Case Of TM Polarization Research Articles

Tunable photonic bandgap and reflection phase shift properties of 1D binary photonic crystal consisting of double negative and magnetic cold plasma materials

In this manuscript, by using alternate layers of double negative and magnetic cold plasma materials, we have studied the reflection and reflection phase shift properties of 1D binary photonic crystals. The simulations of the proposed work have been carried out by using the transfer matrix method with the help of MATLAB software. It has been found that the combination of the angle of incidence and external magnetic field under both right hand polarized and left handed polarized configurations can be used for right and left tuning of photonic bandgap (PBG) of the proposed structure under consideration. Under the aforementioned circumstances, the reflection phase shift corresponding to TE and TM waves can be smoothly switched between 0 to π and –π to 0, respectively, across PBGs of the proposed structure. The variation in external magnetic field values from 0 to 6 T and angle of incidence from 0° to 80° can be used for precise tuning of PBG and reflection phase shift between –π and π depending upon TM and TE polarization cases, respectively. This study may open a new gateway for designing externally tunable microwave devices like single to multichannel band-stop filters, buffers that can hold data temporarily, tunable wave plates, and tunable phase retarders.

Magnetic field induced multichannel tunable filter properties of photonic band gap materials

we have explored the tunable multichannel characteristics of one-dimensional (1D) plasma photonic structure in presence of static magnetic field applied externally parallel and anti-parallel to the direction of propagation under normal incidence. We have theoretically examined the transmission characteristics of the binary photonic design consisting of alternate layers of CaF2 and magnetic cold plasma layers by means of transfer matrix method (TMM) which is amongst the one of the popular techniques for simulating 1D multilayer periodic structures based on MATLAB. The proposed structure possess N-1 number of distinct transmission peaks, each of unit transmission called as transmission channels in transmission spectra for given the number of periods N > 1. In this study N varies from 2 to 6 in steps of 1 to get 1 to 5 transmission channels respectively. Further we have also investigated how these transmission channels can be repositioned inside PBG by applying the static magnetic field (B) externally under right hand polarization (RHP) and lift hand polarization (LHP) configurations for given N at B = 0T, 0.02T, 0.04T and 0.06T. The reason behind the existence of these transmission channels is due to the superposition of evanescent and propagating waves inside plasma and dielectric layers respectively. The existence of these transmission channels inside PBG is different from the transmission bands which are formed due to the interference of forward and backward propagating waves. Besides this the tuning sense of the transmission channels at fixed B applied parallel or anti parallel to direction of periodicity, by changing the angle of incidence corresponding to TE and TM polarization case has also been examined to get some more useful and interesting tunable multichannel characteristics of the current design which cannot be obtained in conventional PPCs.

Determination of steep sidewall angle using polarization-sensitive asymmetric scattering

The sidewall angle (SWA) of a nanostructure exerts influence on the performance of the nanostructure and plays an important role in processing nano-structural chips. It is still a great challenge to determine steep SWAs from far field measurements especially when the SWAs are close to 90°. Here, we propose a far-field detection system to determine steep SWA of a cliff-shape step structure on a silicon substrate by combining a split detector with a scanning method. The far-field radiation field is asymmetric due to the scattering of the step structure, and further numerical analysis demonstrates the reliability of this far-field measurement method. In the simulations, two key variables, i.e. the polarization state and the focus position of the incident laser beam, are considered to explore their impacts. By scanning over the structure laterally and longitudinally with both TE and TM polarizations, polarization effects on the far-field occur. These effects show higher sensitivity to steep SWA variation for TM polarization as compared to TE. Furthermore, with a comprehensive longitudinal scanning analysis for the TM polarization case, a feasible focus interval can be optimized to retrieve the steep SWA. As the proposed method is fast, highly sensitive and easy to implement, it provides a powerful approach to investigate the scattering behavior of nanostructures.

Arbitrary power-splitting-ratio achieved in 1×2 hybrid plasmonic multimode interference device by structure symmetry broken

The power-splitting-ratio (PSR) of the 1 × 2 multimode interference (MMI) device based on hybrid plasmonic waveguide is studied theoretically. Other than the finite and fixed PSR in conventional MMI, by rational breaking the symmetry of the structure, arbitrary PSR can be achieved, while the original advantages of MMI devices including large fabrication tolerance, wide operation bandwidth, and compact size (1 × 1.1–1.5 μm2) are well-kept. Besides, unlike the regular hybrid-plasmonic-waveguide based device suitable only to TM polarization, the power splitter design presented here could be also possible available to TE polarization incidence. Introducing tapered structure may further improve its performance on both TE and TM polarization cases.

On the influence of the medium loss on resonances of surface plasmons in a cylinder

Two-dimensional problem of excitation of a circular cylinder made of a material with negative permittivity by a plane or a cylindrical wave is considered for the case of TM polarization. Conditions under which resonances of surface plasmons arise in cylinders thin compared to the wavelength are found with the use of strict numerical calculations.

A Novel Time-Domain Reflection Coefficient Function: TM Case

In determining electromagnetic transient response of structure placed above the half space, the half space properties can be taken into account via the reflection coefficient (RC) approximation. The choice of an RC function used in RC approximation is often important with regards to accuracy and computational efficiency of the overall method. In this paper, a new time-domain RC function for the case of TM polarization is presented. The function is derived using Gaver-Stehfest algorithm for numerical inverse Laplace transform and does not require the use of Bessel functions. The resulting formulation is rather simple, and, as the results indicate, accurate and computationally efficient.

Reconstruction of penetrable grating profiles

This paper is concerned with the inverse problem of recovering a penetrable gratingprofile in the TM-polarization case from the scattered field measured only above the structure, corresponding to a countably infinite number ofincident quasi-periodic waves.A sampling method is proposed to reconstruct the penetrable grating profile based ona near field linear operator equation in $l^2$.The mathematical justification of the sampling method is establishedand numerical results are presented to show the validity of the inversion algorithm.

CONVERGENT ADAPTIVE FINITE ELEMENT METHODS FOR PHOTONIC CRYSTAL APPLICATIONS

We prove the convergence of an adaptive finite element method for computing the band structure of two-dimensional periodic photonic crystals with or without compact defects in both the TM and TE polarization cases. These eigenvalue problems involve non-coercive elliptic operators with discontinuous coefficients. The error analysis extends the theory of convergence of adaptive methods for elliptic eigenvalue problems to photonic crystal problems, and in particular deals with various complications which arise essentially from the lack of coercivity of the elliptic operator with discontinuous coefficients. We prove the convergence of the adaptive method in an oscillation-free way and with no extra assumptions on the initial mesh, beside the conformity and shape regularity. Also we present and prove the convergence of an adaptive method to compute efficiently an entire band in the spectrum. This method is guaranteed to converge to the correct global maximum and minimum of the band, which is a very useful piece of information in practice. Our numerical results cover both the cases of periodic structures with and without compact defects.

Scattering from cylinders using the two-dimensional vector plane wave spectrum: addendum

The solution for the vector plane wave spectrum scattering from multiple cylinders by Pawliuk and Yedlin [J. Opt. Soc. A28, 1177 (2011)] only provided the single scattering coefficients for the TM polarization case. The TE solution is similar except for the form of the single scattering coefficients. Here we describe the single scattering coefficients for both polarizations and three types of cylinders: dielectrics, perfect electric conductors, and perfect magnetic conductors.

DIFFRACTION BY DIELECTRIC-LOADED MULTIPLE SLITS IN A CONDUCTING PLANE: TM CASE

A new and exact series solution for the scattering and coupling problems by dielectric-loaded multiple slits in a perfectly conducting screen is presented. The case of normal incidence and TM polarization is considered. The scattered and transmitted flelds are represented in terms of an inflnite series of radial modes. By applying the appropriate boundary conditions, the coe-cients of scattered and transmitted flelds are obtained and some numerical results are given.

Analysis of electromagnetic field due to a buried coated PEMC circular cylinder

An analytical solution for the scattering of an electromagnetic plane wave from a coated perfect electromagnetic conducting (PEMC) circular cylinder, buried in the dielectric half space, is presented. Scattering characteristics of a buried PEMC cylinder when coated by double-positive (DPS) or double-negative (DNG) materials is investigated. The cylinder as well as coating layer is of infinite length (2-D problem). Plane wave spectral representations of the fields have been used to solve the problem. Saddle point method is used to solve the integral arising in the analysis. All the multiple interactions between the buried geometry and the dielectric interface separating the two half spaces have been considered in the analysis. The derivation includes both TM and TE polarization cases. It is observed that the response of the coated PEMC cylinder can be used to detect the underground pipes and other buried objects having a cylindrical shape.

Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings

The total-field-scattered-field formulation of the finite-difference time-domain method (FDTD) is used to analyze the diffraction of finite incident beams by finite-number-of-periods holographic and surface-relief gratings. Both second-order and fourth-order FDTD formulations are used with various averaging schemes to treat permittivity discontinuities and a comparative study is made with alternative numerical methods. The diffraction efficiencies for gratings of several periods and various beam sizes, for both TE and TM polarization cases, are calculated and the FDTD results are compared with the finite-difference frequency-domain (FDFD) method results in the case of holographic gratings, and with the boundary element method results in the case of surface-relief gratings. Furthermore, the convergence of the FDTD results to the rigorous coupled-wave analysis results is investigated as the number of grating periods and the incident beam size increase.

Plane-Wave Impulse Response of a Debye Half Space

This report describes the computation of the time-domain reflection coefficient for a transient plane wave incident on a planar interface between free space and a Debye medium. Both the TE and TM polarization cases are considered. The reflection coefficients are written in a simple, compact form and involve a single convolution between exponential and Bessel functions. The use of the expressions in the characterization of Debye materials is explored.

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TM polarization

Diffraction of TM-polarized Gaussian beams by N equally spaced slits (finite grating) in a planar perfectly conducting thick screen is treated. We extend to the TM polarization case the results of a previous paper where the TE polarization was considered. The far-field diffraction patterns, the transmission coefficient tau, and the normally diffracted energy E as a function of several optogeometrical parameters are analyzed within the so-called vectorial region. The existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits is shown. In addition, the property E=Ntau/lambda, valid in the scalar region, is extended to the TM polarization case in the vectorial region, lambda being the wavelength. The coupling between slits is analyzed, giving an oscillating amplitude-decreasing function as the separation between slits increases, where the period for these oscillations is the wavelength lambda. Finally, the extraordinary optical transmission phenomena that appear when the wavelength is larger than the slit width (subwavelength regime) are analyzed.

Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section

The diffraction of an electromagnetic wave by a cylindrical object with arbitrary cross section is studied by taking advantage of recent progress in grating theories. The fast Fourier factorization method previously developed in Cartesian coordinates is extended to cylindrical coordinates thanks to the periodicity of both the diffracting object and the incident wave with respect to the polar angle theta. Thus Maxwell equations in a truncated Fourier space are derived and separated in TE and TM polarization cases. The new set of equations for TM polarization is resolved numerically with the S-matrix propagation algorithm. Examples of elliptic cross sections and cross sections including couples of nonconcentric circles show fast convergence of the results, for both dielectric and metallic materials, as well as good agreement with previous published results. Thus the method is suitable for an extension to conical (out-of-plane) diffraction, which will allow studying mode propagation along microstructured fibers.

ELECTROMAGNETIC SCATTERING FROM A CIRCULAR TARGET ABOVE OR BELOW ROUGH SURFACE - ABSTRACT

The electromagnetic scattering from a perfectly electric conducting (PEC) target located above or below rough surface is investigated, for the case of TM polarization, using the Method of Moments (MoM). The rough surface with Gaussian profile is used to emulate the realistic situation of a statistically-rough surface, while the tapered incident wave is chosen to reduce the truncation error. The Monte-Carlo procedure is employed to calculate the angular correlation function (ACF), which is dependent on the depth, size and horizontal position of the buried target, as well as the moisture content in the soil, and the properties of the rough surface. The enhancement of the ACF on the non-memory line can be used to detect a target below the rough surface. The analysis on the statistical characteristics is also carried out, in view of the study on target detection.

Electromagnetic Scattering from a Circular Target above or below Rough Surface

The electromagnetic scattering from a perfectly electric conducting (PEC) target located above or below rough surface is investigated, for the case of TM polarization, using the Method of Moments (MoM). The rough surface with Gaussian profile is used to emulate the realistic situation of a statistically-rough surface, while the tapered incident wave is chosen to reduce the truncation error. The Monte-Carlo procedure is employed to calculate the angular correlation function (ACF), which is dependent on the depth, size and horizontal position of the buried target, as well as the moisture content in the soil, and the properties of the rough surface. The enhancement of the ACF on the non-memory line can be used to detect a target below the rough surface. The analysis on the statistical characteristics is also carried out, in view of the study on target detection.

Coupled Maxwell-pseudospin equations for investigation of self-induced transparency effects in a degenerate three-level quantum system in two dimensions: Finite-difference time-domain study

We extend to more than one spatial dimension the semiclassical full-wave vector Maxwell-Bloch equations for the purpose of achieving an adequate and rigorous description of ultrashort pulse propagation in optical waveguides containing resonant nonlinearities. Our considerations are based on the generalized pseudospin formalism introduced by Hioe and Eberly [Phys. Rev. Lett. 47, 838 (1981)] for treatment of the resonant coherent interactions of ultrashort light pulses with discrete-multilevel systems. A self-consistent set of coupled curl Maxwell-pseudospin equations in two spatial dimensions and time for the special case of a degenerate three-level system of quantum absorbers is originally derived. Maxwell's curl equations are considered to be coupled via macroscopic medium polarization to the three-level atom model for the resonant medium. Two distinct sets of pseudospin equations are obtained corresponding to the TE- and TM-polarized optical waves. For the case of TM polarization, the electromagnetic wave is polarized in a general direction in the plane of incidence inducing two dipole transitions in a degenerate three-level system by each E-field component along the propagation axis and in transverse direction. We introduce a dipole-coupling interaction Hamiltonian allowing Rabi flopping of the population difference along and perpendicular to the propagation axis with frequencies depending on the corresponding field components. The relationship between the induced polarization and the state vector components that describe the evolution of the discrete-level system is derived in order to couple the quantum system equations to the Maxwell's curl equations. The pseudospin equations are phenomenologically extended to include relaxation effects by introducing nonuniform decay times corresponding to the various dipole transitions occurring in a three-level system. The system has been discretized using finite differences on a Yee grid and solved numerically by an iterative predictor-corrector finite-difference time-domain method. Self-induced transparency soliton propagation through a degenerate three-level quantum system of absorbers in two spatial dimensions and time is demonstrated in planar parallel-mirror waveguide geometries.

A new efficient method of analysis for inhomogeneous media shields and filters

In this paper, we discuss the shielding characteristics of an inhomogeneous shield for oblique incidence. The inhomogeneity considered can be modeled via a continuous spatial variation of the permittivity along the power-flow direction and can be taken into account in the mathematical model involving the transmission line equivalent-circuit representation in terms of a longitudinal-line impedance and a transverse-line admittance varying along the same direction. In order to design a filter or a matching line layout with such a material, new analytical expressions of the reflection coefficient and of the shielding factor for nonuniform dielectric slabs are found. Some numerical examples are also presented for both the TE and TM polarization cases.

Scattering of electromagnetic waves by a perfectly conducting cylinder with a thin lossy magnetic coating

We study the scattering interaction of electromagnetic (EM) waves with an infinite cylinder coated with a lossy dielectric material with frequency-dependent material properties. These properties are hypothetical, yet representative of a wide class of available materials. The monostatic and bistatic scattered widths (SW) are evaluated for the TM or TE polarization cases. These calculations require the use of algorithms to evaluate Bessel-Hankel functions of complex arguments. These algorithms are based on a continued fraction approach, which ensures stability of the recursion relations. The bistatic plots of the TM and TE scattering widths for the coated body are displayed in a convenient color-graded scale. The reductions in the scattering widths produced by this type of coating are determined in selected frequency bands and angular sectors, in both polarization cases. It is quantitatively shown how curvature and polarization shift the effectiveness band of the coating. The determined regions in which the SW are minimally affected are the most suitable for target identification purposes.