基于128°Y-X切割LiNbO3的声光调制器的制作分析

Analysis of integrated acousto-optic modulators fabricated on128-deg-rotated Y-cut X-propagation LiNbO3

Juntao Wang

Qun Han

Jiping Ning

Weiyi Zhang

Yang He

Analysis of integrated acousto-optic modulators fabricated on128-deg-rotated Y-cut

X-propagation LiNbO3

Juntao Wang

Qun Han

Jiping Ning

Weiyi Zhang

Yang He

Tianjin University

College of Precision Instrument and Optoelectronics Engineering,and

Optoelectronic Information Science and Technology Laboratory

The State Ministry of Education 300072,Tianjin,China

E-mail:wangjuntao_tju@https://www.360docs.net/doc/b49976615.html, Abstract.The efficiency of integrated acousto-optic(AO)modulators with different optical penetration depths fabricated on128-deg-rotated Y-cut X-propagation lithium niobate(128-deg Y X-LiNbO3)is analyzed theore-

tically for the first time by determining the overlap integral between the optical and acoustic field distribution.The results show that the smaller the optical penetration depth is,the higher the optimum surface-acoustic-wave(SAW)frequency and diffraction efficiency and the larger the band-width will https://www.360docs.net/doc/b49976615.html,pared with TM-polarized light,TE-polarized light offers better performance for modulation.However,for a well-concentrated opti-cal waveguide,TM-polarized light is attractive for AO modulators,which employ a single SAW.?2012Society of Photo-Optical Instrumentation Engineers (SPIE).[DOI:10.1117/1.OE.51.7.074602]

Subject terms:guided-wave acousto-optic devices;surface acoustic wave; 128-deg-rotated Y-cut X-propagation lithium niobate;overlap integral.

Paper120670received May9,2012;revised manuscript received Jun.19,2012; accepted for publication Jun.21,2012;published online Jul.18,2012.

1Introduction

Integrated acousto-optic(AO)modulators have been inves-tigated over many years and used to perform a number of

signal-processing functions including modulation,beam

deflection,tuneable filtering,and spectrum analysis.1 These functions are implemented in devices based on AO

interactions in GaAs,LiNbO3,and quartz,https://www.360docs.net/doc/b49976615.html,pared

with other materials,LiNbO3is more widely used due to

its high electro-mechanical coupling factor,low acoustic transmission loss,and stable physical and chemical proper-

ties.For each application,it is important to obtain detailed

knowledge of overall AO efficiency and bandwidth.Thus a rigorous computation of the basis of AO interaction in

LiNbO3waveguide is necessary.In previous research, Helmut investigated the efficiency of AO interaction in ZY-LiNbO3waveguide theoretically by calculating overlap integral between the acoustic and optical fields.A reasonable

agreement between the calculated results and the measured

results was obtained.2Similarly,the AO interaction in YZ-and XZ-LiNbO3have also been studied,and the results were proved to be useful for the development of guided-wave AO modulators.3,4But,as the substrate of guided-wave AO devices,the ZY-,YZ-,and XZ-LiNbO3have a smaller electro-mechanical coupling constant and a lower surface-acoustic-wave(SAW)velocity when compared with 128-deg YX-LiNbO3,which has been used extensively in guided-wave AO devices.5,6There have been no reports about the investigation on the efficiency of integrated AO modulators fabricated on128-deg YX-LiNbO3,to the best of our knowledge.

In this paper,the propagation characteristics of SAW in

128-deg YX-LiNbO3are theoretically investigated.On the base of propagation characteristics,the efficiency of guided-wave AO modulators fabricated on128-deg YX-LiNbO3

with different optical penetration depths is discussed for

the first time by determining the overlap integral.The results show that there is a peak value of diffraction efficiency,

which is dependent on the optical penetration depth.

The smaller the optical penetration depth is,the higher

the optimum SAW frequency and diffraction efficiency

and the larger the bandwidth will be.Furthermore,compared

with TM polarization,TE polarization offers a higher diffrac-

tion efficiency and a larger bandwidth of several hundred

megahertz.But TM polarization is attractive for AO devices

with a well-concentrated optical waveguide in128-deg YX-LiNbO3when they employ a single SAW.

2Theoretical Model

2.1SAW Field in128-deg Y X-LiNbO3

The analysis of SAW has been given by many authors.Here

we follow the pattern of Campbell and Jones.7

A simplified schematic diagram of guided wave AO inter-

action is shown in Fig.1.The substrate is128deg YX-LiNbO3,and the SAW and the optical wave propagate in the x1-and x2-direction,respectively.In the following

analysis,the SAW field is assumed to be uniform in the

x2-direction and has a decaying field in the x3-direction. Based on the acoustic field theory and the quasi-static approximation of Maxwell’s equations,a set of coupled differential equations for the particle displacement u i, I?1;2;3and the electrical potentialφ?u4can be obtained.The traveling wave solutions can be expressed as:

u i?

X4

m?1

βi m exp??jγm kx3 exp?jeωt?kx1T

i?1:::4;x3≥0;(1)

0091-3286/2012/$25.00?2012SPIE

Optical Engineering51(7),074602(July2012)

where βm i are the amplitude coefficients,γm

are the complex decay coefficients,and k is the SAW vector.

The mechanical displacements are accompanied by an electrostatic field on the piezoelectric crystal given by:

E i ???u

4?x i

;

i ?1;2;3:(2)

Similarly,the elastic deformations caused by mechanical displacement field can be given by the strain displacement relation:

S ij ?12 ?u i ?x j t?u j

?x i ;i;j ?1;2;3;(3)where S ij is the strain component along the x i direction on a surface of an infinitesimal volume whose normal is parallel to the x j direction.

The coupled differential equations under free surface boundary conditions were solved using numerical method in MATLAB.In the calculation,material constants from Kushibiki et al.8have been used.It should be noted that material constants must be transformed with respect to the coordinate system defined in Fig.1before being substituted.The phase velocity of SAW was evaluated to be 3978.55m ∕s ,and the difference is only 0.35m ∕s compared with Kovacs ’s 3978.2m ∕s ,9which is measured by scanning the crystal surface with a laser beam along several parallel lines and applying the angular spectrum of wave theory.Because the agreement between the phase velocities is good,it is reasonable to believe that our analysis is correct.The relative particle displacement and relative electric field of the 128-deg YX -LiNbO 3as a function of normalized depth into crystal on the free-surface boundary condition also can be obtained,which are shown in Figs.2and 3,respectively.From these figures we can see that the relative particle displacement and relative electric field are concen-trated near the crystal surface within one or two wavelengths.The u 3and the E 1are dominant compared with others.2.2SAW-Induced Effective Refractive Index Change It is well known that the SAW changes the effectiveindexof the guided mode by three distinct phenomena:the AO effect,the electro-optic (EO)effect,and the optical waveguide thickness perturbation effect.2,3Since the effective refractive index change caused by waveguide interface perturbations tends to cancel each other in the typical single mode arrangement,it will be ignored in the following discussion.The change of

optical indicatrix ΔB ij ?Δe1∕n 2Tij due to AO and EO effects is given by:

ΔB ij ?p E ijkm S km tr s ijk E k ;

i;j;k;m ?1;2;3;(4)

where p E ijkm and r S

ijk are the strain optic tensor at constant electric field and EO tensor at constant strain,respectively,S km and E k are strain and electric field components of the SAW,respectively.

The strain and electric field components of the SAW have already been calculated in Sec.2.Substituting the SAW fields together with the known AO and EO constants of LiNbO 3(Ref.10)into Eq.(4),the frequency/depth depended change of optical indicatrix ΔB v can be obtained,where the contracted index v counts from one to six using the standard subscript contraction.It should be noted that the AO and EO constants of LiNbO 3must also be transformed carefully with respect to the coordinate system defined in Fig.1before being

substituted.

Fig.1Geometry of guided wave AO

interaction.

Fig.2Relative displacement of 128-deg Y X -LiNbO 3propagation on the free

surface.

Fig.3Relative electric field of 128-deg Y X -LiNbO 3propagation on the free surface.

The normalized overlap integral factor j U av eωx 3Tj ?j ΔB v eωx 3T∕j ΔB v max jj versus normalized depth into the crystal are shown in Fig.4(a)and 4(b)for 128-deg YX -LiNbO 3with TE (v ?1)and TM (v ?3)polariza-tion,respectively,where j ΔB v max j is the maximum of j ΔB v j .As shown in Fig.4,the different contributions from AO effect and EO effect are plotted separately.From the figure it can be seen that compared with the EO contribution,the AO contribution is dominant.

2.3Modulation Efficiency and Overlap Integral The AO diffraction efficiency of guided optical wave,perfectly phase matched to the SAW,is given by the well-known formula:11

η?sin 2"πλcos θF ????????????????????????????1

2M eP s ∕Λ2TL r #

;(5)

where M 2is the AO figure of merit,P s is the input acoustic

power,θis the Bragg angle,λand Λare the optical and acoustical wavelength,respectively,L is the acoustic beam-width and F is the overlap integral between optical and SAW fields.The overlap integral F ,which has a value varying from 0to 1depending on the field distribution of the optical and acoustic waves,is a complication that occurs only for guided-wave structures.It can be seen that the diffraction efficiency is a strong function of j F j ????ωp ,where ωis the angular frequency of SAW.

The frequency dependent overlap integral,taking a value in the range from 0to 1,can be written as

j F eωTj ? R ∞0j U r ex 3Tj 2U av eωx 3Td x 3R ∞0j U r ex 3Tj 2

d x 3

;v ?1;3:(6)For the bulk-wave case,it should be U r ?U av ?1,

F ?1.

The normalized intensity j U r j 2?j E 0∕E ref j 2of the guided mode of a Ti ∶LiNbO 3waveguide can be approximated by a Hermite-Gaussian function in depth:12

j U r ex 3Tj 2?8<:????????

28x 32

p ?????

?πσ3

p exp h ?2ex 3σT2i ;x 3>00;x 3≤0;(7)where σis the transverse width parameter.

3Numerical Results

Substituting Eqs.(4)and (7)into Eq.(6),the overlap integral with different optical penetration depths can be evaluated for the 128-deg YX -LiNbO 3.The overlap integral as a function of the SAW frequency for five different penetration depths (d ?2,4,6,8,10μm)were calculated and shown in Figs.5and 6for TE (v ?1)and TM (v ?3)polarization,respectively.Here the optical penetration depth d ,defined as the 1∕e 2value of maximum intensity and related to σby d ≈1.5σ(Ref.12).

From these two figures it can be seen there is a peak value of the diffraction efficiency dependent on the optical pene-tration depth.The smaller the optical penetration depth is,the higher the optimum SAW frequency and diffraction efficiency and the larger the bandwidth will be compared with TM polarization,TE polarization offers a higher diffrac-tion efficiency and a larger bandwidth of several hundred megahertz.However,128-deg YX -LiNbO 3with TM polar-ization offers better performance on modulation for a well-concentrated optical waveguide when the device is driven by low SAW frequency.Except for the bandwidth limited by the overlap integral,the bandwidth of AO devices is also determined by SAW transducer bandwidth and AO Bragg bandwidth imposed by phase-matching

condition.

Fig.4Normalized overlap integral factors versus x 3∕Λin 128°Y X -LiNbO 3:(a)TE polarization,(b)TM

polarization.

Fig.5Overlap integral for 128-deg Y X -LiNbO 3and TE polarization.

Because the absolute AO Bragg bandwidth is inversely pro-portional to the frequency of SAW,the modulator that employs a single inter digital transducer will have a smaller AO Bragg bandwidth and thus a smaller device bandwidth when the driving SAW frequency is higher.So TM polariza-tion is attractive for AO devices with a well-concentrated optical waveguide in128-deg YX-LiNbO3when they employ a single SAW.

4Conclusion

We have theoretically investigated efficiency of guided-wave AO devices fabricated on128-deg YX-LiNbO3for the first time.The SAW field and overlap integral under different optical penetration depths in128-deg YX-LiNbO3were cal-culated for TE-and TM-polarized light.Basis on the results, high diffraction efficiency and large bandwidth can be ob-tained by designing the optical penetration depth and SAW https://www.360docs.net/doc/b49976615.html,pared with TM-polarized light,128-deg YX-LiNbO3with TE-polarized light offers better perfor-mance for modulation.However,TM polarization is attractive for AO devices with a well-concentrated optical waveguide in 128-deg YX-LiNbO3when they employ a single SAW.

Acknowledgments

This work is partially supported by the National Natural Science Foundation of China(No.61107035). References

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Juntao Wang received his BS in electronic

science and technology from Tianjin Univer-

sity,Tianjin,China,in2007,and his MS in

photoelectronics also from Tianjin University

in2009.He is currently working toward his

PhD in photoelectronics at Tianjin University.

He is engaged in research on integrated

acousto-optic

interactions.

Qun Han received the BS degree in physics

from Liaocheng Teacher's College(now

Liaocheng University),Shandong,China,in

2000,the MS degree in optics from Nankai

University,Tianjin,China,in2003,and the

PhD degree in physical electronics from

Tianjin University,Tianjin,China,in2006.He

is now an associate professor at the College

of Precision Instrument and Opto-electronics

Engineering,Tianjin University,China.His

current research interests are mainly focused on fiber sensors,fiber lasers and amplifiers.He is the author or co-author of more than50scientific papers and3

patents.

Jiping Ning received her PhD from Tianjin

University and is a PhD adviser.She has

been involved in photoelectronic technology.

In particular,she has been contributed to the

development of fiber lasers and amplifiers,

both pulsed and cw,including an all-solid-

state laser operating in the visible and near-

infrared wavelength regions,since1986. Biographies and photographs of the other authors are not

available. Fig.6Overlap integral for128-deg Y X-LiNbO3and TM polarization.