High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed Generalize
d Source Method in the curvilinear coordinates, which has theoretical $Oleft(Nlog Nright)$ asymptotic numerical complexity, a new method formulation is developed for gratings with sharp edges. It is shown that corrugation corners can be treated as effective medium interfaces within the rationale of the method. Moreover, the given formulation is demonstrated to allow for application of the same derivation as one used in classical electrodynamics to derive the interface conditions. This yields continuous combinations of the fields and metric tensor components, which can be directly Fourier factorized. Together with an efficient algorithm the new formulation is demonstrated to substantially increase the computation accuracy for given computer resources.
The paper presents a method for calculation of non-spherical particle T-matrices based on the volume integral equation and the spherical vector wave function basis, and relies on the Generalized Source Method rationale. The developed method appears t
o be close to the invariant imbedding approach, and the derivations aims at intuitive demonstration of the calculation scheme. In parallel calculation of single columns of T-matrix is considered in detail, and it is shown that this way not only has a promising potential of parallelization but also yields an almost zero power balance for purely dielectric particles.
The paper presents a derivation of analytical components of S-matrices for arbitrary planar diffractive structures and metasurfaces in the Fourier domain. Attained general formulas for S-matrix components can be applied within both formulations in th
e Cartesian and curvilinear metric. A numerical method based on these results can benefit from all previous improvements of the Fourier domain methods. In addition, we provide expressions for S-matrix calculation in case of periodically corrugated layers of 2D materials, which are valid for arbitrary corrugation depth-to-period ratios. As an example the derived equations are used to simulate resonant grating excitation of graphene plasmons and an impact of silica interlayer on corresponding reflection curves.
Implementing the modal method in the electromagnetic grating diffraction problem delivered by the curvilinear coordinate transformation yields a general analytical solution to the 1D grating diffraction problem in a form of a T-matrix. Simultaneously
it is shown that the validity of the Rayleigh expansion is defined by the validity of the modal expansion in a transformed medium delivered by the coordinate transformation.
The article demonstrates uncommon manifestation of spatial dispersion in low refractive index contrast 3D periodic dielectric composites with periods of about one tenth of the wavelength. First principles simulations by the well established plane wav
e method reveal that spatial dispersion leads to appearance of additional optical axes and can compensate anisotropy in certain directions.
The article encloses a new Fourier space method for rigorous optical simulation of 3D periodic dielectric structures. The method relies upon rigorous solution of Maxwells equations in complex composite structures by the Generalized Source Method. Ext
remely fast GPU enabled calculations provide a possibility for an efficient search of eigenmodes in 3D periodic complex structures on the basis of rigorously obtained resonant electromagnetic response. The method is applied to the homogenization problem demonstrating a complete anisotropic dielectric tensor retrieval.
