Propagation Of TM Waves Research Articles

Nonlinear simulation of TM mode free electron laser in rectangular waveguide with ion-channel

By considering the propagation of TM waves in a rectangular waveguide, the radiated power of a free electron laser is calculated during beam–wave interaction in a planar wiggler. A set of self-consistent equations are derived for discerption of this system which includes some electrostatic and electromagnetic fields, equation of motions and evolution equations of amplitude and phase. The evolution equations of amplitude and phase are determined using an averaging method on the wave equation. By writing a 3D simulation code, the variation in power during electron beam propagation is investigated and then the role of various ion channel density on efficiency is examined. Numerical results show that there is a significant increase in the radiation power of TM waves in comparison with the TE waves in the proposed configuration.

Nonlinear Surface Waves in a Symmetric Three-Layer Structure That Is Composed of Optical Media with Different Formation Mechanisms of Nonlinear Response

We consider the propagation of surface TM waves in a three-layer structure the inner layer of which is formed by a plate of a crystal with a Kerr type focusing nonlinearity, while its outer layers are uniaxial photorefractive crystals with the diffusion nonlinearity formation mechanisms. Nonlinear surface waves that differ in the character of their decay can propagate along the interfaces between the layers. The amplitudes of waves of one type decrease without oscillations with increasing distance from the interface as the waves propagate into the depth of the outer layers of the photorefractive crystals, while the amplitudes of waves of the other type decrease with oscillations. The wave profiles can be either symmetric or antisymmetric with respect to the center of the three-layer structure. The waves with the symmetric profile distribution, the amplitudes of which decrease into the depth of the photorefractive crystals either with or without oscillations, can be of two types, while those with the antisymmetric distribution can be only of one type. For the long-wavelength propagation regime of surface waves, explicit analytical dependences of the propagation constant on the characteristics of the layered structure are found and the conditions for their existence are determined.

Нелинейные поверхностные волны в симметричной трехслойной структуре из оптических сред с различными механизмами формирования нелинейного отклика

The propagation of surface TM waves in a three-layer structure, which is a crystal thickness plate with a focusing nonlinearity of a Kerr type, sandwiched between uniaxial photorefractive crystals with a diffusion mechanism for the formation of nonlinearity is considered. Nonlinear surface waves with different attenuation patterns can propagate along the interfaces between the layers. Waves of one type attenuate with distance from the interfaces without oscillations into the depth of the outer layers of photorefractive crystals, and the waves of other type attenuate with oscillations. Wave profiles can have two forms of symmetry about the center of a three-layer structure: symmetric and antisymmetric. The two waves with a symmetric distribution exist with nonperiodic damping and the damping without oscillations. The waves only with antisymmetric distribution exist with nonperiodic damping and the damping without oscillations. The dependences of the propagation constant on the characteristics of the layered structure for the long-wave mode of surface wave propagation are found in an explicit analytical form. The conditions for their existence are indicated.

Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides

Problems on the propagation of surface TE and TM waves in an inhomogeneous anisotropic two-layered planar or cylindrical magneto-dielectric waveguide are considered. The problem is reduced to the analysis of a Sturm-Liouville problem of a special kind with boundary conditions of the third kind, nonlinearly depending on the spectral parameter. The conditions under which TE and TM waves can propagate are obtained, and the regions of localization of the corresponding propagation constants are determined.

Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity

The paper focuses on the problem of monochromatic electromagnetic TM wave propagation in a two-layer circular cylindrical dielectric waveguide. The space outside the waveguide is filled with isotropic medium having constant permittivity. The inner core of the waveguide is filled with isotropic medium having constant permittivity; the cladding of the core is filled with isotropic inhomogeneous nonlinear permittivity (the nonlinear term is expressed by Kerr law). Existence of guided modes which depend harmonically onz(the waveguide axis coincides withz-axis) is proved and their localization is found. Numerical results including different type of nonlinearities are presented. A comparison with the linear case is given. The existence of a new propagation regime is predicted.

Propagation of 2D Electromagnetic Wave in Lossy Lorentz Media Based on Auxiliary Differential Equation of Finite-Difference Time-Domain Method

In order to study the reflection of electromagnetic wave in Lorentz media, A finite-difference time-domain method based on the auxiliary differential equation (ADE) technique is used to obtain the formulation of 2-D TM wave propagation in lossy Lorentz media. In 1-D case, the reflected coefficients calculated by ADE-FDTD method and exact theoretical result are excellent agreement. This expresses that the 2-D formulas of electromagnetic wave propagation in lossy Lorentz media are right. Furthermore, Plane wave reflected by Lorentz media layer is calculated and simulated. Results display that reflected effect is evident.

Application of ADE-FDTD Method in Lossy Lorentz Media

A finite-difference time-domain method based on the auxiliary differential equation (ADE) technique is used to obtain the formulation of 2-D TM wave propagation in lossy Lorentz media. In the paper, the reflected coefficients calculated by ADE-FDTD method and the exact theoretical result are better agreement.

TM-waves guided by a nonlinear film with complex permittivity

The propagation of TM-waves in a planar waveguide with a nonlinear film surrounded by semi-infinite linear media is studied. The film is assumed to be nonmagnetic, anisotropic and it is defined by complex permittivity with a Lipschitz continuous nonlinearity. In the film Maxwell’s equations are reduced to a system of two Volterra integral equations. By the Banach fixed point theorem it is shown that the unique solution exists as a uniform limit of iterations. The dispersion relation is presented and some numerical examples are given.

On the problem of nonlinear coupled electromagnetic transverse-electric–transverse magnetic wave propagation

Coupled electromagnetic TE and TM wave propagation in a nonlinear plane layer is considered. Nonlinearity inside the layer is described by Kerr law. Physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. It is proved that TE and TM waves that form (nonlinear) coupled TE-TM wave can propagate at different frequencies ωE and ωM, respectively. These frequencies can be chosen independently. Existence of coupled surface TE and TM waves is proved. Intervals of localization of coupled eigenvalues are found.

Effective Surface Impedance of a Printed-Circuit Tensor Impedance Surface (PCTIS)

The surface impedance and dispersion equation of a printed-circuit tensor impedance surface (PCTIS) are derived using a modified transverse resonance technique. A PCTIS consists of a subwavelength-patterned metallic cladding over a grounded dielectric substrate. The metallic cladding is analytically modeled as a tensor impedance sheet. An explicit expression is derived for the effective surface impedance of the PCTIS using a transmission-line approach. First, the surface-impedance expression is found for a printed-circuit scalar impedance surface using the transverse resonance technique. Next, a modified transverse resonance technique is applied to an idealized tensor impedance boundary condition (TIBC) to find its dispersion equation. Finally, the analysis of the printed-circuit scalar impedance is combined with that of the idealized TIBC to find the tensor surface impedance and dispersion equation of a PCTIS. A discussion of the principal axes and the propagation of TM and TE waves is provided. The special case of electrically thin PCTISs is also analyzed and discussed.

TM waves in cylindrical superlattices (LANS) bounded by left-handed material (LHM)

The investigation of TM wave propagation inside a cylindrical waveguide composed of antiferromagnetic/nonmagnetic superlattices (LANS), bounded by left-handed material (LHM), is presented. We have derived the eigenmode equation and obtained the solutions for TM propagation modes. We found that the waveguide supports backward TM waves since both electric permittivity and magnetic permeability of the LHM are negative. We also illustrated the dependence of the wave index nx on the magnetic fraction f1 and the reduced radius of the LANS. The largest propagation lengths of TM waves and the best confinement are achieved for the thinnest LANS of less magnetic material. Moreover, we displayed the influence of the magnetic permeability μh and the electric permittivity eh of the LHM on the power flow of TM waves. Larger wave indices have been switched by increasing μh and eh.

Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity

The problem of electromagnetic TM wave propagation through a layer with Kerr nonlinearity is considered. The layer is located between two half-spaces with constant permittivities. This electromagnetic problem is reduced to the nonlinear boundary eigenvalue problem for ordinary differential equations. It is necessary to find eigenvalues of the problem (propagation constants of an electromagnetic wave). The dispersion equation (DE) for the eigenvalues is derived. The DE is applied to nonlinear metamaterial as well. Comparison with a linear case is also made. In the nonlinear problem there are new eigenvalues and new eigenwaves. Numerical results are presented.

Propagation of TM waves in a layer with arbitrary nonlinearity

A boundary value problem for Maxwell’s equations describing propagation of TM waves in a nonlinear dielectric layer with arbitrary nonlinearity is considered. The layer is located between two linear semi-infinite media. The problem is reduced to a nonlinear boundary eigenvalue problem for a system of second-order nonlinear ordinary differential equations. A dispersion equation for the eigenvalues of the problem (propagation constants) is derived. For a given nonlinearity function, the dispersion equation can be studied both analytically and numerically. A sufficient condition for the existence of at least one eigenvalue is formulated.

Analsys of the properties of tunable prohibited band gaps for two-dimensional unmagnetized plasma photonic crystals under TM mode

The piecewise linear current density recursive convolution (PLCDRC) on finite-difference time-domain (FDTD) method is applied to study the properties of prohibited band gaps for TM wave propagation in the two-dimensional unmagnetized plasma photonic crystal. In frequency-domain, the transmission coefficient of electromagnetic differential Gaussian pulses are computed and we analyzed the effect on properties of tunable prohibited band gaps for the two-dimensional unmagnetized plasma photonic crystals by its relative permittivity of column, lattic constant, dielectric column radius, periodic constant and parameters of plasma. The results showed that the prohibited band gaps can not be broadened by inceasing periodic constant and plasma collision frequency, but can be broadened by increasing relative permittivity of column and plasma frequency. The prohibited gaps also can be widened by decreasing the lattic constant and dielectric column radius for fill rate of a certain value.

The method of lines and cylindrical waveguides with constant arbitrary cross sections

AbstractA modified method of lines is developed for propagation of TM waves in waveguides with constant arbitrary cross sections. The proposed method finds the eigenmodes and associated wave functions in a very practical manner. Numerical performance and accuracy of the proposed method are examined for waveguides with well known characteristics and are found to be very satisfactory. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:1–5, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25624

TM-wave propagation controlled by split ring resonator array

We propose a new approach to control the propagation of electromagnetic (EM) wave with certain polarization by a split ring resonator (SRR) array. Interactions between SRR and the EM wave in the array are analyzed and it is found that the H field is always perpendicular to the SRR plane around the magnetic resonance frequency. Based on this property, a semicircular waveguide is designed to realize a 180 degrees bending with high performance. The structure of this approach is simple and feasible, providing an alternative way to construct bending waveguide with low loss.

Frequency-domain modeling of TM wave propagation in optical nanostructures with a third-order nonlinear response

An enhanced method is developed for analysis of third-order nonlinearities in optical nanostructures with a scalar magnetic field frequency-domain formulation; it is shown to produce fast and accurate results for 2D problems without a superfluous vector electric field formalism. While a standard TM representation using cubic nonlinear susceptibility results in an intractable implicit equation, our technique alleviates this problem. In addition to a universal approach, simpler, more efficient solutions are proposed for media having solely either a real (lossless Kerr-type medium) or an imaginary (nonlinear absorbing medium) nonlinearity. Combining these solutions with a finite-element method, we show simulation examples validated with alternative approaches.

A Staggered Upwind Embedded Boundary (SUEB) Method to Eliminate the FDTD Staircasing Error

In spite of its flexibility and second-order accuracy in a homogeneous medium, Yee's finite-difference time-domain (FDTD) method suffers from serious degradation when treating material interfaces, greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors. Indeed, such so-called staircasing approximation may lead to local zeroth-order and global first-order errors. In this work, an embedded FDTD scheme, the staggered upwind embedded boundary (SUEB) method, is developed for the solution of oneand two-dimensional Maxwell's equations. This simple embedded technique uses upwind conditions in the FDTD method to correctly represent the location and physical conditions of material and metallic boundaries, hence eliminating problems caused by the staircasing approximation. Accuracy analysis has been made to show that the SUEB method maintains a second-order accuracy globally. Since the entire problem has been embedded into the simple staggered grid similar to that employed by the Yee's scheme, extra effort is only needed when treating the grid points close to the interfaces. Therefore, little additional computational cost is needed over Yee's scheme. The SUEB method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the TM wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder.

A novel Fourier based 3D full-vectorial beam propagation method

In this paper a Fourier based full-vectorial beam propagation method (BPM) with perfectly matched layer (PML) absorbing boundary conditions is presented. The method starts with the slowly varying envelope coupled wave equations, including coordinate-stretching type PMLs, which are discretised using the Galerkin method with Fourier basis functions in the transversal direction. The proposed method is then assessed in a wide variety of situations, including 2D propagation of TE and TM waves and 3D full-vectorial situations. The obtained results show that good accuracy can be obtained even for complex strongly-guiding waveguides with a small number of basis functions.

Novel numerical method for the analysis of 2D photonic crystals: the cell method

The Cell Method, a new efficient numerical method suitable for working with periodic structures having anisotropic inhomogeneous media with curved shapes, is proposed in order to calculate the band gap of 2D photonic crystals for in-plane propagation of TM and TE waves. Moreover some numerical comparisons with other numerical methods will be provided.