# Physics of Wave Processes and Radio Systems

Peer-review quarterly journal.

### Editor-in-chief

- Prof. Dmitry S. Klyuev, Dr. Sci. (physics)

ORCID iD: 0000-0002-9125-7076

### Publisher

- Povolzhskiy State University of Telecommunications & Informatics (Samara, Russia)

### Journal founders

- Samara National Research University

https://ssau.ru/ - Povolzhskiy State University of Telecommunications & Informatics

https://www.psuti.ru/

### About

“Physics of Wave Processes and Radio Systems” is theoretical and scientific peer-reviewed academic journal published quarterly since 1998. The journal considers for publication original papers including but not limited to next disciplines:

- radio physics;
- optics;
- radio engineering including TV systems;
- antennas, high frequency devices and its technologies;
- solid-state electronics, radio electronics components, micro- and nanoelectronics, quantum effect devices.

### Types of manuscripts to be accepted for publication

- results of original research
- reviews
- letters to the editor

### Publications

- quarterly, 4 issues per year
- free of charge for authors (no APC)
- in English and Russian
- Open Access, under the Creative Commons Attribution 4.0 International License (CC BY 4.0)

## Current Issue

### Vol 26, No 2 (2023)

#### Articles

##### Thermal entanglement in two-atom Tavis–Cummings model with taking into account the dipole-dipole interaction

###### Abstract

**Background.** Interest in the study of entangled states of systems of natural and artificial atoms (qubits) interacting with selected modes of microwave resonators is associated with their use as logic elements of quantum computers. At the same time, the most important task of the physics of quantum computing is the choice of the most effective mechanisms for manipulating and controlling the entangled states of qubits in such devices. **Aim.** The dynamics of the entanglement of two dipole-coupled superconducting Josephson qubits induced by a thermal noise of a coplanar resonator is studied for various initial states of the qubits. **Methods.** Based on the exact solution of the quantum Liouville equation for the whole density matrix of the system under consideration, the time behavior of the qubit entanglement parameter (negativity) is found for chaotic thermal, pure separable, and entangled initial states of qubits. **Results.** It is shown that the entanglement of qubits induced by the thermal noise of the resonator is possible for both the chaotic thermal states and separable states of qubits, except the case when both qubits are excited. It has also been found that, for small values of the dipole–dipole interaction parameter, taking this interaction into account leads to an increase in the degree of entanglement. For values of the dipole-dipole interaction parameter greater than some limit value, the opposite effect takes place. It is found that for entangled initial states of qubits, the inclusion of direct interaction has a small effect on the entanglement dynamics. It is shown that the initial coherence of qubit states can lead to a significant increase in the degree of their entanglement in the presence of a dipole–dipole interaction. **Conclusion.** The dipole-dipole interaction can be used as an effective mechanism for qubits entanglement manipulation and controlling.

**Physics of Wave Processes and Radio Systems**. 2023;26(2):9-17

##### Four-wave mixing on thermal and resonant nonlinearities with feedback for object and signal waves

###### Abstract

– **Background.** The need to create highly efficient four-wave radiation converters in order to use them in adaptive optics systems, for real-time processing of complex spatio-temporal fields, in interferometry, quantum cryptography, etc. requires along with the use of traditional methods to increase the efficiency of such converters by increasing the interaction length, radiation power density, effective value of the nonlinear susceptibility of the development of new methods. One of these methods is a method based on the imposition of feedback on one or more interacting waves. **Aim.** The influence of feedback on the amplitude reflection coefficient of the degenerate four-wave radiation converter on thermal and resonant nonlinearities has been considered. **Methods.** The amplitude reflection coefficient of a degenerate four-wave radiation converter on thermal and resonant nonlinearities in the presence of feedback for both object and signal waves has been analyzed by a numerical method based on the multiple passage of the signal and object waves of the nonlinear layer in the ring resonator. **Results.** It was shown, that the difference in the reflection coefficients in the presence and absence of feedback for both object and signal waves increase monotonically with a growth in the pumping waves intensity and does not depend on the parameter characterizing the relationship between thermal and resonant nonlinearities at the approximation of a small reflection coefficient. **Conclusion.** The range of values of the absorption coefficient in which the imposition of feedback for both object and signal waves leads to an increase in the efficiency of the four-wave radiation converter has been established.

**Physics of Wave Processes and Radio Systems**. 2023;26(2):18-26

##### The structure of the radiation field of a symmetric slot line perpendicular to the edge of an infinite half-plane, taking into account the cross-polarization component

###### Abstract

– **Background.** Symmetric slot lines on a perfectly reflecting half-plane are good mathematical models for slot antennas on an ideal plane of finite dimensions, which in practice have a high gain and operate over a wide frequency band. These antennas are used in ultra-fast information processing systems based on microwave and optical volume integrated circuits. **Aim.** The work presents a solution to the problem of radiation of a perfectly reflecting half-plane, which was excited by a symmetric slot line with a different law of slot expansion. **Methods.** The problem was solved by the Fourier variable separation method, by which the Green tensor function was obtained, which connects the two components of the antenna radiation field with the excitation field in the gap. **Results.** It is shown that in the far zone, the radiation field of an ideally reflecting half-plane has two components: the main and crosspolarization. The Green tensor function has a complex form and consists of two terms. The analysis of the Green tensor function shows the participation of each term in the formation of a field in the far zone, demonstrates the mechanism of radiation and leads to known special cases for slot radiators. **Conclusion.** The validity of the presented mathematical model is confirmed by experimental research.

**Physics of Wave Processes and Radio Systems**. 2023;26(2):27-35

##### Development of a mathematical model of a chiral metamaterial based on a cylindrical helical elements accounting for the dispersion and concentration of elements

###### Abstract

**Background.** Interest in the study of microwave metamaterials is associated with the possibility of using them to achieve the required frequency and polarization selective properties of interaction with electromagnetic radiation, which can’t be obtained for structures based on homogeneous media. **Aim.** The mathematical model of a chiral metamaterial based on a periodic matrix of arbitrarily oriented conducting thin-wire cylindrical helices located in a homogeneous isotropic container creation is considered. Unlike known models, it takes into account the explicit form of the dependence of the effective permittivity and the relative chirality parameter on the helices concentration. **Methods.** The heterogeneity of a chiral metamaterial based on the Maxwell Garnett formula, which makes it possible to determine the effective dielectric permittivity from the permeabilities of the container and the region occupied by conducting mirror asymmetric inclusions is taken into account when creating a mathematical model. The dispersion of permittivity using the quadratic Lorentz formula and the dispersion of the chirality parameter based on the Condon model are taken into account. **Results.** Analytical frequency-dependent expressions for the effective permittivity and the chirality parameter taking into account the concentration of helices and their geometric parameters, were obtained in the work. The expression for the relationship between the dimensionless volume concentration of inclusions and the distance between adjacent elements is obtained. The quasi-static approach is used to calculate the resonant frequency of conducting thin-wire cylindrical helices. **Conclusion.** The proposed method for constructing a mathematical model can be applied to chiral metamaterials based on periodic matrices of conductive elements of an arbitrary mirror asymmetric spatial configuration

**Physics of Wave Processes and Radio Systems**. 2023;26(2):36-47

##### The effect of docking defects on a metal-dielectric shielded waveguide in the EHF frequency range

###### Abstract

**Background.** To improve the accuracy of navigation and radar systems, functional nodes of the EHF wavelength range are used. At the same time, an increase in the operating frequency increases the requirements for the accuracy of manufacturing and docking devices. Analysis of the propagation of electromagnetic waves, subject to the presence of defects in the waveguide paths, will allow determining sufficient manufacturing accuracy and evaluating physical processes in an irregular area. **Aim.** The aim of this work was to study the effect of sharp irregularities on the characteristics of the digital twin of a broadband shielded dielectric waveguide operating in the frequency range from 90 to 100 GHz. **Methods.** Using a numerical experiment, two variants of irregularity were investigated. They are presented in the form of displacement of sections of shielded dielectric waveguides in the vertical and horizontal planes. **Results.** According to the values of the transfer characteristic of the waveguide path, the regularities of the attenuation of the electromagnetic wave energy from the magnitude of the irregularity are revealed and the permissible manufacturing accuracy is proposed. **Conclusion.** To solve the problems of sewerage of weak signals, the authors recommend using a non-jointed manufacturing technology.

**Physics of Wave Processes and Radio Systems**. 2023;26(2):48-57

##### The accuracy of measuring the coefficients of transmission and reflection of materials in the presence of random errors in the formation of fields

###### Abstract

**Background.** One of the characteristic features of the current stage in the development of military equipment is the widespread use of special structural materials and coatings with specified properties of interaction with electromagnetic fields, which are subject to measurement during production and operation. Most often, measurements are carried out in quasi-flat radiation and reception fields. At the same time, the regularities of the influence of random errors in the formation of flat fields on the accuracy of measuring the characteristics of special structural materials and coatings have not been studied enough. **Aim.** The purpose of this work is to establish quantitative patterns of the influence of random phase errors in the formation of flat fields on the errors in measuring the transmission and reflection coefficients of materials and coatings. **Methods. **Studies of the influence of random phase errors in the formation of flat fields of irradiation and signal reception on the accuracy of measuring the transmission and reflection coefficients of objects were carried out using the methods of mathematical modeling and statistical radio engineering. **Results.** Calculation relations are obtained for estimating the magnitude of errors in measuring the transmission and reflection coefficients. **Conclusion.** With small errors and a small interval of spatial correlation, the errors of the measured average values of the transmission and reflection coefficients are proportional to the errors in the formation of the irradiation and reception fields and the relative value of the spatial correlation interval must exceed 22 degrees.

**Physics of Wave Processes and Radio Systems**. 2023;26(2):58-63

##### Practical realization of space-time filtering of satellite navigation signals in real time

###### Abstract

– **Background.** The problem of satellite navigation signals’ jamming-protected receivers design is quite relevant due to the high vulnerability of such signals to the influence of interferences whose sources number is constantly increasing. **Aim.** To design a space-time adaptive filter and to implement its work in real-time as a part of jamming-protected satellite navigation system. **Methods.** The space-time filtering method fitted for the real-time realization is obtained based on the satellite signal space processing algorithm. The apparatus chosen for the satellite navigation signals reception, the filtering algorithm practical realization and the processed signal demodulation is described. The computer modeling of the signals records filtering and demodulation using the obtained algorithm as well as the real-time experiments in satellite signals processing with different numbers of outer jammers using the constructed jamming-protected receiver are carried out. **Results.** As a result of modeling and experiments with the designed set the values of performance characteristics of the jamming-protected navigation system are yielded which correspond to a good quality solution of the interference mitigation problem in a satellite navigation signal. **Conclusion.** The digital processing model based on the obtained space-time filter adequately describes the interference mitigation process in a real satellite signal. The obtained jamming-protected satellite navigation signal receiver is functional and can be used in practice.

**Physics of Wave Processes and Radio Systems**. 2023;26(2):64-69