Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory.Two kinds of completeness of the system of eigenvectors are proven,in terms of those of the compositions of two block operators in the off-diagonal operator matrices.Using these results,the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed.Moreover,we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.     

Fano resonance in quadratic waveguide arrays

We study resonant light scattering in arrays of channel optical waveguides in which tunable quadratic non-linearity is introduced as nonlinear defects by periodic poling of single (or several) waveguides in the array. We describe novel features of wave scattering that can be observed in this structure and show that it is a good candidate for observation of Fano resonance in nonlinear optics.     

Modeling a waveguide with a nonlinear insert with a quadratic nonlinearity

The scalar problem of the scattering of a wave from a nonlinear insertion lying in the interior of a waveguide is reduced by the incomplete Galerkin method to the boundary value problem for a Hamiltonian system. The cases in which this problem admits a solution in finite terms are indicated. Examples are given to illustrate specific phenomena due to the nonlinearity of the problem.     

Soliton emission at a phase-mismatch boundary in a quadratic nonlinear film waveguide

We report the experimental demonstration of spatial nonlinear beam displacement caused by an interface between periodically modulated and uniform quadratic nonlinearity. We observe intensity- and phase-mismatch-dependent spatial beam displacement at 1548 nm in lithium niobate waveguides. The device has the potential to provide a soliton-emission-based, ultrafast all-optical switch.     

Phase transitions of nonlinear waves in quadratic waveguide arrays

We study two-color parametric nonlinear modes in waveguide arrays with a quadratic nonlinear response. We predict theoretically and observe experimentally a new type of phase transition manifested in an abrupt power-controlled change of the mode structure from unstaggered to staggered, due to the interplay of localization and synchronization in parametrically driven discrete systems.     

Quantum waveguide theory of a fractal structure

The electronic transport properties of fractal quantum waveguide networks in the presence of a magnetic field are studied. A Generalized Eigen-function Method (GEM) is used to calculate the transmission and reflection coefficients of the studied systems unto the fourth generation Sierpinski fractal network with node number N=123$N=123$. The relationship among the transmission coefficient T, magnetic flux Φ and wave vector k is investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux Φ are observed and discussed, and compared with the results of the tight-binding model.     

On the theory of transition radiation in a waveguide

The transition radiation from a particle that intersects the waveguide perpendicular to its axis is considered. The expressions are derived for the radiation fields and intensities. The example of a rectangular waveguide is used to investigate the properties of the radiation, and the conditions which determine the Vavilov-Cerenkov radiation spectrum are derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 2, pp. 191–195, February, 1972.     

Mode interplay via quadratic cascading in a lithium niobate waveguide for all-optical processing

The effects of the nonlinear interplay between modes of a lithium niobate channel waveguide are numerically investigated. Based on the nonlinear phase-shift obtainable via up- and down-conversion of each mode at the input frequency into and from the second-harmonic modes generated through Type I and Type II interactions, the waveguide can operate as an all-optical transistor with large small-signal-gain, and as a mode-mixing device capable of spatial switching and routing. It exhibits good switching contrast at 1.55 m with low driving powers.     

Toward a theory of dual-beam charged-particle acceleration in plasma waveguide

The results of a theoretical study of dual-beam charged-particle acceleration in a plasma waveguide in a string longitudinal magnetic field are presented. It is shown that effective charged-particle acceleration can be realized by using electric-field nonuniformity over the waveguide cross section. It is established that optimal acceleration conditions can be achieved when the particles enter the accelerating field that corresponds to the region of the first amplitude maximu. The maximum electron energy of the accelerated beam is determined as a function of the guiding-beam current. It is established that the current of accelerated electrons that have maximal energy is 5–10% of the total beam current.Khar'kov Physics and Engineering Institute, Academy of Sciences of the Ukrainian SSSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 8, pp. 947–955, August, 1991.     

Kinetic theory of a cyclotron-undulator hybrid fel in circular waveguide

In this paper, we model the cyclotron-undulator hydrid instability using the kinetic theory in circular waveguide geometry, following the generalized method of the field expansion in the guiding center coordinate system; and derive in detail the coupling coefficient for a cyclotron-undulator hybrid FEL operating at the fundamental harmonic of gyration and undulation. In our discussion, the effect of the transverse structure of the radiation fields is taken into account, but the undulator is considered as an ideally longitudinal one.     

Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasiclassical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from noncompact real simple algebras with nonsimple complexification, where we impose that a nondegenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem and obtain sufficient conditions on integrable cocycles of quasiclassical Lie algebras in order to preserve nondegenerate quadratic Casimir operators by the associated linear deformations. The text was submitted by the authors in English.     

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.     

Cosmological solutions of a quadratic theory of gravity with torsion

Following the general approach of Hehl, and Hayashi and Shirafuji, we give the gravity equations for the lagrangian $\text{L}\text{=(}\text{e}\text{/2L}{}^2\text{)(F+}\text{1}\text{2}\text{×F}{}^2\text{) +}\text{L}{}_{\mathrm{M}}$. We have found the explicit Einstein-de Sitter solutions for a spinless dust. We have discussed in this case the singularity problem for the metric and for the torsion.     

Self-consistent theory of cyclotron autoresonance maser in a uniform planar waveguide

A general dispersion relation for the cyclotron autoresonance maser (CARM) that takes into account self-consistent couplings between TE, TM and ac space charge perturbations in a uniform planar waveguide is derived. The dispersion relation predicts enhanced growth rate due to ac space charge effects. Results from computer simulations of a planar CARM amplifier are presented to support this finding.