TE-polarized Electromagnetic Waves Research Articles

Numerical Study of the Spectrum of TE-Polarized Electromagnetic Waves of a Goubau Line Coated with Graphene

Numerical Study of the Spectrum of TE-Polarized Electromagnetic Waves of a Goubau Line Coated with Graphene

TE-Polarized Electromagnetic Wave Diffraction by a Circular Slotted Cylinder

The problem of diffraction of a TE-polarized electromagnetic wave by a circular slotted cylinder is investigated. The boundary value problem in question for the Helmholtz equation is reduced to an infinite system of linear algebraic equations of the second kind (SLAE-II) using integral summation identities (ISI). A detailed study of the matrix operator of the problem is performed and its Fredholm property in the weighted Hilbert space of infinite sequences is proven. The convergence of the truncation method constructed in the paper for the numerical solution of SLAE-II is justified and the results of computations are presented and discussed, specifically considering the determination of resonance modes.

Refinement of the Heuristic Solution for the Problem of TE-Polarized Electromagnetic Wave Diffraction on a Half-Plane with Two-Sided Impedance Boundary Conditions

A technique for obtaining refined heuristic solutions for problems with electromagnetic wave diffraction by scatterers with non-ideal boundary conditions is proposed. Based on the method of fundamental components for the problem of TE-polarized wave diffraction on a “semitransparent” half-plane with two-sided impedance boundary conditions, an improved heuristic solution for the scattered field is obtained by replacing the primary heuristic formula. A quantitative and qualitative assessment of the accuracy of the heuristic relationship is carried out as well as a physical interpretation of the rigorous solution based upon them. A classification of heuristic solutions is proposed according to the purpose of their application in practical problems.

Heuristic solution to the problem of diffraction of a TE-polarized electromagnetic wave on a semitransparent half-plane

Using the method of fundamental components for the problem of diffraction of a TE-polarized wave on a half-plane with two-sided impedance boundary conditions a heuristic solution is obtained that approximately describes the scattered field. The verification and adjustment of heuristic formulas using a rigorous solution by the Wiener–Hopf method are carried out. A physical interpretation of the rigorous solution based on the obtained heuristic relations is proposed.

NONLINEAR PROPAGATION OF LEAKY TE-POLARIZED ELECTROMAGNETIC WAVES IN A METAMATERIAL GOUBAU LINE

Propagation of leaky TE-polarized electromagnetic waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear metamaterial medium is studied. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

Influence of Graphene Coating of the Elements in a Two-Dimensional Parabolic Mirror Consisting of Parallel Cylinders on Radio Wave Focusing

We model the diffraction of a plane TE-polarized electromagnetic wave by a parabolic structure consisting of N parallel circular cylinders, where N ∼ 50. The problem of diffraction of a plane wave by a cylinder with arbitrary coordinates of its center is solved. The coupling of individual structural elements is not allowed for in the performed calculations. The field behavior in the vicinity of the focus of the considered parabolic antenna is studied for cylinders made of a dielectric, a dielectric with a graphene monolayer, and perfectly conducting cylinders. It is found that a layer of graphene can lead to an almost twofold increase in the maximum amplitude of the field in the focus, which makes the focusing properties of the dielectric antenna rather close to those of an antenna consisting of perfectly conducting cylinders. It is shown that the field amplitude in the focus oscillates strongly as the frequency increases, and the focus itself moves slightly off the center of the reflector system. The size of the focal spot is studied as a function of the incident-field frequency, cylinder radii, and the distance between the individual reflectors. It is shown that the field in the vicinity of the considered structure has certain features, such as slow and fast oscillations of the field amplitude, which occur as the frequency of the incident wave varies.

On the Existence of an Infinite Number of Leaky Complex Waves in a Dielectric Layer

The problem of propagation of TE-polarized electromagnetic waves in a dielectric layer is considered. The waves existing in the structure under study are classified. It is rigorously proved that, in the dielectric layer, there are no surface complex TE waves, but there are infinitely many complex leaky TE waves.

Theory of TE-polarized waves in a lossless cubic-quintic nonlinear planar waveguide

TE-polarized electromagnetic waves, guided by a three-layer slab structure consisting of a central film with quartic permittivity placed between two half spaces with Kerr permittivity, are studied. Traveling-wave solutions of Maxwell's equations are expressed in terms of Weierstrass's elliptic function $\ensuremath{\wp}$. A general dispersion relation is derived and evaluated by using a phase diagram analysis. Emphasis is placed on the conditions of existence and solvability of the dispersion relation. Numerical results are presented.

Magnetic-field-driven surface electromagnetic states in the graphene-antiferromagnetic photonic crystal system

The surface electromagnetic states (SEMSs) on graphene, which has a linear carrier dispersion law and is placed in an antiferromagnetic photonic crystal, are theoretically studied in the terahertz frequency range. The unit cell of such a crystal consists of layers of a nonmagnetic insulator and a uniaxial antiferromagnet, the easy axis of which is parallel to the crystal layers. A dc magnetic field is parallel to the easy axis of the antiferromagnet. An expression that relates the SEMS frequencies to the structure parameters is obtained. The problem of SEMS excitation by an external TE-polarized electromagnetic wave is solved, and the dependences of the transmission coefficient on the dc magnetic field and the carrier concentration are constructed. These dependences are shown to differ substantially from the case of a conventional two-dimensional electron gas with a quadratic electron dispersion law. Thus, the positions of the transmission coefficient peaks related to resonance SEMS excitation can be used to determine the character of carrier dispersion law in a two-dimensional electron gas.

Ultrahigh refractive index sensitivity of TE-polarized electromagnetic waves in graphene at the interface between two dielectric media

The behavior of the TE and TM electromagnetic waves in graphene at the interface between two semi-infinite dielectric media is studied. The dramatic influence on the TE waves propagation even at very small changes in the optical contrast between the two dielectric media is predicted. Frequencies of the TE waves are found to lie only in the window determined by the contrast. We consider this effect in connection with the design of graphene-based optical gas sensor. Near the frequency, where the imaginary part of the conductivity of graphene becomes zero, ultrahigh refractive index sensitivity and very low detection limit are revealed. The considered graphene-based optical gas sensor outperforms characteristics of modern volume refractive index sensors by several orders of magnitude.

Diffraction of an electromagnetic wave by gaps between plates

The problem of diffraction of a plane TE-polarized electromagnetic wave by gaps between metal plates located in the same plane is investigated. The diffraction problem is formulated as a boundary-value problem for the Helmholtz equation with the boundary conditions on metal and a given asymptotic behavior at the edges of the screens. The solutions are sought in the class of waves propagating to infinity. The problem under consideration is reduced to an integral equation with a strongly singular kernel with respect to the trace of the electric field vector in the gap. In turn, the integral equation is reduced to an infinite system of linear algebraic equations with respect to the expansion coefficients of the derivative of the sought function. Some singular integrals involving generalized Chebyshev polynomials are analytically calculated.

Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption

A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves) of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.

Imaging properties of triangular lattice photonic crystal at the lowest band

The propagation of electromagnetic (EM) waves in two-dimensional triangular-lattice photonic crystals (PCs) is investigated through dispersion characteristics analysis and numerical simulation of field pattern. We examine different surface terminations of the PC slab for getting a high-quality image. In the lowest photonic band both the TM and TE polarized EM waves can undergo negative refraction and imaging effect even at frequencies above the light line. The dependence of the image on the object distance and sample thickness is also discussed.

Enhanced backscattering from a metallic cylinder with a random rough surface

The scattering of a TE-polarized electromagnetic wave from a metallic cylinder with a slightly random rough surface is studied by means of the stochastic functional approach. The incoherent scattering distribution can be calculated from the Wiener coefficients up to the second order and demonstrates the enhanced backscattering peak, which is attributed to the participation of the surface plasmon waves supported by the cylindrical metal surface as the intermediate scattering processes in multiple scattering.

Propagation of TE waves in cylindrical nonlinear dielectric waveguides

The propagation of TE-polarized electromagnetic waves along a Kerr-type nonlinear dielectric, nonabsorbing, nonmagnetic, and isotropic (circular) cylindrical waveguide is investigated. For axially (azimuthal) symmetric solutions the problem is reduced to a cubic-nonlinear integral equation that is solved by iteration leading to a sequence uniformly convergent to the solution of the integral equation. The dispersion relations associated to the exact and iterate solutions, respectively, are derived and solved, subject to certain constraints. The roots of the exact dispersion relation are approximated by the roots of the dispersion relations generated by the iterate solutions. All statements of existence and convergence are based on results of a previous paper. Numerical results (concerning solutions of dispersion relations, field patterns, dependence of the propagation constant and of the cutoff radius on the nonlinearity parameter, power flow) are included.

Integral equation approach to reflection and transmission of a plane TE-wave at a (linear/nonlinear) dielectric film with spatially varying permittivity

A method is proposed for obtaining certain solutions (TE-polarized electromagnetic waves) of the Helmholtz equation, describing the reflection and transmission of a plane monochromatic wave at a (linear or nonlinear) dielectric film situated between two linear semi-infinite media. All three media are assumed to be lossless, nonmagnetic and isotropic. The permittivity of the film is modelled by (i) a continuously differentiable real-valued function of the transverse coordinate, and by (ii) a Kerr-nonlinearity. It is shown that the solution of the Helmholtz equation exists in the form of a uniformly convergent series (in case (i)) and in the form of a uniformly convergent sequence (in case (ii)) of iterations of the equivalent Volterra integral equation. Numerical results of the approach are presented.

Integral Equation Approach for the Propagation of TE-Waves in a Nonlinear Dielectric Cylindrical Waveguide

We consider the propagation of TE-polarized electromagnetic waves in cylindrical dielectric waveguides of circular cross section filled with lossless, nonmagnetic, and isotropic medium exhibiting a local Kerr-type dielectric nonlinearity. We look for axially-symmetric solutions and reduce the problem to the analysis of the associated cubic-nonlinear equation. We show that the solution in the form of a TE-polarized electromagnetic wave exists and can be obtained by iterating a cubic-nonlinear integral equation. We derive the associated dispersion equation and prove that it has a root that determines this solution.

A new family of first-order boundary conditions for the Maxwell system: derivation, well-posedness and long-time behavior

This work deals with the time-dependent Maxwell system in the case of TE-polarized electromagnetic waves, when associated with a family of first-order local boundary conditions. The boundary conditions are derived by using a micro-diagonalization method, actuated by the standard one of M.E. Taylor and involving pseudodifferential technics. The conditions differ from an arbitrary function and any of them leads to a well-posed mixed problem that is described by a continuous semi-group. The arbitrary function can be seen as a parameter and an asymptotic analysis in time shows that it can be chosen so that the resulting boundary condition is absorbing: the system is related to an energy functional that converges towards zero as time tends to infinity. By involving an invariant space for the Maxwell system, the limit state can be explicitly written as a solution to a boundary-value problem depending on the initial data. The long time behavior of the solution is then completely analyzed.

Solutions to the Helmholtz equation for TE-guided waves in a three-layer structure with Kerr-type nonlinearity

We study certain solutions (TE-polarized electromagnetic waves) of the Helmholtz equation on the line describing waves propagating in a nonlinear three-layer structure consisting of a film surrounded by semi-infinite media. All three media are assumed to be lossless, nonmagnetic, isotropic and exhibiting a local Kerr-type dielectric nonlinearity. The linear component of the permittivity is modelled by a continuous real-valued function of the transverse coordinate. We show that the solution of the Helmholtz equation in the form of a TE-polarized electromagnetic wave exists and can be obtained by iterating the equivalent Volterra equation. The associated dispersion equation has a simple root (if the semi-infinite media are linear and if the nonlinearity parameter of the film is sufficiently small) that uniquely determines this solution.

TE-polarized waves guided by a lossless nonlinear three-layer structure

We study TE-polarized electromagnetic waves guided by a three-layer structure consisting of a film surrounded by semi-infinite media. All three media are assumed to be lossless, nonmagnetic, isotropic, and exhibiting a local Kerr-like dielectric nonlinearity. We present general necessary and sufficient conditions for the existence of ``physical'' (real, nonnegative, bounded, and consistent with the dispersion relation) field intensities. As a physical consequence, the parameters ${a}_{\ensuremath{\nu}},{\overline{\ensuremath{\epsilon}}}_{\ensuremath{\nu}}{,n,E}_{0}^{2}{,k}_{0}d$ associated with realizable waves can be specified. To illustrate the procedure, analytical and numerical results for the allowed normalized thickness of the film and patterns of the field intensities as functions of the effective wave number and the intensity of the electric field at the lower surface of the nonlinear dielectric film are presented and the occurrence of singular field intensities is investigated. Finally, the particularization of the results to the three-layer structure containing a linear substrate and film and a nonlinear cladding is briefly discussed.