Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms

We introduce a Domain Decomposition Spectral Method (DDSM) as a solution for Maxwell's equations in the frequency domain. It will be illustrated in the framework of the Aperiodic Fourier Modal Method (AFMM). This method may be applied to compute the electromagnetic field diffracted by a large-scale surface under any kind of incident excitation. In the proposed approach, a large-size surface is decomposed into square sub-cells, and a projector, linking the set of eigenvectors of the large-scale problem to those of the small-size sub-cells, is defined. This projector allows one to associate univocally the spectrum of any electromagnetic field of a problem stated on the large-size domain with its footprint on the small-scale problem eigenfunctions. This approach is suitable for parallel computing, since the spectrum of the electromagnetic field is computed on each sub-cell independently from the others. In order to demonstrate the method's ability, to simulate both near and far fields of a full three-dimensional (3D) structure, we apply it to design large area diffractive metalenses with a conventional personal computer.

Automated summary

We introduce a Domain Decomposition Spectral Method (DDSM) for solving Maxwell's equations in the frequency domain. This method is applied to compute the diffraction of electromagnetic fields by a large-scale surface. It decomposes the large-scale problem into smaller sub-problems and uses a projector to connect them. The method is suitable for parallel computing and can be used to design large area diffractive metalenses.