In the problem of light scattering by ice crystals of cirrus clouds, two exact methods (FDTD – finite difference time domain and DGTD – discontinuous Galerkin time domain) and the physical-optics approximation are used for numerical calculations of the Mueller matrix in the case of ice hexagonal plates and columns. It is shown that for the crystals larger than 10 μm at the wavelength of 0.532 μm the exact methods and physical-optics approximation closely agreed within three diffraction fringes about the centers of the diffraction patterns. As a result, in the case of random orientation of these crystals, the physical-optics approximation provides accuracy 95% for the averaged Mueller matrix.
Previous experimental measurements and numerical simulations give evidence of strong electric and magnetic field interaction between split-ring resonators in dense arrays. One can expect that such interactions have an influence on the second harmonic generation. We apply the Discontinuous Galerkin Time Domain method and the hydrodynamic Maxwell-Vlasov model to simulate the linear and nonlinear optical response from SRR arrays. The simulations show that dense placement of the constituent building blocks appears not always optimal and collective effects can lead to a significant suppression of the near fields at the fundamental frequency and, consequently, to the decrease of the SHG intensity. We demonstrate also the great role of the symmetry degree of the array layout which results in the variation of the SHG efficiency in range of two orders of magnitude.