任意截面介质波导导模的叠代矩量法分析

本文提出用以计算任意截面介质波导色散关系的叠代矩量法,并给出用叠代矩量法计算椭圆介质波导、三角形波导、平切圆波导、蛋形截面波导等的传播特性的实例.计算结果与有限元法、点匹配法等精确数值计算结果符合很好.本方法简便易行,计算工作量较小.     

Comparison of a vectorial and new semivectorial finite-difference approach for optical waveguides

In this article, a new semivectorial finite-difference method is presented. By comparing the results obtained by the new approach with a vectorial method, it is shown that the accuracy is still very high with costs reduced by a factor of two. This revised version was published online in November 2006 with corrections to the Cover Date.     

Unified treatment for accurate and fast evaluation of the Fermi-Dirac functions

A new analytical approach to the computation of the Fermi-Dirac(FD) functions is presented,which was suggested by previous experience with various algorithms.Using the binomial expansion theorem,these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions.This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation,should such limits be required in practice.Some numerical results are presented for significant mapping examples and they are briefly discussed.     

Tunnelling leaky modes on optical waveguides

The lossless dielectric waveguide of circular cross section with an index of refraction greater than its surround supports trapped modes in addition to two subclasses of leaky modes: refracting and tunnelling modes. Refracting modes leak because their fields are formed by waves that undergo refraction at the core-cladding interface. Tunnelling modes leak because their fields are formed by waves that undergo a form of electromagnetic tunnelling at the core-cladding interface due to the curvature of its cross section. Tunnelling modes have a very slow leakage compared to refracting modes and are therefore important for the understanding of propagation in multimode, optical waveguides of circular cross section.     

A search-and-track algorithm for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles

A search-and-track algorithm is proposed for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles. The algorithm starts with an initial guess point in the parameter space that supports a specific number of guided modes. Then, it searches for, and tracks, the boundaries of this space or another space supporting different number of modes. It does so by monitoring the sign of a unified cutoff dispersion function. The algorithm is applied to both symmetric and asymmetric silicon-based parabolic-index waveguides. It shows that unlike asymmetric waveguides, the single-mode condition of symmetric waveguides is controlled by TM-, as opposed to TE-, polarization. This abnormal polarization control is strongest for high index contrast waveguides of sub-micrometer core sizes. The results are verified by full-vectorial beam propagation method.     

Low-loss surface modes and lossy hybrid modes in metamaterial waveguides

We show that waveguides with a dielectric core and a lossy metamaterial cladding (metamaterial-dielectric guides) can support hybrid ordinary-surface modes previously only known for metal-dielectric waveguides. These hybrid modes are potentially useful for frequency filtering applications as sharp changes in field attenuation occur at tailorable frequencies. Our results also show that the surface modes of a metamaterial-dielectric waveguide with comparable electric and magnetic losses can be less lossy than the surface modes of an analogous metal-dielectric waveguide with electric losses alone. Through a characterization of both slab and cylindrical metamaterial-dielectric guides, we find that the surface modes of the cylindrical guides show promise as candidates for all-optical control of low-intensity pulses.     

Exact transcendental equation for scalar modes of rectangular dielectric waveguides

Conclusion A Fourier operator method has been used to derive for the first time an exact closed-form eigenvalue equation for the scalar mode propagation constants of a buried rectangular dielectric waveguide. The new method has been implemented and the results used to determine the accuracy of the scalar finite-difference approach. It is hoped that the exact results obtained here may assist in the validation of the accuracy of the other numerical and semi-analytical methods.     

Disappearance of modes in planar Bragg waveguides

We show how the forbidden bands of a Bragg reflector may shrink to points and how some classes of the guided modes of a planar Bragg waveguide may disappear altogether by shrinking with the forbidden bands. We derive the general conditions to determine the missing modes and explain these conditions with examples. It is possible, for example, to design a Bragg waveguide that rejects all antisymmetric modes and supports only symmetric modes for the TE polarization. We also highlight the effect of Brewster incidence on the interpretation of the missing modes for the TM polarization.     

The novel boundary integral equation method for solving arbitrary cross-section waveguides

A novel method for solving arbitrary cross-sectionn waveguides is presented. The novel method is a modification of the eigen-weighted boundary integral equation method; the EWBIEM is modified by using the eigenfunction of a fictitious regular boundary as weighting function, whose eigenvalue may be the known value, and meanwhile using the domain-bases. To confirm the validity of the novel method, numerical analysis are presented for circular groove guide as an example.The Project Supported by National Natural Science Foundation of P.R. China     

Proper and improper modes of the left-handed material waveguides

The guided, complex, and virtual modes of the planar left-handed material waveguides are studied. The modal dispersion and field distributions are analyzed for the systems with step and parabolic profiles of dielectric permittivity and magnetic permeability. It is shown that anomalously high magnitudes of the magnetic fields may be observed in such structures. Effects of material nonlinearity and spatial dispersion are discussed.     

Higher harmonic generation in nonlinear waveguides of arbitrary cross-section

This article concerns the generation and properties of double harmonics in nonlinear isotropic waveguides of complex cross-section. Analytical solutions of nonlinear Rayleigh-Lamb waves and rod waves have been known for some time. These solutions explain the phenomenon of cumulative double harmonic generation of guided waves. These solutions, however, are only applicable to simple geometries. This paper combines the general approach of the analytical solutions with semi-analytical finite element models to generalize the method to more complex geometries, specifically waveguides with arbitrary cross-sections. Supporting comparisons with analytical solutions are presented for simple cases. This is followed by the study of the case of a rail track. One reason for studying nonlinear guided waves in rails is the potential measurement of thermal stresses in welded rail.     

Finite difference scheme for planar waveguides with arbitrary index profiles and its implementation for anisotropic waveguides with a diagonal permitivity tensor

A finite difference scheme with a uniform mesh for planar waveguides with arbitrary refractive index profiles that takes full account of any smooth index variation and index discontinuity is derived for TE and TM-polarized waves. Discretizations that lead to a second-order error in the effective indices are given for TE and TM polarizations. At the computational boundaries, transparent boundary conditions are used. The scheme was implemented for anisotropic waveguides with a diagonal permitivity tensor and examined by using samples with various refractive index profiles, ranging from simple step- and graded-index up to complicated refractive index profile structures composed of either isotropic or anisotropic materials. For simple cases where the results of other methods are available in the literature, the proposed scheme shows very good agreement.     

Bounds on phase velocities of guided modes in open waveguides

Guiding of waves along cylinders with a surface impedance or along low velocity sound channels lead to eigenvalue problems in unbounded domains. Variational and comparison methods are used to find bounds on the discrete eigenvalues, which are related to the phase velocities of the guided modes. The variational methods yield upper bounds only, but they can be applied systematically to a large class of problems. The comparison methods yield upper and lower bounds, but are restricted to a smaller class of problems.     

An accurate variational analysis of single-mode diffused channel waveguides

We present a procedure based on the variational principle to obtain the modal propagation characteristics of single-mode diffused channel waveguides with arbitrary index profiles. The only assumption in our method, in addition to the scalar approximation, is that the trial field is separable along the depth and the width directions. The method is iterative, with each cycle of iteration requiring the solution of two planar waveguide propagation problems. The convergence is usually achieved within 2–3 cycles of iteration. Comparisons with other methods show that our method gives much better accuracy.     

Selective excitation of high-order modes in circular waveguides

The excitation of very high-order modes in circular waveguides has been performed in a cavity with a connected up-taper with a geometry similar to those used in gyrotrons. A Gaussian beam was coupled to the cavity which was made translucent by an array of holes. With the help of a special optics, the amplitude as well as the phase distribution of the beam was matched to the mode to be excited in the resonant cavity. By simple rotation of one mirror to adjust the phase distribution together with the change of frequency to match the resonance condition, a large number of modes could be produced with one experimental set-up. Field measurements in the output waveguide show a high mode purity of the radiation and confirm the calculations. The method can be used for cold tests of electrodynamic systems operating with these modes, e.g. quasi-optical converters for gyrotrons.