Characteristics of an Electric Dipole in a Plane Waveguide with an Inhomogeneous Filling in the Long-Line Approximation

Within the framework of the long-line approximation, we obtain the expressions for the current distribution, input impedance, and admittance of a nonsymmetric thin electric dipole whose ends are connected to perfectly conducting walls of a plane waveguide filled by an inhomogeneous dielectric. The use of this approximation allows one to qualitatively interpret the results of rigorous solution of the problem of the effect of the medium inhomogeneity on the radiation characteristics of the antenna.     

Estimation of field in plane impedance waveguide with local geometrical irregularity. II

The author investigates effect on the field of a point source in a plane impedance waveguide of an irregularity in the form of spherical surface that projects from (or is embedded into) the plane of the, ionospheric wall of the waveguide. In a scalar approximation, the problem is reduced to a two-dimensional integral equation over the surface of the irregularity. A solution is constructed by successive approximations, for which the solution of the problem for a regular impedance waveguide is used as the initial approximation. Numerical results are given for estimation of the effect of a local ionospheric irregularity on the field of an electric dipole in the earth-ionosphere waveguide.St. Petersburg State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 6/7, pp. 569–578, June–July, 1992.     

Calculation of VLW fields in a waveguide with A 3-D local inhomogeneity

The problem of a point-source field in an irregular impedance waveguide is solved. The 3-D inhomogeneity of one of the walls of the waveguide is given by an area-inhomogeneous impedance. To obtain a solution within the framework of the method of integral equations, we develop a procedure for asymptotic transformation of the 2-D equation into an 1-D equation with allowance for the waves reflected from all the inhomogeneity boundaries. The obtained 1-D integral equation for points that belong to both the path line and boundary contour of the inhomogeneity is solved numerically using an original algorithm. The results of model calculations in a near-earth waveguide for the case of ionospheric perturbations that are large on the wavelength scale are given.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1312–1322, December, 1995.     

Wave Propagation in a Waveguide with Resonance Periodic Inhomogeneity of the Surface Impedance

In this paper, we study the influence of periodic inhomogeneity of the surface impedance on the field of an electric dipole located in a waveguide. The inhomogeneity period is assumed to be close to the wavelength of the source in free space. An analytical representation for the field in the waveguide channel is obtained. We estimate the inhomogeneity period for which a mode of a given number is excited most efficiently.     

Diffraction of Electromagnetic Waves by an Anisotropic Cylindrical Inhomogeneity in a Planar Waveguide

We consider diffraction of electromagnetic waves by an anisotropic cylindrical inhomogeneity located in a planar waveguide with perfectly conducting walls. Anisotropy is allowed for by using the uniaxial-crystal approximation. A rigorous analytical solution is represented in the form of double sums over eigenfunctions of a planar waveguide with perfectly conducting walls and azimuthal eigenfunctions of a cylinder. Different components of the intensity of the electric field scatttered by an anisotropic inhomogeneity are numerically calculated. The influence of the anisotropy and sizes of the inhomogeneity on the scattered field is analyzed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 605–615, July 2005.     

Diffraction of a sound wave by the open end of a flanged waveguide with impedance walls

Diffraction of a plane sound wave by the open end of an impedance-wall waveguide connected to an opening in an impedance screen is considered. The plane wave is incident on the waveguide from a free half-space. Two versions of the problem are considered: for a semi-infinite waveguide and for a finite-length waveguide with a specified bottom impedance; the impedances of the walls, screen, and waveguide bottom can be different. The finite-length waveguide can be treated as an open cavity in the impedance screen. For the cavity of zero length, the problem is reduced to the diffraction by an impedance insert in the impedance screen. The solution in the external region determines the scattered field; the solution in the internal region allows one to determine the directional pattern of an array of receivers located in the cavity. The problem is solved using the integral Helmholtz equation with a specially selected Green’s function that provides the fulfillment of the boundary conditions. Formally, the problem is reduced to an infinite system of algebraic equations. The computational results obtained for bistatic and monostatic scattering patterns are presented.     

Effect of large-scale boundary irregularity on the ELF waveguide field

The effect of boundary irregularity on the ELF field in a waveguide is studied by the full-wave/ray method using the focusing-factor equation. The displacement of the normal-wave trajectories into the complex region and the field along them are estimated, and the applicability conditions of a longitudinal approximation of field phase and amplitude in a two-dimensionally irregular waveguide are determined. The transverse scale of an inhomogeneity that changes the qualitative dependence of the field on distance is found.Scientific-Research Institute, St. Petersburg University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1576–1586, December, 1994.     

Directional properties of an array of sound receivers positioned in an impedance screen recess

Expressions for calculating the directional characteristics of an array of sound receivers positioned in a waveguide with impedance walls are obtained from the solution to the problem on the diffraction of a plane sound wave by the waveguide open end with impedance flanges. The waveguide can be of a finite length, and, in this case, it can be considered as an open cavity in an impedance screen. The solution of the integral equation for the sound pressure distribution over the opening area is reduced to the solution of an infinite system of algebraic equations for the coefficients of the field expansion in normal waveguide waves. Examples of calculated directional characteristics are presented for arrays with receivers positioned at different distances from the opening and for different values of the impedances of the waveguide walls and flanges.     

Diffraction Radiation from a Slot in the Impedance End of a Semi-Infinite Rectangular Waveguide

Using the induced magnetomotive force method, we obtain an approximate analytical solution of the problem of diffraction of the H₁₀ mode by a narrow slot which is cut in the impedance finite-thickness wall on the end of a semi-infinite rectangular waveguide and radiates into free half-space over an infinite, perfectly conducting screen. The scattering-matrix coefficients of a slotted waveguide radiator are studied numerically for the values of the complex surface impedance which correspond to some particular types of a thin-film coating of the waveguide end wall.     

On solution of the vector 3-D locally irregular waveguide problem

The vector 3-D problem of a point-source field in a plane waveguide with a large-scale local inhomogeneity on one of its walls is considered. The field components on the boundary surfaces comply with the Leontovich conditions, which are used as a basis for obtaining expressions for the derivatives of the field vectors normal to the boundaries; these expressions reflect the 3-D nature of the inhomogeneity. The problem is reduced to a system of 2-D integral equations allowing for overexcitation and depolarization of the field scattered by the irregularity. The system of 2-D integral equations is asymptotically transformed over the inhomogeneity region on the surface of the walls bounding the waveguide space into a system of linear integral equations, for which the integration contour is represented by the line between the source and observation point, as well as by the linear geometric contour of the irregularity.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 8, pp. 785–803, August, 1995.     

Depolarization of the electromagnetic field in a locally inhomogeneous earth-ionosphere waveguide

This paper presents a further development of the numerical-analytical method for the solution of three-dimensional problems in the theory of radio wave propagation. We consider a vector problem of the electromagnetic field of a vertical electric dipole in a plane Earth-ionosphere waveguide with a local large-scale irregularity on the anisotropic ionosphere wall. The possibility of lowering (elevating) of the local region of the upper waveguide wall with respect to the regular ionosphere level is taken into account. The field components on the boundary surfaces obey the Leontovich impedance conditions. The problem is reduced to a system of two-dimensional integral equations taking into account the overexcitation and depolarization of the field scattered by the irregularity. Using asymptotic (with respect to the parameter kr ≫1) integration along the direction perpendicular to the ray path, we transform this system to a system of one-dimensional integral equations. The system is solved numerically in the diagonal approximation, combining direct inversion of the Volterra integral operator and the subsequent iterations. The proposed method reduces the computer time required for solving the problem and is useful for the study of both small-scale and large-scale irregularities. We obtained estimates of the TE field components that are not excited by the source considered and originate entirely from field scattering by a three-dimensional irregularity disturbing the geometric regularity of the ionospheric waveguide wall. State University of St. Petersburg, Russia Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 7, pp. 617–629, July, 2000.     

Study of the vertical electric dipole in an earth-ionosphere waveguide with a smooth stochastic inhomogeneity of the upper boundary impedance

We study the effect of a smoothly inhomogeneous stochastic disturbance in the impedance of the upper wall of a plane Earth-ionosphere waveguide on the field of the vertical electric dipole placed in the waveguide channel. The case where the disturbance variance is comparable to the mean impedance is considered. An expression for the Hertz potential is found, and the conditions for use of the Bourre approximation are specified. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 4, pp. 457–471, April, 1997.     

Electromagnetic-wave excitation and diffraction by metal cylinder inside flat waveguide

Electromagnetic-wave excitation by a vertical electric dipole located inside a flat waveguide containing a vertical circular metal cylinder is examined. An exact solution is obtained, and the diffracted field inside the waveguide is analyzed. Algorithms are provided for electromagnetic-field calculation in a Rayleigh approximation and in a short-wave approximation. Results of numerical calculations of fields and directivity characteristics are presented. The effect of the cylinder on the radiation power of the dipole in the waveguide is analyzed.Nizhny Novgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 11, pp. 965–976, November, 1993.     

The peculiarities of cross-correlation between two secondary precursors – Radon and magnetic field variations,induced by stress transfer changes

A model of precursor manifestation mechanisms, stimulated by tectonic activity and some peculiarities of observer strategy, whose main task is the effective measurement of precursors in the spatial area of their occurrence on the Earth's daylight, are considered. In particular, the applicability of Dobrovolsky's approximation is analyzed, when an unperturbed medium (characterized by the simple shear state) and the area of tectonic activity (local inhomogeneity caused by the change only of shear modulus) are linearly elastic, and perturbation, in particular, surface displacement is calculated as a difference of the solutions of two independent static problems of the theory of elasticity with the same boundary condition on the surface. Within the framework of this approximation a formula for the spatial distribution (of first component) of magnetic field variations caused by piezomagnetic effect in the case of perturbed regular medium, which is in simple shear state is derived. Cogent arguments in favor of linear dependence between the radon spatial distribution and conditional deformation are obtained.Changes in magnetic field strength and radon concentrations were measured along a tectonomagnetic profile of the total length of 11 km in the surroundings of the ”Academician Vernadsky” Station on the Antarctic Peninsula (W 64°16′, S 65°15′). Results showed a positive correlation between the annual surface radon concentration and annual changes of magnetic field relative to a base point, and also the good coincidence with theoretical calculation.     

Low-frequency radio wave propagation in the earth-ionosphere waveguide disturbed by a large-scale three-dimensional irregularity

In this paper, we develop further the analytical and numerical method of solving three-dimensional problems in the theory of radio wave propagation, including three-dimensional local inhomogeneities (ionospheric disturbances or Earth’s surface irregularities). To model the Earth-ionosphere waveguide, we use the surface impedance concept, by which the irregularity extending beyond one waveguide wall has an arbitrary smooth shape, and its surface can be described by the impedance. In the scalar approximation, this problem is reduced to a two-dimensional integral equation for the irregularity surface, which, by asymptotic (kr ≫ 1) integration over the coordinate transverse to the propagation path (with allowance for terms of the order of (kr)⁻¹), is reduced to a one-dimensional integral equation, in which the integration contour is the linear contour of the irregularity. The equation is solved numerically, combining the inversion of a Volterra integral operator and successive approximations. By reducing the computer times, this method enables one to study both small-scale and large-scale irregularities. The results of numerical simulation of radio wave propagation in the presence of a powerful three-dimensional ionospheric disturbance are presented as an example. State University, St. Petersburg, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 5, pp. 588–604, May, 1998.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

The diffraction of sound by an impedance sphere in the vicinity of a ground surface

The problem of sound diffraction by an absorbing sphere due to a monopole point source was investigated. The theoretical models were extended to consider the case of sound diffraction by an absorbing sphere with a locally reacting boundary or an extended reaction boundary placed above an outdoor ground surface of finite impedance. The separation of variables techniques and appropriate wave field expansions were used to derive the analytical solutions. By adopting an image method, the solutions could be formulated to account for the multiple scattering of sound between the sphere and its image near a flat acoustically hard or an impedance ground. The effect of ground on the reflected sound fields was incorporated in the theoretical model by employing an approximate analytical solution known as the Weyl-van der Pol formula. An approximation solution was suggested to determine the scattering coefficients from a set of linearly coupled complex equations for an absorbing sphere not too close to the ground. The approximate method substantially reduced the computational time for calculating the sound field. Preliminary measurements were conducted to characterize the acoustical properties of an absorbing sphere made of open cell polyurethane foam. Subsequent experiments were carried out to demonstrate the validity of the proposed theoretical models for various source/receiver configurations around the sphere above an acoustically hard ground and an impedance ground. Satisfactory comparative results were obtained between the theoretical predictions and experimental data. It was found that the theoretical predictions derived from the approximate solution agreed well with the results obtained by using the exact solutions.     

Space-charge field of a photorefractive grating in a planar waveguide based on a cubic crystal

We consider the initial stage of formation of photorefractive gratings in planar waveguides based on cubic electrooptic crystals. We have obtained solutions for the components of the space-charge field for arbitrary ratios between parameters characterizing the spatial inhomogeneity of the light interference pattern in the waveguide as well as the diffusion length. The dependence of the component of the space-charge field parallel to the grating vector on its period in the initial section of the recording is also determined by the sum and difference of the transverse propagation constants of the interacting waveguide modes. We show that for waveguide interactions characterized by a small transverse scale of spatial inhomogeneity, the distributions of the space-charge field and the light intensity in the interference pattern are substantially different. These effects must be considered in analysis of the nonlinear interactions occurring in a refractive index grating due to the electrooptical effect. Tomsk University of Control Systems and Radioelectronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, pp. 65–73, June, 1997.     

Magnetic-Type Waves in a Tapered Waveguide of Subwavelength Cross Section

The characteristics of electromagnetic waves in a narrowing waveguide are investigated. A method for field analysis is developed based on the application of transverse modes parametrically dependent on the longitudinal coordinate. For a circular cross section waveguide, a system of equations for the wave amplitudes is obtained, the waves being coupled owing to a variable tilt of the walls. It is shown that in the adiabatic approximation, there exist independent eigenwaves whose structure reflects the field energy density variation due to the waveguide radius variation. A detailed analytical and numerical investigation of these fields has been carried out for a waveguide with a special profile of hypergeometric type. The applicability of the adiabatic approximation is studied and conversion of the fundamental mode into higher-order modes is assessed. The amplitudes of the higher-order modes are obtained using the Green function for ordinary differential equations. The region of the waveguide parameters is found where the higher-order mode amplitudes are not great and the adiabatic approximation is highly accurate. The dependence of the transmittance of a semi-infinite waveguide on the input radiation characteristics is obtained. It is established that the field amplitudes at the waveguide output strongly depend on the wavelength of the input radiation, on its transverse structure, and the waveguide profile steepness. The greatest output fields take place in the case of an abrupt dependence of the waveguide radius on the longitudinal coordinate.     

Dictums for problem solving and approximation in mathematical acoustics: examples involving low-frequency vibration and radiation

A sequence of dictums for mathematical acoustics is given representing opinions intended to be regarded as authoritative, but not necessarily universally agreed upon. The dictums are presented in the context of the detailed solution for a class of problems involving the forced vibration of a long cylinder protruding half-way into a half-space bounded by a compliant surface (impedance boundary) characterized by a spring constant. One limiting case corresponds to a cylinder vibrating within an infinite rigid baffle, and another limiting case corresponds to a vibrating cylinder on the compliant surface of an incompressible fluid. The second limiting case is identified as analogous to that of a floating half-submerged cylinder whose vibrations cause water waves to propagate over the surface. Attention is focused on vibrations at very low frequencies. Difficulties with insuring a causal solution are pointed out and dictums are given as to how one overcomes such difficulties. Various approximation techniques are described. The derivations involve application of the theory of complex variables and the method of matched asymptotic expansions, and the results include the apparent entrained mass in the near field of the cylinder and the radiation resistance per unit length experienced by the vibrating cylinder.