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     

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.     

Scattering from a conductive rectangular plate covered by a thickdielectric layer and excited from a dipole source or a plane wave

The scattering of electromagnetic radiation from a conductive rectangular plate of infinitesimal thickness covered by a dielectric parallelepiped of arbitrary size is analyzed. An integral equation formulation is employed in terms of the electric field inside the dielectric layer and the surface current density on the conductive plate, and is solved approximately by using entire domain Galerkin technique. The electric field inside the dielectric layer is described in terms of a superposition of exponential waves while, in describing the surface current density on the conductive plate, two types of entire domain basis functions are utilized: either Fourier-exponential series or Chebyshev series type finite-term expansions are employed alternatively. Numerical results are computed and presented for several scatterer sizes and excitation types     

全向波导裂缝阵列天线的数值分析

介绍了一种新的分析全向矩形波导裂缝阵列天线方向图的方法 .以电场积分方程为基础 ,选用Rao ,Wilton和Glisson的RWGfunction作为矩量法计算的基函数和检验函数 ,计算了裂缝波导内外壁上的电流分布 ,继而对全向波导裂缝阵的辐射方向图作了计算。数值计算结果也验证了T .Takeshima的实验结论即裂缝对矩形波导的E面全向辐射特性及波导高度对方向图不圆度的影响。同时也说明了文中所介绍的方法的有效性。     

Generalized admittance matrix for a slotted parallel-platewaveguide

An integral equation for the slot electric field in transverse magnetic (TM) scattering and radiation by a slotted parallel-plate waveguide is solved using the moment method. By using piecewise sinusoidal functions for expansion and testing in the moment-method technique, a generalized admittance matrix associated with the slot is obtained in functional form as opposed to numerical integration     

Diffraction from an abruptly terminated dielectric slab waveguide in the presence of a cylindrical scatterer

The efficiency of using an adaptor lens in front of an abruptly terminated symmetric slab optical waveguide is examined analytically in this paper. The adaptor lens is assumed to be of cylindrical shape with a constant refractive index. The coupling of the modes propagating inside the slab guide into radiation waves in the presence of the lens is treated by integral equation methods. In the first step an integral equation is derived for the Green's functionG(r/r')of an abruptly terminated slab waveguide. The integral equation is solved approximately by an iterative procedure giving accurate results when the difference of the refractive indices between the slab waveguide and substrate-cover regions is small. The Green's function is then used to formulate another integral equation for the unknown field inside the adaptor lens. The latter integral equation for the cylindrical lens cross section area is solved by adopting a cylindrical partial wave expansion for the unknown interior field. After determining this field, the reflection-coupling coefficients for the guided modes propagating in the opposite direction of the incident wave, are computed by using the Green's functionG(r/r'). Radiation patterns are also derived in the far field region for an incident slab guided mode. Numerical results are computed and presented for several guide dimensions, lens radii, and refractive indices.     

多量子阱波导场的等效折射率近似分析

当多量子阱周期与芯区厚度之比趋于零时,利用转移矩阵技术,证明了任意折射率分布多量子阱波导的场分布与其等效折射率波导的场分布近似相等,为利用等效折射率方法分析多量子阱波导特性充实了理论基础,文中的数值实例表明了理论的正确性。     

A Theoretical Analysis of Discrete Reflecting Beam Waveguide with Parabolic Cylindrical Reflectors

A discrete reflecting beam waveguide with parabolic cylindrical reflectors, proposed by M. Kamimura, is theoretically analyzed. Electric field elementary waves on the reflector and the exciting primary electric field from the launcher are represented in the elliptic cylindrical coordinate system, and boundary conditions on the reflector are introduced to derive simultaneous integral equations regarding the reflector current. By solving these integral equations approximately, the integral representation of the secondary electric field in the beam waveguide is obtained, and poles and residues of the integrand are calculated to obtain the propagation constant of the beam waveguide and beam waveguide modes. The beam waveguide mode reflected toward the transmitting side when an obstacle is placed in the beam waveguide is obtained.     

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     

ELF and VLF fields of a horizontal electric dipole

The waves in the spherical guide between the earth and ionosphere are excited by a horizontal electric dipole. The guide boundaries are characterized by surface impedances and the resulting waves are expressed as a superposition of TM and TE modes. The wavenumbers, excitation factors, height-gain functions, and height-dependent impedances are examined for both types of modes. A thin-shell approximation of the radial wave functions is shown to be adequate for phase velocity estimates; but other propagation parameters are of restricted validity in the VLF range where Airy integral approximations provide more reliable data. A horizontal electric dipole is shown to provide a nearly omnidirectional coverage of horizontal field components in the frequency range of the lower Schumann resonances. For an elevated source the horizontal fields are essentially omnidirectional also in the VLF range. Near fields are expressed as a summation of waveguide modes. The vertical field components vanish at the antipode, but the horizontal components remain of finite magnitude.     

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     

Transient fields of a horizontal electric dipole on a multilayereddielectric medium

The transient electric fields of a horizontal electric dipole excited by a short pulse current and located on a layered dielectric medium were analyzed using the Cagniard-de-Hoop method. The fields are expressed as the convolution of the exciting current with the layered medium response. The layered medium response is obtained directly from the integral representation for the electric fields in the frequency domain and is expressed as a finite integral. In contrast to the conventional frequency synthesis approach, the Cagniard-de-Hoop (1960) method proves to be computationally more efficient and numerically more stable. Compared with the asymptotic approach, the solution involves no approximation. The nature of the various waves, reflected waves (guided wave and leaky wave), and lateral waves can be easily recognized on the Cagniard integral path. Numerical results are obtained to provide a rigorous forward modeling for the geo-radar operating on layered media     

Self-switching in hollow waveguides with a Kerrlike nonlinearpermittivity

The dispersion relations, stability, and excitation of the stationary nonlinear transverse electric (TE) waves guided by a nonlinear hollow waveguide are examined numerically. This waveguide consists of a self-focusing nonlinear film bounded by two identical linear claddings of the higher refractive index. Since a minimum power for guidance of the stationary waves always exists, the nonlinear hollow waveguide acts as a lower threshold device. A stability analysis using the beam propagation method shows that all the stationary TE_n modes, including the asymmetric TE₀ mode, are stable on the positively sloped branch (dP/dβ>0) of the nonlinear dispersion curve. The lower threshold device using the nonlinear hollow waveguide exhibits very sharp power-switching characteristics, and the required device length is fairly short     

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.     

Simulation of three-dimensional optical waveguides by a full-vectorbeam propagation method

Simulations of optical guided waves in three-dimensional waveguide structures by a full vector beam propagation method are described. Two sets of coupled equations governing the propagation of the transverse electric and magnetic fields are derived systematically. Polarization dependence and coupling due to the vectorial nature of the electromagnetic fields are considered in the formulations. The governing equations are solved subsequently by finite-difference schemes. The vector BPM is first assessed for a step-index circular fiber by comparing the numerical results with the exact analytical solutions. The guided modes of a rib waveguide are then investigated in detail. Comparisons among the scalar, semi-vector and full-vector simulations of the rib waveguide are made. Finally polarization rotation of a periodically loaded rib waveguide operated fully based on the vector nature of the electromagnetic waves is modeled and simulated     

A new approach to diffraction analysis of conductor grids. II.Perpendicular-polarized incident plane waves

For pt.I see ibid., vol.37, no.1, p.84-88 (1988). Diffraction analysis is given for infinite planar conducting-strip grids illuminated by normally incident (perpendicular-polarized) plane waves, the electric fields of which are perpendicular to the strip axes. Iris-surface electric field integral equations are used which are based on the equivalent waveguide theory, and then the electric field is solved for using the moment method. This is a universal approach applicable to infinite planar grids made of conducting strips of rectangular cross section, uniform or periodic, dense or sparse, single layer or multilayer     

Finite element analysis of MMIC structures and electronic packagesusing absorbing boundary conditions

In this paper, a three-dimensional finite element method (FEM) is employed in conjunction with first and second-order absorbing boundary conditions (ABC's) to analyze waveguide discontinuities and to derive their scattering parameters. While the application of FEM for the analysis of MMIC structures is not new, to the best of the knowledge of the authors the technique for mesh truncation for microstrip lines using the first and higher-order ABC's, described in this paper, has not been reported elsewhere. The scattering parameters of a microstrip discontinuity are computed in two steps. As a first step, the field distribution of the fundamental mode in a uniform microstrip is obtained by exciting the uniform line with the quasi-static transverse electric field, letting it propagate, and then extracting the dominant mode pattern after the higher order modes have decayed. In step two, the discontinuity problem is solved by exciting the structure by using the fundamental mode obtained in step one. The scattering parameters based on the voltage definition are calculated by using the line integral of electric fields underneath the strip. Numerical solutions for several waveguide discontinuities and electronic packages are obtained and compared with the published data     

Analysis of longitudinal slots in ridged waveguides using a hybridfinite element-Galerkin technique

A hybrid approach, combining the finite element method (FEM) with an integral equation formulation of the tangential electric field, is developed for the solution of longitudinal slots cut in the broad wall of finite thickness of a ridged waveguide. The system of integral equations formulated at both interfaces of the slot, is solved using the Galerkin approach with sinusoidal basis and testing functions. The Green's function for the internal waveguide region, as called for in the integral equation formulation, is generated numerically, utilizing the eigenvalues and eigenfunctions of the waveguide as computed by the FEM with Lagrangian fourth order polynomials. This approach is quite general, allowing for arbitrary waveguide cross sections and compositions. Computations of the dot characteristics performed in this way agree very well with previously documented as well as our own experimental results     

Propagation and coupling properties of integrated opticalwaveguides-an integral equation formulation

The propagation and coupling properties of integrated optical waveguides are analyzed by means of the electric field integral equation approach. The kernel of the integral equation is the Green's function of a two-layered medium. The Galerkin's method is then employed to solve the integral equation numerically. The set of basis and test functions consists of entire domain plane wave functions. Fast convergence and superior accuracy are the advantages of the chosen set of basis and test functions. The method is used to compute the propagation and coupling properties of several structures. Very good agreement is observed with previously published results. Field distributions of several coupled mode structures, such as the symmetrical and asymmetrical coupler are also investigated and presented. Finally, the same method is used to produce the field distribution of waveguides having more complex cross section like the trapezoidal waveguide     

A Planar transversal junction of two planar waveguides

A rigorous analytic method is used to solve the wave-propagation problem for a planar transversal junction of two planar waveguides. The problem is reduced to an iteratively solved system of integral equations of the second kind. Dependences of the transmission and reflection coefficients of guided waves, radiation patterns, and the power of the radiation field on the ratios of the waveguide thicknesses and the waveguide permittivities are obtained.