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.

Over the last few years, broken symmetry within crystals has attracted extensive attention since it can improve the control of light propagation. In particular, low-symmetry Bravais crystal can support shear polaritons, which has great potential in thermal photonics. In this work, we first use the fluctuation-dissipation theorem to investigate mechanisms of near-field thermal radiation (NFTR) in a low-symmetry Bravais crystal. The NFTR between such crystal slabs is nearly four orders of magnitude larger than the blackbody limit, demonstrating its remarkable potential for noncontact heat dissipation for nanoscale circuits or other devices. Moreover, we report a form of twist-induced near-field thermal control system employing the low-symmetry Bravais crystal medium (β-Ga2O3), showing that this crystal can serve as an excellent platform for twist-induced near-field thermal control. Due to the intrinsic shear effect, the twist-induced modulation supported by low-symmetry Bravais crystal exceeds that by high-symmetry crystal. We further clarify how the shear effect affects the twist-induced thermal-radiation modulation supported by hyperbolic and elliptical polaritons and show that the shear effect significantly enhances the twist-induced thermal control induced by the elliptical polariton mode. These results open directions for thermal-radiation control in low-symmetry materials, including geological minerals, common oxides, and organic crystals.

Using the self-consistent Born approximation, we study a topological phase transition appearing in bulk HgCdTe crystals induced uncorrelated disorder due to both randomly distributed impurities and fluctuations in Cd composition. By following the density-of-states evolution, we clearly demonstrate the topological phase transition, which can be understood in terms of the disorder-renormalized mass of Kane fermions. We find that the presence of a heavy-hole band in HgCdTe crystals leads to the topological phase transition at much lower disorder strength than is expected for conventional three-dimensional topological insulators. Our theoretical results can also be applied to other narrow-gap zinc-blende semiconductors such as InAs, InSb, and their ternary alloys InAsSb.