Rigorous Coupled-Wave Approach for Sandwich Gratings

Xuehui Xiong,Ping Lu

doi:10.4236/jamp.2016.48148

Abstract

Rigorous Coupled-Wave Approach (RCWA) has been used successfully and accurately to study simple grating structures, such as one-layer gratings, one-whole gratings. In this paper, RCWA is expanded to solve Sandwich gratings (SG), which is composed of two identical planar dielectric gratings adjoined by thin metallic or dielectric film. The electromagnetic analytic expressions for each layer of SG structure are given and rigorous coupled-wave equations are deduced. The numerical investigations for the diffraction spectra of SG by our theoretical and computer programs are in good agreement with the results of classical RCWA in the condition when a Sandwish grating is simplified to a classical one-layer grating. The calculations by our programs of another condition when a Sandwish grating is degenerated to a classical single planar structure also conform to the results of classical electromagnetic theory. The research results above indicate that the extended theoretical formula has backwards compatibility and is self-consistent with the classical theory.

Highlights

Over the past 30 years Rigorous Coupled-Wave Approach (RCWA) formulated by Moharam and Gaylord [1]-[5] has been used successfully and accurately to analyze periodic structures including holographic gratings [1] [2] and arbitrary profiled dielectric or metallic surface-relief gratings [3] [6]-[8]
RCWA is adopted to solve sandwich gratings (SG) structure, which is composed of two identical planar dielectric gratings adjoined by thin metallic or dielectric film
To verify the theory presented in the paper, the proposed RCWA for SG and classic electromagnetic theory are respectively used to research two degenerative SG structures, namely classical single grating and classical single planar structure

Summary

Introduction

Over the past 30 years RCWA formulated by Moharam and Gaylord [1]-[5] has been used successfully and accurately to analyze periodic structures including holographic gratings [1] [2] and arbitrary profiled dielectric or metallic surface-relief gratings [3] [6]-[8]. RCWA is almost used to study relatively simple structure, such as one-layer gratings [1]-[5] and one-whole gratings [6]-[13] which have arbitrary profiled surface-relief on both of top and bottom of monolithic materials. (2016) Rigorous Coupled-Wave Approach for Sandwich Gratings. RCWA is adopted to solve sandwich gratings (SG) structure, which is composed of two identical planar dielectric gratings adjoined by thin metallic or dielectric film. The electromagnetic analytic expressions for each layer of SG structure are given and rigorous coupled-wave equations are deduced. To verify the theory presented in the paper, the proposed RCWA for SG and classic electromagnetic theory are respectively used to research two degenerative SG structures, namely classical single grating and classical single planar structure. The results indicate that RCWA for SG has backwards compatibility and is self-consistent with the classical theory

The Sandwich Grating Structure and Theoretical Formulas

Numerical Calculations and Discussions

Conclusion