Related papers: Exact solutions for radiative transfer with partia…
An efficient direct solver for solving the Lippmann-Schwinger integral equation modeling acoustic scattering in the plane is presented. For a problem with $N$ degrees of freedom, the solver constructs an approximate inverse in…
The Lifshitz formula is derived by making use of the spectral summation method which is a mathematically rigorous simultaneous application of both the mode-by-mode summation technique and scattering formalism. The contributions to the…
The difficulty of description of the radiative transfer in disordered photonic crystals arises from the necessity to consider on the equal footing the wave scattering by periodic modulations of the dielectric function and by its random…
We present two novel additions to the semi-analytic solution of Lyman $\alpha$ (Ly$\alpha$) radiative transfer in spherical geometry: (1) implementation of the correct boundary condition for a steady source, and (2) solution of the…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
We solve the radiative transfer equation (RTE) in anisotropically scattering media as an infinite series. Each series term represents a distinct number of scattering events, with analytical solutions derived for zero and single scattering.…
The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…
We theoretically revisit the problem of the propagation of coherent light pulses through a linear medium when the carrier frequency of the pulses coincides with the minimum of a narrow dip in the medium transmission. Considering realistic…
A unique perspective approach based on an analogy method is presented to solve the ray equation in a model of a continuous inhomogeneous medium, which has a spherically symmetric distribution. Basically, in the standard undergraduate…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
This paper deals with the optimal synthesis of aperture fields for (radiating) near-field communications in obstructed environments. A physically consistent model based on knife-edge diffraction is used to formulate the problem as a…
We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…
We found an exact analytical solution of the wave equation for a transient electromagnetic field of synchrotron radiation in the frequency domain. The exact solution represents the field which consists of the coherent and incoherent…
Employing tight-binding approximation we derive a transfer matrix formalism for one-dimensional single photon transport through a composite scattering center, which consists of parallel connected resonator optical waveguides. By solving the…
We investigate elliptic fractional equations in the whole space, involving zero order perturbations of the fractional Laplacian $(-\Delta)^s$, $0<s<1$. Our main objective is to determine appropriate radiation conditions at infinity that…
This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…
We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…
We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from two-dimensional Helmholtz transmission problems in multi-layered periodic structures or gratings. Employing suitably parametrized…
We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian…