Complex and Backward-Wave Modes in Inhomogeneously and Anisotropically Filled Waveguides

A rigorous analysis of lossless inhomogeneously and anisotropically filled waveguides of arbitrarily shaped cross section is presented. The mode propagation constants squared appear as eigenvalues of a real infinite-dimensional characteristic matrix, which is, in the general case, nonsymmetric. Complex conjugate pairs of eigenvalues are then possible, which give rise to complex modes. Modes at cutoff are shown to be either TE or TM with real cutoff frequencies. An investigation of the power flow shows that backward-wave modes may exist as well. Different orthogonality relations are derived from which the power coupling between complex modes is investigated.     

Rigorous Analysis of the Scattering of Surface Waves in an Abruptly Ended Slab Dielectric Waveguide

The reflection and the scattering properties of even TE and TM surface waves incident in an abruptly ended dielectric slab waveguide are analyzed. The discontinuity is regarded as a junction between two open waveguides namely the dielectric slab waveguide and the free space waveguide. The boundary conditions acting together with the orthogonality provide singular coupled integral equations on the discrete and the continuous wave amplitudes at the discontinuity. These singular coupled intergral equations with Cauchy kernels and infinite limits of integration are solved by iteration via the Neuman series. Numerical results are presented for the reflectivity of the even TE/sub 0/ and TM/sub 0/ fundamental modes, together with their mode conversion on even TE/sub 2/ and TM/sub 2/ in a slab where two guided modes can propagate. Reflectivity and mode conversion of higher order excitations are also investigated     

Response of circular symmetric multiconductor microstrip line to an electromagnetic field

The primary-secondary field idea is used to determine the response of a circular symmetric multiconductor microstrip line (CSMSL) to an external electromagnetic plane wave. The primary field is obtained analytically for the cases of oblique TM/sup z/ and TE/sup z/ polarized incidence. The secondary field is determined using excited multiconductor transmission line theory. The method is examined to obtain the effect of external illumination on a four-strip CSMSL and some useful results are obtained.     

Accurate analysis and modeling of laminated multilayered 3-D optical waveguides

The theoretical investigation of waveguides having nonuniform cross-sections is an attractive and challenging problem which deserves serious interest. In this paper, we present a novel analysis of laminated multilayered three-dimensional waveguide, based on two modes: 1) a new coupled transmission line approach that considers the sloping of the layers along the longitudinal direction and 2) a transmission line matrix integral equation (TLMIE) modeling that complete and extends the investigation of the field propagation. In method 1), we neglect radiation modes and their EM coupling. All physical effects instead are accounted for by the full-wave TLMIE method. By using TLMIE, we validate the EM analysis and calculate TE/TM losses, arising from radiation modes.     

Mode Conversion in Tapered Waveguides At and Near Cutoff

The coupling coefficient between the TE/sub 11/ mode and the TM/sub 11/ mode in tapered circular waveguides is derived, and at cutoff frequency it tends to approach an infinity of the order of 0/sup -1/4/. It is surprising to discover that the corresponding coupling coefficient between the TE/sub 10/ mode and the TM/sub 12/ mode in tapered rectangular waveguides approaches instead a zero of the order of 0/sup 1/4/ at cutoff frequency. Accordingly, for the modes concerned, the choice of using circular or square waveguides as tapers for transition at and near cutoff frequency is significant in reducing mode conversion level. At and near cutoff frequency a "synthesized" square taper is better in that it is shorter than a "synthesized" circular taper for the same mode conversion levels. On the other hand, for frequencies far away from cutoff the choice is insignificant. Design procedures for "synthesized" waveguide tapers at and near cutoff are presented, and the results of measurements are in agreement with the theoretical calculations.     

On the Mode and Square Correspondence Between Circular Multimode Tapered Waveguides

In an axially straight multimode circular waveguide taper excited with a pure TE/sup /spl circle// /sub 11/ dominant mode, the first and only converted mode at and near cutoff is the TM/sup/spl circle// /sub 11/ mode. It is shown that in an axially straight multimode square waveguide taper excited with a pure TE/sup/spl square// /sub 10/ dominant mode, the TM/sup/spl square// /sub 12/ mode corresponding to the TM/sup/spl circle// /sub 11/ mode in circular case is not the only first converted mode at and near cutoff. The overall behavior or coupling mechanism of waveguides is similar whether the waveguide is rectangular, square, circular, or elliptical: i.e., the overall coupling coefficient at cutoff of a converted mode or modes approaches an ininfinity of the order 0/sup -1/4/.     

Cyclotron Autoresonance with TE and TM Guided Waves

The electron cyclotron autoresonance is of both theoretical and practical interest for acceleration of charged particles and for generation of microwave radiation in various gyro-devices. In this paper a unified first-principles approach is applied to the analysis of the interaction of gyrating electrons with electromagnetic waves with different characteristic impedance. In contrast to the previous works that consider the underlying autoresonance integral only for the case of plane transverse waves and TE modes our analysis is applied also to TM modes. An approximate constant of motion is derived for the latter case from which it follows that the requirements for autoresonance can be satisfied easily in comparison to the TE modes. Some fundamental relations which follow from the analysis are discussed as well.     

用谱域导抗法计算铁氧体加载鳍线的传输特性

本文从Maxwell方程出发,经过Fourier变换和坐标旋转,将铁氧体中的非寻常波分解成TE和TM波,并给出它们的波导纳。利用边界条件,忽略TE和TM波间耦合的影响后,将鳍线用一等效网络表示。本文方法与T.Itoh提出的谱域导抗法比较,在等效网络中引入了理想变压器元件。最后对铁氧体加载单侧鳍线的正反向传播常数进行了数值计算,其结果与有关文献中数据吻合得很好。     

Analysis of a line-defect waveguide on a silicon-on-insulator two-dimensional photonic-Crystal slab

This paper describes the investigation of the waveguide properties of a silicon-on-insulator (SOI)-based two-dimensional photonic-crystal slab. It is found that coupling between transverse-electric (TE)-like defect modes and transverse-magnetic (TM)-like slab modes occurs in some frequency range due to structural asymmetries in the vertical direction. This TE-TM coupling, together with the smaller refractive-index contrast between the slab and dielectric cladding, results in propagation losses for a line-defect waveguide in an SOI structure. The paper also presents optimization methods for obtaining a wide lossless propagation band using such a line defect.     

Analysis of TE and TM modes in DFB lasers by two-dimensional theory

The two-dimensional theory of a distributed feedback (DFB) laser (which was previously presented and applied to the analysis of the laser threshold conditions for the transverse-electric (TE) mode in a simple three-layer waveguide structure) is developed to treat both TE and transverse-magnetic (TM) modes in a four-layer waveguide structure with a thin grating layer, which more closely reflects actual DFB laser structure. The differences between TE and TM modes for the dispersion relations and the laser threshold conditions are clarified. The effects of the waveguide structure (including grating layer thickness, refractive indexes of layers, coupling constant, and corrugation period) on the threshold gains and the gain differences between the two longitudinal modes on both sides of the Bragg frequencies are studied in detail for both TE and TM modes     

Scattering of the TE/sub 01/ and TM/sub 01/ Modes on Transverse Discontinuities in a Rod Dielectric Waveguide-Application to the Dielectric Resonators

Our purpose is to determine the resonance frequency together with the radiation quality factor of dielectric resonators. To do that, the reflection and the scattering properties of the TE/sub 01/ and TM/sub 01/ modes, incident on an abruptly ended dielectric rod, are analyzed. After the building of the complete mode spectrum on each side of the discontinuity, the continuity relations in the discontinuity plane associated with the orthogonality properties lead to a coupled integral equation system. That one is solved by means of an iterative procedure, providing all the characteristics of the discontinuity (reflection or coupling coefficients, radiation losses). Then, these solutions are used to determine the resonant frequency and the radiation quality factor of cylindrical resonators which are considered as waveguide lengths between two interacting discontinuities.     

Mode Coupling Between Surface Wave Transmission Lines

The eigenvalue equation describing the mode coupling between two Goubau surface wave lines is derived utilizing the point matching method for solutions of boundary value problems. Excellent agreement is obtained between theoretical and experimental results. A method for obtaining the hybrid wavenumbers of coupled surface wave lines is proposed for a finite set of TE and TM modes.     

Modes of a symmetric slab optical waveguide in birefringent media, part II: Slab with coplanar optical axis

We study the modes of a symmetric thin-film slab waveguide composed of birefringent crystalline material in the film and in the equivalent substrate and superstrate. In addition we assume that the optical axes of the uniaxial materials of film and substrate are parallel to each other and also parallel (coplanar) to the plane of the film. This simple anisotropic waveguide has interesting properties. It supports only hybrid modes but in the limit of propagation along the optical axis and at right angles to it the modes become almost of the TE and TM type. Moreover, some of the modes become leaky waves as they propagate at increasingly larger angles relative to the optical axis of the dielectric material. For guides made of materials whose ordinary refractive index nois larger than the extraordinary index ne, the extraordinary wave modes, which approximate TE modes, become leaky; and forn_{e} > n_{o}, the ordinary wave modes, which approximate TM modes, become leaky. The leakage losses are large near a "critical angle," where leakage begins to appear but may be insignificant at larger angles, measured between the optical axis and the direction of propagation.     

TE-TM mode conversion of an optical beam wave in thin-film opticalwaveguides

The TE-TM mode conversion efficiency when a Gaussian beam wave propagates in thin-film optical waveguides is discussed. For film thicknesses at which strong coupling between the TE and TM modes is obtained, two hybrid modes have oppositely rotating circular polarizations, or linear polarizations perpendicular to each other with equal magnitude of TE-wave and TM-wave components. In the former (i.e. circular polarization), complete TE-TM mode conversion is impossible. In the latter (i.e. linear polarization) complete TE-TM mode conversion is available. These claims are based on the fact that the direction of power flow of the hybrid modes depends on the polarization     

Radiation modes of a five-layer symmetric slab waveguide

The radiation modes of a five-layered symmetric slab waveguide are treated in detail. Since the slab is assumed to be infinitely extended in the yz plane, all field quantities are considered to be independent of y. The analysis is based on modal expansion formulation and the modes can be classified as TE and TM as well as even and odd ones. Applying the boundary conditions at interfaces, the expansion coefficients of the field components are easily calculated. In addition, the normalization factors and the orthogonality properties are determined by deriving appropriate integrals over the cross section of the waveguide. Finally, the validity of the orthogonality relations between the radiation modes and the guided ones, which propagate in such a waveguide, is proved explicitly.     

Nondestructive Measurement of a Dielectric Layer Using Surface Electromagnetic Waves

In this investigation, the possibility of nondestructively measuring the thickness and dielectric constant of a layer of dielectric material on a conducting substrate by surface electromagnetic waves (SEW) has been demonstrated. The theoretical approximate dispersion relations near cutoff were derived for both the TE and TM modes and found to be linear functions of frequency, the thickness and dielectric constant were then calculated as simple algebraic functions of the slope and intercept of the dispersion curve. An experimental apparatus utilizing a prism-coupler was constructed to excite surface electromagnetic waves in a dielectric layer whose characteristics were known. By suitable measurements of the frequency and the coupling angle of the source, the dispersion curve was determined experimentally and the resulting dielectric constant and thickness of the layer calculated.     

Fundamental and Higher Mode Inversion of Dispersed GPR Waves Propagating in an Ice Layer

Dispersion of ground-penetrating radar (GPR) waves can occur when they are trapped in a layer. In this paper, we analyze the modal propagation of GPR pulses through a layer of ice that is overlying water. Dispersed transverse electric (TE) waves that are trapped in the waveguide have larger amplitudes than the critically refracted waves that travel through air, whereas the transverse magnetic (TM) critically refracted waves traveling through air are more dominant than the trapped dispersed TM waves. This can be explained by the leaky waveguide behavior of the ice layer. The reflection coefficients for the waves incident on the ice-water interface show that the TM modes are more leaky than the TE modes. Still, clear dispersion is observed in both cases, which depends on the permittivity and thickness of the ice. Similar to inversion of dispersed Rayleigh waves, these parameters can be estimated by calculating phase-velocity spectra, picking dispersion curves, and inverting the dispersion curves using a combined local and global minimization procedure. Synthetic data show several higher order modes of which separate and combined inversions return the input modeling parameters accurately. Experimental data acquired on a frozen lake show strong dispersion for the TE and TM modes. The phase-velocity spectra of the field data show three TE and four TM modes of which separate and combined inversion of different modes return similar values for the ice thickness and known permittivity of ice. Due to the more leaky behavior of the TM modes, the TE inversion is better constrained and more suitable for inversion.     

A polarization independent GaAs-AlGaAs electrooptic modulator

Two designs for polarization independent GaAs-AlGaAs interferometric electrooptic modulators are described. One design uses the linear electrooptic effect to couple degenerate TE/TM eigenmodes of a single-mode waveguide. In the other design the eigenmodes need only be near degenerate. The design using the coupling between near degenerate TE/TM modes utilizes a novel biasing scheme. A novel polarization independent GaAs-AlGaAs interferometric optical modulator based on this design has been fabricated and characterized at 1.3 μm. This modulator is fabricated as a traveling wave modulator incorporating 50 Ω, phase velocity matched, low microwave loss electrodes for maximum electrical bandwidth     

Reflection and transmission of guided electromagnetic waves at anair-chiral interface and at a chiral slab in a parallel-plate waveguide

Recently, the concept of chirowaveguides, which exhibit some novel and interesting properties due to electromagnetic chirality, was introduced and studied elsewhere. In this paper, the authors analyze theoretically another problem associated with chirowaveguides, namely, the problem of reflection and transmission of guided waves at an air-chiral interface and at a chiral slab located transversely in a parallel-plate waveguide. The notable features and the role of chirality of the medium on the reflected and transmitted guided waves are discussed, and physical insights into these results are provided. It is found that since the guided modes inside the chiral region of the waveguide are hybrid, in order to satisfy the boundary conditions at interfaces, the reflected and transmitted guided modes in the air regions of the waveguides need to be of TE and TM modes. The motivation behind this study is the potential applications of this problem to the design of novel measurement techniques for determining material parameters of chiral composites     

An effect of excitation of a transverse magnetic creeping wave when a transverse electric wave crosses the line of the coincidence of propagation constants

Transverse electromagnetic electric (TE) and transverse magnetic (TM) creeping waves on a surface with an anisotropic impedance boundary condition are considered. An asymptotic theory is developed for creeping waves. The theory is valid near the line where the attenuation parameters of two different types of waves coincide and, therefore, standard asymptotics are inapplicable. Asymptotic formulas describing physical effects that occur when a creeping wave propagates across the degeneracy line are derived. It is found that, behind the degeneracy line, a propagating TE wave excites a TM wave with a small amplitude (of order O(k ^−1/6)) and a propagating TM wave excites a TE wave.