大学物理波动光学英文实验报告

Diffraction grating modeling by RCWA and CM methods: diffraction efficiency synchronism studies

Ivan Richter,Petr Honsa,and Pavel Fiala

Czech Technical University in Prague,Faculty of Nuclear Sciences and Physical Engineering

Department of Physical Electronics,B?ehová7,11519Prague l,CZECH REPUBLIC

Phone:+420221912285,Fax:+42026884818,Email:richter@troja.fjfi.cvut.cz

Abstract:This contribution concentrates on modeling of diffraction processes in optical

diffraction gratings(ODG).First,the approach to characterization of mechanisms and diffraction

processes is briefly presented,together with the regions with typical diffraction regimes.Different

types of diffraction efficiency volume phase synchronism are then described.Different situations

are analyzed and compared concerning ODG of different types,different refractive index/relief

modulation profiles,various modulation strengths,and incident wave polarization influence.As

examples,the cases of conical and Littrow mounts are discussed in detail.As rigorous modeling

tools,both rigorous coupled wave analysis,and coordinate transformation methods are used,

implemented,and modified.

2002Optical Society of America

OCIS codes:050.1950Diffraction gratings,050.1970Diffractive optics

1.Introduction and modeling tools

In the last years,diffractive optics modeling,i.e.both analysis(direct problem)and synthesis(inverse problem)in diffractive optics has obtained an immense attention and interest,especially due to an increasing amount of practical applications of optical diffraction gratings(ODG)and diffractive optical elements and systems.Technological possibilities of grating fabrication methods to produce e.g.high-aspect ratio diffractive structures with periods(or minimum feature sizes)comparable and smaller than the wavelength of light have also enlarged rapidly.Hence, originally-used scalar theoretical methods(analytical methods of transmittance,two wave Kogelnik's methods,thin film decomposition,etc.)became inapplicable soon,and the rigorous methods had to start their developments and beings.Apart from design,fabrication and application driven rigorous modeling,diffraction processes characterization in ODG is also important itself since it can provide a deep insight into the physical mechanisms,can separate and identify their influences,and allows to find some regions(of important parameters)with typical diffraction regimes.In this sense,it is very useful and needful for all other types of modeling.Therefore,based on our previous studies[1-8],the purpose of this contribution is mainly to present,discuss and interpret on various examples new and physically interesting results concerning the behavior of the diffraction efficiency synchronism for selected grating and experimental parameters of diffraction gratings.

As rigorous modeling tools,both rigorous coupled wave analysis(RCWA)and coordinate transformation methods(CM)have been implemented and applied within this contribution.RCWA,as a standard technique for the analysis of diffraction grating properties,nowadays represents an efficient and stable modelling tool[9].Our RCWA model has implemented several modifications and improvements,and was successfully applied in our previous studies[10].The coordinate transformation method has also shown a great potential in rigorous diffraction modelling,and become a strong counterpart of RCWA methods,efficiently applicable especially to specific types of surface-relief gratings[11].This method is based on the introduction of a new coordinate system transforming a generally complicated grating surface corrugation into a simple plane surface,hence simplifying the boundary-matching problem by a great extent.Our CM model,based mainly on the Li's valuable reformulation[12]and modifications of the classical algorithm,has also been recently successfully implemented and tested.We have confirmed that while CM has appeared fast and efficient for smooth profiles,and for both input polarizations,it has showed considerably slower convergence for profiles with discontinuities.On the other hand,RCWA is practically ideal for gratings with multilevel profiles.Both methods have been found complementary,with different areas of applicability,and thus both methods are used within this contribution.

2.Diffraction efficiency synchronism

As has been shown in[1-3,7],by using the proper way of interpretation,i.e.by studying the diffraction efficiency of a given diffraction order in the representation defined by the relevant independent variables(as e.g.the period to wavelength ratio(Λ/λ) and the grating depth to wavelength ratio(d/λ) ? for a fixed angle of incidence),it is possible to efficiently describe and explain the complex behavior of grating diffraction efficiencies.The main advantage of such a description is that the whole class of gratings can be described altogether,and character of the diffraction efficiency synchronization(i.e.volume phase synchronism[1,2])can thus be effectively studied.This also allows one to determine the regions with typical diffraction regimes in the(Λ/λ, d/λ)representation,as has been studied previously[1,2],the synchronism periodicity and structuring[7],as well as to study the behavior within resonant regions of diffraction(threshold and guiding effects[3,8]).From a practical point of view,however,the effects of varying some important grating and diffraction setup parameters,using mainly the(Λ/λ, d/λ)synchronism,are of great importance.Hence,in this contribution,these influences have been studied and will be presented(the effects of the angle of incidence,of grating relief profiles,of input polarization,and of the value of refractive index).

3.The case of conical diffraction

As an example,Fig.1shows a comparison of volume phase synchronisms for the case of conical mount(90deg.) and classical mount(0deg.),for both TE and TM polarizations,for the case of binary gratings,with the incidence angle of30deg.As can be seen,whereas the classical mount provides the Bragg synchronization,in the case of conical mount,there is no such effect.

4.Different types of synchronisms,the case of Littrow mount

The diffraction efficiency dependence characterization is clearly a complicated multi-parameter problem,complexly describable using some type of proper characterization.In this sense,although the selected(Λ/λ, d/λ)synchronism appears as one of the most beneficial,other types can be also very useful(angular synchronism,combined

synchronisms).As the second example,Fig.2shows a comparison of such combined synchronisms,again for the case of binary gratings,comparing both TE and TM polarizations.Here,at each periodΛ/λ,the incident angle is appropriately changed in order to ensure the proper Littrow mount.In the contribution,the interpretation of such behavior will be given,and usefulness of the approach will be shown.

5.Conclusions

To summarize the contribution,we have contributed to a better understanding of diffraction processes in optical diffraction gratings,by presenting and interpreting various simulation results based on rigorous diffraction modeling of RCWA and CM.The influence of important parameters on the synchronism has been evaluated,and different situations have been analyzed and discussed.

6.Acknowledgments

This work has been partially supported by the Grant Agency of Czech Republic with contract No.202/01/D004and by the Ministry of Education of the Czech Republic Research plan CEZ:J04/98:210000022.

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