Hybrid-matrix algorithm for rigorous coupled-wave analysis of multilayered diffraction gratings

This paper presents an alternative approach called the hybrid-matrix or H-matrix algorithm for the stable and efficient implementation of the rigorous coupled-wave analysis of multilayered diffraction gratings. The H matrix is superior to both the T and R matrices because of its numerical stability across the whole range of large and small layer thicknesses. It is also more concise and simple than the S matrix in obviating the need to invoke auxiliary reference layers or two consecutive layers. For high efficiency, the stack H-matrix recursive algorithm is derived in terms of eigen-submatrices directly without any auxiliary layer matrix. Compared with the enhanced transmittance matrix (partial-solution) approach, the enhanced H-submatrix approach achieves 30% higher computation efficiency and requires less memory.