Elastic Modes of an Anisotropic Ridge Waveguide

Abstract EN

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.