Efficient Rigorous Coupled-Wave Analysis Without Solving Eigenvalues for Analyzing One-Dimensional Ultrathin Periodic Structures

Abstract

Based on the first-order Taylor expansion, an efficient Rigorous Coupled-Wave Analysis (RCWA) for one-dimensional ultrathin periodic structures is proposed in this paper. The derivation of the ultrathin form RCWA method is completed by using the first-order Taylor expansion to rearrange the matrix in the equations of boundary conditions. Then, the reliability of the proposed algorithm is verified by two examples. Finally, it is concluded that the proposed algorithm can reduce the CPU time of TE polarization and TM polarization by more than 50%. Meanwhile, compared with the conventional algorithm, the proposed algorithm also needs less memory.INDEX TERMS RCWA, eigenvalues and eigenvectors, computational efficiency, ultrathin periodic structures.

Efficient and Explicit Fourier Modal Method for Ultrathin Metallic Gratings

“…() has no relation with the eigenvalue and eigenvector of matrix , which means that the process of solving the eigenvalue and eigenvector of matrix can be avoided, so the calculation time and memory can be reduced. Compared to our previous work [ 12 ] , is replaced by matrix and avoids the inverse of , which is the source of the numerical instability of the FMM algorithm, especially for ultrathin metallic gratings. However, Eq.…”

“…The normalized CPU time and its cube root of different methods under different truncation orders (Algorithm 1 [ 6 ] , Algorithm 2 [ 7 ] , Algorithm 3 [ 8 ] , Algorithm 4 [ 12 ] ). (a) TE‐polarization; (b) TM‐polarization…”

“…The condition number of different methods under different truncation orders (Algorithm 1 [ 12 ] ). (a) TE‐polarization; (b) TM‐polarization…”

“…This method converts boundary problems into algebraic eigenvalue problems by expanding the electromagnetic field and permittiv-ity in the grating region. Various improvements to different aspects of the method have been proposed in the literature [9][10][11][12][13]. The convergence rate is greatly improved by rearranging Maxwell's curl equations [9] .…”

“…The computational efficiency of FMM is improved by introducing the form of auxiliary equations [10] . In our previous works, efficient FMM methods for binary gratings [11] and ultrathin one-dimensional periodic structures [12,13] were proposed. However, the implementation of our previous work still involves the inverse of large dimensional matrices and no explicit solution expressions are given.…”