An efficient method for calculating cutoff frequencies in optical fibers with arbitrary index profiles

An accurate and simple method of calculating the cutoff frequencies of scalar modes in a fiber having an arbitrary refractive-index profile, including discrete numerical data from profile measurements, is proposed. First, the cutoff problem is transformed into a general matrix eigenvalue problem and then cutoff frequencies as the eigenvalues of a real symmetric matrix are evaluated. Representative test examples have been computed to illustrate the accuracy, reliability, and efficiency of the algorithm proposed.     

Analysis of dielectric-loaded waveguide

The calculation of eigenvalues including propagation constants and cutoff wavelengths of longitudinal section electric and magnetic modes of different orders (LSE_nm and LSM_nm modes) in homogeneous and inhomogeneous lossless dielectric-slab-loaded rectangular waveguides using a modified variation-iteration method is presented. The initial eigenvalues used in the iteration are selected on the basis of a physical consideration. As shown in numerical examples, this method is very efficient for finding all the eigenvalues of LSE_nm and LSM_nm modes by a given free-space propagation constant calculation and a given lower bound of the cutoff wavelength for the cutoff wavelength calculation. In addition, the importance of the adaptive update factor in preventing the possibility of missing existing eigenvalues is also discussed     

Computation of cutoff wavenumbers of TE and TM modes in waveguidesof arbitrary cross sections using a surface integral formulation

A procedure is described for obtaining the cutoff wave numbers of transverse electric (TE) and transverse magnetic (TM) modes in waveguides of arbitrary cross section. A surface integral equation approach is used in which the E-field equation has been transformed into a matrix equation using the method of moments. An iterative technique is used to pick the eigenvalues of the solution matrix which corresponds to the waveguide cutoff wave numbers. The salient features of this technique are its speed, its simplicity, and the absence of any spurious modes when waveguides of arbitrary cross section are treated. The first four modes are tabulated for various waveguides, and the results are in very good agreement with published data     

Cutoff frequencies of transmission lines consisting of pair ofcylinders

The paper presents a method of evaluation of cutoff frequencies of higher-order modes of transmission line of parallel cylinders by transforming them into a parallel plate configuration using cotangent hyperbolic transformation. Application of the method of finite difference to the weighted Helmholtz equation leads to a set of simultaneous equations. The eigenvalues related to cutoff frequencies are determined from the characteristic equation expressed in terms of matrices obtained from the simultaneous equations. Numerical data are presented     

圆锥波导中电磁场的一种新的等效表达式

本文提出了一种新的等效圆波导半径表达式,改进了计算圆锥波导内电磁场的传播常数,波阻抗和场分量的计算精度,运用数值对比方法,证明新的表达式在高次模和近截止区仍有较好的适用性,最后结合实例讨论了相关的插值方法,以便处理工程设计中常邮的特征值非整数时的计算问题。     

The spectrum of electromagnetic waves guided by a plasma layer

The modal spectrum of a lossless, homogeneous and isotropic planar plasma layer is shown to contain contributions from surface waves and complex modes in addition to the usual continuous spectrum characteristic of open structures. These discrete contributions are only of the E-mode type and occur whenever the plasma dielectric constant εpis negative. The surface waves may be of the forward or the backward type and they carry power in opposite directions in the plasma and air regions. The complex modes are shown to appear always in degenerate pairs and as a consequence they carry no real power but may account for large reactive fields in the neighborhood of sources. For E modes with positive values of εp, and for all H modes, the spectrum is purely continuous; however, nonspectral leaky ways are then present which are significant in radiation considerations.     

Analysis of elliptical waveguides by differential quadrature method

A new approach for elliptical waveguide analysis is presented in this paper. This approach applies the global method of a differential quadrature (DQ) to discretize the Helmholtz equation and then reduces it into an eigenvalue equation system. All the cutoff wavelengths from low-to high-order modes can be simultaneously obtained from the eigenvalues of the equation system. The present solver is general, which can be applied to elliptical waveguides with arbitrary ellipticity. It is demonstrated in this paper that the DQ results are in excellent agreement with theoretical values using just a few grid points and, thus, requiring very small computational effort     

Eigenvalue approach to the efficient determination of the hybridand complex spectrum of inhomogeneous, closed waveguide

Many hybrid modes are required in computing the fields scattered from discontinuities in structures such as finline, coplanar waveguide, or microstrip. The authors present a new analytical method based on an eigenvalue formulation of the generalized telegrapher's equations discretized by using the modes at cutoff as an expanding set. This approach produces a compact theoretical model while providing at the same time an effective algorithm for finding the characteristics of many modes, including their below cutoff and complex behaviour. The theoretical approach gives some direct insights about the appearance of complex modes. Due to the explicit formulation of the eigenvalue equation for the complex propagation constant, the proposed method overcomes some of the typical drawbacks of the currently used algorithms, such as the limited numerical accuracy and efficiency, the numerical degeneracy and appearance of spurious solutions, the inability to trace the characteristics of degenerate modes. Numerical results for ordinary and complex propagation in finline show excellent agreement with existing data     

Guided modes on open chirowaveguides

Surface wave modes on an open chiral rod and a planar chiral slab are studied. It is shown that the effect of chirality is to split each mode in the nonchiral case to a pair of modes, the cutoff frequencies of which are above and below that of the nonchiral case. The mode with the lower cutoff frequency is dominantly right circularly polarized (RCP) mode while the mode with the higher cutoff frequency is dominantly left circularly polarized (LCP) mode near their respective cutoff frequencies. At sufficiently higher frequencies, all modes tend to become RCP (assuming a right handed chiral medium). Closed form expressions for modal cutoff frequencies on the planar chiral slab and chiral circular rod are derived. The surface wave modes are classified as HE and EH modes and a suitable definition for these mode types, that reduces to well known definitions in the nonchiral case, is proposed     

Intrinsic modes in a wedge-shaped taper above an anisotropicsubstrate

Intrinsic modes yield exact solutions away from the tip in a wedge-shaped taper with penetrable boundaries. Unlike adiabatic modes, they are uncoupled and pass smoothly through the cutoff transition. This model has been generalized to accommodate stratified multiwave substrates and weakly range-dependent environments. Here, a wedge-shaped taper above an anisotropic substrate is considered. In the spectral representation of intrinsic modes, the plane wave reflection coefficient from the substrate depends on the orientation of the optic axis, which, in turn, affects the cutoff condition and the direction of the leakage field in the substrate. Since the phase propagation vector and average power flow vector are usually nonparallel in anisotropic media, the field in the substrate is substantially different from that in isotropic cases     

Radiation propagating transverse to the external magnetic field from an electromagnetic source in an unbounded plasma

The radiation characteristics of a line source of magnetic current embedded in an unbounded plasma are investigated for the case in which a uniform magnetic field is impressed externally throughout the medium in the direction of the source. The plasma is assumed to be a homogeneous and macroscopically neutral mixture of compressible gas of electrons and ions. A two-fluid continuum theory of plasma dynamics is employed. It is shown that it is possible to define three suitable wave functions which satisfy separately simple wave equations whose solutions are written down by inspection. These wave functions specify the three possible modes which are identified, respectively, to be the modified forms of the electromagnetic, the electron plasma and the ion plasma modes. The limiting behavior of these modes are discussed for the following two cases: 1) infinite source frequency and 2) vanishing external magnetic field. The dispersion relations for the three modes are examined in detail for the general case using a perturbation procedure. It is shown that the modified ion plasma (MIP) mode propagates for all frequencies whereas both the modified electron plasma (MEP) mode and the modified electromagnetic (MEM) mode have a low-frequency cutoff. Explicit expressions for the cutoff frequencies are obtained. The power radiated in each of the three modes is also evaluated. It is found that the power radiated in the MEM mode is always lower than that due to the line source in free space, whereas the power radiated in the two plasma modes is higher than that value for certain ranges of frequency.     

A Penetrable Dielectric Waveguide with Periodically Varying Circular Cross Section

For a penetrable dielectric waveguide with a periodically varying circular cross section, the modes that are exponentially decreasing in the cladding are considered. Their axial wavenumbers are determined by the null field approach and some plots are given showing their frequency dependence. From the numerical results, it is observed that two modes propagating in opposite directions interact destructively when the real parts of their axial wavenumbers differ by a multiple of the wavenumber of the corrugations. Both an upper and a lower cutoff frequency exists above (below) which only leaky modes exist.     

Propagation in a Dielectric-Loaded Parallel Plane Waveguide

A theoretical analysis of wave propagation in a parallel plane waveguide partially filled with a dielectric is performed. This transmission line is a symmetrical three-region structure consisting of two infinite parallel conducting planes with a dielectric slab of rectangular cross section between and contacting each of the planes. It has been found that TEM and TM modes cannot propagate on this structure. This investigation is concerned with TE modes, although hybrid modes can also propagate on this line. The lowest order TE mode, which is the dominant mode, has no cutoff and hence is inherently suited to extremely wide bandwidth operation. Equations have been presented for the field components, guide wavelength, cutoff criteria, power handling capabilities, wall losses, and dielectric losses as a function of the operating wavelength, waveguide dimensions, and material constants. In the case of the dominant mode, design curves covering a large range of wavelengths, dimensions, and dielectric constants are presented. For a loosely bound wave, the losses are comparable or less than those of conventional rectangular waveguide and the power handling capacity is an order of magnitude greater.     

Waveguides of Arbitrary Cross Section by Solution of a Nonlinear Integral Eigenvalue Equation

The problem of electromagnetic wave propagation in hollow conducting waveguides of arbitrary cross section is formulated as an integro-differential equation in terms of fields at the waveguide boundary. Cutoff wave numbers and wall currents appear as eigenvalues and eigenfunctions of a nonlinear eigenvalue problem involving an integro-differential operator. A variational solution is effected by reducing the problem to matrix form using the method of moments. A specific solution of the problem is developed using triangle expansion functions in the method of moments. The solution is simplified by symmetry considerations and is implemented by two digital computer programs. Listings and full documentation of these programs are available. This solution yields accurate determinations of cutoff wave numbers, wall currents, and distributions of both longitudinal and transverse modal field components for the first several modes. Illustrative computations are presented for the single-ridge waveguide, which has a complicated boundary shape that does not lend itself to exact solution.     

Resonant Modes of a Dielectric Rod Resonator Short-Circuited at Both Ends by Parallel Conducting Plates

This paper describes a generalized study for the resonant modes of a dielectric rod resonater placed between two parallel conducting plates. Dielectric and conductor losses are ignored. It is shown that there are two resonant states in this resonator, trapped and leaky states. In order to determine the cutoff and resonat frequencies in the trapped state, numerical results are given for the cutoff conditions and dispersive characteristics of a dielectric rod waveguide. The field patterns for the hybrid modes are also presented. For the resonant modes in the leaky state, it is shown to be useful to introduce a complex angular frequency. Numerical results are given for the various modes with different values of the dielectric constant. Generalized mode charts covering both states and including the cutoff conditions are presented. The existence of both states has been verified by experiments.     

Spectral analysis and synthesis options for short pulse radiationfrom a point dipole in a grounded dielectric layer

Formal exact alternative spectral representations for the electromagnetic fields radiation from a pulsed electric current element embedded in a grounded dielectric layer are derived. Starting from the standard spectral decomposition into the real frequency domain and the real spatial wavenumber domains corresponding to the transverse coordinates perpendicular to the direction of stratification, alternative treatments of the spectral integrands in the various complex spectral planes lead to exact steepest descent path representations which are well suited for subsequent asymptotic reduction into the time domain (TD). Of special interest is the nonconventional synthesis strategy, which performs frequency inversion before spatial wavenumber inversion, thereby utilizing in one of the options TD leaky modes with complex frequency and real spatial wavenumbers, and also TD trapped modes, as basis fields. This is contrasted with the conventional approach built around time-harmonic real-frequency leaky modes with complex spatial spectra. The spectral strategies employed here are applicable also to layered structures     

The effect of device geometry on lateral mode content of stripe geometry lasers

The dielectric profile of stripe geometry injection lasers is modeled with an objective of structure design requirements for fundamental lateral mode operation. Heterostructure lasers are modeled with a dielectric step profile using an effective dielectric discontinuity based on the gain/loss profile of the active layer as well as the overall geometrical structure. The analysis provides a quantitative comparison of the performance of two important double-heterostructure lasers: 1) the oxide-stripe geometry laser and 2) the channeled-substrate planar (CSP) laser. Modes of oxide-stripe lasers have lateral gain confinement, whereas, modes of CSP devices have strong lateral index confinement. To isolate the influence of geometry on the effective dielectric profile we assume that the real refractive index of the active layer is position independent. Resulting calculations show that a stripe geometry laser inherently has a depressed effective index in the active region below the metallic contact. This phenomenon alone produces index anti-guiding. In actual devices, both geometry and free carrier injection into the active region produce lateral index antiguiding. Lateral mode cut-off conditions are calculated as functions of the effective complex dielectric step and the stripe width. The results show that cutoff is related in a unique fashion to the ratio of the real and imaginary parts of the complex dielectric step; the ratio is positive for index guided modes and negative for gain guided ones.     

Revealing stable and unstable modes of denoisers through nonlinear eigenvalue analysis

In this paper, we propose to analyze stable and unstable modes of black-box image denoisers through nonlinear eigenvalue analysis. We aim to find input images for which the denoiser output is proportional to the input. We treat this as a generalized nonlinear eigenproblem. Potential implications are wide, as most image processing algorithms can be viewed as black-box operators. We introduce a generalized nonlinear power-method to solve eigenproblems for such operators. This allows us to reveal stable modes of the denoiser: optimal inputs, achieving superior PSNR in noise removal. Analogously to the linear case, such stable modes show coarse structures and correspond to large eigenvalues. We also provide a method to generate unstable modes, which the denoiser suppresses strongly, which are textural with small eigenvalues. We validate the method using total-variation (TV) and demonstrate it on the EPLL (Zoran–Weiss) and the Non-local means denoisers. Finally, we suggest an encryption–decryption application.     

Approximate eigenvalues for a circular rod of arbitrary relative permittivity

A simple and useful approximate expression for the eigenvalues of a circular dielectric or glass waveguide of arbitrary relative permittivity are found. Although the approximation is derived for conditions far from cutoff, it is accurate except close to cutoff.     

The Theory of Characteristic Modes Revisited: A Contribution to the Design of Antennas for Modern Applications

The objective of this paper is to summarize the work that has been developed by the authors for the last several years, in order to demonstrate that the Theory of Characteristic Modes can be used to perform a systematic design of different types of antennas. Characteristic modes are real current modes that can be computed numerically for conducting bodies of arbitrary shape. Since characteristic modes form a set of orthogonal functions, they can be used to expand the total current on the surface of the body. However, this paper shows that what makes characteristic modes really attractive for antenna design is the physical insight they bring into the radiating phenomena taking place in the antenna. The resonance frequency of modes, as well as their radiating behavior, can be determined from the information provided by the eigenvalues associated with the characteristic modes. Moreover, by studying the current distribution of modes, an optimum feeding arrangement can be found in order to obtain the desired radiating behavior.