Beam‐to‐mode conversion of a high‐frequency Gaussian P‐wave input in an elastic plate embedded in vacuum

Abstract

Gaussian beams, either individually or as synthesizing basis fields, provide useful models for the response due to Gaussian or more generally shaped high‐frequency source inputs, respectively. When propagating into a layered environment, an initially well‐collimated beam undergoes diffusion after successive reflections, and is converted essentially into the oscillatory pattern of one or more guided modes. The diffusion process is accelerated in the presence of multiwave coupling at interfaces, for example, the P‐SV coupling at the free boundary of an elastic solid. This phenomenology is examined here for a two‐dimensional P‐wave beam input into an elastic plate embedded in vacuum. The beam is modeled via the complex source point method whereby a Gaussian‐waisted input is generated from a line forcing function by assigning complex values to the source coordinates. This scheme avoids the need for plane‐wave spectral decomposition and synthesis, but the analytic continuation to complex source coordinates of ...