Asymptotic solutions for high-frequency trapped wave propogation

Abstract

A technique is developed by which high-frequency trapped scalar wave problems are reduced to finding solutions for a sequence of equations which are independent of the frequency. The technique is applied to whispering gallery waves, ducted waves, edge waves and surface waves. Several successful comparisons are made between the asymptotic expansions of exact analytic solutions and the results obtained by using the technique while one numerical comparison shows that such results can be extremely accurate even when the frequency is low. The range of validity of the solutions is discussed with particular reference to numerical solutions.