The directivity of a radiating line array slightly deflected from vertical in a waveguide

The azimuth directivity of a line array in a waveguide is studied for the case of its deflection from the vertical under the effect of underwater currents. The modal composition and the interference pattern of the field radiated by such an array is considered.     

Radiation directivity pattern of a semiinfinite planar dielectric waveguide with a multilayer transformer

Mowsow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 2, pp. 222–225, February, 1990.     

Observation of a radiating bulk strain soliton in a solid-state waveguide

The appearance and propagation of a radiating bulk elastic strain soliton is experimentally detected for the first time in layered nonlinearly elastic waveguides with nonideal contact between the layers. The nature of such waves is explained in terms of a model using coupled Boussinesq equations.     

Path-integral analysis of propagation in a waveguide with random inhomogeneities

The method of path integration is applied to the analysis of wave propagation in both a graded-index optical waveguide and in an otherwise homogeneous infinite medium whose refractive indices have random statistical inhomogeneities superposed upon a regular variation of refractive index with suitable averaged properties. The authors use techniques originally employed in the context of electron propagation in a set of random scatterers to calculate the averaged Green function describing paraxial wave propagation in a medium whose refractive index has statistical inhomogeneities. The concept of an averaged density of modes is introduced, and the paper presents detailed calculations of this quality for two limiting case. In the first, the correlation length associated with the distribution of inhomogeneities is zero along the direction of propagation. In the second, the Feynman variational technique is used to describe the propagator in a medium whose statistical inhomogeneities have an infinite correlation length along the direction of propagation. Comments are made about the intermediate case which is of greater relevance to real waveguides.     

Sound absorption by resonators in a cylindrical waveguide

The problem on the scattering of a zero-order axisymmetric mode by a ring of equally spaced identical monopole-dipole resonators positioned in the cross section of a wide circular pipe is considered. The solution to the problem is used to formulate the requirements for a set of resonators that provide a complete absorption of the zero-order mode in the pipe.     

Joint statistical moments of mode amplitudes at different frequencies in a random acoustic waveguide

This paper considers an approximate ray-based analytical approach for evaluating the joint statistical moments of mode amplitudes in an acoustic waveguide with large-scale sound speed fluctuations. Explicit analytic expressions for the statistical moments are derived from an approximate analytical solution of the mode-coupling equations. The analytic solution allows one to deduce a scaling law establishing the connection between amplitudes of modes with the same ratio of the mode number to frequency. The applicability of the ray-based approach for evaluating the joint statistical moments of modes amplitudes including the moments at different frequencies is demonstrated using the Monte Carlo simulation of sound fields in a model of the underwater acoustic waveguide in a deep ocean. Numerical simulation also shows different manifestations of the scaling law. In particular, it is shown how this law manifests itself in the acoustic energy distribution between normal modes, in the jump-like range variations of statistical moments, and in the shape of the correlation function between amplitudes of different modes at different frequencies.     

Sound propagation in two-dimensional waveguide with circular wavefront

Sound propagation through a waveguide is generally modeled by the Webster horn equation which assumes a planar pressure wavefront. However, most of the sources are non-planar in nature. In this work, a 1-D model is derived for sound propagation through a 2-D waveguide with circular wavefront. The model is derived from the 2-D Helmholtz equation using the weighted residual method. The model assumes a uniform pressure across the angular coordinate at a given radial distance. A 2-D finite element model is used to validate the results for different waveguide geometries and it shows good agreement.     

Sound scattering by a body in a planar layered waveguide

In the framework of the theory of integral equations, the problem of sound diffraction by pressure-release and acoustically stiff inhomogeneities of an oceanic waveguide is considered. The iteration method is used to obtain recurrent relations for the surface currents. The relations describe the diffraction process as a sequence of interactions between the body and the waveguide boundaries (multiple reflections). The validity condition for the zero-order approximation, which ignores multiple reflections, is formulated and physically justified.     

The theory of long waveguide structures radiating lower hybridwaves into a plasma

It is shown that the radiation into a plasma from the structures composed of many waveguides is well described by the theory of the infinite structures. This theory results in the efficient numerical code which is appropriate for the study of the nonlinear response of the plasma ill front of the grill. Both the infinite conventional grill and the structure built up from the infinite series of identical N-waveguide multijunction sections are investigated. It is proved that the spectrum of the last structure is the superposition of N spectra of the infinite conventional grills with the specially selected phase shifts. The theoretical results for three long structures (24-waveguide conventional grill on ASDEX and two multijunction arrays, namely a 32-waveguide grill on JET and a 30-waveguide grill proposed for T15) are compared with the predictions of the theory for the corresponding infinite structures. and the agreement is good     

Features in the diagnosis of random time-varying nonuniformities in a waveguide using complex pulse signals

Applied Physics Institute of the Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 12, pp. 1370–1379, December, 1990.     

Minimal size of the focal spot when focusing a field in a waveguide using a vertical array

The paper considers the problem of using a vertical array to focus a monochromatic field in the vicinity of a given point of an underwater sound channel. The solution to the problem is discussed, which has been obtained with a limitation on the initial grazing angles of the emitted waves. The limitation is introduced to increase the stability of the solution to the influence of random perturbations of the sound velocity field. Then, the radiated field represents a wave beam propagating along a reference ray that connects the center of the array and the focusing point. In the geometric optics approximation, analytic estimates of the smallest possible dimensions of the focal spot are obtained. A simplified version of the formula is obtained for the vertical scale of the spot convenient for rough express estimates and comparison of the focusing properties of waveguides with different sound velocity profiles.     

Dispersion properties of an inhomogeneous piezoelectric waveguide with attenuation

Dispersion relations are investigated for a transversely inhomogeneous piezoelectric layer with attenuation. Using the complex modulus concept, the problem is reduced to a first-order matrix differential equation with complex coefficients. Characteristic structural features of dispersion relations are studied both analytically and numerically. An asymptotic analysis is performed for the low-frequency region.     

Optical imaging system with a waveguide

The problem of image transmission through a waveguide is considered. The transfer function of a step rectangular waveguide is obtained, and it is concluded that direct image transmission is possible over large distances without significant loss of quality. An optical system with a waveguide in which an image is formed with a single objective is proposed. The process of image transmission through a step planar dielectric waveguide is experimentally investigated, and the influence of parameters of the waveguide on the resulting image is revealed. The conditions for image transmission through waveguides of other types are discussed.     

一个全局耦合不连续映像格子中的冻结化随机图案模式

本文研究了一类既不连续又不可逆分段线性映像构成的全局耦合映像格子系统中的一类典型集体动力学行为, 即冻结化随机图案模式. 计算了平均同步序参量和最大李雅普诺夫指数随耦合强度的变化. 结果显示, 当耦合强度超过某个阈值后, 在给定动力学变量的初始下, 系统几乎都能达到完全或部分同步状态, 出现冻结化随机图案. 这些现象表明, 耦合映像格子系统中存在着多个共存的吸引子. 因此, 其冻结化图案的结构和分布敏感地依赖于格点动力学变量初始值的选取. 感兴趣地是, 即使当单映像处于混沌状态时, 格点间的耦合仍能将系统调制到规则的运动状态, 这种特征对于混沌控制具有重要的利用价值. 上述丰富动力学行为的出现是由于单映像中不连续性和不可逆性相互作用的结果.     

On the acoustic field in a Pekeris waveguide with attenuation in the bottom half-space

The acoustic field in a Pekeris channel with an attenuating basement is critically examined, based on contour integrations of the wave number integrals for the two domains. In both regions, the field consists of a finite sum of proper (square integrable) normal modes plus a branch line integral around a hyperbolic cut. For low bottom attenuation, only "trapped" modes exist but as the loss increases additional "dissipation" modes contribute to the mode sum. A Newton-Raphson iterative procedure is introduced for finding the complex eigenvalues of the modes and a new expression is derived which shows that the total number of proper (trapped plus dissipation) modes supported by the waveguide increases essentially linearly with rising bottom attenuation. Approximations for the complex shape functions of the modes in the water column and the basement are developed and compared with the exact shape functions determined from the Newton-Raphson procedure. An expression derived for the modal attenuation coefficient scales in proportion to the square of the mode number and inversely with the square of the frequency. Stationary-phase approximations for the branch line integrals for both domains are developed, which serve to illustrate the asymptotic range dependence of the lateral wave but otherwise have little utility.