TM-polarized Electromagnetic Waves Research Articles

Tunable optical bistability at microwave frequency based on 1D sandwich photonic structure consisting of a nonlinear dielectric slab and two magnetized cold plasma layers

In this paper, tunable optical bistability that denotes the relationship between input intensity and output intensity is numerically investigated in the microwave frequency region based on the one-dimensional (1D) sandwich photonic structure consisting of a Kerr-type nonlinear material slab and two magnetized cold plasma layers. Results show that, in the case of TM-polarized electromagnetic wave, width and switching thresholds of the bistability loops are dependent on the working frequency, initial incidence angle, layer thickness, plasma density, and external magnetic field, which should be judiciously selected to obtain a required bistability behavior. Compared to the case of switch-down threshold, the switch-up threshold in the bistability loop is more sensitive to the changes of parameters. Through this study, the suggested 1D sandwich photonic structure is beneficial to the all-optical signal processing.

Three-periodic 1D photonic crystals for designing the photonic optical devices operating in the infrared regime.

We investigate theoretically and numerically one-dimensional three-periodic photonic crystals of the structure [(SiO2/TiO2)N(Al2O3/ZrO2)M]K, formed by dielectric oxides SiO2, TiO2, Al2O3, and ZrO2 (N and M are the number of subperiods, and K is the number of superperiods). We study the transmission spectra, energy and power fluxes of TE- and TM-polarized electromagnetic waves for a photonic crystal, characterized by the sharp PBG edges, and narrow and pronounced peaks of defect modes. The angular distance (difference in the incidence angles) between the transmission peaks of different polarizations is shown to be about 1.5°, which is 5 times more than in the ternary photonic crystals. The results can be useful for designing highly efficient optical devices operating in the infrared regime on the side-surface of the photonic crystal, such as polarization-sensitive couplers and angle sensors for optical fiber systems.

Modification of transfer-matrix method for electromagnetic waves in layered superconductor in presence of dc magnetic field

In the present paper, we modify the transfer-matrix method to study the dissipation-free transition of electromagnetic waves of terahertz range through a plate of layered superconductor embedded in the dielectric environment in the presence of external direct current (dc) magnetic field. In this work, we сonsider TM-polarized electromagnetic waves. The setup is arranged in such a way that the dielectric and superconducting layers in the plate are perpendicular to its interface, and the external magnetic field is directed along the plate and parallel to the layers. We consider the case of a weak external dc field at which magnetic vortices do not penetrate the plate. Due to the nonlinearity of the Josephson plasma formed in the layered superconductor, the dc magnetic field penetrates non-uniformly into the plate and affects the electromagnetic wave. Hence, the magnitude of the external dc magnetic field can be used as a variable parameter to tune various phenomena associated with the propagation of an electromagnetic waves in layered superconductors. In the presence of the external homogeneous dc magnetic field, linear electromagnetic waves in the layered superconductor turn out to be non-exponential. Therefore we cannot directly apply the transfer matrix method, in which the amplitudes of the corresponding exponents are compared. However, in the present paper, it is shown that for a sufficiently thick plate, the matrices describing the wave transfer through the plate can be introduced. The analytical expressions for these matrices are derived explicitly in terms of special Legendre functions. The obtained transfer-matrices can be used for the further study of the wave transfer through the layered superconductor in the presence of an external dc magnetic field.

Propagation of electromagnetic waves through non-uniform dielectric layers

The propagation of TE- and TM-polarized electromagnetic (EM) waves through a dielectric layer with spatial variation of the refractive index is reported in this paper. The relative permittivity of the layer is assumed to be graded along the thickness direction, and its spatial variation is described by a quartic polynomial. The corresponding mode equations are Helmholtz equations with variable coefficients that can be transformed to a triconfluent Heun equation, a local exact solution of which is expressed in terms of triconfluent Heun functions. The solutions cover many particular cases owing to a variability of four optional parameters (coefficients) of the quartic polynomial. The general local solution for a TE-polarized EM wave is employed for the calculation of transmission properties of a periodic one-dimensional photonic crystal using the Floquet theory.

Wide-angle transmissions of electromagnetic fields through the sandwiched transparent epsilon-near-zero metamaterial screen.

We propose a sandwiched transparent epsilon-near-zero (ENZ) metamaterial screen to release the obliquely incident electromagnetic fields. More specifically, the transmission properties through ENZ metamaterials are investigated when incorporated with an interlayer of a meta-surface having periodic complementary spiral-resonator-matrixes. We show that both TE- and TM-polarized electromagnetic waves are capable of penetrating the ENZ metamaterials under a wide-angle range of illuminations, and the greatly enhanced transmissions are turning out to be frequency dispersionless for different polarized electromagnetic fields with different incident angles. Our design, breaking the notion of the angular filter of ENZ metamaterials, should readily be applied to other extreme-parameter materials and pave the way to explore more unexpected transmission properties of these metamaterials.

Control Problems for 2-D Electromagnetic Wave Scattering Model

We consider the control problem for two-dimensional model of the electromagnetic field, which describes the scattering TM-polarized electromagnetic waves in an infinite homogeneous medium containing permeable dielectric obstacle with a covered for masking boundary. The role of control function is played by index of refraction of the dielectric obstacle. We prove the solvability of the control problem, derive the optimality system, which describes the necessary conditions of an extremum and develop an efficient numerical algorithm for the solution of the control problem.

Multilayer graphene waveguides

We study dispersion properties of TM-polarized electromagnetic waves guided by a multilayer graphene metamaterial. We demonstrate that both dispersion and localization of the guided modes can be efficiently controlled by changing the number of layers in the structure. Remarkably, we find that in the long wavelength limit, the dispersion of the fundamental mode of the N-layer graphene structure coincides with the dispersion of a plasmon mode supported by a single graphene layer, but with N times larger conductivity. We also compare our exact dispersion relations with the results provided by the effective media model.

Shape identification of anisotropic diffraction gratings for TM-polarized electromagnetic waves

This paper concerns the shape identification problem of anisotropic periodic structures which are known as diffraction gratings. We study the so-called Factorization method as a tool for reconstructing the anisotropic periodic media from measured spectral data involving scattered electromagnetic waves in TM modes. This sampling method provides a simple criterion to compute a picture of shape of diffraction gratings in a rapid way. We propose a rigorous analysis for the method as well as numerical experiments to examine its performance.

Nonlinear effects in the problem of propagation of TM electromagnetic waves in a Kerr nonlinear layer

The dispersion equation for the problem of propagation of TM-polarized electromagnetic waves in a Kerr nonlinear layer is presented. The propagation constants are calculated. Qualitative differences of the dispersion curves in the nonlinear and linear cases are demonstrated.

Design of reconfigurable metallic slits for terahertz beam modulation

We analyze the interaction of electromagnetic waves with double-layered subwavelength metallic slits on a dielectric substrate. This structure allows efficient transmission of an incident TM-polarized electromagnetic wave into the dielectric substrate, due to the presence of surface modes which couple the incident wave to the TEM waveguide modes supported by the subwavelength metallic slits. Our study shows that electromagnetic transmission through double-layered subwavelength metallic slits is strongly geometry dependent. Based on this observation, a terahertz modulation scheme is presented which, compared to existing terahertz modulator solutions, has the promise of significant enhancement in modulation index over a broad range of terahertz frequencies.

Excitation of oblique surface electromagnetic waves at an anisotropically conducting artificial interface by means of the attenuated-total-reflection method

In this paper, we present the theoretical analysis of excitation of well-bounded oblique surface electromagnetic waves propagating along an anisotropically conducting interface of two different dielectrics by means of the attenuated-total-reflection method. The flat surface of the interface contains a one-dimensional array of thin metal wires. It has been assumed that both the lattice constant of the array and the diameter of the wires are far less than the wavelengths of the surface waves. The surface electromagnetic waves may propagate along the interface at frequencies that are far lower than the plasma frequency of a metal, and the electric field of the waves is always perpendicular to the wires in any propagation directions. It has been shown that the oblique surface electromagnetic waves can be excited by the TM-polarized electromagnetic wave which becomes partially polarized during the excitation.

Boundary Eigenvalue Problem for Maxwell Equations in a Nonlinear Dielectric Layer

The propagation of TM-polarized electromagnetic waves in a dielectric layer filled with lossless, nonmagnetic, and isotropic medium is considered. The permittivity in the layer defines by Kerr law. We look for eigenvalues of the problem and reduce the issue to the analysis of the corresponding dispersion equation. The equivalence of the boundary eigenvalue problem and the dispersion equation is proved. We show that the solution of the problem exists and from dispersion equation it can be numerically obtained. Using this solution the components of electromagnetic field in the layer can be numerically obtained as well. Transition to the limit in the case of a linear medium in the layer is proved. Some numerical results are presented also.

Terahertz transmission properties of an individual slit in a thin metallic plate

We report on the terahertz transmission properties through a single slit in a thin metallic film. The properties are studied by comparing the transmissions of TE- and TM-polarized electromagnetic waves over a broad spectral range from the geometrical regime to the subwavelength limit. In the geometrical regime, the remarkable terahertz transmission due to guided modes is observed even without the contribution of surface waves. Whereas in the subwavelength limit, the surface charge oscillations associated with the TM-polarized guided mode give rise to strong transmission enhancement. The nature of the mechanisms for the terahertz transmission is elucidated using theoretical simulations of the near-field distributions and electromagnetic energy flow.

Cross-polarization of light at a dielectric-biisotropic medium interface

The problem of reflection and refraction of TE- and TM-polarized electromagnetic waves at oblique incidence on a dielectric-biisotropic medium interface has been solved. Conditions for the Brewster angles, at which the reflected wave field contains only the cross-polarized component, are established and the influence of the chirality and nonreciprocity parameters on the reflection coefficients is analyzed. It is shown that the appearance of cross-polarization upon reflection from the biisotropic medium is caused by the presence of nonreciprocity in addition to chirality.

A nonlinear boundary eigenvalue problem for TM-polarized electromagnetic waves in a nonlinear layer

We consider the propagation of TM-polarized electromagnetic waves in a nonlinear dielectric layer located between two linear media. The nonlinearity in the layer is described by the Kerr law. We reduce the problem to a nonlinear boundary eigenvalue problem for a system of ordinary differential equations. We obtain a dispersion relation and a first approximation for eigenvalues of the problem. We compare the results with those obtained for the case of a linear medium in the layer.

Total reflection of electromagnetic waves propagating from an isotropic medium to an indefinite metamaterial

The existence conditions for total reflection and the corresponding critical angle at the interface separating an isotropic medium and an indefinite metamaterial for TE- and TM-polarized electromagnetic waves are obtained. For different kinds of indefinite metamaterial, there appear different total reflection phenomena. Particularly, the anomalous total reflection in which the incident angle is smaller than the critical angle and the Brewster’s angle can be smaller than the critical angle can occur for anti-cutoff medium. Furthermore, the omnidirectional total reflection exists for the always cutoff medium and anti-cutoff medium. The total reflection depends on the thickness of indefinite metamaterial when the indefinite metamaterial is finite, and the photon tunneling phenomenon can occur when the thickness of indefinite metamaterial is smaller than wavelength.

Total transmission of electromagnetic waves at interfaces associated with an indefinite medium

We investigate the problem of total transmission at the interface separating an isotropic regular material and an indefinite medium [Phys. Rev. Lett.90, 077405 (2003)] in which not all of the principal elements of the permeability and permittivity tensors have the same sign, for TE- and TM-polarized electromagnetic waves. We make a detailed investigation on the existence conditions of total transmission and the corresponding Brewster's angles when an electromagnetic wave is incident on the interface from an isotropic regular material. We show that the propagation characteristics of electromagnetic waves at such interfaces are quite different from those at regular interfaces. For both TE and TM waves, total transmission is possible at the interfaces containing an indefinite medium; in particular, normally incident total transmission and omnidirectional total transmission are also allowed, provided that suitable physical parameters for the two materials across the interface are chosen.

Diffraction of a tm-polarized electromagnetic wave by two-dimensional thin screens and obstacles with edges

The solution to the scattering of an E-polarized plane wave from perfectly conducting infinite cylinders having arbitrary cross-sections and a finite number of edges is constructed by the polynomial expansions-Fourier transforms (PE-FT) method. The proposed method is based on the idea of reformulation of the integral equation in terms of the dual series equations with the trigonometrical kernel and the use of the properties of the orthogonal Gegenbauer polynomials. The initial problem is reduced to the problem of scattering from N bodies. As the result, the integral equation of the first kind with logarithmic singularity is reduced to N coupled systems of linear algebraic equations of the second kind. Particular cases of the circular cylindrical strip and the bodies with circular cylindrical facets are considered and analysis of scattering from the obstacles is presented.

A novel approach to the 2D-TM inverse electromagnetic medium scattering problem

The 2D inverse electromagnetic scattering problem of reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is considered. The material properties are reconstructed using scattering data from time-harmonic TM-polarized electromagnetic plane waves. A novel method which ensures physically meaningful material properties is proposed to numerically solve this nonlinear optimization problem. Numerical examples illustrate the efficiency of the algorithm.

Parametric interaction of surface waves guided by a plasma layer

We study the linear stage of the parametric instability of high-frequency surface waves guided by a homogeneous plasma layer on a metallic substrate when a TM-polarized plane electromagnetic wave is incident on the layer. The instability growth rate and the threshold value of the pumping wave amplitude are determined. It is shown that the instability can be thresholdless in a certain range of permittivities and thicknesses of the layer.