An exact Dyson equation for averaged over electromagnetic crystal unit cell propagating total wave electric field is
derived, with supposing the incident wave electric field to have the Floquet property. The mass operator related to
periodic structure effective tensor dielectric permittivity is written as double Fourier transform from electric field Tscattering
operator of the structure unit cell. The Lippmann-Swinger equation for the unit cell T-scattering operator,
written in terms of the unit cell T-scattering operator in free space and the electric field lattice tensor Green function
interaction part, is resolved by quasi-separable method. This recently presented quasi-separable approach to unit cell Tscattering
operator enables one to consider unit cell containing several particles, with coupling between them directly
inside the cell as well as through the structure via above lattice Green function interaction part. The obtained quasiseparable
unit cell T-scattering operator is applied to study double diamagnetic-paramagnetic narrow peak in artificial
periodical material with unit cell including the coupled plasmonic particles. Actually this magnetic phenomenon is
appeared as combination result of space-group resonance between two small dielectric spheres and plasmonic resonance
inside a single sphere. Studying the magnetic response of disordered media, we use Dyson self-consistent exact equation
for ensemble averaged wave electric field inside dense discrete random media, with a random mass operator having been
put under averaging sign. The random mass operator was written in terms of particles’ correlations functions of all orders
and particles’ clusters’ T-scattering operators. We discuss comparison between the unit cell T-scattering operator of
periodic discrete structure and a cluster T-scattering operator of random discrete structure and consider the above double
diamagnetic–paramagnetic peak also in random discrete structure of coupled small plasmonic dielectric spherical
particles.
An approach is proposed of near field introscopy of a left-handed material (LHM) layer, i.e. Veselago's lens, without
using any waveguides: the near field image of an inhomogeneity in a tested homogeneous LHM layer appears on the
wave receiver placed near a wave source provided that this layer is illuminated by source in a way that inside Veselago's
lens focus appears near inhomogeneity considered. We extend the traditional potential wave multiple scattering theory to
analytical study an inhomogeneous and absorbing LHM slab focusing properties by the Green function method. A
specific multiplicative quasistatic singularity of the Green function is revealed provided a weak and thin linelike
inhomogeneity is placed near focus inside perfect LHM slab. This sort of singularity is directly linked with concept
about spatial transformation media. Modelling the linelike scatterer by non-local separable scattering potential reveals a
resonance property of the scattering amplitude related to singular behaviour of the Green function for waves propagated
inside perfect LHM slab. These resonance properties were previously lost in the Born's approximation.
Reflection spectra of one dimensional diffraction gratings are calculated on the basis of an exact, fast approach, uniting
several modern methods, to the theory of electromagnetic wave multiple scattering in two dimensional inhomogeneous
dielectric media which uses the technique of matrix Riccati equation. The sensitivity of computed reflection spectra to
distortions of a grating shape (strip like, triangular, trapezoidal) for metal and dielectric structures is demonstrated.
Distortions of the lamellar grating shape are simulated by the roundness of sharp edges of the grating. In particular, the
computations shows that the roundness of grating ruling (150 nm wide and 300 nm hegh) edges with a curvature radius
as small as 10 nm can be detected by changing the intensity of specular reflected light (500 nm wavelength) provided
that the grating has a subwavelength period (300 nm) even in the case of low dielectric contrast.
A theoretical study is presented of transmission spectra formation of perfect two dimensional (2D) photonic crystals (PCs) composed of dielectric cylinders arranged parallel to the electromagnetic wave's electric vector in the square lattice. Layer-by-layer transmission spectra are computed on the basis of a Riccati equation for the matrix wave reflection coefficient from a 2D PC slab and Poynting theorem, regarding 2D PCs as a stack of conservative gratings (layers of non-absorptive rods). The lowest (main) and high-order Mie resonances in a single cylinder and the Bragg-like multiple scattering of electromagnetic waves are determined as three mechanisms of formation and frequency position of two opaque bands, with narrow peaks in one of the bands in the transmission spectra of 2D PCs. It is argued that higher-order Mie resonances are responsible for the transmission peaks within the additional band of a perfect crystal. The possibility of opaque band engineering is discussed. In particular, it is demonstrated that filling fraction of volume occupied by cylinders as small as under half a percent does not destroy the opaque band of 2D PCs.
A recently derived radiative transfer equation with three Lorentzian kernels of delay is applied to an albedo problem on a scalar wave field quasi-monochromatic pulse diffuse reflection from a semi-infinite random medium consisting of resonant point-like scatterers. The albedo problem is solved exactly in terms of the Chandrasekhar consisting of resonant point-like scatterers. The albedo problem is solved exactly in terms of the Chandrasekhar H-function, extended analytically into the single scattering complex albedo (lambda) -plane. Simple analytical asymptotics for the non- stationary scattering function is obtained in the limit related to large values of the time variable. The exact analytic solution for the time-evolution of a diffusely reflected short pulse is used to analyze an accuracy of the non-stationary scattering function calculated in the diffusion approximation. It is shown that the diffusion asymptotics describes the exact solution with a relative error not exceeding one percent only at larger values of dimensionless wave propagation time t equals t/to > 200 where to stands for a mean free time of wave radiation between scattering events defined in terms of the wave phase in a random medium consisting of point-like scatterers tuned to the Mie resonance. Besides, the accuracy of the diffusion asymptotics falls off providing that wave scattering approaches the resonance conditions.
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