The RCWA method--a case study with open questions and perspectives of Algebraic computations

Diffraction of light on periodic media represents an important problem with numerous physical and engineering applications. The Rigorous Coupled Wave Analysis (RCWA) method assumes a specific form of gratings which enables a straightforward separation of space variables. Using Fourier expansions, th...

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Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 31; p. 331
Main Authors Hench, John J, Strakos, Zdenek
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.04.2008
Subjects
Diffraction
Electric waves
Electromagnetic radiation
Electromagnetic waves
Fourier transformations
Matrices
Czech Republic
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ISSN1068-9613
1097-4067

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Summary:Diffraction of light on periodic media represents an important problem with numerous physical and engineering applications. The Rigorous Coupled Wave Analysis (RCWA) method assumes a specific form of gratings which enables a straightforward separation of space variables. Using Fourier expansions, the solutions of the resulting systems of ordinary differential equations for the Fourier amplitudes can be written, after truncation, in form of matrix functions, with an elegant formulation of the linear algebraic problem for integrating constants. In this paper, we present a derivation of the RCWA method, formulate open questions which still need to be addressed, and discuss perspectives of efficient solution of the related highly structured linear algebraic problems. A detailed understanding of the RCWA method for the two-dimensional grating is, in our opinion, necessary for the development of a successful generalization of the method to practical problems. Key words. Diffraction of electromagnetic waves, Maxwell's equations, periodic gratings, RCWA, truncated Fourier expansions, matrix functions, structured matrices, scattering amplitude. AMS subject classifications. 78A45, 42A20, 42A85, 35Q60, 65L10, 65F10, 65F30.
ISSN:1068-9613
1097-4067