Domain integral equation analysis of integrated optical channel andridge waveguides in stratified media

A domain integral equation approach to computing both the propagation constants and the corresponding electromagnetic field distributions of guided waves in an integrated optical waveguide is discussed. The waveguide is embedded in a stratified medium. The refractive index of the waveguide may be graded, but the refractive indices of the layers of the stratified medium are assumed to be piecewise homogeneous. The waveguide is regarded as a perturbation of its embedding, so the electric field strength can be expressed in terms of domain integral representation. The kernel of this integral consists of a dyadic Green's function, which is constructed using an operator approach. By investigating the electric field strength within the waveguide, it is possible to derive an integral equation that represents an eigenvalue problem that is solved numerically by applying the method of moments. The application of the domain integral equation approach in combination with a numerically stable evaluation of the Green's kernel functions provides a new and valuable tool for the characterization of integrated optical waveguides embedded in stratified media. Numerical results for various channel and ridge waveguides are presented and are compared with those of other methods where possible     

一种特殊的双包层圆柱光波导的研究

本文研究了一种双包层阶跃型光波导，内包层的折射率大于芯及外包层的折射率，因而可作为导波层。文中严格地推导了柱坐标下该光波导的特征方程，详细计算了ＴＥ波和ＴＭ波的传播常数、场分布及功率分布；作出了相应的曲线，表明了导波层的厚度、折射率及工作波长对此类光波导传播特性的影响。     

Diffraction of guided waves by the end face of a dielectric slab waveguide terminated with a finite conductive strip

The diffraction of guided waves by the end face of a dielectric slab waveguide short circuited with a finite conductive strip is analyzed. An integral equation technique is employed to formulate the corresponding boundary problem. The unknown term in this integral equations is the electric field E(x) on the terminal plane of the waveguide. The homogeneous term is determined from the incident guided wave. A method of moments technique is employed to compute approximately the electric field E(x) by using Laguerre functions as describing and testing functions. The reflection coefficients of the guided waves are computed by using the approximate expression of the E(x) field. Numerical results are given for several guide and conductor plate dimensions.     

Analysis of a Longitudinal Gyroelectric Discontinuity Inside a Fiber Waveguide

The scattering of guided electromagnetic waves from a finite-length longitudinal gyroelectic discontinuity inside a fiber waveguide is treated analytically. An integral equation approach is employed to formulate the corresponding boundary-value problem. The induced field inside the gyroelectic discontinuity region is expanded into a Fourier-type series in terms of the well-known cylindrical waves M and N plus a purely longitudinal wave Q. Then the method of moments is applied to decouple the basic integral equation. The resulting infinite coupled system of equations is truncated and solved numerically. After determining the field inside the discontinuity, the scattered far field inside the dielectric-rod waveguide is computed by employing a steepest descent integration technique. Numerical results for the scattering coefficients of an incident HE/sub 11/ dominant mode are obtained. Finally, design principles are discussed for practical components based on the treated longitudinal gyroelectric discontinuity.     

Discontinuities in a Rectangular Waveguide Partially Filled with Dielectric

The modal spectrum for a rectangular waveguide with a dielectric slab at the bottom of the guide is obtained following the Characteristic Green's Function method developed by Marcuvitz. Then a four-terminal network is found as equivalent to the junction of the partially filled waveguide and an empty rectangular waveguide. An integral equation is written for the electric field at the plane of the junction and variational expressions are derived for the parameters of the four-terminal network connecting the transmission line equivalent to the partially filled waveguide to the transmission line equivalent to the empty guide. A reasonable guess for the electric field at the discontinuity gives approximate values for the parameters of the four-terminal network. These values agree with experiment. The parameters of the network are plotted vs frequency and thickness of the slab.     

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     

Scattering of Guided Modes Caused by an Arbitrarily Shaped Broken End in a Dielectric Slab Waveguide

Electromagnetic scattering of guided modes in a dielectric slab waveguide caused by an arbitrarily shaped broken end is analyzed theoretically by using the integral equation method. By solving the integral equations iteratively, the tangential components of the electric and magnetic fields on the broken end surface are determined, from which the reflected mode power, the radiation wave power and field patterns, and the total scattered power are obtained. Numerical results are presented for the plane-perpendicular, plane-tilted, and arc-shaped end surfaces. Both TE and TM modes are assumed as an incident wave.     

Theoretical analysis of a coated single-mode fiber termination

The antireflection efficiency of a single layer coating in front of an abruptly terminated monomode optical fiber is treated analytically by means of an integral equation, that is appropriate to solve the corresponding boundary value problem. Both guided and radiation modes are taken into account, when describing the field inside the optical fiber region. Then the integral equation is solved approximately by a Neumann series procedure giving highly accurate results when the weakly guidance condition holds, which is a case of practical interest in the optical communications area. The reflection coefficient and the radiation pattern of this configuration are computed. Numerical results are given for several values of the parameters of the geometry under consideration.     

Scattering from an abruptly terminated dielectric-slab waveguide

Scattering of surface waves from an abruptly terminated dielectric-slab waveguide is investigated analytically, by means of an integral equation appropriate for the boundary-value problem of TE modes. In order to obtain a tractable solution to the equation, a Neumann Series iterative procedure is applied. Numerical results are given in several cases of abruptly ended dielectric slabs. Particular attention is directed to the behavior of electric and magnetic fields at the plane of discontinuity, since field distributions at any other region depend directly on these surface values.     

Sensitivity enhancement in evanescent optical waveguide sensors

It is shown, that the sensitivity of the effective refractive index on the cladding index in evanescent optical waveguide sensors, can be larger than unity. This implies that the attenuation of a guided wave propagating in a waveguide immersed in an absorptive medium can be made larger than that of a free-space wave propagating through the same medium. The conditions and physical explanation for this puzzling behavior are identified and as a practical application, an absorption sensor, based on a suspended silicon slab waveguide, is proposed where the sensitivity is enhanced by a factor of 1.35     

Scattering and mode conversion of guided modes by an arbitrary cross-sectional cylindrical object in an optical slab waveguide

The scattering and mode conversion of guided modes caused by a cylindrical scatterer of arbitrary cross section embedded in, or placed on, a dielectric slab waveguide are investigated theoretically. The method employed for the analysis is the surface current integral equation technique. The total scattered power, mode-conversion coefficients, and scattering patterns for the typical numerical examples are shown.     

Domain-integral analysis of channel waveguides in anisotropicmultilayered media

A domain-integral equation method is presented to determine both propagation constants and the electromagnetic field distributions of guided surface wave modes in integrated optical waveguides. Both the waveguide and its multilayered embedding are anisotropic. The permittivity tensor of the embedding is assumed to be piecewise homogeneous. The kernels of the domain-integral equations consist of Green's tensors. The integral equations form an eigenvalue problem where the electric field strength represents the eigenvector. This problem is solved numerically by applying the method of moments. Numerical results are presented for an anisotropic ridge waveguide, embedded in an anisotropic multilayered medium     

Coupling phenomena in concentric multi-applicator phased arrayhyperthermia systems

The coupling between the waveguide applicators of a four-element phased array hyperthermia system irradiating a three-layered cylindrical tissue model of circular cross section is analyzed theoretically. The fields inside the tissue layers are expressed in terms of cylindrical vector wave functions satisfying the corresponding wave equations, while the fields inside each waveguide are expanded in terms of guided and evanescent normal modes. Then, by implementing the appropriate boundary conditions, a system of four coupled integral equations is derived in terms of the unknown electric field distributions on the open waveguide apertures. This system is solved by expanding the unknown electric field on each aperture into waveguide normal modes and by applying a Galerkin's procedure. The self reflection coefficient and the mutual coupling coefficients are then determined and numerical results for a four-element phased array hyperthermia system are computed and presented for different waveguide applicator sizes and settings     

Confinement factors and gain in optical amplifiers

A new identity is derived which relates the gain and the field distribution (or confinement factor) in a dielectric waveguide with complex refractive indices. This identity is valid for any guided mode of waveguides with an arbitrary cross section. It provides a new check of the accuracy of mode solvers. Also, it can be used in a variational approach to predict the gain or loss of a guided mode based on knowledge of confinement factors. It is shown that a previous analysis that is often used, is not correct. In addition, approximate expressions for the gain in slab waveguides are presented     

Analysis of Wave Propagation in Inhomogeneous Dielectric Slab Waveguides

The propagation characteristics of the guided modes in an inhomogeneous dielectric slab waveguide are analyzed by tbe regularized WKBJ method. The corrected propagation constants of the guided modes in a near parabolic index medium are derived in analytic form. The effects of the refractive index profile and the homogeneous cladding on the guided modes can be expressed in terms of the mode indices and evaluated numerically.     

EM analysis of a conducting scatterer in optic dielectric waveguide

A method to compute the scattered field of curved mirrors and gratings in a dielectric slab waveguide is proposed. In contrast to the beam propagation method (BPM) for this kind of problems, the method of moment is adopted. By introducing the dyadic Green's function in a slab waveguide, the electric field integral equations for induced current distribution on the conducting obstacles are derived. To improve the computational efficiency, the modified Green's function is incorporated into the computation program. With this study, the effects of grooves of gratings and the finite extent of the mirrors in dielectric waveguides can be investigated in more detail     

Scattering from structured slabs having two-dimensional periodicity

The problem of a plane wave incident on a structured slab is examined. To analyze the problem, an electric field integral equation (EFIE) is derived that has as its unknown the equivalent surface currents on the plates in the unit cell. The integral equation is discretized and solved approximately using the method of moments with subdomain basis and testing functions. The periodic Green's function is efficiently calculated using the Poisson summation formula. The interaction of the structure with the surrounding environment is described in terms of a generalized scattering matrix. Results are presented showing the reflection coefficient as a function of frequency for arrays of zigzagging strips and honeycomb slabs     

Analysis of the power coupling from a waveguide hyperthermiaapplicator into a three-layered tissue model

The power deposition from a rectangular-aperture flanged waveguide into a three-layered stratified tissue medium is analyzed theoretically. The fields inside the tissue layers are expressed in terms of Fourier integrals satisfying the corresponding wave equations, while the fields inside the waveguide are expanded in terms of the guided and evanescent normal modes. An integral equation is derived on the aperture plane of the flanged waveguide by applying the continuity of the tangential electric and magnetic fields. This integral equation is solved by expressing the unknown electric field in terms of the waveguide mode fields and by applying a Galerkin procedure. The electromagnetic fields inside the tissue medium are then determined and patterns of the deposited power at frequencies of 432 MHz and 144 MHz for apertures of 5.6×2.8 cm² and 16.5×8.3 cm², respectively, are computed and presented     

Analysis of wraparound microstrip phased array by infinite arrayapproach

A moment method analysis of an infinite array of wraparound microstrip antennas fed with idealized current probes on a cylindrical body is presented. The integral equation is formulated through the use of periodic grounded dielectric slab Green's function. The method accounts for the blind angles and allows efficient computation of the reflection coefficient at all other angles. Illustrative results are given     

Analysis of radiating slots in a rectangular waveguideinhomogeneously loaded with a dielectric slab

Longitudinal and transverse radiating slots in the broad wall of a rectangular waveguide inhomogeneously loaded with a dielectric slab are analyzed. The formulation used involves the moment method solution of a pair of coupled integral equations containing the dyadic Green's function of the inhomogeneously loaded waveguide. Both an edge-condition for the electric field in the slot aperture and the correct form of the ψ=constant waveguide mode are included in the analysis. Computed and measured results are compared to verify the theoretical analysis