Visnyk of V.N. Karazin Kharkiv National University, series “Radio Physics and Electronics”

Mode decomposition of fields into solenoidal and potential components in a closed waveguide

S. M. Shulga — 2025-07-01

Background. At the end of the last century, it became necessary to solve the problem of excitation of unsteady fields in closed and open electrodynamic structures. In the 1980s, the Department of Theoretical Radiophysics proposed an alternative to the Fourier method, the mode basis method for closed hollow resonators. In this paper, we consider an electrodynamic problem on the excitation of an unsteady field in an open cylindrical waveguide. At the very beginning, the original system of Maxwell's equations is divided into two systems of equations for solenoidal and potential vectors.

Objectives. To show the possibility of applying the mode basis method for superposition of solenoidal and potential fields in a waveguide with dielectric filling.

Materials and methods. When solving some spectral electrodynamic problems for solenoidal and potential components of the electromagnetic field vectors, the orthogonality of these eigenvectors in the waveguide volume is proved, taking into account the condition of field boundedness at the waveguide ends when the longitudinal component of a cylindrical waveguide tends to plus/minus infinity.

Results. Under the assumption of completeness of the found eigenfunctions, the desired field is represented as the sum of the expansion by the elements of the mode basis for solenoidal and potential fields with time-dependent coefficients. The first-order differential equations are obtained for the time coefficients.

Conclusions. In this paper, using the example of an infinite cylindrical waveguide with dielectric and diamagnetic filling, a type of mode basis is proposed, when at the initial stage of solving Maxwell's equations, the vector quantities of the initial problem are represented as the sum of solenoidal and potential components. After proving the orthogonality of the eigenvector functions for the potential and solenoidal fields and assuming their completeness, the paper presents the solutions for waveguide excitation by nonstationary sources in the form of an expansion by eigenfunctions with unknown time coefficients.

Kirchhoff migration method in the problem of detecting hidden metal objects using ultra-wideband GPR

V.A. Plakhtii — 2025-07-01

Background: Ultra-wideband (UWB) GPR systems are widely used to detect hidden objects. However, efficient data processing, especially in complex environments with heterogeneities, remains a pressing problem. The accuracy of determining the depth of such objects largely depends on the correct application of migration methods and signal preprocessing.

Objectives: To solve the model problem of determining the depth of a metal pipe in a homogeneous and heterogeneous environment using the Kirchhoff migration method for further application of the approach to real GPR data.

Materials and method: The environment model included a homogeneous region and a region with a trench containing a metal pipe. The FDTD method with a Gaussian pulse of 0.6 ns duration was used to model signal propagation. B-scan images were generated from 15 antenna positions, and the data were subjected to pre-processing and Kirchhoff migration. In the case of an inhomogeneous medium, the change in dielectric constant was taken into account.

Results: A clear image of the pipe was obtained after applying the migration method, which coincides with the actual depth of the object in both homogeneous and inhomogeneous media. In case of ignoring local changes in the dielectric constant, an error is observed that can reach a value close to the pipe diameter.

Conclusions: The Kirchhoff migration method is effective for determining the depth of metal objects in a model environment, provided that the parameters of the environment are correctly estimated

Energy analysis of a transient wave process excited by a rectangular pulse

D. I. Havrylenko — 2025-07-01

Background. With the rapid advancement of ultrawideband technologies, pulsed antennas are becoming increasingly essential tools in applications involving radio communication, location, and remote sensing. Unlike harmonic sources, whose dynamics are well-described in the frequency domain, real pulsed emitters operate with finite-duration excitations, which significantly alter both the nature of the electromagnetic field and the process of energy transfer. One of the physically realistic excitation scenarios is the rectangular pulse, which models a situation where the source is active for a limited time interval and then turned off. This type of pulse more accurately reflects the actual operating conditions of pulsed systems than idealized step-like excitation. Investigating the energy characteristics in the time domain not only deepens the understanding of radiation mechanisms but also contributes to the improved design of efficient antennas and sources. Such insights directly impact the enhancement of range, noise immunity, and accuracy in communication and observation systems, as well as the reduction of energy losses and near-field exposure. Analyzing the transformation of pulsed energy at different stages of excitation, from the formation of wavefronts to their propagation, is key to developing high-fidelity models of the electromagnetic field.

Objectives. To derive analytical and numerical dependencies that describe the energy characteristics of the electromagnetic field excited by a rectangular pulse. Specifically, the aim is to obtain expressions for the energy flux through the transverse plane at an arbitrary distance from the aperture, as well as to determine the total wave energy at different stages of its spatiotemporal evolution. Where analytical solutions are unattainable, apply numerical methods. Provide a physical interpretation of the obtained results, and assess the influence of pulse duration on wave behavior.

Materials and methods. The problem is formulated as a transient three-dimensional propagation scenario of an -wave excited by a rectangular pulse from a circular aperture into the free half-space. General field solutions are constructed using the evolutionary approach. These solutions are expressed through the evolutionary coefficients, which are obtained as solutions of the inhomogeneous Klein-Gordon equation using the Riemann function method. To determine the energy flux, the longitudinal component of the Poynting vector is used. Numerical computations are carried out via the Gauss-Kronrod method.

Results. Exact analytical expressions for the energy flux and total energy at the aperture under rectangular excitation have been obtained. Generalized formulas have been derived for arbitrary planes, taking into account the temporal and spatial evolution of the field. A comparison with the far-field approximation shows that it may overestimate energy values in the near zone. A three-dimensional visualization of the spatiotemporal dynamics has been constructed, clearly demonstrating the formation and interaction of wavefronts. The process of energy accumulation in the near field has been analyzed, along with the manifestation of the “electromagnetic missile” effect, where the excitation exists in the form of a compact energy pulse.

Conclusions. This study presents, for the first time, analytical and numerical models for rectangular excitation of an -wave from an aperture radiator in the time domain. It is shown that, in the case of finite-duration pulses, the field exhibits more complex temporal dynamics than under step-like excitation. It is established that the energy flux near the aperture arises from the interaction of static and wave components, which render far-field approximations inaccurate at low values of the longitudinal coordinate. The slow decay of energy with distance indicates that a significant portion is concentrated in a compact front that retains its structure during propagation. The analysis refines the applicability conditions of approximate models and provides a foundation for further research aimed at optimizing pulsed antennas and radiation systems.

Prediction of electromagnetic waves scattering on complex shape large objects

M.M. Legenkiy — 2025-07-01

Relevance. Currently, the question radar cross-section (RCS) modelling of real targets arises. Experimental measurement is difficult to implement, and existing methods of theoretical calculation usually require a lot of time. Therefore, it is necessary to develop new methods of collecting and processing experimental data and theoretical modeling, which will allow to speed up the assessment of the RCS of various objects. An important task now is to create a radar that will be able to detect even well-camouflaged targets. On the other hand, there is a need to mask one's own objects. Given the latest trends in the use of low-visibility targets, the reflected signal from which can be almost at the noise level, it is necessary to learn how to distinguish it from the signals of other objects. Thus, the current task is to create effective methods for predicting scattering on typical radar targets, the use of which will not require a lot of time for modeling.

Objective Obtaining an equation for calculating the effective scattering surface of a system of bright point reflectors with different radiation patterns.

Methods. Using physical and geometric optics methods to obtain the equation of the radar cross-section of bright point reflector systems. Using the Python programming language, as well as its libraries NumPy and Matplotlib for calculations and plotting.

Results. An equation for calculating the radar cross-section of bright point reflector systems has been obtained for the cases of isotropic reflectors and different angular dependence of the effective scattering surface. Graphs have been constructed for cases where the RCS of each scatter is constant and varies according to certain laws.

Conclusions. The final formula for calculating the RCS of bright point reflector systems was obtained, and regularities were found for different RCS values of the reflectors.

Pressure of electromagnetic radiation on very thin conductors

N.G. Kokodii — 2025-07-01

Background.. We use the mechanical action of laser radiation in the optical range for levitation, holding and moving of microparticles. We use that fact that the radiation beam presses on the particle, pulls it into a region of high field intensity and holds it there. We use the effect of strong absorption and scattering of microwave radiation by very thin conductors - metal wires, graphite and semiconductor fibers, to overcome difficulties caused by comparable large focal spot of the beam in the microwave range.

Objectives. To provide an analysis of the possibility of levitation and control of the movement of thin metal targets, which can be metal conductors with a diameter of several micrometers and a length of several millimeters, using microwave radiation without focusing on the target.

Results. We provide a theoretical analysis of the effect of microwave radiation strong pressure on thin conductors. We derive a condition for the maximum of radiation pressure - the relationship between the radiation wavelength, the diameter of wire and its conductivity. Also, we provide results of measurement of forces acting on thin conductors. For such purpose, we have used a torsion bar scales with a wire suspension with a diameter of several micrometers and an optical rotation angle reading. We show the good agreement between the calculation and experimental results.

Development of a methodology for transitioning from a spectral equation relative to a spatial variable to a differential equation relative to a spectral parameter in the Sturm-Liouville problem for a one-dimensional periodic two-layer photonic crystal

O. V. Kazanko — 2025-07-01

Relevance. In connection with solving the problem of scattering of electromagnetic waves (diffraction problem) on objects such as photonic crystals (one-dimensional periodic unbounded), it is important to study the dispersion relation. This involves solving the wave equation with subsequent application of the separation of variables method (For the diffraction structures considered in the paper, the specified method of separation of variables allows obtaining a solution to the wave equation, which in this case turns out to be an equation with periodic coefficients, in the explicit form) and transition to the Sturm-Liouville problem on an unbounded interval . The dispersion relation allows us to understand the conditions under which the Sturm-Liouville problem can be solved and connects these conditions with the parameters of the diffraction problem, and therefore becomes an indispensable step on the way to obtaining solutions to this wave equation. This work continues a series of previously published works on the development of approaches to studying the specified dispersion relation through understanding the behavior of the solution of the spectral equation in the Sturm-Liouville problem. The transfer matrix method for a wave equation with periodic coefficients makes it possible to take into account the specifics of its solution on an unlimited interval , and to achieve the fulfillment of a component condition under which the Sturm-Liouville problem is solvable – the condition of self-adjointness of the differential operator in this problem. This is on the one hand, and on the other hand, such a method clearly indicates the place occupied by the solution of the spectral equation in the dispersion relation.

The aim of the work is to simplify the previously obtained equation, which is a consequence of the spectral equation in the Sturm-Liouville problem for a one-dimensional periodic two-layer photonic crystal. In particular, to integrate some of the constituent terms of the linear representation of the 1st and 2nd derivatives of the solution of the spectral equation in the Sturm-Liouville problem.

Methods. The separation of variables method is used to solve the wave equation. The transfer matrix method for a wave equation with periodic coefficients makes it possible to take into account the specifics of its solution on an unlimited interval and achieve the fulfillment of a component condition under which the Sturm-Liouville problem is solvable – the condition of self-adjointness of the differential operator in this problem. To take the integral of the individual component terms of the linear representation of the 1st and 2nd derivatives of the solution of the spectral equation in the Sturm-Liouville problem, the method of integration by parts is used.

Results. The work showed that in the course of a series of successive transformations, the coefficient at zero derivative in the reduced differential equation (the equation relative to the spectral parameter to which the transition is made – according to the title of the work) is subject to simplification. In particular, the square of the coefficient of the linear representation of the 1st derivative of the solution of the spectral equation in the Sturm-Liouville problem was integrated.