Planar dielectric waveguides play an important role in electrooptics and in the submillimeter regions. In many laser configurations and integrated optical components, grooves are etched in the planar surface or overlays are deposited on it. The step is an idealization of such discontinuity. In this paper, the problem of an arbitrary large step under multimode excitation is solved by means of a rigorous variational approach. A rapidly converging expression for the scattering matrix of the step is derived, which is analogous to the one previously derived for transverse discontinuities in closed waveguides. Two choices as to the basis functions are compared: one is constituted by optimally scaled Laguerre functions and the other by the surface waves of both slabs complemented by Laguerre functions. Both the electric field and the magnetic field formulations of the problem have been investigated for the TE case. Numerical results are presented for the scattering matrix of the step under monomode and multimode excitation as well as for its radiation pattern. The accuracy and limitations of existing small step approximations are discussed. The technique is applicable to other transverse discontinuities in open structures.

Rigorous Analysis of the Step Discontinuity in a Planar Dielectric Waveguide

This paper presents the calculation of the diffraction of axisymmetric borehole waves by bed boundary discontinuities. The bed boundary is assumed to be horizontal and the inhomogeneities to be axi...

Diffraction of axisymmetric waves in a borehole by bed boundary discontinuities

A novel approach for analyzing discontinuity problems in optical waveguides is presented. The method is a combination of the vector-finite-element method and the least-squares boundary residual method. The vector-H-field-finite-element method is capable of providing accurate eigenvalues and eigenvectors for a wide range of optical waveguide problems, including arbitrary shape, arbitrary index distribution, and anisotropic materials. The least-squares boundary residual method matches the continuity of tangential fields in the least-squares sense, taking into account many modes at the discontinuity plane, to give the general scattering matrix. A few results are presented to show the usefulness of the approach. >

Analysis of optical waveguide discontinuities

A novel approach to analyze the discontinuities in open-type transmission lines is proposed. The method used is the least squares boundary residual technique which has been applied previously to treat the boundary-value problems in closed-type transmission lines. As an example of application of our approach the reflected, transmitted, and radiated waves caused by the transverse displacement at the junction of two dielectric slab waveguides are calculated.

Analysis of Discontinuities in Dielectric Waveguides by Means of the Least Squares Boundary Residual Method

We have developed a rigorous mode matching approach for the exact semi-analytical analysis
of surface plasmon propagation across non-uniform semi-infinite dielectric-metal interfaces. We address two key deficiencies of related approaches in the literature: firstly, we resolve issues of accuracy and convergence and secondly, while we focus on the analysis of two-dimensional problems, we present a framework for three-dimensional problems for the first time. Analytical derivations of coupling coefficients between guided and radiation modes allow an efficient scattering matrix formulation to describe general structures with multiple discontinuities. Studies of the reflection, transmission and radiation of surface plasmons incident on both dielectric and metallic surface discontinuities show a correspondence with an effective Fresnel description. We also model a surface plasmon Distributed Bragg Reflector (DBR) capable of reflecting between 80% and 90% of incident surface plasmon power. Radiation mode scattering ultimately limits the DBR’s reflection performance rather than the intrinsic absorption of the metal. Thus alternative plasmonic geometries that suppress radiation modes, such as gap and channel structures, could be superior for the design of strongly reflective DBRs for integration in high Q-factor nano-scale cavities. We anticipate that this method will be an invaluable tool for the efficient and intuitive design of plasmonic devices based on structural non-uniformities.

http://xlab.me.berkeley.edu/pdf/10.1103_PhysRevB.76.035408.pdf

Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities

A theoretical treatment is presented of the scattering of a surface-wave mode on a planar surface waveguide at an abrupt axial transition. The latter is due to a dielectric obstacle that covers the line completely up to a given height. The analysis involves the matching of the tangential fields, expressed in terms of complete sets of eigenmodes, on the transition plane. The problem arises in certain obstacle detection schemes currently being proposed for guided transportation, which use the principle of guided RADAR.

J.C. Beal

Papers

Scattering of Surface Waves at a Dielectric Discontinuity on a Planar Waveguide