A detailed derivation of rigorous coupled wave algorithms for three-dimensional periodic liquid-crystal microstructures

Abstract

This paper offers a detailed derivation of the rigorous coupled-wave algorithms for three-dimensional periodic liquid-crystal media. The media are treated as multi-layer stacks with two-dimensional periodic microstructures, and the algorithm is formulated for the stacks of microstructures with isotropic or birefringent materials in an arbitrary order. It is shown that the near-field transmittances approximate to those obtained by the Jones method as the angles of the dominant diffraction are small, while the far-field diffractions are verified by the finite-difference time-domain method, indicating the validity of the algorithms.

Keywords:

• rigorous coupled wave theory
• diffraction
• birefringence
• periodic microstructure

Acknowledgements

This work was supported in part by the National Science Council of the Republic of China under Contract Numbers NSC 99-2811-E-001-003 and NSC 98-2622-E-001-001-CC2.