TE and TM modes in circularly shielded slot waveguides

Cutoff wavenumbers and the field of TE and TM modes are evaluated in circularly shielded, single- or double-slot waveguides in the case of infinitely thin fins. The formulation, based on field equivalence principles, is exact and leads to Carleman-type singular integral or integrodifferential equations for the equivalent surface magnetic current across the slot(s). The solution of these equations is based on Neumann's expansion of the Hankel kernels and leads to numerically stable and efficient algorithms regardless of the slot widths. Numerical results for the cutoff wavenumbers, both TE and TM, are presented. By lowering the cutoff frequencies of the TE modes and by raising the corresponding ones of the TM modes, considerable increase in the operating frequency bandwidth may be achieved after suitably selecting the various geometrical parameters of the configuration     

求解渐变折射率分布平面光波导模式的数值方法

本文用多种数值方法（积分插值法、有限元法及幂法）对具有渐变折射率分布的平面光波导率征方程进行了理论计算。这些方法不仅适用于任意的折射率分布，而且能够达到较高的计算精度。作为一个例子，作者对高斯分布波导进行了具体计算。计算结果表明，Arun Kumar等人用的微扰法是较好的方法。此外，本文作者通过迭代求出了更精确边界条件下的本征模。     

空心平板光波导中二脉冲TE模的光子回波

讨论了空心平板光波导中二脉冲TE模光子回波问题(包括单阶模和多阶模两种情况),所得结果表明,空心平板光波导中的光子回波与非波导情况下的相比,具有许多不同的性质.     

非线性介质膜波导中高阶TE模的色散特性

用微扰方法对非线性波动方程求解,导出了各阶近似下非线性介质膜波导中高阶TE模的色散方程和截止波长。研究了高阶TE模的色散特性。计算结果表明,具有功率激发阈值的高阶模的一个传播功率可能对应两个不同的传播常数,具有光学开关的特性。     

Properties of the slab modes in photonic crystal optical waveguides

We show that by placing a slab of semiconductor material between two photonic bandgap (PBG) mirrors, waveguide modes at frequencies out of the PBG can be obtained. These modes are similar to the modes of a conventional dielectric slab waveguide. Using these modes, we can obtain very good coupling between a PBG waveguide and a dielectric slab waveguide with similar slab properties. We discuss the properties of these slab modes and outline the guideline for the optimization of the PBG waveguides based on these properties     

Exact solutions for TM modes in graded index slab waveguides

Three continuous profiles for the dielectric constant are derived, which allow exact solutions of the vector wave equation, including all terms in the gradient of the profile, for both TE and TM modes on slab waveguides. The dielectric constant has been assumed to be a scalar quantity; i.e., the medium is isotropic.     

Computation of TM and TE modes in waveguides based on a surfaceintegral formulation

The surface integral formulation is used for the computation of TM and TE modes propagating in dielectric loaded waveguides. This formulation makes use of the surface equivalence principle whereby the field at any point internal or external to the waveguide can be expressed in terms of equivalent surface currents. This procedure reduces the original problem into a set of integro-differential equations which is then reduced to a matrix equation using the method of moments. The solution of this matrix equation provides the propagation characteristics of the waveguide and the equivalent surface currents existing on the waveguide walls. The equivalent surface currents can be used to compute the fields at all points, both inside and outside the waveguide. The surface integral method has been used to compute the propagation characteristics of waves propagating in dielectric loaded waveguides. The computed results agree very well with analytical and published data. A method that can be used to remove spurious modes is illustrated     

Hybrid modes of graded-index optical fibres

The profile dependence of the hybrid wave structure of graded-index optical-fibre modes is discussed. It is shown that the generally accepted definitions for HE and EH modes should be altered for certain classes of refractive-index profile.     

Eigenvalue equations of N-parallel graded-index waveguides: WKBanalysis

The eigenvalue equations of N-parallel graded-index waveguides are derived in a recursive form for the first time by using the WKB method and the transfer matrix method. For the derivation, trial solutions are defined which not only converge at turning points but also approximate the conventional WKB solutions. It is confirmed through the computer simulation that the results of the derived WKB eigenvalue equations are in good agreement with those of the finite-difference method in the well-guided regions     

Local field analysis of bent graded-index planar waveguides

A local field analysis is proposed for bent planar waveguides with arbitrary refractive index profiles. Exact vector wave equations that include the gradient index, or polarization correction, term are derived for both transverse electric and transverse magnetic modes from Maxwell's equations in a local bent coordinate system. The approximate local field and correction to the propagation constants are obtained by perturbation analysis. As an example of the method, an infinitely extended parabolic index profile is studied     

Explicit formulas for cutoff values of TE modes on symmetric dielectric slab waveguide with Kerr-like permittivity

Based on the perturbation method, very simple expressions are derived which give accurate approximations for the cutoff values of TE modes in the symmetric slab waveguide with a Kerr-like nonlinear thin film.<>     

渐变折射率平板波导的传输特性及实验研究

分析了渐变折射率平板波导(GISLAB)的工作特性.理论推导表明GISLAB在折射率渐变方向具有与自聚焦透镜完全一样的传输矩阵与成像性质,分析讨论了GISLAB输出光束的传输特性.并通过实验验证了GISLAB的工作特性.     

Modal analysis of step discontinuities in graded-index dielectricslab waveguides

The modal solutions of the TE- and TM-modes of an arbitrary graded-index dielectric slab waveguide have been derived by applying the generalized telegraphist's equations to the equivalent inhomogeneous parallel-plate waveguide model with electric or magnetic walls. These modal solutions have been employed in a mode-matching procedure to calculate the transmission properties of step discontinuities in arbitrarily graded-index dielectric slab waveguides such as diffused optical waveguides having exponential, Gaussian and complementary error-function index profiles. For slab waveguides containing an abrupt offset, the radiated power is found to increase smoothly with increasing displacement. Power loss calculations for an abrupt change in diffusion depth for which the dominant mode is in the vicinity of cutoff, exhibit a sharp transition from almost zero loss to nearly total radiation loss     

Modes in inhomogeneous slab waveguides

In this correspondence we have developed the perturbation approach for the calculation of propagation constants for some of the practical slab waveguides and have shown the applicability of the approach to systems of practical interest.     

Determination of the TE and TM modes in arbitrarily shaped waveguides using a hypersingular boundary element formulation

In this paper a procedure based on the hypersingular element method is applied to find the TE and TM modes in arbitrarily shaped waveguides. To show the accuracy of this method, various examples are solved and the results are compared to those analytical, when there is an analytical solution, and those presented in the literature. The proposed method did not present spurious modes, and in all the examples presented showed excellent results considering a reasonable number of elements in the boundary.     

An improved finite-difference vector beam propagation formulationfor graded-index waveguides

An improved finite-difference vector beam propagation formulation for graded-index waveguides is presented. The modification over the existing version involves a more accurate representation of the Fresnel operator in finite-difference form that accounts for the gradient of the refractive index in the vector Hehmholtz equation. The modified scheme is assessed by calculating the TM mode propagation constants of single-mode planar guides that yield better agreement to the exact values over the existing scheme. Furthermore, the calculated coupling lengths of a vertical directional coupler show improved comparison to experimental data     

Numerical stability analysis and the route to chaos for TE/sub 1/ waves in nonlinear slab waveguides

The stability characteristics of TE/sub 1/ waves guided by a dielectric slab bounded by semi-infinite, Kerr-type nonlinear media are investigated numerically using variational methods. It is shown that portions of the solutions are not only unstable but follow a route to chaos through period doubling as the guided-wave power increases. The results are presented by means of a bifurcation diagram.<>     

Characterization of asymmetric graded-index planar optical waveguides from the knowledge of TE/sub 0/-TE/sub 1/ mode cutoff wavelengths

The authors have proposed (1991) a simple method for predicting the index profile parameter (the profile exponent q in case of a power law profile or the aspect ratio S in case of trapezoidal index profile) of a graded-index optical fiber which is single moded in the 1.3-1.55 mu m wavelength range from a measurement of the LP/sub 11/ and LP/sub 02/ cutoff wavelengths. They extend the method with appropriate modification to determine the asymmetry parameter sigma , the maximum refractive index n/sub f/ and the characteristic thickness d of the guiding layer of a few-moded graded-index asymmetric planar optical waveguide from a measurement of the TE/sub 0/ and TE/sub 1/ cutoff wavelengths. The method is simple and can give firsthand information about these parameters with reasonably good accuracy.<>     

片状固体激光器的基模

片状固体激光器片内的光束在上下表面产生全内反射,按之字形路径传输,提高了激活介质的利用率,从而可获得较高的能量输出.更重要的是,与传统的棒状固体激光器相比,它能补偿激光介质内部因温度不均匀而造成的光学畸变,因而引起了人们的广泛注意.本文试图用矩阵光学来分析它的补偿性.同时对这种结构的基模进行分析.由于片状固体激光器的菲涅耳数N(?)1,因而适于用矩阵光学来进行分析.