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Grating interferometer is a state of art x-ray imaging approach, which can simultaneously acquire information of x-ray attenuation, phase shift, and small angle scattering. This approach is very sensitive to micro-structural variation and…
The recently proposed concept of metagrating enables wavefront manipulation of electromagnetic (EM) waves with unitary efficiency and relatively simple fabrication requirements. Herein, two-dimensional (2D) metagratings composed of a 2D…
The $T$-matrix, often obtained with Waterman's extended boundary condition method (EBCM), is a widely-used tool for fast calculations of electromagnetic scattering by particles. Here we investigate the quasistatic or long-wavelength limit…
A topology optimization method is presented and applied to a blazed diffraction grating in reflection under conical incidence. This type of gratings is meant to disperse the incident light on one particular diffraction order and this…
We study the diffraction produced by a slab of purely reflective PT-symmetric volume Bragg grating that combines modulations of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex…
Light diffraction at an aperture is a basic problem that has generated a tremendous amount of interest in optics. Some of the most significant diffraction results are the Fresnel-Kirchhoff and Rayleigh-Sommerfeld formulas. These theories…
A problem of diffraction of a symmetrical transverse magnetic mode $ \text{TM}_{0l} $ by an open-ended cylindrical waveguide corrugated inside is considered. A depth and a period of corrugations are supposed to be much less than the…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are…
The Rayleigh conjecture about convergence up to the boundary of the series representing the scattered field in the exterior of an obstacle $D$ is widely used by engineers in applications. However this conjecture is false for some obstacles.…
We calculate the radiative heat transfer between two identical metallic one-dimensional lamellar gratings. To this aim we present and exploit a modification to the widely-used Fourier modal method, known as adaptive spatial resolution,…
The fractional diffraction optics theory has been elaborated using the Green function technique. The optics-fractional equation describing the diffraction X-ray scattering by imperfect crystals has been derived as the fractional matrix…
The Rayleigh conjecture on the representation of the scattered field in the exterior of an obstacle $D$ is widely used in applications. However this conjecture is false for some obstacles. AGR introduced the Modified Rayleigh Conjecture…
Phase gradient metagratings/metasurfaces (PGMs) have provided a new paradigm for light manipulations. In this work, we will show the existence of gauge invariance in PGMs, i.e., the diffraction law of PGMs is independent of the choice of…
The equations describing the T-violating photon scattering by a diffraction grating have been obtained. It is shown, that the T-violating rotation of the photon polarization plane appear under diffraction in a noncenter symmetrical…
Diffraction of multi-level atoms by an evanescent wave reflective diffraction grating is modeled by numerically solving the time-dependent Schr\"{o}dinger equation. We are able to explain the diffraction observed in experiments with…
This work presents the implementation, numerical examples and experimental convergence study of first- and second-order optimization methods applied to one-dimensional periodic gratings. Through boundary integral equations and shape…
We study the Cauchy problem for a system of equations corresponding to a singular limit of radiative hydrodynamics, namely the 3D radiative compressible Euler system coupled to an electromagnetic field through the MHD approximation.…
We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…