Light diffraction in photonic hypercrystals studied by finite-difference frequency-domain method

Structuring of a medium on the wavelength and subwavelength scales significantly enriches its interaction with light leading to new optical effects. As a result, it fuels the interest in planar artificial structures like photonic crystals, metasurfaces and plasmonic crystals, which have found tremendous success in light manipulation and applications in sensing, routing, light localization, enhancement of the nonlinear effects. The deep insight into optical phenomena in artificial structures requires necessarily numerical simulations. For periodic structures such as photonic crystals and diffraction gratings, numerical methods like finite-difference time-domain method (FDTD) and rigorous coupled-wave analysis (RCWA) are widely used. These methods have definite drawbacks, as the FDTD requires large computer memory to store the field values in the nodes of a 3D mesh, and high computational effort for the time simulation; the RCWA demands extra labor for the accurate treatment of a grating made of metal or anisotropic materials. Because the optical effects in highly anisotropic metal-based artificial structures like hypercrystals are of practical interest, we have proposed hybrid finite-difference frequency-domain (FDFD) approach for the calculation of light diffraction in such periodic structures. The improvement is achieved by handling the direct values instead of Fourier series, which is the core of the RCWA. Using this approach, we predict the excitation of the Dyakonov plasmons in hypercrystal formed by trenches in hyperbolic metamaterials.