Hybrid-matrix RCWA for anisotropic gratings: computational advances and SiC applications

We present an optimized RCWA implementation based on the Hybrid-matrix (H-matrix) approach, extended to uniaxial and biaxial media with axes aligned to grating directions. The method supports planar and conical incidence and uses an enhanced submatrix strategy for reflection analysis, reducing complexity while maintaining accuracy. Numerical stability is ensured for lossy anisotropic materials, enabling multilayer computations that combine isotropic, uniaxial, and biaxial media. The H-matrix is derived analytically for substrates with different anisotropy types, eliminating singularities at specific incidence configurations. Instabilities at lossless interfaces are resolved by introducing minimal loss in critical tensor directions, ensuring stability and physically relevant behavior for complex stacks.