Energy leakage and reflection in slowly varying waveguides

Abstract

A new technique is presented which is called the method of slowly varying dispersion relations, for approximately determining the modes near cutoff in two-layer slowly varying waveguides. The depth of the upper layer is finite while the lower layer is semi-infinite. The method is presented for the penetration problem, where the density and sound speed ratios are O(1), which was analyzed previously by different methods. It was shown that all of the energy propagating in the upper layer was lost into the underlying layer. The method is also applied to the case where the lower layer is hard and fast compared to the upper layer. It is shown that in this case energy is both lost into the lower layer and reflected back into the waveguide.