Abstract
A two-dimensional scalar Helmholtz equation is derived for a transverse electric mode transverse gyrotropic grating. In the frame of a rigorous coupled-wave analysis, a Bloch-type wave solution and a Fourier expansion of the dielectric tensors are substituted into the Helmholtz equation to obtain a system of ordinary dierential equations, and an Airy-like internal-reflection series is applied for better convergence. In the derivation, no approximation or estimate has been employed, and it is easy to implement. Finally, the numerical method is tested with various parameters.
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