other?ber lasers.This is the prevalent pumping scheme in SM diffraction-limited?ber lasers with>3kW output power[30],[81],[82].

Finally,both MM TFBs and SM-to-MM TFBs have been used together to demonstrate multi-kW?ber laser outputs[83] First,single-emitter diodes are combined by91:1MM TFBs to produce900W pump modules,which are used to cladding-pump SM?ber lasers.Seven such SM?ber lasers were then combined with SM-to-MM combiners to produce>4kW MM output beam.The limit in power scaling of pump and/or signal fused TFBs will be ultimately set by the NA and power handling capabilities of coating materials.

C.Active Ion Spectroscopy and Pump Wavelength Selection A number of rare-earth dopants have been incorporated suc-cessfully into optical?bers,using modi?ed chemical vapor deposition(MCVD)process[84],to form lasers.They in-clude Nd3+[85],Er3+[86],Er3+/Yb3+[87],Yb3+[88], Tm3+[89],and Ho3+[90].From the extended range of dopants used in?ber lasers,we consider here only the Yb3+and Tm3+ ions,which so far have shown excellent power scaling with output powers exceeding1kW(see Fig.22).

Yb3+comprises a simple two-level system and provides ef?-cient lasing around the1μm window.Fig.9(a)shows a typical energy diagram of Yb3+ions in silica,with indicative sub-level Stark splitting.The exact sub-level splitting depends on the glass composition and Yb3+concentration[91],[92].Stark splitting enables three-or four-level-system operation,depending on the choice of pump and lasing wavelengths.Fig.9(b)plots typi-cal emission and absorption cross-sections in aluminosilicate and phosphosilicate?bers[93].The emission and absorption spectra details and level lifetimes depend on the host

mate-Fig.9.(a)Typical energy level diagram of Yb3+ions in silica,(b)typical emission and absorption cross-sections in aluminosilicate(thicker lines)and phosphosilicate(thinner lines)?bers(the arrow shows the peak emission and absorption for phosphosilicate

?bers).

Fig.10.(a)Typical energy level diagram of Tm3+ions(only lower levels are shown),and(b)typical emission and absorption cross-sections in alumi-nosilicate?bers[96].

rial[94].Although phosphosilicate glasses reduce considerably the emission and absorption cross-sections,they allow for much larger dopant concentrations,without signi?cant clustering ef-fects[95],and reduce or even eliminate photo-darkening effects (see Section III-D).The simplicity of the Yb3+energy-level structure also eliminates other ef?ciency reduction effects,such as excited-state absorption,multiphonon non-radiative decay and concentration quenching.

Yb3+shows a broadband absorption spectrum,extending from~850to~1080nm,enabling multi-pump or multi-wavelength pumping schemes,which in turn facilitate power scaling.The broadband absorption spectrum also enables the use of unstabilized and low cost pumps,simplifying the design and reducing the overall cost and long-term stability of high power?ber lasers.Interestingly,the small but?nite absorption in the1010–1020nm band enables in-band(or tandem)pump-ing with high brightness?ber lasers,which is key for the power scaling to multi-kW levels[26],[30].In addition,the broadband emission spectrum enables wide wavelength coverage and tun-ability,from980nm to about1100nm and short pulse(down to few10s of fs)ampli?cation.

The Tm3+ion,on the other hand,shows a much more complex energy-level structure.Fig.10(a)shows the lower en-ergy levels of a Tm3+ion.The diagram indicates the main

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW

0904123

Fig.11.Typical ef?ciency budget for Yb3+-doped?ber lasers.

ground-state absorption transitions and the most important, in the context of this review,lasing transition around2μm. Fig.10(b)shows typical Tm3+emission and absorption cross-sections in aluminosilicate?bers[96].The most technologically important absorption bands are the one around1600nm,which enables in-band pumping with high power Er3+-doped?ber lasers,and the790nm band,which can make ef?cient use of available powerful diode pumps through the cross-relaxation process[97].Cross-relaxation creates two excited Tm3+ions in the upper laser level for every absorbed pump photon and can potentially result in100%optical-to-optical ef?ciency.Cross-relaxation in Tm3+-doped?ber lasers pumped at790nm has resulted in record74%ef?ciency and provides the root for ef?-cient power scaling[97].

D.Fiber Laser Ef?ciency Budget

Emission and absorption cross-sections de?ne also to a large extent the ef?ciency of a laser system.Along with the?ber parameters,they de?ne the signal saturation energy and power extraction ef?ciency.The choice of pumping wavelength de?nes the fundamental heat dissipation limit through the quantum de-fect(pump/signal wavelength ratio),as well as,the absorption and total?ber length.Fig.11shows a typical power ef?ciency budget for Yb3+doped?ber lasers.In addition to the fun-damental loss due to the quantum defect,there are inevitable loss contributions from excess pump and signal losses and non-optimized cavity.These losses can be minimized by proper choice of core and cladding materials and proper cavity design (choice of optimum re?ector wavelength and strength). Losses due to the quantum defect depend on the choice of pumping and lasing wavelengths.In the case of in-band(or tandem)pumping,the quantum defect can be very small(~1%) and the optical-to-optical output ef?ciency can be increased considerably.However,if the conversion ef?ciency of the(?ber or disc)pump laser is taken into account,the overall ef?ciency drops again to the levels shown above.Nevertheless,in-band pumping is a powerful approach for effective heat management, and power scaling SM?ber lasers beyond3kW relies almost exclusively on

it.Fig.12.(a)Beam quality for different modes as a function of V number of step-index?ber,(b)M2of highest-order mode(dashed line),average M2 (assuming mode equipartition)(and measured M2for different V-number?ber lasers(experimental data taken from Ref.[103]).

E.Beam Quality

Laser beam quality can be de?ned in a number of different ways.The M2de?nition,based on the second moment of the beam intensity pro?le,is the most commonly used method[98],

[99].From a practical point of view,though,the“quality”of

a laser beam depends on the speci?c application for which the beam is intended for.The M2parameter denotes also how many times faster the beam diverges compared to a diffraction-limited Gaussian beam with the same waist diameter.Therefore,it can be de?ned as the ratio of the beam-parameter product(BPP B) of the beam in question divided by the BPP G of a diffraction-limited Gaussian beam,namely[99]:

M2=

BPP B

BPP G

=

ωBθB

ωGθG

=

π

λωBθB(3) whereωB andθB are the mode-?eld radius and far-?eld diver-gence of the beam.For Gaussian beams M2=1,while for any other practical beam M2>1.The beam quality of a?ber laser output can be tailored by proper?ber design.

Fig.12(a)shows the M2variation,calculated by the sec-ond moment of the corresponding mode intensity pro?le,as a

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER 2014

function of the normalized frequency (V number)of a step-index ?ber,for different modes.The M 2of the fundamental mode (FM)LP 01is shown to depart considerably from 1for V <1.5.This is due to the increased evanescent extension into the cladding and departure from the Gaussian pro?le.It fol-lows closely the LP 01mode-to-core radius ratio variation with V number,as approximated by Marcuse’s formula [100].The same behavior is observed for all modes as they approach cut-off and their ?eld extends deep into the cladding.The modes LP m 1,corresponding to skew rays or whispering gallery modes with high orbital momentum,show considerably lower M 2,which grows at a much slower rate compared to other LP m n modes of the family characterized by the same composite mode number p =2n +m [101].Within each p family,the LP 0n modes,which correspond to meridional rays or modes with no orbital momentum,show the highest and fastest growing M 2.This resembles the M 2behavior of elegant Laguerre–Gaussian (LG)modes,compared with the standard LG modes supported by cavities with cylindrical symmetry [102].In the case of real ?bers with complex refractive-index pro?les (RIPs)the mode intensity distributions differ from the corresponding mode distributions of the step-index ?ber and,therefore,show differ-ent values of M 2.

The M 2of an incoherent MM beam is given by the weighted average of the M 2of the participating modes [104].In this case,the centroid of the beam is stationary [105],[106].Using simple arguments applicable to MM ?bers [107],it can be shown that the M 2of the group of modes characterized by the composite mode number p is given by M 2p =πr co θout

p λ=πp /4,where θout

p

is the half-angle divergence of the mode in free space.The weighted-average of a MM beam can then be approximated by M 2

≈π(2p max +1)/12=π/12+V /3,where p m ax =2V/πand both polarizations are counted [108].The weighted-average is obtained when all supported modes are equally excited.For a given V number,the M 2of the highest-order mode group (p =p m ax )can be approximated by M 2

max

=V /2.Fig.12(b)plots the weighted average and the M 2

max of a step index ?ber,as a function of the V number.It also shows the measured M 2of the output of kW-level ?ber lasers as a function of the V-number of the active ?ber [103].In prac-tice,the number of modes and their relative power depends on the gain saturation level,their overlap with the active region and effective modal re?ectivities [109].For relatively low V numbers (V <8)the lower-order modes dominate and the M 2remains small.For higher V-number ?bers,though,the higher-order modes (HOMs)attain substantial power and the output beam quality approaches the equipartition value.From the relations derived above and Eqn.(A-2),it can be deduced that the brightness of a MM beam is inversely proportional to the core V number squared.A similar relation (∝1/D 2)has been predicted for MM VCSEL devices in the limit of large D [110].

A drastically different situation arises in the case of coherent MM beams in large-mode area (LMA)?bers.Even with large HOM content (e.g.,30%LP 11)the resulting M 2can be decep-tively low (M 2<1.1),depending on the relative phase between LP 01and HOMs.However,signi?cant changes in beam shape,

peak intensity,and pointing stability can occur by varying the relative phase of the constituent ?ber modes [106],[111].F .Fiber Types

High power ?ber lasers require the development of active and passive LMA ?bers,in order to reduce peak intensities and di-minish nonlinear effects.In most occasions these ?bers end up being multimoded,and they are operated in the SM or low-mode (LM)regime by introducing suf?cient HOM differential losses,without increasing signi?cantly the FM loss.This becomes in-creasingly challenging as the ?ber dimensions increase and the mode effective index differences decrease.Additionally,in the presence of unavoidable small external perturbations,such as ?ber drawing or packaging-induced microbending,small modal effective index differences enhance modal cross-coupling be-tween FM and HOMs.This results in ef?ciency and beam qual-ity deterioration.

1)Active Fibers:Modality in MM ?bers is generally con-trolled by properly matching the FM at the input [112],launch-ing through a mode-?eld adapter (MFA)[113],[114]and/or by properly bending of the ?ber [115].However,in the last case,care should be taken to avoid excessive bending,which exceeds the safe bend-induced stresses level.This level depends on the ?ber outer diameter.Depending on the core radius and NA in ac-tive ?bers,bending does not always reduce modality or improves output beam quality.This is due to induced mode coupling,modal deformation and modal gain competition [116],[117].Furthermore,in high-power lasers and ampli?ers short LMA active ?ber lengths and small cladding diameters are needed in order to maximize pump absorption and minimize length-dependent nonlinear effects.However,small cladding diameter and low-NA LMA ?bers have the disadvantage of being ex-tremely sensitive to external perturbations,which has adverse effects on ef?ciency and optical beam quality [112],[118].Another issue associated with low-NA,LMA active ?bers is related to the uniformity of the refractive index across the core area.Making low NA,highly doped Yb 3+?bers requires high phosphorous concentration to increase dopant solubility.This,in addition to increasing the core refractive index,results usually in refractive index central dips due to uncontrolled phosphorous evaporation in MCVD fabricated ?bers.Such refractive index feature can deteriorate the beam quality and power stability of LMA ?ber lasers.

An alternative method has been demonstrated,which places much less stringent requirements on the MCVD process.Solid rod has been fabricated,with small index step and quasi-uniform doping to form the core region of a LMA photonic crystal ?ber (PCF)laser,by repeated “stacking and drawing”[119]of Yb 3+-doped and undoped silica.The ensemble therefore can form an effective-index medium with V <1.3.The composite doped rod has been then stacked along with silica capillaries to form a PCF in the usual manner [120].Solid active ?bers with similar novel core structures composed of small doped cores to give a LMA structure with a low effective core NA and without a central dip have also been demonstrated [121],[122].In another approach,based on PCF technology,by adjusting the hole size and spacing of the air-holes around the LMA doped core,effectively single

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW0904123

mode operation has been achieved for core diameters up to

100μm[123].

LMA?bers have been demonstrated using solid-core PCF

technology utilizing the“modal sieve”effect[124].LMA oper-

ation has been extended even further with very large-mode-area

(VLMA)?ber designs using large-pitch PCFs(LPFs).These

?bers use claddings with hole-to-hole spacing of~10–30times

the operating wavelength.The aforementioned designs offer

different degrees of HOM leakage or delocalization into the

cladding[125],[126].Compared to LMA PCFs,LPFs relax con-

siderably the fabrication tolerances and have resulted in record

core diameters of135μm and mode?eld diameter(MFD)of ~130μm in passive operation.In order to avoid bend-induced MFD collapse,such rod-type?bers have to be kept straight dur-

ing operation.However,under high power operation thermally-

induced waveguide changes have been observed in Yb3+-doped

LPF,resulting in substantial fundamental MFD reduction and

increased modality[127].

An alternative LMA?ber design is based on the chirally-

coupled core(CCC)concept,which provides resonant?ltering

of HOMs and enables effective SM index-guiding.Single-mode

CCC?bers have been produced with core sizes exceeding stan-

dard50μm[128].Being resonant thought their length,CCC

LMA?bers require tight fabrication tolerances.

Finally,LMA MM active?bers can be operated effectively in

the SM regime by tailoring the dopant distribution inside the core

to provide gain and favor predominantly the FM[129].Fiber

lasers based on gain-guided,index antiguiding mechanism are

another interesting approach to achieving LMA operation and

power scaling[130].These waveguides,though,are fundamen-

tally leaky and additional measures should be taken to manage

the leaking power during high power operation.

2)Passive Fibers:LMA passive?bers play an important role in the construction of high performance,high power?ber lasers,particularly in delivering ef?ciently the generated power into the work-piece.In some applications,delivery?bers up to10–20m long are required.Optical power LMA delivery ?bers should be designed properly to avoid excessive spectral broadening and onset of temporal instabilities due to non-linear interactions,such as stimulated Raman scattering(SRS),stim-ulated Brillouin scattering(SBS),self-phase modulation(SPM) and four-wave mixing,as well as,beam quality degradation due to modal scrambling.

Standard step-index(SI)?bers with core diameters of ~30μm and effective areas~360μm2can be SM at a5cm bending radius with NA of~0.06,which is considered to be the lowest limit that can be achieved repeatedly and it is manufac-turable with current?ber fabrication techniques[131].When kept straight,SI?bers can maintain single mode operation for diameters below~15μm[12].

A number of different?ber designs have been proposed and

experimentally demonstrated,which extend the FM area well

beyond the SI capabilities.These?bers are fundamentally mul-

timoded but utilize different techniques to?lter out HOMs.An

early example is the W-type?ber,which uses a refractive-index

dip around the core to drive the second-order mode beyond cut-

off into leakage[132]or LMA segmented-cladding?bers,which

leak out HOMs[133].Recently more advanced

leakage-channel Fig.13.Nonlinearity enhancement factor as a function of ampli?er gain,for L0=15m and NA=0.1.

?bers(LCFs)have been demonstrated using a small number of

air holes inserted in the silica cladding,providing differential

loss for the HOMs.LCFs with core diameters in the range of

170μm have been demonstrated,with effective areas in excess

of10000μm2[134].In another approach,modal?ltering is

achieved by inserting small cores around the main MM core,

which are resonant to the HOMs.The HOMs are then leaking

out of the main core through evanescent coupling[135].

Lately,state-of-the-art hollow microstructured?bers have

been used for high peak power delivery.In such?bers optical

nonlinearities are contained effectively,since the vast majority

of the power(>99%)is guided in air.Hypocycloid core Kagome

lattice microstructured?bers have been used for delivering high

beam quality,high peak power500fs,1mJ pulses over10m

length,without beam quality degradation.The energy threshold

damage was found to be>10mJ,with output power density af-

ter focusing approaching TW/cm2.This opens up the possibility

of using such?bers for practical high peak power delivery[136].

III.N ONLINEAR AND O THER P ARASITIC E FFECTS

Most of the?ber nonlinearities areχ(3)based and are in-

tensity and?ber length dependent.Hence they become more

severe in pulsed,high peak power and CW kW-level oper-

ation.Despite the very small nonlinear coef?cient in silica

(n2=3.2×10?16cm2/W)),due to the high intensities and

lengths involved,the nonlinearity enhancement factor(NEF),

which compares the strength of the nonlinear interaction in

?bers with that of a focused beam in bulk glass(see Appendix

B)can take quite large values.

Fig.13plots the NEF,given by Eqn.(B.3),as a function

of ampli?er gain,for different V numbers.Forλ=1μm,a

?ber length L0=15m and NA=0.1,the obtained NEF is ~105.This actually makes optical?bers one of the highest nonlinearity media.It is shown that the NEF decreases with

gain.This is because the power distribution varies signi?cantly

along the length for higher gains.Also,NEF decreases with V

number,because in this case the FM effective radius increases.

For V>10,the NEF reduces by about one order of magnitude.

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER2014

From Eqn.(B.3)to(B.5),it can be shown that the NEF is

inversely proportional to wavelength,and therefore,moving to λ=2μm is expected to half the nonlinearity strength. Nonlinear effects are one of the most limiting factors in

scaling-up the power in?ber lasers.In general,they transfer

energy in unwanted spectral regions and can potentially desta-

bilize laser operation.They can be reduced signi?cantly by

special?ber designs and/or appropriate spectral?ltering.

A.Stimulated Brillouin and Stimulated Raman Scattering SBS and SRS are related to inelastic nonlinear processes and involve power interactions with acoustic and optical phonons, respectively[137].

1)Stimulated Raman Scattering:Under controlled condi-tions and special?ber designs,both effects can be either min-imized or used effectively to enhance wavelength coverage of available?ber laser output spectrum.In high peak power pulsed lasers,SRS can be minimized by employing short lengths of phosphosilicate?bers[138].Fibers with wavelength-selective transmission can suppress the Stokes wave of Raman scattering and result in length-independent nonlinearity threshold,which could be particularly advantageous for high power lasers and ?ber beam delivery in material processing applications[139], [140].Residual backre?ections at splices or?ber ends can de-crease considerably the SRS threshold[20].

SRS is in general a non-catastrophic effect,resulting in only

in power transfer to longer wavelengths.Such spectral broad-

ening can complicate the design of focusing optics and result in

effective focal shifts that can compromise processing capabili-

ties.In some cases,the presence of strong forward and backward

SRS can destabilize?ber laser cavities.

Fig.14(a)shows the output power overshoot(relaxation os-

cillation)of a pump-modulated?ber laser.By inserting appro-

priate spectral?lters,the total forward propagating beam can be

analyzed into its signal content(centered around1070nm de-

termined by FBGs)and the forward propagating SRS(centered

around1130nm).The SRS threshold is shown to be~250W.A

small ripple starts appearing after the?rst overshoot.Fig.14(b)

shows the output overshoot at higher pump power.In addition

to forward signal and SRS,it plots the backward SRS,measured

on the HR side of the cavity.It is shown that the?rst overshoot is

terminated abruptly by a sharp,high peak power backward prop-

agating SRS.This is then followed by a secondary relaxation

oscillation,modulated at the cavity roundtrip.This behavior is

repeatable and predictable,occurring each time there is strong

enough backward SRS.

2)Stimulated Brillouin Scattering:Techniques to suppress SBS,while maintaining FM operation,include increasing the mode area with appropriate NA reduction[141],using?bers with tailored acoustic speed pro?les[142],increasing the ef-fective linewidth via phase modulation[143]–[145],laser gain competition[146],and using highly doped?bers to absorb the pump light in a short length.Self-heating and strong temperature gradients due to pump absorption can contribute to substantial SBS threshold increase[147].11.2dB suppression of SBS in an Yb3+-doped,Al/Ge co-doped LMA gain?ber is demonstrated with a ramp-like acoustic index pro?le exhibiting an acoustic

in-Fig.14.Output power overshoot(relaxation oscillation)of a pump modulated ?ber laser.(a)Total forward power(signal+SRS),Signal and SRS traces resolved,(b)total forward power(signal+SRS),forward signal and backward SRS traces.

dex contrast of0.09and acoustic index slope of0.01/μm[148]. It is shown that SBS can be effectively suppressed by broadening the signal linewidth to a value above0.07nm[149].

SBS in an Yb3+-doped double-clad pulsed?ber ampli?er with multi-ns-duration can break-up the original pulse and pro-duce high peak-power sub-pulses.Fig.15(a)shows three differ-ent cases of backward-propagating1st-Stokes SBS measured at the input of a ns pulsed?ber ampli?er.SBS is stochastic in nature and the backward SBS pulses are usually characterized by a sharp(~10ns)spike followed by a longer tail.Fig.15(b) shows the corresponding ampli?ed forward pulses with200ns duration and output peak power of~15kW.It is shown that strong backward SBS excitation results in forward pulse distor-tion[150],as power is transferred into acoustic waves,as well as,generation of forward propagating2nd Stokes,appearing as superimposed sharp~10ns spikes.Generation of forward propagating2nd Stokes is usually followed by optical damage and catastrophic?ber failure(see Section IIC).

In MM?bers,in addition to normal backward SBS,SBS in a forward direction(FSBS)has been observed,transferring power between LP01and LP11forward propagating modes. FSBS is possible because although the overlap between?exural ?ber modes and the light is small,the phonon lifetime is much longer than in conventional SBS.Unlike in normal SBS,FSBS does not depend signi?cantly on the laser linewidth,and may also be the?rst example of a nonlinear effect,which for a given power is actually enhanced by increasing the optical mode area[151].FSBS can take place in both active and passive?bers and can transfer power from the FM into HOMs and potentially destabilize the output beam.

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW

0904123

Fig.15.(a)Backward-propagating1st-Stokes SBS measured at the input of a ns pulsed?ber ampli?er,(b)corresponding ampli?ed forward pulses with forward propagating second Stokes.

B.SPM and FWM

A direct consequence of the Kerr effect is the nonlinear intra-pulse phase shift,which results in SPM and equivalent fre-quency shifts.The SPM-induced spectral broadening depends on the pulse shape and it is more pronounced for pulses with steep leading and trailing edges.SPM is a limiting factor in short-pulse energy scaling when using phase locking or coher-ent combination of multiple lasers.

Four-wave mixing(FWM)in?bers is an elasticχ(3)nonlin-ear process involving two pump photons,which annihilate to create one Stokes and one anti-Stokes photon with frequencies de?ned by the energy conservation principle.FWM is a coherent process and its ef?ciency depends critically on the exact phase matching between the waves involved.In high power?ber lasers and ampli?ers the signal beam serves as the FWM pump and increases exponentially along the length.This results in sub-stantial FWM generation despite the phase mismatching[152], [153].FWM generation is also enhanced in birefringent or MM ?bers,since phase matching is greatly facilitated by the fact that the Stokes and anti-Stokes beams can propagate in different ?ber modes with the appropriate group velocities[17],[154]. Instead of being always parasitic,SRS and FWM can co-operate and be bene?cial in specially designed?bers for certain applications,such as ef?cient supercontinuum generation.High peak powers enhance the spectral broadening via FWM and Raman shifting and result in record bandwidth and spectral density supercontinuum sources[155]–[157].

The ultimate limit in high power can be set by self-focusing (SF)in?bers[158],[159].SF is the only nonlinearity that de-pends on power rather than intensity and,therefore,cannot

be Fig.16.SBS induced damage.

mitigated just by scaling the mode size.For1060nm operation, SF in silica?bers occurs at a power of~4–5MW[160]and, therefore,it can only be relevant to ultrashort pulse propaga-tion[161].Surprisingly,transmission of powers of~20MW, much higher than the widely accepted limit,have been reported using highly MM?bers[162].However,?ber core design can affect the SF threshold.Numerical results suggest that optical ?bers with a strong central dip at the center of the refractive index pro?le can guide stable fundamental modes at more than10x the bulk silica critical power for SF[163].SF threshold increases to~6–8MW with the use of circularly-polarized light[164], [166].SF threshold has a wavelength squared dependence and, therefore,operating at2μm results in quadrupling the afore-mentioned thresholds.The onset of SF can potentially result in spatial beam collapse and optical damage.

C.Optical Damage

Optical damage for ns and sub-ns pulses is a catastrophic ef-fect associated usually with electron avalanche effects[164], [165].Damage initiates if the electron density exceeds2×108μm?3,beyond which the plasma frequency approaches the optical frequency and the propagating light is strongly absorbed. The deposited energy is then suf?cient to melt or fracture the sil-ica glass.For pulses longer than~50ps the bulk optical damage irradiance is found to be constant at~4.75kW/μm2,which makes the threshold?uence linearly-dependent on the pulse du-ration.For shorter pulses,the electron avalanche effects evolve slower than the pulse envelope,so that the threshold?uence increases and departs from the above linearity.Preliminary re-sults indicate that Yb3+doping does not affect appreciably the aforementioned optical damage thresholds[164].By proper pol-ishing of end-faces,surface damage is measured to be equal to the bulk value[165].

Optical damage of a different type is associated with the onset of strong SBS in pulsed?ber lasers or self Q-switched highly inverted?ber ampli?ers.This damage is caused by internal stresses induced by the acoustic waves generated by the SBS material/light interaction.Fig.16shows SBS induced damage in the core and cladding a pulsed?ber ampli?er.The?ber has turned into white powder over a~2–3cm length,while the coating remains intact.This damage mechanism is different to the optical fuse effect[167],and appears to be similar to the fast optical discharge mechanism observed in?bers[168].

D.Photodarkening

High power?ber lasers based on Yb3+-doped silicate glasses are known to suffer from light-induced optical losses,known as photodarkening(PD).The optical losses are believed to be due

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER

2014

Fig.17.Power evolution with time in high-power Yb3+-doped cladding-pumped?ber lasers.[multimode(MM),single-mode,diode pumped(SM-DP),single-mode,tandem pumped(SM-TP),and coherent beam combination (CBC)].

to formation of color centers in the glass matrix,which in-

crease the background loss and reduce the output power.The

exact color-center formation mechanisms are still under debate.

There have been a number of studies showing that the PD rate

and saturated level are dependent on the Yb3+inversion[169],

[170].The order of the inversion dependence,however,varies

between3.5[169]and7[170].It has also been observed that

photodarkening in LMA?bers is non-uniformly distributed over

the?ber cross-section[171].The PD-induced loss is also non-

uniformly distributed along the length of the active?ber[172],

following closely a dependence to the calculated Yb3+inversion

to the power of2.It is shown that increasing(decreasing)the

operating temperature results in decrease(increase)of the laser

output power,reaching the new equilibria over time scales of ~200h[172].However,the occurrence of PD is entirely depen-dent on the materials composing the?ber core[173].The Yb3+

concentration and co-dopants such as aluminum[174],[175],

phosphorous[176]or cerium[177]can reduce signi?cantly or

even eliminate PD.Photodarkening has also been observed in

Tm3+doped?bers[178],[179].

IV.H IGH P OWER F IBER L ASERS

In the last decade,?ber technology has grown quite diverse

and mature and can provide an excellent platform for fabricating

robust,high performance laser systems.The core and cladding

structures can be tailored appropriately to control the beam

modality,optical nonlinearities and scale-up the power.

A.Single Fiber,Single-Mode Continuous-Wave(CW)Output In addition to?ber technology advancements,power evolu-tion in?ber lasers with near diffraction-limited output has fol-lowed and depended critically on the maturity of the pumping technologies,and their progress from low brightness diodes to combined high-brightness diode modules,and lately to in-band tandem pumping[30].

Fig.17shows the power evolution of single mode(SM)

near diffraction-limited Yb3+-doped?ber lasers,when entirely

diode pumped(SM-DP)and with the?nal ampli?er in-band

tandem pumped(SM-TP).Introduction of high brightness diode

pump modules after year2000has resulted in a fast increase

of Fig.18.Brightness enhancement in high-power Yb-doped cladding-pumped ?ber lasers.[single-mode(SM),multimode(MM)-direct diode(DD)is shown also for comparison].

SM outputs.It has been predicted that if the?ber’s MFD could be increased arbitrarily,about36kW of diffraction-limited power could be obtained from single?ber lasers or ampli?ers.This power limit is imposed primarily by thermal and SRS effects, and does not take into account modal instability effects,which can reduce it considerably[180].As already mentioned,scal-ing the SM?ber laser power above3kW requires in-band(or tandem)pumping to reduce the thermal load on the?nal power ampli?er,which has resulted in SM output of20kW[181].It has been predicted that in-band pumping can extend the SM operation to about70kW[182].Scaling the power to such high SM levels involves very large diameter?bers and stable SM operation will prove quite challenging.It is conceivable that robust?ber lasers can reach~25kW quasi-diffraction-limited SM output.

Fig.17also includes the case of MM outputs obtained with geometric incoherent combination,currently reaching the100 kW level[181].Such power levels promise even higher?ber laser penetration into the industrial and directed energy appli-cation space.Fig.17?nally includes the power evolution of single beam,near diffraction-limited output obtained with co-herent combination of SM?ber lasers[183]–[187].Currently, coherently-combined?ber lasers have demonstrated multi-kW quasi-Gaussian outputs[186],[187].Coherent combination dis-tributes effectively the optical gain and thermal load among several contributory?ber strands and can break the vicious circle of increased-power/increased-heat-generation/increased-nonlinearities and potentially provide high quality output beams with power increased well above the current single?ber strand limits.

In addition to raw power scaling,one of the most impor-tant characteristics of diode-pumped?ber lasers is the achieved brightness enhancement.The generated laser output beams are characterized by much higher brightness than that of the pump sources.Fig.18compares the brightness of SM and MM?ber lasers and the corresponding diode pump modules[188]as a function of power.It is shown that the experimentally observed SM output brightness increase in the range of10+3–10+4is in very close agreement with the theoretical predictions shown in Fig.6.The SM?ber brightness increases monotonically with the output power,although it is showing signs of saturation.

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW0904123

Power scaling in direct diode(DD)output,on the other hand,

relies on various geometrical beam shaping techniques and the

resulting brightness decreases with power.Due to the geomet-

rical incoherent combination,MM?ber laser outputs show a

brightness increase~1–2orders of magnitude smaller,almost

independent of the power level.

B.Pulsed Fiber Laser Parameter Space

Although?ber lasers are ideal for average power scaling,it is

generally perceived that they suffer in terms of energy storage

and peak power handling.However,even in this front,progress

in?ber technology has enabled substantial improvements in

pulsed?ber laser performance and has resulted in increased

penetration into the industrial and scienti?c application space.

Q-switched?ber lasers have been used extensively in the

?eld of low-cost laser marking[7].They combine con?gura-

tion simplicity and substantial pulse energies[189]–[194].As

a practical approximate rule of thumb,the extractable energy

from a?ber laser or ampli?er is limited to about ten times the

saturation energy[190]and can be controlled by?ber design.

The pulse duration in Q-switched?ber lasers is directly propor-

tional to the round trip time of the laser cavity.It also depends

on the inversion level and it reduces with increasing inversion

levels and,therefore,increasing small-signal gain.Q-switched

?ber laser has been demonstrated producing pulse durations

well below10ns by using a short length Yb-doped rod-type

photonic crystal?ber as gain medium.Pulse energies up to0.5

mJ and average powers in excess of30W have been obtained

in single-transverse mode beam quality,at repetition rates up

to100kHz[192].At low repetition rates,below the ytterbium

inverse?uorescence lifetime,the generated ASE can reduce the

inversion and limit the pulse energies.Optimized pump modula-

tion can minimize the effects of intra-pulse ASE and maximize

the extractable energy[193],[194].

MOPAs based on a diode-seeded nanosecond?ber system

offer adaptive pulse shape control[195],[196]that can cover

an extremely large range of pulse duration(from ps to CW)and

repetition rates(from pulse-on-demand to MHz).They combine

the fast dynamics and turn-on characteristics of semiconductor

lasers and the high gain,high average power capabilities of?ber

ampli?ers,resulting in high performance pulsed laser systems

with energies and beam qualities suitable for a number of diverse

applications,such as marking and material micro-processing

[197],[198].

Fig.19summarizes the progress in peak power,pulse en-

ergy and average power achieved by nanosecond pulsed?ber

lasers within the last decade.The main results are catego-

rized in terms of beam quality:single-mode(SM–M2<1.5),

low-moded(LM–M2~3)and multimoded(MM–M2~6–8). Most of the record results presented in Fig.19have been ob-

tained using large core rod-type?bers and SM to LM output

beams.Q-switched60ns pulses with26mJ pulse energy and

near diffraction-limited beam quality(M2<1.3)with average

output power of130W and peak power of500kW is achieved,

using a large-pitch?ber with a core diameter of135μm[199].

A micro-chip seed,Yb-doped?ber MOPA produced1-ns-long,

4.3mJ pulses,with average power of42W,peak power

of Fig.19.Nanosecond pulsed?ber laser performance parameter space.

4.5MW and near-Gaussian,single-transverse-mode pro?le of M2~1.3,using a100μm-core rod-like PCF used as the?nal ampli?er[200].

Fig.19shows that high performance nanosecond pulsed?ber lasers with SM and LM output beams have shown output pow-ers below250W.In order to circumvent this limitation spectral beam combination has been used to achieve1.1kW,5ns pulsed laser[201].Spectral and coherent beam combination(CBC) will be required to extend the SM/LM nanosecond?ber laser performance to the high average/high energy parameter space region(highlighted in Fig.19).Such beam combination tech-niques will be necessary to avoid modal instability issues,likely to be encountered in this regime(see discussion below). Ultrashort pulse lasers have opened up new scienti?c and in-dustrial application areas,such as time-resolved material and chemical studies,nonlinear microscopy,metrology and preci-sion material https://www.360docs.net/doc/907866321.html,pared to solid-state crys-tal counterparts,?ber lasers are characterized by broad emis-sion spectra and offer themselves for ultrafast tens-of-fs op-eration[14],[202]–[205].Chirp and nonlinear propagation in ?bers can also be combined to achieve even shorter pulses[206]. Lately,signi?cant power scaling in superfast pulse?ber lasers has been achieved based on the powerful chirped-pulse ampli?-cation(CPA)technique[207]and special?bers,such as the ones using rod-type PCF?ber technology[13],[204],[205].Com-pared to diode-pumped solid-state crystal and thin-disc lasers,?ber ultrashort pulse lasers offer superior thermo-mechanical behavior and more robust operation.They offer the potential for highly integrated and passively cooled ultrashort pulse sources. Fig.20summarizes the progress in pulse energy and av-erage power achieved ultrafast(ps and fs)pulsed?ber lasers within the last decade.High average powers,in excess of800W, and moderate pulse energies(E p≤10μJ)have been demon-strated[204].This was achieved by using27μm)MFD pixilated core[120]and500μm outer diameter JAC?bers.At the other extreme,appreciably high energies(>2mJ)and moderate av-erage powers(>10W)with record(~4GW)peak power have

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER

2014

Fig.20.Ultrafast pulsed?ber laser parameter space.

been achieved[208],using large pitch PCF?bers with105μm MFD.

Scaling up the average power requires special?bers with in-creasingly large diameters.However,exceeding100W in the high pulse energy regime(E p≤10μJ)[209]or1kW in the lower energy regime(E p≤10μJ)[204],delineated by the

dashed line,the power?ber ampli?er operation is severely lim-ited by TMIs[204],[211],resulting in signi?cant output power variations and beam pointing drift.The limit is established ex-perimentally and it is related to the?ber effective core diameters. This currently appears to be a hard limit and intensive research is underway to understand the root cause and develop robust solutions to the modal instability effects[210]–[229].

C.Transverse Mode Instabilities

In high power LMA?ber ampli?ers,TMI manifests itself as sharp and rapid output beam pro?le deterioration above an out-put power threshold.For near single fundamental-mode input excitation,the output beam shows large content of and strong competition with HOMs(dominantly LP11mode),after a cer-tain threshold has been reached.A number of research groups have recently reported on TMI effects in PCF and LPF high power Yb3+-doped?ber ampli?ers[211]–[218].Lately,TMI has been observed also in standard solid-core LMA?ber ampli-?ers[219],[220].

Fig.21plots the TMI threshold power as a function of the active?ber nominal diameter.The highest TMI thresholds to date has been obtained with actively cooled,step index?ber of 22μm[210]and~30μm core diameter(SI-MC)[204].The ?bers had micro-structured doped core to achieve low NA and was bent to preferentially attenuate HOMs.Fig.21includes also results obtained with short length,straight rod-type PCFs and LPFs(PCF-LPF#1:[211]–[214],DMF#1-#3:[215]),as well as,longer bendable PCFs(PCF-B1:[216],PCF-B2:[217], PCF-SAT:[218]).It also includes more conventional

step-index Fig.21.Transverse mode instability threshold versus nominal core diameter. (PCF-LPF#1:[211]-[214],DMF#1-#3:[215],PCF-B1:[216],PCF-B2:[217],PCF-SAT:[218],SI-MC:[204],(SI-NS):[210],SI&SI-GT:[219], PM25:[220]).

?bers,with and without gain tailoring(SI and SI-GT:[219]), as well as,polarization-maintaining step-index?bers(PM25: [220]).PM25is monolithic,fully-spliced ampli?er,in contrast with all the other con?gurations,which are free-standing and end-pumped.

Fig.21shows that the TMI threshold generally decreases with the nominal core diameter,irrespective of the?ber type used.TMI threshold,however,has been observed to be affected by a number of other ampli?er characteristics.In the case of DMF[215],it is shown that HOM excess leakage results in approximately double the TMI threshold.Also,in the case of SI-GT[219],gain tailoring results in substantial(~x3)TMI threshold increase.However,gain tailoring is not as effective in the case of PCF-GT[214].In the case of PCF-SAT[218], the TMI threshold has been shown to increase substantially by ef?cient?ber cooling.Finally,in the case of PM25polarization-maintaining?ber it is observed that increasing the input power and pumping the ampli?er off the absorption peak results in almost double the TMI threshold.Interestingly,in this case, a similar non-PM?ber shows no TMI instability up to1kW level[220].It should be also remarked that an all-?ber,spliced-up and coiled ampli?er with core diameter of20μm showed no signs of TMI for>2kW output power[230].To the best of our knowledge,so far there has been no TMI observed in?ber ampli?ers with core diameter smaller than20μm.Finally,It should be mentioned that due to lack of experimental details, it is not clear if all the observed TMI effects follow the same evolution patterns[213],or are all due to the same root cause. Different theoretical models have been proposed for the root cause of the observed TMI effects[221]–[229].All models con-sider thermo-optically induced refractive-index gratings as the main mechanism of forward mode coupling.The instability has been attributed to either stimulated thermal Rayleigh scatter-ing(STRS)[221],[223]–[227]or other thermal mode coupling effects[222],[228],[229].So far,the proposed models have had different degrees of success in predicting mode coupling and instabilities.However,to the best of our knowledge,there has been limited success to quantitatively predict instability

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW

0904123

Fig.22.Fiber laser wavelength coverage and maximum output power achieved to date.

evolution and dynamics.This is not surprising,given the lack of experimental details and other uncertainties regarding published data.Specially designed experiments are required to prove or disprove proposed theories.

V.O THER F IBER L ASERS

Fiber lasers can cover an extended range of wavelengths by simply doping the core with different active dopants.Fig.16 shows schematically the wavelength ranges offered by dopants such as Nd3+,[231],[232]Er3+/Yb3+[233],[234]and Tm3+ [235].Power scaling in Nd3+and Er3+/Yb3+doped?ber lasers has been severely hampered by the relative large quantum de-fect and excessive thermal management requirements.Tm3+-doped?ber lasers operate around the eye-safe2μm region and have been scaled up to kW level and appear to be promising for new directed energy and industrial applications[236].A monolithic,robustly single-mode,resonantly cladding-pumped Ho3+-doped?ber laser producing more than400W of out-put power in the2.05–2.15μm wavelength range[237].Using nonlinear processes such as SRS,high power lasers emitting in the spectral regions shown in Fig.22can be used as pumps and, combined with properly designed and optimised?bers,can offer substantial power in almost any spectral region in the1–2.5μm span.

Fiber lasers have also been used as seeds to produce high per-formance supercontinuum sources[238].CW supercontinuum generation extending to the visible spectral region has been demonstrated by pumping photonic crystal?bers at1.07μm with a400W single mode CW Ytterbium?ber laser.The con-tinuum spans over1300nm with average powers up to50W and spectral power densities over50mW/nm[157].High-energy pulsed supercontinuum spanning the450–1750nm region with energy spectral density in excess of1nJ/nm in the visible,suit-able for STED microscopy,has also been generated[156]. Fiber distributed-feedback(DFB)lasers[239]–[241]can pro-vide high purity,single frequency,single polarization[242],low phase noise seeds ideal for advanced high power MOPA con?g-urations,sensors[243]and other applications[244].It should be mentioned that in the highest power laser MOPA system, demonstrated to date in the world at the National Ignition Facil-ity,the only laser used is actually a?ber DBF laser[245].

TABLE I

C OMPARISON OF

D IFFERENT H IGH P OWER L ASER T ECHNOLOGIES

.

VI.I NDUSTRIAL F IBER L ASERS AND A PPLICATIONS Industrial high power?ber lasers are almost exclusively based on all-?ber monolithic con?gurations,exploiting the excellent power scaling capabilities of?ber ampli?ers in MOPA con-?gurations.In such monolithic con?gurations,a high power all-?ber laser seed is followed usually by one matched,low-gain and well saturated?ber ampli?er[23]–[30].Additionally, hybrid high power?ber laser systems have been demonstrated, using free-space optics for pump coupling and laser cavities with mirrors butt-coupled or directly deposited onto the?ber facets[22].

All-?ber MOPA con?gurations offer the possibility of using multiple pump power injection points and therefore distribute evenly the pump absorption and thermal load,providing service-free,reliable industrial laser systems.

Table I shows a comparison of the wall-plug ef?ciency (WPE),expected lifetime,maintenance requirements and?ber delivery capabilities for the main industrial high power laser technologies.It is shown?ber lasers outperform all other tech-nologies combining record>30%WPE,100k hours lifetime (de?ned by the single-emitter(SE)diode pumps)and mainte-nance free operation.

Fig.23compares the typical beam quality,quanti?ed by the beam-parameter product(BPP=ω0θ0)variation with output power for the most common laser applications in material pro-cessing and manufacturing to date.It also superimposes the BPP and power requirements for the main materialprocessing laser applications.The contours show parameters averaged over different operational conditions and materials.These applica-tions are based primarily on thermal processes,such as heating, melting and vaporization.In addition to replacing traditional mechanical or chemical techniques,lasers have also enabled a number of novel https://www.360docs.net/doc/907866321.html,ser cutting,for example,allows repeatable high-precision patterns at high speeds that cannot be produced via conventional methods.Also use of lasers enables welding of dissimilar materials,like steel and aluminum,which is of growing interest to shipbuilding and car industries and known to be impossible in conventional welding.

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER

2014

Fig.23.BPP and average power requirements for laser applications&BPP versus average output power for main industrial lasers[4].

In automotive industry,welding car bodies,transmission and engine components,air bags,exhaust systems,etc.,are now made robotically using laser systems.In healthcare,lasers are used for welding deep brain stimulator implants,pacemakers and prosthetics.In electronics industry,for drilling and cutting of printed circuit boards.In photovoltaics for scribing,drilling and cutting of Si-wafer,ablation of conduction or dielectric layers of thin?lm solar and crystalline Si solar cells.More recently in additive manufacturing,3-D rapid prototyping and manufacturing by selective sintering,melting and3-D cladding directly from CAD?les is enabled by lasers.Rapid prototyping has evolved from polymer components to tool-free rapid manu-facturing of high quality metallic parts using materials,such as titanium,aluminum and cobalt chrome powders.

So far most of the industrial applications are based on lasers operating predominantly in CW or relatively long pulse mode. Recently,advances in laser technology have resulted in industry-worthy ultrashort laser systems capable of ef?cient material processing.Femtosecond pulses can extend the laser processing capabilities into materials inaccessible by traditional lasers.For example,transparent materials can be processed ef?ciently by focusing fs pulses tightly to induce nonlinear absorption through a combination of athermal effects,such as multiphoton absorp-tion,tunneling ionization,and avalanche ionization.As a result, the induced structural changes are con?ned into tiny volumes with nm precision and are ideal for3-D micromachining.This area of highly nonlinear matter/light interaction is still in its infancy and is expected to take?ber laser material processing to a new level,with a number of novel applications expected in the near future.

One of the main attributes of high power?ber lasers is their superior beam quality at high powers.For the same collimated beam size,higher beam quality radiation result in smaller spot size at the work-piece.Alternatively,for the same spot size at the work-piece,higher beam quality requires smaller and therefore lighter focusing beam optics.This results in lighter processing heads and higher processing speeds.Finally,for the same beam size and focusing optics,as well as,same spot size,beams with higher beam quality can be focused further away enabling remote material processing[188].

However,with the development of high-power,high-brightness near-diffraction-limited?ber laser sources it has be-come more challenging to achieve stable focal position of the focused beam at the work-piece,because of the time dependent thermal lensing and optical distortions in the transmitting optics inside the laser processing head[188],[246].It is rather ironic that although eliminating the thermal lensing from the laser cav-ity is one of the major contributors to scaling-up the diffraction-limited?ber laser output,this deleterious effect“sneaks”back into the processing head optics.To gain the full potential and make ef?cient use of high power?ber lasers with diffraction-limited beam quality new processing heads have been devel-oped[188],[247],[248].

VII.S UMMARY—F UTURE P ROSPECTS

Fiber lasers have come of age and are currently fast increasing their share in the industrial applications market.They uniquely combine high average powers,unparalleled beam quality,small footprint,and record ef?ciencies.They gradually replace con-ventional laser technologies offering substantially lower cost of ownership,higher processing speeds in existing applications while enabling new ones.

In this paper,we have summarized the fundamental properties and reviewed the latest developments in high power ytterbium-doped?ber lasers.The review has been focused primarily on the main?ber laser con?gurations,used in industrial applications, have considered issues related to cladding pumping.Special at-tention has been placed on pump combination techniques and the parameters that affect the brightness enhancement observed in high power?ber lasers.The review also included the major limitations imposed by?ber nonlinearities and other parasitic effects,such as optical damage,TMI and photodarkening.The paper?nally summarized the power evolution in continuous-wave and pulsed ytterbium-doped?ber lasers and highlighted their impact on material processing and other industrial appli-cations.

Following the spectacular progress in their performance so far,future innovations in materials and?ber designs are ex-pected to continue pushing the performance boundaries with new radical?ber laser solutions.

So far,the tremendous success of?ber lasers has been al-most entirely based on Yb3+-doped?bers operating around 1μm.However,moving forward extending the output beam wavelength into the mid-infrared(mid-IR)will be bene?cial for a large number of existing or enable novel new applica-tions[235],[249].For industrial material processing applica-tions,such as plastic welding,or glass processing,?ber laser sources in the mid-IR with substantial power(>100W)will be required.Processing glass will require robust laser sources in the3–5μm range.At present,there are no industrial-grade,?ber-based lasers in this spectral region.Emission in this spec-tral region relies entirely on ZBLAN or possibly chalcogenide glasses[235],the power handling capabilities of which have not been proven yet.

Further power scaling with diffraction limited outputs,well beyond the current single-?ber performance,can be achieved by spectral(SBC)and/or CBC of high power SM?ber lasers [182],[185].SBC and CBC distribute spatially the thermal load and intensity and can effectively mitigate thermal and nonlinear effects,which set the hard limits to the power generated and

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW0904123 transmitted in currently used?bers.In addition to power scaling,

CBC and SBC increase the output beam spatial brightness.SBC

though is limited by the ampli?cation bandwidth of the active

medium and results in spectral brightness deterioration,which

might complicate the processing head design.Four2kW?ber

lasers have been spectrally combined to provide8.2kW of

output power[250].The beam quality was retained to M2<1.5

up to2.5kW and degraded to M2~3.5at full power due to

the onset of TMI.

CBC has been already demonstrated by tiling eight SM?ber

lasers side-by-side in the near?eld(tiled aperture)to provide

a record4kW of diffraction-limited beam(M2=1.25)[186].

Using a single diffractive optical elements(?lled aperture)?ve

SM?ber lasers have been combined coherently into one beam

with M2=1.1,exceeding that of the contributory lasers[187].

Power scaling in CBC is achieved by increasing the number of

tiled contributory?ber lasers.So far,a maximum of64?ber

lasers have been combined successfully combined coherently

[251],making CBC an extremely powerful technique for future

?ber laser power scaling.SBC and CBC can also be combined

for multidimensional power scaling[252].

In addition to average power scaling,research is now con-

centrated into novel techniques for scaling the pulse en-

ergy and peak power in ultrafast laser systems,using re-

cently demonstrated promising techniques such as divided-

pulse ampli?cation[253]–[255]and/or the stack-and-dump

concept[256].Currently,these are areas of intensive re-

search and new exciting results are expected in the near

future.

Finally,?ber lasers offer themselves for massive“paral-

lelism”and can go beyond the classic MOPA con?gurations

into schemes such as the coherent ampli?er network(ICAN).

Such radical concepts can potentially produce pulses with en-

ergies of>10J at repetition rates of several kHz,as required

for the next-generation particle accelerators[257].Given the

size,power requirements and expected cost,practical imple-

mentation of such future coherent ampli?ed network concepts

can only be realized by the?ber laser technology,which can

provide10s of kW of diffraction-limited beams,with record

wall-plug ef?ciencies(>30%)robustly in small foot-print and

low cost.

A PPENDIX A

B EAM B RIGHTNESS

The brightness(or radiance)of a beam(B)is de?ned as the

beam power(P)per unit area(A)and unit solid angle(Ω),

namely[99],[259]:

B=

P

.(A.1)

For circular cross-sections A=πr2andΩ=πNA2,where r is the radius and NA the numerical aperture.The brightness can also be given in terms of beam quality as

B=

P

π2BPP2

=

P

(M2λ)2

.(A.2)

For rectangular cross-sections[110],A=d x d y and

Ω=4sin?1

sin

θx

2

sin

θy

2

≈θxθy(A.3)

where d x and d y are the lengths andθx,θy are the divergence

full angles in the two orthogonal directions.Again,brightness

is given in terms of beam quality parameters as

B=

P

d x d yθxθy

=

P

16(BPP x BPP y)

=

π

4

2P

M2x M2yλ2

.

(A.4)

There are two important theorems that govern brightness in

a passive optical system.First,assuming that both object and

image spaces have the same index of refraction,the brightness

theorem states that the brightness of beam produced by an imag-

ing system cannot be greater than the original source brightness.

The brightness is preserved only when the system is lossless.

The underlying principle is conservation of energy,or conser-

vation of number of rays.The second theorem states that the

brightness of a collection of mutually incoherent beams cannot

be higher than the brightness of the brightest beam.

These two theorems imply that there is an upper limit to the

brightness achieved by a combined pump module,which de?nes

to large extend the ef?ciency of the various cladding pumping

schemes.

The above theorems are sometimes expressed in terms of

′e tendue,which is de?ned as

E=n2AΩ(A.5)

where n is the surrounding medium refractive index.Etendue

describes the light gathering power or acceptance of an optical

system.

Finally,the spectral brightness or spectral brilliance is es-

sentially the brightness per unit optical bandwidth,expressed in

W/(μm2sr Hz).

A PPENDIX B

N ONLINEARITY E NHANCEMENT F ACTOR

The NEF is a?gure of merit that compares the strength of

the nonlinear interaction in?bers with that of a focused beam in

bulk silica.For a Gaussian beam of power P0and focused waist

radiusω0,the(intensity)x(effective length)product is given

by[258]:

IL bulk=

P0

λ(B.1)

where the effective length is equal to Rayleigh length.A quasi-

Gaussian beam with waist radiusω0,propagating in a?ber

ampli?er of length L0and gain G=P out/P in=exp(γL0),

where P out=P0,is characterized by(intensity)x(effective

length)product

IL amp=

L

I in eγz dz=I0

G?1

γG

(B.2)

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER2014

where I0=P0

πω20

=GI in andγis the gain coef?cient.

The NEF is then de?ned as

NEF=IL amp

IL bulk

=

λ

πω20

G?1

G ln G

L0.(B.3)

In the quasi-Gaussian approximation,the fundamental?ber mode is given by[100]:

ω0≈r0

0.65+

1.619

V3/2

+

2.879

V6

(B.4)

and

r0=λ

V

2πNA

.(B.5)

A CKNOWLEDGMENT

The authors would like to thank helpful discussions and fruit-ful collaboration over the years with colleagues and coworkers in SPI(Dr.S.R.Norman,Dr.M.P.Varnham,Dr.M.K.Durkin, Dr.F.Ghiringhelli,and Dr.L.Walker)and the ORC(Prof.D.N. Payne,Prof.J.Nilsson,Prof.W.A.Clarkson,Prof.J.K.Sahu, and Prof.D.J.Richardson).

R EFERENCES

[1] E.Snitzer,“Proposed?ber cavities for optical masers,”J.Appl.Phys.,

vol.32,pp.36–39,1961.

[2] C.J.Koester and E.Snitzer,“Ampli?cation in a?ber laser,”Appl.Opt.,

vol.3,pp.1182–1186,1964.

[3]T.H.Maiman,“Stimulated optical radiation in ruby,”Nature,vol.187,

pp.493–494,1960.

[4] A.E.Willner,R.L.Byer,C.J.Chang-Hasnain,S.R.Forrest,H.Kressel,

H.Kogelnik,G.J.Tearney,C.H.Townes,and M.N.Zervas,“Optics and

photonics:Key enabling technologies,”Proc.IEEE,vol.100,pp.1604–1643,2012.

[5] A.E.Siegman,https://www.360docs.net/doc/907866321.html,l Valley,CA,USA:Univ.Science,1986.

[6]H.Injeyan and G.D.Goodno,High Power Laser Handbook.New

York,NY,USA:McGraw-Hill,2011.

[7]Strategies Unlimited,“The worldwide market for lasers,”Mountain View,

CA,USA,2013.

[8] E.Snitzer,“Glass lasers,”Appl.Opt.,vol.5,pp.1487–1499,1966.

[9]L.D.DeLoach,S.A.Payne,L.L.Chase,L.K.Smith,W.L.Kway,

and W.F.Krupke,“Evaluation of absorption and emission properties of Yb3+doped crystals for laser applications,”IEEE J.Quantum Electron., vol.29,no.4,pp.1179–1191,Apr.1993.

[10]O.G.Okhothikov,Fiber Lasers.Weinheim,Germany:Wiley,2012.

[11]V.Ter-Mikirtychev,Fundamentals of Fiber Lasers and Ampli?ers,vol.

181.New York,NY,USA:Springer(Springer Series in Optical Sci-ences),2014.

[12] D.J.Richardson,J.Nilsson,and W.A.Clarkson,“High power?ber

lasers:Current status and future perspectives,”J.Opt.Soc.Amer.B, vol.27,pp.B63–B92,2010.

[13]J.Limpert,F.Roser,S.Klingebiel,T.Schreiber,C.Wirth,T.Peschel,

R.Eberhardt,and A.Tunnermann,“The rising power of?ber lasers and ampli?ers,”J.Sel.Topics Quantum Electron.,vol.13,pp.537–545,

2007.

[14]L.Jintong,L.Dan,and D.Yitang,“A review of?ber lasers,”China

Commun.,vol.9,pp.1–15,2012.

[15]J.L.Archabault and S.G.Grubb,“Fiber gratings in lasers and ampli-

?ers,”J.Lightw.Technol.,vol.15,no.8,pp.1378–1390,Aug.1997. [16]M.J.Cole,W.H.Loh,https://www.360docs.net/doc/907866321.html,ming,M.N.Zervas,and S.Barcelos,

“Moving?bre/phase mask-scanning beam technique for enhanced?ex-ibility in producing?bre gratings with uniform phase mask,”Electron.

Lett.,vol.31,no.17,pp.1488–1490,1995.

[17]J.Limpert,S.Hofer,A.Liem,H.Zellmer,A.Tunnermann,S.Knoke,

and H.V oelckel,“100-W average-power,high-energy nanosecond?ber ampli?er,”Appl.Phys.B,vol.75,pp.477–479,2002.[18]S.Bohme,S.Fabian,T.Schreiber,R.Eberhardt,and A.Tunnermann,

“End cap splicing of photonic crystal?bers with outstanding quality for high power applications,”Proc.SPIE,vol.8244,824406,2012. [19]Y.Jeong,J.K.Sahu,D.N.Payne,and J.Nilsson,“Ytterbium-doped

large-core?ber laser with1.36kW continuous-wave output power,”

Opt.Exp.,vol.12,pp.6088–6092,2004.

[20] C.-H.Liu,B.Ehlers,F.Doerfel,S.Heinemann,A.Carter,K.Tankala,

J.Farroni,and A.Galvanauskas,“810W continuous-wave and single-transverse-mode?bre laser using20μm core Yb-doped double-clad ?bre,”Electron.Lett.,vol.40,pp.1471–1472,2004.

[21]J.Nilsson,W.A.Clarkson,R.Selvas,J.K.Sahu,P.W.Turner,

S.U.Alam,and A.B.Grudinin,“High-power wavelength tunable cladding-pumped rare-earth-doped silica?ber lasers,”Opt.Fiber Tech-nol.,vol.10,pp.5–30,2004.

[22]J.D.Minelly,L.Spinelli,R.Tumminelli,https://www.360docs.net/doc/907866321.html,orkov,D.Anthon,

E.Pooler,R.Pathak,D.Roh,D.Grasso,D.Schleuning,B.Perilloux,

and P.Zambon,“All-glass kW?bre laser end-pumped by MCCP-cooled diode stacks,”in Proc.12th Eur.Quantum https://www.360docs.net/doc/907866321.html,sers Electro-Opt.Eur.,2011,p.1.

[23]V.Gapontsev,D.Gapontsev,N.Platonov,O.Shkurikhin,V.Fomin,

A.Mashkin,M.Abramov,and S.Ferin,“2kW CW Ytterbium?ber

laser with record diffraction-limited brightness,”in https://www.360docs.net/doc/907866321.html,sers Electro-Opt.Eur.,2005,p.508.

[24]S.Norman,M.N.Zervas,A.Appleyard,P.Skull,D.Walker,P.Turner,

and I.Crowe,“Power scaling of high power?ber lasers for microma-chining and materials processing applications,”Proc.SPIE,vol.6102, p.61021P,2006.

[25]S.Norman and M.N.Zervas,“Fiber lasers prove attractive for industrial

applications,”Laser Focus World,vol.43,no.8,pp.93–96,2007. [26] D.Gapontsev,“6kW CW single mode ytterbium?ber laser in all-?ber

format,”Proc.21st Annu.Solid State Diode Laser Technol.Rev.,p.258, 2008.

[27]W.Rath,“Lasers for industrial production processing:Tailored tools with

increasing?exibility,”in Proc.SPIE,2012,vol.8239,823908. [28] D.A.V.Kliner,“4-kW?ber laser for metal cutting and welding,”Proc.

SPIE,vol.7914,791418,2011.

[29]M.N.Zervas,“High power?ber lasers:From lab experiments to real

world applications,”in Proc.AIP Conf.Emerging Trends Novel Mater.

Photon.,2010,vol.1288,pp.63–66.

[30]M.O’Connor and B.Shiner,“High power?ber lasers for industry and

defense,”in High Power Laser Handbook,H.Injeyan and G.D.Goodno, Eds.New York,NY,USA:McGraw-Hill,2011.

[31] E.Snitzer,H.Po,F.Hakimi,R.Tumminelli,and B.C.McCollum,

“Double-clad,offset core Nd?ber laser,”presented at the Opt.Fiber Commun.Conf.,New Orleans,LA,1988,Paper PD5.

[32]H.Po,E.Snitzer,R.Tuminelli,L.Zenteno,F.Hakimi,N.M.Cho,and

T.Haw,“Double clad high brightness Nd?ber laser pumped by GaAlAs phased array,”presented at the Opt.Fiber Commun.Conf.,Houston,TX, 1989,Paper PD7.

[33]N.A.Mortensen,“Air-clad?bers:Pump absorption assisted by chaotic

wave dynamics?,”Opt.Exp.,vol.15,pp.8989–8996,2007.

[34]M.N.Zervas,A.Marshall,and J.Kim,“Effective absorption in cladding-

pumped?bers,”Proc.SPIE,vol.7914,p.79141T,2011.

[35]M.H.Muendel,“Optimal inner cladding shapes for double-clad?ber

lasers,”presented at the https://www.360docs.net/doc/907866321.html,sers Electro-Opt.,Washington,,DC, USA,1996,p.209.

[36] A.Liu and K.Ueda,“The absorption ef?ciency of circular,offset,and

rectangular double-clad?bers,”https://www.360docs.net/doc/907866321.html,mun.,vol.132,pp.511–518, 1996.

[37] A.Liu,J.Song,K.Kouichi,and K.Ueda,“Effective absorption and

pump loss of double-clad?ber lasers,”Proc.SPIE,vol.2986,pp.30–38, 1997.

[38]P.Leproux,S.Fevrier,V.Doya,P.Roy,and D.Pagnoux,“Mod-

eling and optimization of double-clad?ber ampli?ers using chaotic propagation of the pump,”Opt.Fiber Technol.,vol.6,pp.324–339, 2001.

[39]V.Doya,O.Legrand,and F.Mortessagne,“Optimized absorption in a

chaotic double-clad?ber ampli?er,”Opt.Lett.,vol.26,pp.872–874, 2001.

[40] D.Kouznetsov,J.Moloney,and E.Wright,“Ef?ciency of pump absorp-

tion in double-clad?ber ampli?ers—Part I:Fiber with circular symme-try,”J.Opt.Soc.Amer.B,vol.18,pp.743–749,2001.

[41] D.Kouznetsov and J.Moloney,“Ef?ciency of pump absorption in

double-clad?ber ampli?ers—Part II:Broken circular symmetry,”J.Opt.

Soc.Amer.B,vol.19,pp.1259–1263,2002.

ZERV AS AND CODEMARD:HIGH POWER FIBER LASERS:A REVIEW0904123

[42]J.J.Morehead and M.H.Muendel,“Nearly circular pump guides,”Proc.

SPIE,vol.7914,79142Y,2011.

[43]J.K.Sahu,C.C.Renaud,K.Furusawa,R.Selvas,J.A.Alvarez-Chavez,

D.J.Richardson,and J.Nilsson,“Jacketed air-clad cladding pumped

ytterbium-doped.Fibre laser with wide turning range,”Electron.Lett., vol.37,pp.1116–1117,2001.

[44]W.J.Wadsworth,R.M.Percival,G.Bouwmans,J.C.Knight,

T.A.Birks,T.D.Hedley,and P.S.J.Russell,“Very high numerical aperture?bers,”IEEE Photon.Technol.Lett.,vol.16,no.3,pp.843–845,Mar.2004.

[45]R.Selvas,J.K.Sahu,L.B.Fu,J.N.Jang,J.Nilsson,A.B.Grudinin,

K.H.Yl¨a-Jarkko,S.U.Alam,P.W.Turner,and J.Moore,“High-power,low-noise,Yb-doped,cladding-pumped,three-level?ber sources at980nm,”Opt.Lett.,vol.28,pp.1093–1095,2003.

[46]M.Aslund,S.D.Jackson,J.Canning,A.Teixeira,and K.Lyytikainen-

Digweed,“The in?uence of skew rays on angular losses in air-clad ?bres,”https://www.360docs.net/doc/907866321.html,mun.,vol.262,pp.77–81,2006.

[47] A.Liu and K.Ueda,“Propagation losses of pump light in rectangular

double-clad?bers,”Opt.Eng.,vol.35,pp.3130–3134,1996.

[48] D.A.V.Kliner,J.P.Koplow,L.Goldberg, A.L.G.Carter,and

J.A.Digweed,“Polarization-maintaining ampli?er employing double-clad bow-tie?ber,”Opt.Lett.,vol.26,pp.184–186,2001.

[49] C.Pare,“In?uence of inner cladding shape and stress-applying parts

on the pump absorption of a double-clad?ber ampli?er,”Proc.SPIE, vol.5260,pp.272–277,2003.

[50] D.Gloge,“Bending loss in multimode?bers with graded and ungraded

core index,”Appl.Opt.,vol.11,pp.2506–2513,1972.

[51] D.Marcuse,“Coupled power equations for lossy?bers,”Appl.Opt.,

vol.17,pp.3232–3237,1978.

[52]J.Nilsson,S.U.Alam,J.A.Alvarez-Chavez,P.W.Turner,

W.A.Clarkson,and A.B.Grudinin,“High power and tunable opera-tion of erbium-ytterbium co-doped cladding-pumped?ber lasers,”IEEE J.Quantum Electron.,vol.39,no.8,pp.987–994,Aug.2003.

[53] A.Tunnermann,T.Schreiber,and J.Limpert,“Fiber lasers and ampli-

?ers:An ultrafast performance evolution,”Appl.Opt.,vol.49,pp.F71–78,2010.

[54]V.Filippov,Y.Chamorovskii,J.Kerttula,K.Golant,M.Pessa,and

O.G.Okhotnikov,“Double clad tapered?ber for high power applica-tions,”Opt.Exp.,vol.16,pp.1929–1944,2008.

[55]X.P.Cheng,P.Shum,J.Zhang,and M.Tang,“Analysis of nonlinear

effective absorption coef?cient of double cladding?ber,”presented at the IEEE Region Conf.TENCON,Hong Kong,Nov.2006.

[56] C.L.Bonner,T.Bhutta,D.P.Shepherd,and A.C.Tropper,“Double-clad

structures and proximity coupling for diode-bar-pumped planar wave-guide lasers,”IEEE J.Quantum Electron.,vol.36,no.2,pp.236–242, Feb.2000.

[57] D.P Shepherd,S.J Hettrick, C.Li,J.I.Mackenzie,R.J.Beach,

S.C.Mitchell,and H.E.Meissner,“High-power planar dielectric wave-guide lasers,”J.Phys.D,Appl.Phys.,vol.34,pp.2420–2432,2001. [58]H.X.Kang,H.Zhang,P.Yan,D.S.Wang,and M.Gong,“An end-

pumped Nd:Y AG planar waveguide laser with an optical to optical conversion ef?ciency of58%,”Laser Phys.Lett.,vol.5,pp.879–881, 2008.

[59]T.Y.Fan,“Ef?cient coupling of multiple diode laser arrays to an optical

?ber by geometric multiplexing,”Appl.Opt.,vol.30,pp.630–632,1991.

[60] D.J.DiGiovanni and A.J.Stentz,“Tapered?ber bundles for cou-

pling light into and out of cladding-pumped?ber devices,”U.S.Patent 58646441999.

[61] A.Kosterin,V.Temyanko,M.Fallahi,and M.Mansuripur,“Tapered

?ber bundles for combining high-power diode lasers,”Appl.Opt.,vol.43, pp.3893–3900,2004.

[62]L.Goldberg,B.Cole,and E.Snitzer,“V-groove side-pumped1.5μm

?bre ampli?er,”Electron.Lett.,vol.33,pp.2127–2129,1997.

[63]G.Canat,J.C.Mollier,J.P Bouzinac,G.M.Williams, B.Cole,

L.Goldberg,Y.Jaou¨e n,and G.Kulcsar,“Dynamics of high-power erbium–ytterbium?ber ampli?ers,”J.Opt.Soc.Amer.B,vol.22, pp.2308–2318,2005.

[64] E.Snitzer,H.Ho,R.P.Tumminelli,and F.Hakimi,“Optical?ber lasers

and ampli?ers,”U.S.Patent4815079,1989.

[65]Q.Xiao,P.Yan,S.Yin,J.Hao,and M.Guo,“100W ytterbium-doped

monolithic?ber laser with fused angle-polished side-pumping con?gu-ration,”Laser Phys.Lett.,vol.8,pp.125–129,2011.

[66]V.P.Gapontsev and I.Samartsev,“Coupling arrangement between a

multimode light source and an optical?ber through an intermediate optical?ber length,”U.S.Patent5999673,1999.[67]P.Ou,P.Yan,M.Gong,W.Wei,and Y.Yuan,“Studies of pump light

leakage out of couplers for multi-coupler side-pumped Yb-doped double-clad?ber lasers,”https://www.360docs.net/doc/907866321.html,mun.,vol.239,pp.421–428,2004.

[68] A.B.Grudinin,J.Nilsson,P.W.Turner,C.C.Renaud,W.A.Clarkson,

and D.N.Payne,“Single clad coiled optical?ber for high power lasers and ampli?ers,”presented at the https://www.360docs.net/doc/907866321.html,sers Electro-Opt.,Baltimore, MD,USA,1999,Paper CPD26.

[69] A.B.Grudinin,D.N.Payne,P.W.Turner,J.Nilsson,M.N.Zervas,M.

Ibsen,and M.K.Durkin,“Multi-?bre arrangements for high power?ber lasers and ampli?ers,”U.S.Patent6826335,2000.

[70]P.Polynkin,V.Temyanko,M.Mansuripur,and N.Peyghambarian,“Ef-

?cient and scalable side pumping scheme for short high-power optical ?ber lasers and ampli?ers,”IEEE Photon.Technol.Lett.,vol.16,no.9, pp.2024–2026,Sep.2004.

[71]Y.Wang,“Heat dissipation in kilowatt?ber power ampli?ers,”IEEE J.

Quantum Electron.,vol.40,no.6,pp.731–740,Jun.2004.

[72]J.R.Leger and W.C.Goltsos,“Geometrical transformation of linear

diode-laser arrays for longitudinal pumping of solid-state lasers,”IEEE J.Quantum Electron.,vol.28,no.4,pp.1088–1100,Apr.1992. [73]S.R.Karlsen,R.K.Price,M.Reynolds,A.Brown,R.Mehl,S.Patterson,

and R.J.Martinsen,“100-W,105-μm,0.15NA?ber coupled laser diode module,”Proc.SPIE,vol.7198,719829,2009.

[74]JDSU Product Catalogue,JDS Uniphase Corporation,CA,USA,2013.

[75]Y.Xiao,F.Brunet,M.Kanskar,M.Faucher,A.Wetter,and N.Holehouse,

“1-kilowatt CW all-?ber laser oscillator pumped with wavelength-beam-combined diode stacks,”Opt.Exp.,vol.20,pp.3296–3301,2012. [76] B.S′e vigny,P.Poirier,and M.Faucher,“Pump combiner loss as a function

of input numerical aperture power distribution,”Proc.SPIE,vol.7195, 719523,2009.

[77] A.Wetter,M.Faucher,M.Lovelady,and F.S′e guina,“Tapered fused-

bundle splitter capable of1kW CW operation,”Proc.SPIE,vol.6453, 645301,2007.

[78]Q.Xiao,P.Pan,J.He,Y.Wang,X.Zhang,and M.Gong,“Tapered fused

?ber bundle coupler capable of1kW laser combining and300W laser splitting,”Laser Phys.,vol.21,pp.1415–1419,2011.

[79]H.–S.Seo,J.T.Ahn,B.J.Park,J.H.Song,and W.Chung,“Ef?cient

pump beam multiplexer based on single-mode?bers,”Jpn.J.Appl.Phys., vol.51,010203,2012.

[80]S.U.Alam,A.T.Harker,R.J.Horley,F.Ghiringhelli,M.P.Varnham,

P.W.Turner,M.N.Zervas,and S.R.Norman,“All-?bre,high power, cladding-pumped1565nm MOPA pumped by high brightness1535nm pump sources,”presented at the https://www.360docs.net/doc/907866321.html,sers Electro-Opt.,San Jose,CA, USA,2008,Paper CWJ4.

[81]V.Gapontsev,V.Fomin,D.Gapontsev,and V.Ivshin,“Advances in

multi-kW?ber lasers,”presented at the Advanced Laser Appl.Conf.

Expo.,Michigan,MI,USA,Sep.2006.

[82]J.Zhu,P.Zhou,Y.Ma,X.Xu,and Z.Liu,“Power scaling analysis

of tandem-pumped Yb-doped?ber lasers and ampli?ers,”Opt.Exp., vol.19,pp.18645–18654,2011.

[83]M.H.Muendel,R.Farrow,K.H.Liao,D.Woll,J.Luu,C.Zhang,

J.Morehead,J Segall,J.Gregg,K.Tai,B.Kharlamov,H.Yu,and L.Myers,“Fused?ber pump and signal combiners for4-kW Ytterbium ?ber laser,”Proc.SPIE,vol.7914,p.791431,2011.

[84]S.B.Poole,D.N.Payne,and M.E.Fermann,“Fabrication of low-loss

optical?bres containing rare-earth ions,”Electron.Lett.,vol.21,no.17, pp.737–738,1985.

[85]R.J.Mears,L.Reekie,S.B.Poole,and D.N.Payne,“Neodymium

doped silica single-mode?bre lasers,”Electron.Lett.,vol.21,no.17, pp.738–740,1985.

[86]R.J.Mears,L.Reekie,S.B.Poole,and D.N.Payne,“Low-threshold

tunable CW and Q-switched?bre laser operating at1.55μm,”Electron.

Lett.,vol.22,no.3,pp.159–160,1986.

[87]M.E.Fermann, D.C.Hanna, D.P.Shepherd,P.J.Suni,and

J.E.Townsend,“Ef?cient operation of an Yb-sensitised Er?ber laser at

1.56mm,”Electron.Lett.,vol.24,pp.1135–1136,1988.

[88] D.C.Hanna,R.M.Percival,I.R.Perry,R.G.Smart,P.J.Suni,and

A.C.Tropper,“Yb-doped monomode?bre laser:broadly tunable oper-

ation from1.010μm to1.62μm and three-level operation at974nm,”

J.Modern Opt.,vol.37,pp.329–331,1987.

[89]J.Suni,J.E.Townsend,and A.C.Tropper,“Continuous-wave oscillation

of a monomode thulium-doped?ber laser,”Electron.Lett.,vol.24,no.19, pp.1222–1223,1988.

[90] D.C.Hanna,R.M.Percival,R.G.Smart,J.E.Townsend,and

A.C.Tropper,“Continuous-wave oscillation of holmium-doped silica

?ber laser,”Electron.Lett.,vol.25,no.9,pp.593–594,1989.

0904123IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS,VOL.20,NO.5,SEPTEMBER/OCTOBER2014

[91]P.Barua,E.H.Sekiya,K.Saito,and A.J.Ikushima,“In?uences of

Yb3+ion concentration on the spectroscopic properties of silica glass,”

J.Non-Crystalline Solids,vol.354,pp.4760–4764,2008.

[92]Y.Qiao,L.Wen,B.Wu,J.Ren,D.Chen,and J.Qiu,“Preparation and

spectroscopic properties of Yb-doped and Yb–Al-codoped high silica glasses,”Mater.Chemistry Phys.,vol.107,pp.488–491,2008. [93]H.M.Pask,R.J.Carman,D.C.Hanna,A.C.Tropper,C.J.Mackechnie,

P.R.Barber,and J.M.Dawes,“Ytterbium-doped silica?ber lasers:Ver-satile sources for the1–1.2μm region,”IEEE J.Sel.Topics Quantum Electron.,vol.1,no.1,pp.2–13,Apr.1995.

[94]M.J.Weber,J.E.Lynch,D.H.Blackburn,and D.J.Cronin,“Depen-

dence of the stimulated emission cross section of Yb3+on host glass composition,”IEEE J.Quantum Electron.,vol.QE-19,no.10,pp.1600–1608,Oct.1983.

[95] F.Auzel and P.Goldner,“Towards rare-earth clustering control in doped

glasses,”Opt.Mater.,vol.16,pp.93–103,2001.

[96]S.D.Jackson and T.A.King,“Theoretical modelling of Tm-doped silica

?ber lasers,”J.Lightw.Technol.,vol.17,no.5,pp.948–956,May1999.

[97]S.D.Jackson,“Cross relaxation and energy transfer upconversion pro-

cesses relevant to the functioning of2μm Tm3+-doped silica?bre lasers,”https://www.360docs.net/doc/907866321.html,mun.,vol.230,pp.197–203,2004.

[98] A.E.Siegman,“How to(maybe)measure laser beam quality,”in DPSS

Lasers:Applications and Issues,M.W.Dowley,Ed.Washington,DC, USA:OSA,1998,pp.184–199.

[99]T.S.Ross and https://www.360docs.net/doc/907866321.html,tham,“Appropriate measures and consistent stan-

dard for high energy laser beam quality,”J.Directed Energy,vol.2, pp.22–58,2006.

[100] D.Marcuse,“Loss analysis of single-mode?ber splices,”Bell System Tech.J.,,vol.56,no.5,pp.703–718,1977.

[101] D.Gloge,“Optical power?ow in multimode?bers,”Bell System Tech.

J.,vol.51,pp.1767–1783,1972.

[102]S.Sagha?and C.J.R.Sheppard,“The beam propagation factor for higher order Gaussian beams,”https://www.360docs.net/doc/907866321.html,mun.,vol.153,pp.207–210, 1998.

[103]Y.Jeong, A.J.Boyland,J.K.Sahu,S.Chung,J.Nilsson,and

D.N.Payne,“Multi-kilowatt single-mode Ytterbium-doped large-core

?ber laser,”J.Opt.Soc.Korea,vol.13,pp.416–422,2009.

[104] A.E.Siegman and S.W.Townsend,“Output beam propagation and beam quality from multimode stable-cavity laser,”IEEE J.Quantum Electron., vol.29,no.4,pp.1212–1217,Apr.1993.

[105]Y.Shamir,Y.Sintov,E.Sha?r,and M.Shtaif,“Beam quality output of a few-modes?ber seeded by an off-center single-mode?ber source,”Opt.

Lett.,vol.34,pp.1795–1797,2009.

[106]S.Wielandy,“Implications of higher-order mode content in large mode area?bers with good beam quality,”Opt.Exp.,vol.15,pp.15402–15408, 2007.

[107] D.Gloge,“Optical power?ow in multimode?bers,”Bell Syst.Tech.J., vol.51,pp.1767–1783,1972.

[108]M.N.Zervas,“High power Ytterbium-doped?ber lasers:Fundamentals and applications,”Int.J.Mod.Phys.B,vol.28,1442009,2014. [109]Z.Jiang and J.R.Marciante,“Impact of transverse spatial-hole burning on beam quality in large-area Yb-doped?bers,”J.Opt.Soc.Amer.B, vol.25,pp.247–254,2008.

[110]J.F.Seurin,G.Xu,Q.Wang,B.Guo,R.Van Leeuwen,A.Miglo, P.Pradhan,J.D.Wynn,V.Khal?n,and C.Ghosh,“High-brightness pump sources using2D VCSEL arrays,”Proc.SPIE,vol.7615,76150F, 2010.

[111]H.Yoda,P.Polynkin,and M.Mansuripur,“Beam quality factor of higher order modes in a step-index?ber,”J.Lightw.Technol.,vol.24,no.3, pp.1350–1355,Mar.2006.

[112]M.E.Fermann,“Single-mode excitation of multimode?bers with ultra-short pulses,”Opt.Lett.,vol.23,pp.52–54,1998.

[113]Y.Jung,Y.Jeong,G.Brambilla,and D.J.Richardson,“Adiabatically tapered splice for selective excitation of the fundamental mode in a multimode?ber,”Opt.Lett.,vol.34,pp.2369–2371,2009.

[114]H.Zimer,M.Kozak,A.Liem,F.Flohrer,F.Doerfel,P.Riedel,S.Linke, R.Horley,F.Ghiringhelli,S.Demoulins,M.N.Zervas,J.Kirchhof, S.Unger,S.Jetschke,T.Peschel,and T.Schreiber,“Fibers and?ber-optic components for high power?ber lasers,”Proc.SPIE,vol.7914, 791414,2011.

[115]J.P.Koplow,D.A.V.Kliner,and L.Goldberg,“Single-mode operation of a coiled multimode?ber ampli?er,”Opt.Lett.,vol.25,pp.442–444, 2000.

[116]R.T.Schermer,“Mode scalability in bent optical?bers,”Opt.Exp., vol.15,pp.15674–15701,2007.[117]Z.Li,J.Zhou,W.Wang,B.He,Y.Xue,and Q.Lou,“Limitations of coiling technique for mode controlling of multimode?ber lasers,”

presented at the CLEO/Paci?c Rim,Shangai,China,2009.

[118] B.Sevigny,X.Zhang,M.Garneau,M.Faucher,Y.K.Lize,and N.Holehouse,“Modal sensitivity analysis for single-mode operation in large-mode area?ber,”Proc.SPIE,vol.6873,68730A,2008. [119]S.A.Cerqueira,Jr,“Recent progress and novel applications of photonic crystal?bers,”Rep.Prog.Phys.,vol.73,024401,2010.

[120]W.J.Wadsworth,R.M.Percival,G.Bouwmans,J.C.Knight,and P.S.J.Russell,“High power air-clad photonic crystal?bre laser,”Opt.

Exp.,vol.11,pp.48–53,2003.

[121]G.Canat,S.Jetschke,S.Unger,L.Lombard,P.Bourdon,J.Kirchhof, V.Jolivet,A.Dol?,and O.Vasseur,“Multi?lament-core?bers for high energy pulse ampli?cation at1.5μm with excellent beam quality,”Opt.

Lett.,vol.33,pp.2701–2703,2008.

[122]G.Canat,R.Spittel,S.Jetschke,L.Lombard,and P.Bourdon,“Analysis of the multi?lament core?ber using the effective index theory,”Opt.

Exp.,vol.18,pp.4644–4654,2010.

[123] F.Di Teodoro,M.K.Hemmat,J.Morais,and E.C.Cheung,“High peak power operation of a100μm-core Yb-doped rod-type photonic crystal ?bre ampli?er,”Proc.SPIE,vol.7580,758006,2010.

[124]P.S.J.Russell,“Photonic crystal?bers,”Science,vol.299,pp.358–362, 2003.

[125]J.Limpert,F.Stutzki,F.Jansen,H.J.Otto,T.Eidam,C.Jauregui,and

A.Tunnermann,“Yb-doped large-pitch?bres:effective single-mode op-

eration based on higher-order mode delocalisation,”Light:Sci.Appl., vol.1,no.4,pp.1–5,2012.

[126]R.Dauliat,D.Gaponov,A.Benoit,F.Salin,K.Schuster,R.Jamier,and P.Roy,“Inner cladding microstructuration based on symmetry reduction for improvement of singlemode robustness in VLMA?ber,”Opt.Exp., vol.21,pp.18927–18936,2013.

[127] F.Jansen,F.Stutzki,H.J.Otto,T.Eidam,A.Liem,C.Jauregui, J.Limpert,and A.Tunnermann,“Theramally induced waveguide changes in active?bers,”Opt.Exp.,vol.20,pp.3997–4008,2012. [128]C-H.Liu,G.Chang,N.Litchinitser,D.Guertin,N.Jacobsen,K.Tankala, and A.Galvanauskas,“Chirally coupled core?bers at1550-nm and 1064-nm for effectively single-mode core size scaling,”presented at the https://www.360docs.net/doc/907866321.html,sers Electro-Opt.,Baltimore,MD,USA,2007,Paper CTuBB3.

[129]J.R.Marciante,“Gain?ltering for single-spatial-mode operation of large-mode-area?bre ampli?ers,”IEEE J.Sel.Topics Quantum Elec-tron.,vol.15,no.1,pp.30–36,Jan.2009.

[130]V.Sudesh,T.Mccomb,Y.Chen,M.Bass,M.Richardson,J.Ballato, and A.E.Siegman,“Diode-pumped200μm diameter core,gain-guided, index-antiguided single mode?ber laser,”Appl.Phys.B,vol.90,pp.369–372,2008.

[131]M.J.Li,X.Chen, A.Liu,S.Gray,J.Wang, D.T.Walton,and L.A.Zenteno,“Limit of effective area for single-mode operation in step-index large mode area laser?bers,”J.Lightw.Technol.,vol.27, no.15,pp.3010–3016,Jan.2009.

[132]S.Kawakami and S.Nishida,“Characteristics of a doubly clad optical ?ber with a low-index inner cladding,”IEEE J.Quantum Electron., vol.10,no.12,pp.879–887,Dec.1974.

[133]V.Rastogi and K.S.Chiang,“Propagation characteristics of a segmented cladding?ber,”Opt.Lett.,vol.26,pp.491–493,2001.

[134]L.Dong,T.W.Wu,H.A.McKay,L.Fu,J.Li,and H.G.Winful,“All-glass large-core leakage channel?bers,”IEEE J.Sel.Topics Quantum Electron.,vol.15,no.1,pp.47–53,Jan.2009.

[135]J.M.Fini,“Design of solid and microstructure?bers for suppression of higher-order modes,”Opt.Exp.,vol.13,pp.3477–3490,2005. [136] B.Beaudou, F.Ger?o me,Y.Y.Wang,M.Alharbi,T.D.Bradley,

G.Humbert,J.-L.Auguste,J.-M.Blondy,and F.Benabid,“Millijoule

laser pulse delivery for spark ignition through kagome hollow-core?ber,”

Opt.Lett.,vol.37,pp.1430–1432,2012.

[137]G.P.Agrawal,Nonlinear Fiber Optics,3rd ed.New York:Academic, 2001.

[138] B.Morasse,E.Gagnon,J.Arsenault-Roy,and J.-P.De Sandro,“High peak power single-mode ampli?cation using highly doped double cladding Ytterbium phosphosilicate?ber,”in presented at the Work-shop Specialty Opt.Fibers Appl.,Sigtuna,Sweden,2013,Paper F2.19.

[139] A.J.Kim,P.Dupriez,C.Codemard,J.Nilsson,and J.K.Sahu,“Sup-pression of stimulated Raman scattering in a high power Yb-doped?ber ampli?er using a W-type core with fundamental mode cut-off,”Opt.

Exp.,vol.14,pp.5103–5113,2006.

ENAS云存储(网盘+文档云)管理系统解决方案

易存云存储系统平台建设 项目方案 北京易存科技 2016-1-25 目录 一、方案概述....................................... (03) 二、方案要求与建设目标.................................0 4 2.1 客户需求分析..................................04 2.2 系统主要功能方案..............................05 三、系统安全方案.................................... (19) 3.1 系统部署与拓扑图...............................19 3.2 文件存储加密...................................21 3.3 SSL协议........................................22 3.4 二次保护机制............................. (23)

3.5 备份与恢复.....................................23 四、系统集成与二次开发.................................24 4.1 用户集成.......................................24 4.2 文件集成.................................... (2) 7 4.3 二次开发.................................... (2) 9 五、典型成功案例.......................................29 六、售后服务体系.................................... (30) 6.1公司概况.......................................30 6.2 服务内容与响应时间............................. 31 一、方案概述 随着互联网时代的到来,企业信息化让电子文档成为企业智慧资产的主要载体。信息流通的速度、强度和便捷度的加强,一方面让我们享受到了前所未有的方便和迅捷,但另一方面也承受着信息爆炸所带来的压力。 传统的文件管理方式已经无法满足企业在业务的快速发展中对文件的安全而高效流转的迫切需求。尤其是大文件的传输与分享,集团公司与分公司,部门与部门之间,乃至与供应商或客户之间频繁的业务往来,显得尤其重要。 文件权限失控严重,版本混乱,传递效率,查找太慢,文件日志无法追溯,历史纸质文件管理与当前业务系统有效整合对接等一系列的问题日渐变的突出和迫切。 该文档描述了北京易存科技为企业搭建文档管理系统平台的相关方案。从海量文件的存储与访问,到文件的使用,传递,在线查看,以及文件的流转再到归档

小学奥数之容斥原理

五.容斥原理问题 1.有100种赤贫.其中含钙的有68种,含铁的有43种,那么,同时含钙和铁的食品种类的最大值和最小值分别是( ) A 43,25 B 32,25 C32,15 D 43,11 解:根据容斥原理最小值68+43-100=11 最大值就是含铁的有43种 2.在多元智能大赛的决赛中只有三道题.已知:(1)某校25名学生参加竞赛,每个学生至少解出一道题;(2)在所有没有解出第一题的学生中,解出第二题的人数是 解出第三题的人数的2倍:(3)只解出第一题的学生比余下的学生中解出第一题的人数多1人;(4)只解出一道题的学生中,有一半没有解出第一题,那么只解出第二题的学生人数是( ) A,5 B,6 C,7 D,8 解:根据“每个人至少答出三题中的一道题”可知答题情况分为7类:只答第1题,只答第2题,只答第3题,只答第1、2题,只答第1、3题,只答2、3题,答1、2、3题。 分别设各类的人数为a1、a2、a3、a12、a13、a23、a123 由(1)知:a1+a2+a3+a12+a13+a23+a123=25…① 由(2)知:a2+a23=(a3+ a23)×2……② 由(3)知:a12+a13+a123=a1-1……③ 由(4)知:a1=a2+a3……④ 再由②得a23=a2-a3×2……⑤ 再由③④得a12+a13+a123=a2+a3-1⑥ 然后将④⑤⑥代入①中,整理得到 a2×4+a3=26 由于a2、a3均表示人数,可以求出它们的整数解: 当a2=6、5、4、3、2、1时,a3=2、6、10、14、18、22 又根据a23=a2-a3×2……⑤可知:a2>a3 因此,符合条件的只有a2=6,a3=2。 然后可以推出a1=8,a12+a13+a123=7,a23=2,总人数=8+6+2+7+2=25,检验所有条件均符。 故只解出第二题的学生人数a2=6人。 3.一次考试共有5道试题。做对第1、2、3、、4、5题的分别占参加考试人数的95%、80%、79%、74%、85%。如果做对三道或三道以上为合格,那么这次考试的合格率至少是多少? 答案:及格率至少为71%。 假设一共有100人考试 100-95=5 100-80=20 100-79=21 100-74=26 100-85=15 5+20+21+26+15=87(表示5题中有1题做错的最多人数)

云课堂系统解决方案

云课堂 技术解决方案

目录 第1章概述 (2) 第2章现状分析及问题 (3) 2.1方案背景 (3) 2.2教育信息化建设的发展 (3) 2.2云课堂的推出 (4) 第3章云课堂技术解决方案 (5) 3.1云终端方案概述 (5) 3.2云课堂解决方案 (5) 3.2.1 云课堂拓扑图 (5) 3.2.2 云课堂教学环境 (6) 3.2.3 云课堂主要功能 (7) 3.2.4 优课数字化教学应用系统功能 (8) 第4章方案优势 (9) 4.1私密性 (9) 4.2工作连续性 (9) 4.3方便移动性 (9) 4.4场景一致性 (9) 4.5长期积累性 (9) 4.6安全稳定性 (10) 4.7易维护性 (10) 4.8高效性 (10) 第5章实际案例 (11)

第1章概述 随着现代信息技术的飞速发展,越来越多的用户更加注重自身信息架构的简便易用性、安全性、可管理性和总体拥有成本。近几年信息化的高速发展,迫使越来越多的教育机构需要采用先进的信息化手段,解决各机构当前面临的数据安全隔离、信息共享、资源整合等实际问题,实现通过改进机器的利用率降低成本,减少管理时间和降低基础设施成本,提高工作效率。 无论是作为云计算的核心技术,还是作为绿色 IT、绿色数据中心的核心技术,虚拟化已经成为 IT 发展的重要方向,也可以说我们正面临着一场 IT 虚拟化、云计算的革命。这场 IT 虚拟化、云计算的革命正在开始席卷全球。 虚拟化技术在解决信息安全、资源利用率提升、简化 IT 管理、节能减排等方面有着得天独厚的优势,通过虚拟化技术,把数据中心的计算资源和存储资源发布给终端用户共享使用,大幅度提高服务器资源利用率,同时通过严格的访问控制,确保数据中心中所存储的安全性。

数据结构实验指导书(2016.03.11)

《数据结构》实验指导书 郑州轻工业学院 2016.02.20

目录 前言 (3) 实验01 顺序表的基本操作 (7) 实验02 单链表的基本操作 (19) 实验03 栈的基本操作 (32) 实验04 队列的基本操作 (35) 实验05 二叉树的基本操作 (38) 实验06 哈夫曼编码 (40) 实验07 图的两种存储和遍历 (42) 实验08 最小生成树、拓扑排序和最短路径 (46) 实验09 二叉排序树的基本操作 (48) 实验10 哈希表的生成 (50) 实验11 常用的内部排序算法 (52) 附:实验报告模板 .......... 错误!未定义书签。

前言 《数据结构》是计算机相关专业的一门核心基础课程,是编译原理、操作系统、数据库系统及其它系统程序和大型应用程序开发的重要基础,也是很多高校考研专业课之一。它主要介绍线性结构、树型结构、图状结构三种逻辑结构的特点和在计算机内的存储方法,并在此基础上介绍一些典型算法及其时、空效率分析。这门课程的主要任务是研究数据的逻辑关系以及这种逻辑关系在计算机中的表示、存储和运算,培养学生能够设计有效表达和简化算法的数据结构,从而提高其程序设计能力。通过学习,要求学生能够掌握各种数据结构的特点、存储表示和典型算法的设计思想及程序实现,能够根据实际问题选取合适的数据表达和存储方案,设计出简洁、高效、实用的算法,为后续课程的学习及软件开发打下良好的基础。另外本课程的学习过程也是进行复杂程序设计的训练过程,通过算法设计和上机实践的训练,能够培养学生的数据抽象能力和程序设计能力。学习这门课程,习题和实验是两个关键环节。学生理解算法,上机实验是最佳的途径之一。因此,实验环节的好坏是学生能否学好《数据结构》的关键。为了更好地配合学生实验,特编写实验指导书。 一、实验目的 本课程实验主要是为了原理和应用的结合,通过实验一方面使学生更好的理解数据结构的概念

2015国家公务员考试行测:数学运算-容斥原理和抽屉原理

【导读】国家公务员考试网为您提供:2015国家公务员考试行测:数学运算-容斥原理和抽屉原理,欢迎加入国家公务员考试QQ群:242808680。更多信息请关注安徽人事考试网https://www.360docs.net/doc/907866321.html, 【推荐阅读】 2015国家公务员笔试辅导课程【面授+网校】 容斥原理和抽屉原理是国家公务员考试行测科目数学运算部分的“常客”,了解此两种原理不仅可以提高做题效率,还可以提高自己的运算能力,扫平所有此类计算题。中公教育专家在此进行详细解读。 一、容斥原理 在计数时,要保证无一重复,无一遗漏。为了使重叠部分不被重复计算,在不考虑重叠 的情况下,把包含于某内容中的所有对象的数目先计算出来,然后再把计数时重复计算的数 目排斥出去,使得计算的结果既无遗漏又无重复,这种计数的方法称为容斥原理。 1.容斥原理1——两个集合的容斥原理 如果被计数的事物有A、B两类,那么,先把A、B两个集合的元素个数相加,发现既是 A类又是B类的部分重复计算了一次,所以要减去。如图所示: 公式:A∪B=A+B-A∩B 总数=两个圆内的-重合部分的 【例1】一次期末考试,某班有15人数学得满分,有12人语文得满分,并且有4人语、 数都是满分,那么这个班至少有一门得满分的同学有多少人? 数学得满分人数→A,语文得满分人数→B,数学、语文都是满分人数→A∩B,至少有一 门得满分人数→A∪B。A∪B=15+12-4=23,共有23人至少有一门得满分。 2.容斥原理2——三个集合的容斥原理 如果被计数的事物有A、B、C三类,那么,将A、B、C三个集合的元素个数相加后发现 两两重叠的部分重复计算了1次,三个集合公共部分被重复计算了2次。 如图所示,灰色部分A∩B-A∩B∩C、B∩C-A∩B∩C、C∩A-A∩B∩C都被重复计算了1 次,黑色部分A∩B∩C被重复计算了2次,因此总数A∪B∪C=A+B+C-(A∩B-A∩B∩C)-(B∩ C-A∩B∩C)-(C∩A-A∩B∩C)-2A∩B∩C=A+B+C-A∩B-B∩C-C∩A+A∩B∩C。即得到: 公式:A∪B∪C=A+B+C-A∩B-B∩C-C∩A+A∩B∩C

数据结构课后习题

第一章 3.(1)A(2)C(3)D 5.计算下列程序中x=x+1的语句频度 for(i=1;i<=n;i++) for(j=1;j<=i;j++) for(k=1;k<=j;k++) x=x+1; 【解答】x=x+1的语句频度为: T(n)=1+(1+2)+(1+2+3)+……+(1+2+……+n)=n(n+1)(n+2)/6 6.编写算法,求一元多项式p n(x)=a0+a1x+a2x2+…….+a n x n的值p n(x0),并确定算法中每一语句的执行次数和整个算法的时间复杂度,要求时间复杂度尽可能小,规定算法中不能使用求幂函数。注意:本题中的输入为a i(i=0,1,…n)、x和n,输出为P n(x0)。算法的输入和输出采用下列方法 (1)通过参数表中的参数显式传递 (2)通过全局变量隐式传递。讨论两种方法的优缺点,并在算法中以你认为较好的一种实现输入输出。 【解答】 (1)通过参数表中的参数显式传递 优点:当没有调用函数时,不占用内存,调用结束后形参被释放,实参维持,函数通用性强,移置性强。 缺点:形参须与实参对应,且返回值数量有限。 (2)通过全局变量隐式传递 优点:减少实参与形参的个数,从而减少内存空间以及传递数据时的时间消耗 缺点:函数通用性降低,移植性差 算法如下:通过全局变量隐式传递参数 PolyValue() { int i,n; float x,a[],p; printf(“\nn=”); scanf(“%f”,&n); printf(“\nx=”); scanf(“%f”,&x); for(i=0;i

云安全管理平台解决方案.doc

云安全管理平台解决方案 北信源云安全管理平台解决方案北京北信源软件股份有限公司 2010 云安全管理平台解决方案/webmoney 2.1问题和需求分析 2.2传统SOC 面临的问题................................................................... ...................................... 4.1资产分布式管理 104.1.1 资产流程化管理 104.1.2 资产域分布 114.2 事件行为关联分析 124.2.1 事件采集与处理 124.2.2 事件过滤与归并 134.2.3 事件行为关联分析 134.3 资产脆弱性分析 144.4 风险综合监控 154.4.1 风险管理 164.4.2 风险监控 174.5 预警管理与发布 174.5.1 预警管理 174.5.2 预警发布 194.6 实时响应与反控204.7 知识库管理 214.7.1 知识共享和转化 214.7.2 响应速度和质量 214.7.3 信息挖掘与分析 224.8 综合报表管理 245.1 终端安全管理与传统SOC 的有机结合 245.2 基于云计算技术的分层化处理 255.3 海量数据的标准化采集和处理 265.4 深入事件关联分析 275.5 面向用户服务的透明化 31云 安全管理平台解决方案 /webmoney 前言为了不断应对新的安全挑战,越来越多的行业单位和企业先后部署了防火墙、UTM、入侵检测和防护系统、漏洞扫描系统、防病毒系统、终端管理系统等等,构建起了一道道安全防线。然而,这些安全防线都仅仅抵御来自某个方面的安全威胁,形成了一个个“安全防御孤岛”,无法产生协同效应。更为严重地,这些复杂的资源及其安全防御设施在运行过程中不断产生大量的安全日志和事件,形成了大量“信息孤岛”,有限的安全管理人员面对这些数量巨大、彼此割裂的安全信息,操作着各种产品自身的控制台界面和告警窗口,显得束手无策,工作效率极低,难以发现真正的安全隐患。另一方面,企业和组织日益迫切的信息系统审计和内控要求、等级保护要求,以及不断增强的业务持续性需求,也对客户提出了严峻的挑战。对于一个完善的网络安全体系而言,需要有一个统一的网络安全管理平台来支撑,将整个网络中的各种设备、用户、资源进行合理有效的整合,纳入一个统一的监管体系,来进行统一的监控、调度、协调,以达到资源合理利用、网络安全可靠、业务稳定运行的目的。云安全管理平台解决方案 /webmoney 安全现状2.1 问题和需求分析在历经了网络基础建设、数据大集中、网络安全基础设施建设等阶段后,浙江高法逐步建立起了大量不同的安全子系统,如防病毒系统、防火墙系统、入侵检测系统等,国家主管部门和各行业也出台了一系列的安全标准和相关管理制度。但随着安全系统越来越庞大,安全防范技术越来越复杂,相关标准和制度越来越细化,相应的问题也随之出现: 1、安全产品部署越来越多,相对独立的部署方式使各个设备独立配置、管理,各产品的运行状态如何?安全策略是否得到了准确落实?安全管理员难以准确掌握,无法形成全局的安全策略统一部署和监控。 2、分散在各个安全子系统中的安全相关数据量越来越大,一方面海量数据的集中储存和分析处理成为问题;另一方面,大量的重复信息、错误信息充斥其中,海量的无效数据淹没了真正有价值的安全信息;同时,从大量的、孤立的单条事件中无法准确地发现全局性、整体性的安全威胁行为。 3、传统安全产品仅仅面向安全人员提供信息,但管理者、安全管理员、系统管理

根式函数值域定稿版

根式函数值域 HUA system office room 【HUA16H-TTMS2A-HUAS8Q8-HUAH1688】

探究含有根式的函数值域问题 含根式的函数的值域或者最值问题在高中数学的学习过程中时常遇到,因其解法灵活,又缺乏统一的规律,给我们造成了很大的困难,导致有些学生遇到根式就害怕。为此,本文系统总结此类函数值域的求解方法,供学生参考学习。 1.平方法 例1:求31++-=x x y 的值域 解:由题意知函数定义域为[]1,3-,两边同时平方得:322422+--+=x x y =4+()4212+- +x 利用图像可得[]8,42∈y ,又知?y 0[]22,2∈∴y 所以函数值域为[]22,2 析:平方法求值域适用于平方之后可以消去根式外面未知量的题型。把解析式转化为()x b a y ?+=2 的形式,先求y 2 的范围,再得出y 的范围即值域。 2.换元法 例2: 求值域1)12--=x x y 2)x x y 2 4-+= 解:(1)首先定义域为[)+∞,1,令()01≥-=t x t ,将原函数转化为 [)+∞∈,0t ,?? ????+∞∈∴,815y 析:当函数解析式由未知量的整数幂与根式构成,并且根式内外的未知量的次幂保持一致。可以考虑用代数换元的方法把原函数转化成二次函数,再进行值域求解。 (2)首先,函数定义域为[]2,2-∈x ,不妨设αsin 2=x ,令?? ????-∈2,2ππα

则原函数转化为:??? ? ?+=+=4sin 22cos 2sin 2παααy ?? ????-∈2,2ππα,∴??????-∈+43,44πππα 析:形如题目中的解析式,考虑用三角换元的方法,在定义域的前提下,巧妙地规定角的取值范围,避免绝对值的出现。 不管是代数换元还是三角换元,它的目的都是为了去根式,故需要根据题目灵活选择新元,并注意新元的范围。 3.数形结合法 例3:1)求()()8222+-+= x x y 的值域。 2)求1362222+-++-= x x y x x 的最小值。 解:(1)()()8222+-+=x x y 82++-=x x 其解析式的几何意义为数轴上的一动点x ,到两定点2与-8的距离之和,结合数轴不难得到[]+∞∈,10y (2)解析式可转化为()()41312 2+++=--x x y , 定义域为R ,进行适当的变形 ()()=+++--413122x x ()()()()2031012 222----+++x x , 由它的形式联想两点间的距离公式,分别表示点到点的距离与点的距离之和。 点()0,x P 到()1,1A 和()2,3B 的距离之和。即PB PA y +=,结合图形可知 13min =+'=PB A P y ,其中()1,1-'A 析:根据解析式特点,值域问题转化成距离问题,结合图形得出最值,进而求出了值域。 例4:1) 求x x y x 2312 +--+=的值域

雷达原理复习

第一章绪论 1、雷达的任务:测量目标的距离、方位、仰角、速度、形状、表面粗糙度、介电特性。 雷达是利用目标对电磁波的反射现象来发现目标并测定其位置。 当目标尺寸小于雷达分辨单元时,则可将其视为“点”目标,可对目标的距离和空间位置角度定位。目标不是一个点,可视为由多个散射点组成的,从而获得目标的尺寸和形状。采用不同的极化可以测定目标的对称性。 β任一目标P所在的位置在球坐标系中可用三个目标确定:目标斜距R,方位角α,仰角 在圆柱坐标系中表示为:水平距离D,方位角α,高度H 目标斜距的测量:测距的精度和分辨力力与发射信号的带宽有关,脉冲越窄,性能越好。目标角位置的测量:天线尺寸增加,波束变窄,测角精度和角分辨力会提高。 相对速度的测量:观测时间越长,速度测量精度越高。 目标尺寸和形状:比较目标对不同极化波的散射场,就可以提供目标形状不对称性的量度。 2、雷达的基本组成:发射机、天线、接收机、信号处理机、终端设备 3、雷达的工作频率:220MHZ-35GHZ。L波段代表以22cm为中心,1-2GHZ;S波段代表10cm,2-4GHZ;C波段代表5cm,4-8GHZ;X波段代表3cm,8-12GHZ;Ku代表2.2cm,12-18GHZ;Ka代表8mm,18-27GHZ。 第二章雷达发射机 1、雷达发射机的认为是为雷达系统提供一种满足特定要求的大功率发射信号,经过馈线和收发开关并由天线辐射到空间。 雷达发射机可分为脉冲调制发射机:单级振荡发射机、主振放大式发射机;连续波发射机。 2、单级振荡式发射机组成:大功率射频振荡器、脉冲调制器、电源 触发脉冲 脉冲调制器大功率射频振荡器收发开关 电源高压电源接收机 主要优点:结构简单,比较轻便,效率较高,成本低;缺点:频率稳定性差,难以产生复杂的波形,脉冲信号之间的相位不相等 3、主振放大式发射机:射频放大链、脉冲调制器、固态频率源、高压电源。射频放大链是发射机的核心,主要有前级放大器、中间射频功率放大器、输出射频功率放大器 射频输入前级放大器中间射频放大器输出射级放大器射频输出固态频率源脉冲调制器脉冲调制器 高压电源高压电源电源 脉冲调制器:软性开关调制器、刚性开关调制器、浮动板调制器 4、现代雷达对发射机的主要要求:发射全相参信号;具有很高的频域稳定度;能够产生复杂信号波形;适用于宽带的频率捷变雷达;全固态有源相控阵发射机 5、发射机的主要性能指标:

二次函数和几何综合压轴题题型归纳

学生: 科目: 数 学 教师: 刘美玲 一、二次函数和特殊多边形形状 二、二次函数和特殊多边形面积 三、函数动点引起的最值问题 四、常考点汇总 1、两点间的距离公式:()()22B A B A x x y y AB -+-= 2、中点坐标:线段AB 的中点C 的坐标为:??? ??++22 B A B A y y x x , 直线11b x k y +=(01≠k )与22b x k y +=(02≠k )的位置关系: (1)两直线平行?21k k =且21b b ≠ (2)两直线相交?21k k ≠ (3)两直线重合?21k k =且21b b = (4)两直线垂直?121-=k k 3、一元二次方程有整数根问题,解题步骤如下: ① 用?和参数的其他要求确定参数的取值范围; ② 解方程,求出方程的根;(两种形式:分式、二次根式) ③ 分析求解:若是分式,分母是分子的因数;若是二次根式,被开方式是完全平方式。 例:关于x 的一元二次方程()0122 2 =-m x m x ++有两个整数根,5<m 且m 为整数,求m 的值。 4、二次函数与x 轴的交点为整数点问题。(方法同上) 例:若抛物线()3132 +++=x m mx y 与x 轴交于两个不同的整数点,且m 为正整数,试确定 此抛物线的解析式。 课 题 函数的综合压轴题型归类 教学目标 1、 要学会利用特殊图形的性质去分析二次函数与特殊图形的关系 2、 掌握特殊图形面积的各种求法 重点、难点 1、 利用图形的性质找点 2、 分解图形求面积 教学内容

5、方程总有固定根问题,可以通过解方程的方法求出该固定根。举例如下: 已知关于x 的方程2 3(1)230mx m x m --+-=(m 为实数),求证:无论m 为何值,方程总有一个固定的根。 解:当0=m 时,1=x ; 当0≠m 时,()032 ≥-=?m ,()m m x 213?±-= ,m x 3 21-=、12=x ; 综上所述:无论m 为何值,方程总有一个固定的根是1。 6、函数过固定点问题,举例如下: 已知抛物线22 -+-=m mx x y (m 是常数),求证:不论m 为何值,该抛物线总经过一个固定的点,并求出固定点的坐标。 解:把原解析式变形为关于m 的方程()x m x y -=+-122 ; ∴ ???=-=+-0 1 02 2x x y ,解得:???=-=1 1 x y ; ∴ 抛物线总经过一个固定的点(1,-1)。 (题目要求等价于:关于m 的方程()x m x y -=+-122 不论m 为何值,方程恒成立) 小结.. :关于x 的方程b ax =有无数解????==0 b a 7、路径最值问题(待定的点所在的直线就是对称轴) (1)如图,直线1l 、2l ,点A 在2l 上,分别在1l 、2l 上确定两点M 、N ,使得MN AM +之和最小。 (2)如图,直线1l 、2l 相交,两个固定点A 、B ,分别在1l 、2l 上确定两点M 、N ,使得 AN MN BM ++之和最小。

PB常用函数

PB常用函数日期时间类函数 日期时间类函数的功能如下: Date:把日期转换为Date类型。 Time:把时间转换为Time类型。 Day:日期值。 Month:月值。 Year:年值。 DayName:星期几。 DayNumber:一周中的第几天。 DaysAfer:两个日期之间所差的天数。 SecondsAfer:两个时间之间所差的秒数。 Hour:小时。 Minute:分钟。 Second:秒。 Now:系统当前时间。 Today:系统日期和时间。 RelativeDate:指定日期前后的天数值。 RelativeTime:指定时间的前后时间值。 数值计算类函数 数值计算类函数主要的作用就是对数据进行计算,功能如下:Abs:返回数据的绝对值。 Max:求输入的最大值。 Min:求输入的最小值。 Ceiling:返回整数,小数会自动向上进位。 Int:返回整数,小数会自动向下退位。 Round:对数据进行四舍五入操作。 Truncate:删除掉小数点后若干位。 Cos:求余弦值。 Sin:求正弦值。 Tan:求正切值。 Exp:以e为底,输入值为次方的乘方值。 Sqrt:求平方根。 Fact:求阶乘。 Log:求自然对数。 LogTen:求以10为底的对数。 Mod:求余数。 Pi:求与PI的乘积。 Rand:返回1与输入值之间的一个伪随机数。 字符串类函数 字符串类函数的功能如下。 Fill:建立一个指定长度的字符串。 Lower:转换为小写字母。

Upper:转换为大写字母。 WordCap:首写字母大写,其他小写。 Space:由指定字符个数组成的空格字符串。 Left:从字符串左边开始指定字符串。 Right:从字符串右边开始指定字符串。 LeftTrim:删除字符串左边的空格。 RightTrim:删除字符串右边的空格。 Trim:删除左右两边的空格。 Len:返回字符串长度。 Match:判断是否有指定模式的字符。 Mid:取子字符串。 Replace:用指定字符替换另外一个字符串。 String:将数据转换为指定格式的字符串。 信息类函数 信息类函数可以获取数据窗口中的一些信息,函数的功能如下: CurrentRow:获取数据窗口的焦点的行数。 Page:获取当前记录的页数。 PageAcross:获取当前水平方向的页面。 PageCount:获取总页数。 RowHeight:获得记录的高度。 Describe:获取数据窗口对象的属性值。 IsRowModified:获取记录是否修改过,如果修改过返回True。 IsRowNew:获取是否新插入数据,如果插入返回True。 IsSelected:获取记录是否被选中,选中返True。 PageCountAcross:获取水平方向总页面。 RowCount:获取主缓冲区的总记录数。 统计类函数 统计类函数主要是用来对数据库中的数据进行统计操作,统计函数功能如下: Avg:计算字段的平均数,例如Avg(id)。 Max:计算字段的最大值,例如Max(id)。 Min:计算字段的最小值,例如Min(id)。 Median:计算字段的中间值。 Count:计算表或字段的记录数,例如Count(*)。 Frist:返回第一条记录。 Last:返回最后一条记录。 交叉表函数 只能在交叉列表风格的数据窗口中的细节区使用交叉表函数,交叉表的函数功能如下:CrosstabVag:计算字段数据的平均数。 CrosstabCount:计算字段数据的记录数。 CrosstabMax:计算字段数据的最大值。 CrosstabMin:计算字段数据的最小值。 数据类型转换与检查函数 数据类型转换与检查函数用于定义数据窗口的过滤条件、有效性检查和数据类型转换,数据类型转换与检查函数的功能如下:

云管理平台解决方案

随着云计算在企业内应用,大多数企业都认识到了云计算的的重要性,因为它可以实现资源分配的灵活性、可伸缩性并且提高了服务器的利用率,降低了企业的成本。但是随着企业信息化程度的越来越高、信息系统支持的业务越来越复杂,管理的难度也越来越大,所以就需要选择一个合理的解决方案来支撑企业信息系统的管理和发展。 云管理平台最重要的两个特质在于管理云资源和提供云服务。即通过构建基础架构资源池(IaaS)、搭建企业级应用、开发、数据平台(PaaS),以及通过SOA架构整合服务(SaaS)来实现全服务周期的一站式服务,构建多层级、全方位的云资源管理体系。那么有没有合适的云管理平台解决方案可以推荐呢? SmartOps作为新一代多云管理平台,经过6年多的持续研发和实际运营,已经逐渐走向成熟,能通过单一入口广泛支持腾讯云、阿里云、华为云、AWS等超大规模公有云的统一监控、资源编排、资产管理、成本管理、DevOps 等管理功能,同时也支持私有云和物理裸机环境的统一纳管。SmartOps平台具有统一门户、CMDB配置

数据库、IT服务管理、运维自动化和监控告警等主要模块,支持客户自助在线处理订单、付款销账、申报问题、管理维护等商务运营流程,而且对客户的管理、交付、技术支持也都完全在平台上运行,这极大提升了整体运营效率并大幅降低成本,业务交付速度更快、自动化程度更高、成本更具竞争力、用户体验更佳。 同时,SmartOps正在构建适应业务创新发展的云管理平台,实现从服务中提炼普惠性的服务方案,并构建软件化、工具化、自动化的快速上线对外提供服务的通道。SmartOps不仅是一个云管平台,也是一个面向企业用户的服务迭代的创新平台,一切有利于企业用户数字化发展的个性化服务,都有可能在普遍落地后实现技术服务产品化、工具化的再输出。不仅如此,下一步,SmartOps还将融入更多的价值,包括借助人工智能的技术,面向企业用户领导决策提供参考价值。借助平台化的管理工具,为企业财务人员提供有价值的成本参

国考行测暑期每日一练数学运算:容斥原理和抽屉原理精讲

2015国考行测暑期每日一练数学运算:容斥原理和抽屉原理精讲 容斥原理和抽屉原理是国家公务员测试行测科目数学运算部分的“常客”,了解此两种原理不仅可以提高做题效率,还可以提高自己的运算能力,扫平所有此类计算题。中公教育专家在此进行详细解读。 一、容斥原理 在计数时,要保证无一重复,无一遗漏。为了使重叠部分不被重复计算,在不考虑重叠的情况下,把包含于某内容中的所有对象的数目先计算出来,然后再把计数时重复计算的数目排斥出去,使得计算的结果既无遗漏又无重复,这种计数的方法称为容斥原理。 1.容斥原理1——两个集合的容斥原理 如果被计数的事物有A、B两类,那么,先把A、B两个集合的元素个数相加,发现既是A类又是B类的部分重复计算了一次,所以要减去。如图所示: 公式:A∪B=A+B-A∩B 总数=两个圆内的-重合部分的 【例1】一次期末测试,某班有15人数学得满分,有12人语文得满分,并且有4人语、数都是满分,那么这个班至少有一门得满分的同学有多少人? 数学得满分人数→A,语文得满分人数→B,数学、语文都是满分人数→A∩B,至少有一门得满分人数→A∪B。A∪B=15+12-4=23,共有23人至少有一门得满分。 2.容斥原理2——三个集合的容斥原理 如果被计数的事物有A、B、C三类,那么,将A、B、C三个集合的元素个数相加后发现两两重叠的部分重复计算了1次,三个集合公共部分被重复计算了2次。 如图所示,灰色部分A∩B-A∩B∩C、B∩C-A∩B∩C、C∩A-A∩B∩C都被重复计算了1次,黑色部分A∩B∩C被重复计算了2次,因此总数A∪B∪C=A+B+C-(A∩B-A∩B∩C)-(B∩C -A∩B∩C)-(C∩A-A∩B∩C)-2A∩B∩C=A+B+C-A∩B-B∩C-C∩A+A∩B∩C。即得到:公式:A∪B∪C=A+B+C-A∩B-B∩C-C∩A+A∩B∩C

云课堂解决方案

创新管理价值,引导教学未来——云课堂解决方案 一、概述 随着计算机教育的发展,计算机机房在各中小学已经相当普及,这些计算机资源在很大程度上提高了课题的教学效果。同时,随着机房规模的不断扩大,学校需要管理和维护的各种计算机硬件和软件资源也越来越多,而中小学维护力量相对薄弱,如何科学有效地对这些教育资源进行管理已成为各中小学面临的一个难点管理维护问题:很少中小学有专门的机房管理人员,机房维护专业性要求高,工作量大 使用体验问题:PC使用时间一长,运行速度变慢,故障变多 投资保护问题:PC更新换代较快,投资得不到保障 节能环保问题:机房耗电量大,废弃电脑会产生大量电子垃圾 二、方案简介 RCC(Ruijie Cloud Class)云课堂是根据不断整合和优化校园机房设备的工作思路,结合普教广大学校的实际情况编制的新一代计算机教室建设方案。每间教室只需一台云课堂主机设备,便可获得几十台性能超越普通PC机的虚拟机,这些虚拟机通过网络交付给云课堂终端,学生便可体验生动的云桌面环境。云课堂可按照课程提供丰富多彩的教学系统镜像,将云技术和教育场景紧密结合,实现教学集中化,管理智能化,维护简单化,将计算机教室带入云的时代。 三、方案特性 简管理

云课堂采用全新的集中管理技术管理学校所有计算机教室,管理员在云课堂集中管理平台RCC Center中根据教学课程的不同应用软件制作课程镜像, 同步给教室中的云课堂主机设备,老师上课时可根据课程安排一键选择镜像从而随时获得想要的教学环境。 管理员也不用再为记录繁杂的命令而烦恼,云课堂提供全图形控制管理界面,无论虚拟机制作,编辑,还原都只需轻轻一按。云课堂的管理模式可彻底解决机房中常见大量软件安装导致系统臃肿、软件冲突,病毒侵入、教学、考试场景切换工作量大等难题,还可省去Ghost或还原卡的繁杂设置。全校的计算机教室设备监控和软件维护在办公室中即可轻松实现,效率比PC管理提高9倍! 促教学 云课堂三大关键技术,全面提升虚拟机性能,可令终端启动和课程切换加速,教学软件运行更快,并且可以全面控制学生用机行为,杜绝上课开小差的情况发生。 智能镜像加速技术 - 所有定制好的系统镜像会由云课堂主机自动优化,在该技术的支持下,60个虚拟机启动时间只需短短几分钟,同时还提供老师在上课过程中可随时切换学生操作系统的选择,从而轻易改变教学环境,演绎云技术带给传统教学的优化和创新实践。 多级Cache缓存技术 - 实现镜像启动加速、IO加速,使云桌面启动和应用程序运行速度大幅度提升,用户体验远高于市面上其他产品。在该技术帮助下,教师常用教学课件,专用软件启动、运行速度比同配置物理机提升200%,大幅提升用机体验,让学生畅游”云海”,领略“飞”一般的感受! 多媒体教学管理软件防卸载技术–云课堂终端内嵌多媒体教学管理程序,且学生不可见。老师在使用该软件教学时,不会再出现学生因卸载或关闭管理程序而脱离教师的管理现象,大大加强对学生上课行为的控制力度,严肃课堂纪律,教学质量得以保证。 易获得 云课堂是包括课堂主机,课堂终端,多媒体教学管理软件和课堂集中管理平台在内的一套端到端的整体解决方案。其部署过程极其简单,仅需将云课堂主机和云课堂终端相连,在云课堂主机上做一次课程配置,一间全新的计算机教室即建设完成。因省去逐台PC分区设置和系统同传等过程,效率上可提高3小时以上。 同时云课堂终端功耗极低,普通教室不需强电改造即可转型为云课堂,加快校园IT信息化建设的同时,打造绿色校园 更环保 每台云课堂终端设备平均功耗20w,是传统PC机的1/12。且整个终端机身使用一体化设计,无风扇、硬盘等易损元件,寿命比PC机延长20%以上。节省开支的同时大大减少电子垃圾,响应国家倡导的绿色节能号召,创造舒适、低能耗的绿色校园环境。

浪潮私有云平台解决方案

浪潮私有云平台解决方案云计算的发展 近几年,国内外IT信息技术快速发展,以云计算为代表的新兴技术已经为解决传统IT信息化建设困局找到了突破性的解决方案,并已经在国内企业、政府、金融、电信等众多关键领域取得了成功。 云计算是一种按使用量付费的模式,这种模式提供可用的、便捷的、按需的网络访问,进入可配置的计算资源共享池(资源包括网络,服务器,存储,应用软件,服务),这些资源能够被快速提供,只需投入很少的管理工作,或与服务供应商进行很少的交互。 云计算分为三种服务模式:软件即服务(SaaS)、平台即服务(PaaS)、基础设施即服务(IaaS)。 云计算根据部署部署方式的不同分为:公有云(Public Cloud)、私有云(Private Cloud)、社区云(Community Cloud)、混合云(Hybrid Cloud)。 其中私有云是为一个客户单独使用而构建的,因而提供对数据、安全性和服务质量的最有效控制。私有云可部署在企业数据中心的防火墙内,也可以部署在一个安全的主机托管场所,私有云的核心属性是专有资源。主要优势体现在以下方面: 1.数据安全 虽然每个公有云的提供商都对外宣称其服务在各方面都是非常安全,特别是对

数据的管理。但是对企业而言,特别是大型企业以及对安全要求较高的企业而言,和业务有关的数据是其的生命线,是不能受到任何形式的威胁,而私有云在这方面是非常有优势的,因为它一般都构建在防火墙后。 2、SLA(服务质量) 因为私有云一般在防火墙之后,而不是在某一个遥远的数据中心里,所以当公司员工访问那些基于私有云的应用时,它的SLA会非常稳定,不会受到网络不稳定的影响。 3、不影响现有IT管理的流程 对大型企业而言,流程是其管理的核心,如果没有完善的流程,企业将会成为一盘散沙。不仅与业务有关的流程非常繁多,而且IT部门的管理流程也较多,比如在数据管理和安全规定等方面。 客户面临由虚拟化向云服务转型的挑战 服务器虚拟化作为云计算的基础,已经被越来越多的客户认可,虚拟化已经成为数据中心建设过程中的首选方案,将服务器物理资源抽象成逻辑资源,让一台服务器变成几台甚至上百台互相隔离的虚拟服务器,用户将不再受限于物理上的界限,而是让CPU、内存、磁盘、I/O等硬件变成可以动态管理的“资源池”,从而提高资源的利用率,简化系统管理,实现服务器整合,让IT对业务的变化更具适应力。通过部署服务器虚拟化,用户能够获得如下收益: ?降低TCO成本,提高硬件资源利用率,节省了机房空间成本;

云课堂系统解决方案

玄课堂 技术解决方案 目录 第2章现状分析及问题................................................ 错误!未定义书签。 2」方案背景........................................................ 错误!未定义书签。 2.2教育信息化建设的发展 .......................................... 错误!未定义书签。 2.2云课堂的推;h错谋!未定义书签。 第3章云课堂技术解决方案............................................. 错误!未定义书签。 3.1云终端方案概述?错误!未定义书签。 3.2云课堂解决方案?错误!未定义书签。 3.2. 1云课堂拓扑图............................................. 错误!未定义书签。 3. 2. 2 云课堂教学环境.......................................... 错谋!未定义书签。 3. 2. 3云课堂主要功能Z错误!未定义书签。 3. 2. 4优课数字化教学应用系统功能 ............................... 错误!未定义书签。 第4章方案优势...................................................... 错误!未定义书签。 4」私密性.......................................................... 错误!未定义书签。 4.2匸作连续性,错淚!未定义书签。 4.3方便移动性 .................................................... 错误!未定义书签。 4.4场景?致性 ..................................................... 错误!未定义书签。 4.5长期积累性 ..................................................... 错误!未定义书签。 4.6安全稳定性。错误!未定义书签。 4.7易维护性。错误!未定义书签。 4.8高效性,错误!未定义书签。 第5章实际案例,错误!未定义书签。 第1章概述 随着现代信息技术的飞速发展,越来越多的用户更加注重自身信息架构的简便易用性、安全性、可管理性和总体拥有成木。近几年信息化的高速发展,迫使越来越多的教育机构需要采用先进的信息化手段,解决各机构当前面临的数据安全隔离、信息共享、资源整合等实际问题,实现通过改进机

集合与容斥原理

第一讲集合与容斥原理 数学是一门非常迷人的学科,久远的历史,勃勃的生机使她发展成为一棵枝叶茂盛的参天大树,人们不禁要问:这根大树到底扎根于何处?为了回答这个问题,在19世纪末,德国数学家康托系统地描绘了一个能够为全部数学提供基础的通用数学框架,他创立的这个学科一直是我们数学发展的根植地,这个学科就叫做集合论。它的概念与方法已经有效地渗透到所有的现代数学。可以认为,数学的所有内容都是在“集合”中讨论、生长的。 集合是一种基本数学语言、一种基本数学工具。它不仅是高中数学的第一课,而且是整个数学的基础。对集合的理解和掌握不能仅仅停留在高中数学起始课的水平上,而要随着数学学习的进程而不断深化,自觉使用集合语言(术语与符号)来表示各种数学名词,主动使用集合工具来表示各种数量关系。如用集合表示空间的线面及其关系,表示平面轨迹及其关系、表示方程(组)或不等式(组)的解、表示充要条件,描述排列组合,用集合的性质进行组合计数等。集合的划分反映了集合与子集之间的关系,这既是一类数学问题,也是数学中的解题策略——分类思想的基础,在近几年来的数学竞赛中经常出现,日益受到重视,本讲主要介绍有关的概念、结论以及处理集合、子集与划分问题的方法。 1.集合的概念 集合是一个不定义的概念,集合中的元素有三个特征: (1)确定性设A是一个给定的集合,a是某一具体对象,则a或者是A的元素,或者不是A的元素,两者必居其一,即a∈A与a?A仅有一种情况成立。 (2)互异性一个给定的集合中的元素是指互不相同的对象,即同一个集合中不应出现同一个元素. (3)无序性 2.集合的表示方法 主要有列举法、描述法、区间法、语言叙述法。常用数集如:R , ,应熟记。 N, Z Q 3.实数的子集与数轴上的点集之间的互相转换,有序实数对的集合与平面上的点集可以互相转换。对于方程、不等式的解集,要注意它们的几何意义。 4.子集、真子集及相等集 (1)A?? B A?B或A=B; (2)A?B?A?B且A≠B; (3)A=B?A?B且A?B。 5.一个n阶集合(即由个元素组成的集合)有n2个不同的子集,其中有n2-1个非空子集,也有n2-1个真子集。 6.集合的交、并、补运算 x∈} A B={A |且B x∈ x x∈} A B={A |或B x x∈ x?} A∈ {且A =| I x x 要掌握有关集合的几个运算律: (1)交换律A B=B A,A B=B A; (2)结合律A (B C)=(A B) C, A ( B C)=(A B) C;

相关文档
最新文档