We offer a computer technology for modeling a process of optical imaging with a diffractive imaging lens. The central idea of the technology is to evaluate the quality of the optical system by matching the input and output images against criteria adopted in image processing. For this purpose, same-resolution hyperspectral images are fed to the input and generated at the output. Thanks to the large number of spectral components, a fairly accurate reproduction of the effects associated with the dependence of the refractive index on the wavelength is ensured. To compare input and output images in terms of PSNR (peak signal-to-noise ratio), standard three-component RGB images are "assembled" using standard matching functions over the entire optical range. Results of the study of the dependence of the PSNR indicator on the main parameters of the optical system are given: focal length, linear aperture and the number of diffraction orders taken into account.

A problem of optimizing the subwavelength microrelief of a binary cylindrical transmissive diffractive lens (DL) with a 300-mm focal length for a wavelength of λ=141 μm was considered. High-resistivity silicon was chosen as the DL substrate material. The angle of incidence of the illuminating beam was taken to be π/6. The optimization parameters were the height of the DL profile and the fill factor of the groove. The main goal of optimizing the design was to increase the diffraction efficiency of the lens. The DL diffraction efficiency was calculated using a Fourier mod method. The DL was fabricated by plasma-chemical etching (Bosch process) of the surface of a silicon substrate. The diffraction efficiency of the calculated lens was estimated to be 70%. However, a full-scale experiment showed the real efficiency to be much lower. These differences are related to both errors in the manufacturing process of the DL and non-ideal thickness parameters of the silicon wafers.

The work is devoted to the development of the quantum theory of diffractive optical elements. Aspects of quantum optics are considered by the example of light diffraction from a dielectric plate in a resonator. The paper shows the connection between the classical and quantum solution of the problem of diffraction by a dielectric plate. Expressions are obtained for the eigenmodes of such a resonator, as well as for the operators of the vector magnetic potential and the electric field strength. The method proposed in this paper can be easily extended to dielectric plates with a diffractive microrelief, that is, to diffractive optical elements.

We propose a method for calculating the point scattering function (PSF) of an Offner imaging hyperspectrometer with a diffraction grating in the approximation of scalar diffraction theory. The method consistently takes into account limitations and diffraction of a light beam by elements of the hyperspectrometer system in accordance with the physics of image formation. The PSF of the Offner imaging hyperspectrometer is numerically simulated at various beam parameters and wavelengths. The simulation results are verified using analytical relationships, a geometrical optics approach, as well as a comparison with the related works of other researchers.

This work deals with a hot topic of using quantum approaches in advanced telecommunications. Here, the major trend involves exploiting a flow of individual photons for signal transmission, because the photon is impossible to split, measure, copy, or imperceptibly delete. Such manipulations destroy the photon, prohibiting it to reach the recipient. Before the field quantization can be implemented, a problem of the electromagnetic field propagation needs first to be solved within classical electrodynamics, with dynamic quantities then replaced by the corresponding operators. This work describes a procedure for the electromagnetic field quantization in a waveguide with superconducting walls. In an optical fiber with inhomogeneous refractive index, the modes are shown to be non-orthogonal, so that the field can only approximately be quantized using the basis of waveguide modes. Expressions for operators of the electric and magnetic fields are derived, which may prove helpful for calculating both dynamic and other characteristics of the electromagnetic field, including nonclassical states of the electromagnetic field.

In this paper, we developed a mathematical model of image formation that allows a predictive hyperspectral image to be generated. The model takes into account the formation of an optical image using a matrix photodetector. The paper presents a numerical modeling of hyperspectral image formation and gives estimates of spatial and spectral resolution, as well as analyzing the adequacy of the results.

The paper considers paraxial Gaussian laser beams with different polarization states and their characteristics, such as the Poynting vector, gradient force, and force density, which are important for evaluating the effects of radiation on matter. An analysis of the considered characteristics of laser radiation from the point of view of the formation of photoinduced microrelief in an azopolymer film is carried out.

In the presence of a strong electromagnetic field, the spectrum of charge carriers in a Dirac material is changed. The interaction of a linearly polarized field with electrons in the Dirac material leads to anisotropy. The anisotropy axis coincides with the direction of the electric field in the linearly polarized wave. We show that the major contribution to the interaction of electrons with an electromagnetic field comes from elastic scattering processes, whereas taking into account inelastic processes leads to an error of about 2%.

We discuss the nonparaxial focusing of laser light into a three-dimensional (3D) spiral distribution. For calculating the tangential and normal components of the electromagnetic field on a preset curved surface we propose an asymptotic method, using which we derive equations for calculating stationary points and asymptotic relations for the electromagnetic field components in the form of one-dimensional (1D) integrals over a radial component. The results obtained through the asymptotic approach and the direct calculation of the Kirchhoff integral are identical. For a particular case of focusing into a ring, an analytical relation for stationary points is derived. Based on the electromagnetic theory, we design and numerically model the performance of diffractive optical elements (DOEs) to generate field distributions shaped as two-dimensional (2D) and 3D light spirals with the variable angular momentum. We reveal that under certain conditions, there is an effect of splitting the longitudinal electromagnetic field component. Experimental results obtained with the use of a spatial light modulator are in good agreement with the modeling results.

The work is devoted to the study of the caustics of radial beams. Analytical expressions for caustic surfaces of wave fronts created by radially symmetric diffractive optical elements are found. The result is presented in a curvilinear coordinate system consistent with the caustic surface. An asymptotic representation of the Kirchhoff integral near the optical axis is obtained, ensuring the correct calculations in the non-paraxial case.

We describe mathematical tools that enable the reflection of light at a diffraction grating applied on a freeform surface to be modeled. To address the problem, we use an analog of the Kirchhoff's method. By way of illustration, reflection at a diffraction grating applied on a spherical surface is analyzed. To enable the modeling of such systems, the software was developed and numerical study was conducted. The feasibility to generalize the results onto freeform diffractive optical elements is studied.

A new form of the linear augmented cylindrical wave method is proposed. For the construction of basis functions, the electron potential is taken to be spherically symmetric in atomic regions, constant in the intermediate region and cylindrically symmetric in the vacuum regions. The basis functions of the method, obtained from the solution of the Schrodinger equation in the corresponding domains, are sewn on the boundaries of the MT-spheres and the cylindrical surfaces of the tube, forming everywhere continuous and differentiable functions. In order to approve a method, the band structure of the non-chiral semiconductor and metallic single-wall carbon nanotubes was calculated.

In this paper, we have developed a mathematical base for describing the propagation of waves in a metal waveguide in a cylindrical coordinate system. The transformation of a conical wave with circular polarization into a cylindrically polarized vortex beam is shown on the basis of the expansion of the field in vector cylindrical modes. The results of modeling, based on the expansion in plane waves, qualitatively agree with theoretical calculations.

The comparative modeling of focusing of femtosecond Gaussian and Poissonian pulses was presented in this paper. Poissonian spectral shape pulses, as opposed to the Gaussian-shaped ones, allow to avoid negative frequency components. The spectral properties of pulses for various durations are investigated. Calculations showed that a significant difference between the Gauss and Poisson pulses begins only for very short durations (less than 3 fs). A comparative simulation of the focusing of short pulses, as well as the passage of focused pulses through a binary phase plate, is performed. The calculation was carried out on the basis of solutions of the Maxwell equations by the method of finite differences in the time domain.

We discuss the use of variational principles for solving the phase problem in optics. In this paper, we consider the connection between four fundamental problems: the phase problem in optics, the inverse problem of focusing coherent radiation, the Monge – Kantorovich optimal mass transport problem, and the variational methods for solving the equation of a modified Monge – Ampere equation. It is shown that the solution of the phase problem in optics within the framework of the asymptotic approach is closely related to the solution of the problem of optimal mass transport with a nonquadratic cost function.

Работа выполнена при поддержке Федерального агентства научных организаций (соглашение No 007-ГЗ/Ч3363/26) и Российского фонда фундаментальных исследований (РФФИ), гранты NoNo 16-29-09528, 16-29-11744.

We propose mathematical tools and analyze the quality of an image in the detection plane of an Offner imaging hyperspectrometer, evaluating conditional tolerances for the position of the spectrometer elements. The results of modeling of a combined effect of the arrangement errors show that the probability for the hyperspectrometer to be successfully assembled in compliance with the requirements for image quality is not lower than 0.9.

In this paper, we consider a method for solving a system of Maxwell's equations in the case of time-dependent boundary conditions at the end of a waveguide with superconducting walls. An explicit analytical solution is obtained for a quasi-harmonic signal whose pulse width in the frequency domain is much smaller than the carrier frequency. Numerical examples are calculated in the case of a Gaussian pulse as a superposition of modes propagating in a circular hollow metal waveguide. The calculation of dynamic invariants of short pulses propagating in a waveguide with an arbitrarily-shaped conducting shell is considered. A procedure for quantizing an electromagnetic field in a waveguide with superconducting walls is described.

In this paper, explicit expressions for the momentum and angular momentum from the Noether's theorem (ab initio) are obtained. These expressions contain squared modules of the coefficients of a guided mode expansion, weighted by the phase singularity orders present. The expressions obtained are useful for quantizing the electromagnetic field in a waveguide.

In this paper, we simulate the propagation of mode pulses in a waveguide with a one-dimensional grating. The diffraction of continuous radiation and a short pulse on a grating with subwavelength period in a waveguide with reflecting walls is investigated using the FDTD method. The possibility of differentiating the reflected short Gaussian pulse is reported.