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On the Passage of Gaussian Beams through Cusps in Ray Paths

  • Author(s): Tiruviluamala, Neelesh
  • Advisor(s): Ralston, James
  • et al.
Abstract

Gaussian beams are asymptotic solutions to hyperbolic partial differentiable equations which propagate along null bicharacteristic curves in phase space. To build gaussian beams, one constructs a phase and an amplitude by using data along a specific null bicharacteristic. The current construction assumes that the ray path a beam follows in position space is smooth. In this work, we extend the construction to the case in which the ray path has cusps and deduce the phase shift that occurs when a beam passes through these cusps. We also present a new formula for the phase of a gaussian beam.

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