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Background. The article considers the problem of propagation of electromagnetic waves in a dielectric layer filled with a medium whose permittivity is characterized by the integral form of the Kerr law. The main task in describing the process of wave propagation in a waveguide structure is to obtain a dispersion equation for propagation constants and study its solvability. Materials and methods. Maxwell’s equations are solved in the frequency domain. The system contains the dependence on the square of the modulus of the electric field strength. Results and conclusions. A system of dispersion equations is obtained, which in fact is a system of dispersion equations for TM waves in the structure. The results of calculations of propagation constants depending on the parameters of the problem are presented.

The electrodynamic problem is reduced to an integral equation with respect to the current density on the strip conductor. It is solved by the projection method using the Chebyshev basis. A homogeneous system of linear algebraic equations (SLAE) is described with respect to the coefficients of the expansion of the longitudinal and transverse components of the current density in terms of Chebyshev polynomials with weight functions that take into account the specificity of the field at the edges of the strip conductors. On the basis of the condition that the determinant of this system is zero the constants of the natural waves propagation are determined by numerical methods. A procedure for improving the convergence of slowly convergent series for the matrix coefficients of SLAE is carried out. The problem of high-accuracy calculation of the functions represented in the form of infinite slowly convergent series, by means of which the matrix coefficients are determined, is solved. A universal formula independent of the number of layers for calculating the wave impedances of natural waves is obtained. The use of the Chebyshev basis and the improvement of the series convergence made it possible to develop an effective algorithm for calculating the basic electrodynamic parameters of the strip lines - the propagation constants and the wave impedances of the natural waves. The constructed algebraic models of strip lines allow computer simulation to obtain numerical results quickly and with high accuracy irrespectively of the number of dielectric layers and their parameters. On the basis of the developed algorithm we created a set of computer programs for calculating the propagation constants, the coefficients of the current density decomposition in terms of Chebyshev weighted polynomials and the wave impedances of screened strip lines of various types: a single and connected microstrip lines (with side and face communication); coplanar strip line; slit line and coplanar waveguide. These programs allow determining the electrodynamic parameters of the main wave and up to 50 waves of higher types. The results of a numerical analysis of the convergence of the developed algorithm for the calculation of natural waves are presented. This confirms the effectiveness of the constructed models. Numerical results obtained without the procedure for improving the convergence of series for matrix coefficients and results obtained by the projection method using the trigonometric basis are given.

We calculate the amplitudes of surface plasmon-polaritons (SPP) excited at a photonic-crystal–metal interface. Using a three-wave approximation, we evaluate optical fields in the crystal medium. The generation of plasmons at the boundary between the photonic crystal (PhC) and gold substrate is numerically analyzed in the wavelength range of a plane incident wave 400–1,900 nm. The optimum wavelength corresponding to the maximum plasmon amplitude is determined. [ABSTRACT FROM AUTHOR]

We present a four-layer transmitarray antenna using small and dense frequency selective surface (FSS) cells and a horn antenna operated in a Ku band satellite downlink (10.7 to 12.75 GHz in Europe). The FSS offers a full transmission phase range of 360° and low loss between the incident and the transmitted waves: the magnitudes of the transmitted waves were equal to or better than −3.5 dB for incident transverse electric and transverse magnetic waves up to 30° in oblique angle. The transmitarray was fabricated using FR-4 boards with a loss tangent of about 0.02. FR-4 boards with lower loss tangents at the operating Ku band were not used because of the requirement for low cost. We also present the design of the horn antenna used to illuminate the transmitarray. The design applies discrete Jones matrix analysis; the final full transmitarray (333 unit cells) with the horn antenna were co-simulated using a full-wave simulation tool. The measured and simulation results are in excellent agreement. With a cell pitch of 0.39 $\lambda _{0}$ , the transmitarray achieves a dynamic range of 20 dB. The measured gain of the transmitarray prototype is 26.2 dB at a center frequency of 11.7 GHz, resulting in an aperture efficiency of about 62%. The measured results were achieved with a very small transmitarray (backpack-fit versus truck-carried). The −1 dB gain bandwidth of the transmitarray antenna is 12.6% at the center frequency (11.7 GHz). [ABSTRACT FROM AUTHOR]

We consider a two-layer elastic waveguide structure such that its one layer is unbounded in the lateral direction, and the standard boundary conditions are stated on the boundary of another one. We study several kinds of eigenwaves for this structure. In general, they have a complex-valued longitudinal propagation constant (the spectral parameter). On the base of the Green formula we introduce the scalar product of two waves and prove that the system of eigenwaves of the semiopen elastic waveguide is orthogonal. We construct families of waves which belong to discrete and continuous parts of the spectrum. [ABSTRACT FROM AUTHOR]

An integrated beam-forming network analysis for multibeam antennas based on an array of dielectric slotted waveguides in millimeter waves is proposed. The advantages of such networks include low losses, high aperture efficiencies, and design flexibility in comparison with traditional quasitopical systems. A new technique for obtaining the main characteristics by solving eigenwave and diffraction problem of the basic structure of the proposed network has been developed. [ABSTRACT FROM AUTHOR]

Eigen waves in novel materials which have properties of chiral composites and omega structures are considered. The materials can be modeled by uniaxial bianisotropic constitutive relations. Both chiral and omega composites possess promising features, for and one may expect still more interesting effects in more general media. [ABSTRACT FROM AUTHOR]