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Advances in Acoustics and Vibration
Volume 2012 (2012), Article ID 685326, 14 pages
http://dx.doi.org/10.1155/2012/685326
Research Article

Elastic Modes of an Anisotropic Ridge Waveguide

1Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287, USA
2RFIC Design Group, MaxLinear Inc., Carlsbad, CA 92011, USA
3Freeform Wave Technologies, Inc., Los Angeles, CA 90049, USA

Received 11 October 2011; Accepted 17 January 2012

Academic Editor: Rama Bhat

Copyright © 2012 Ameya Galinde et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A semi-analytical method for finding the elastic modes propagating along the edge of an anisotropic semi-infinite plate is presented. Solutions are constructed as linear combinations of a finite number of the corresponding infinite plate modes with the constraint that they decay in the direction perpendicular to the edge and collectively satisfy the free boundary condition over the edge surface. Such modes that are confined to the edge can be used to approximate solutions of acoustic ridge waveguides whose supporting structures are sufficiently far away from the free edge. The semi-infinite plate or ridge is allowed to be oriented arbitrarily in the anisotropic crystal. Modifications to the theory to find symmetric and antisymmetric solutions for special crystal orientations are also presented. Accuracy of the solutions can be improved by including more plate modes in the series. Numerical techniques to find modal dispersion relations and orientation dependent modal behavior, are discussed. Results for ridges etched in single crystal Silicon are found to be in good agreement with Finite Element simulations. It is found that variations in modal phase velocity with respect to crystal orientation are not significant, suggesting that anisotropy may not be a critical issue while designing ridge waveguides in Silicon.