Contour integral solutions of the parabolic wave equation and applications to canonical scattering problems

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• David Hewett (University College London)
• Tuesday 07 February 2023, 15:30-16:15
• Seminar Room 1, Newton Institute.

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MWSW01 - Canonical scattering problems

We present a simple, systematic construction and analysis of solutions of the two dimensional parabolic (or paraxial) wave equation that exhibit far-field localisation near certain algebraic plane curves. Our solutions are complex contour integral superpositions of elementary plane wave solutions with polynomial phase, the desired localisation being associated with the coalescence of saddle points. Our solutions provide a unified framework in which to describe some classical phenomena in two-dimensional high frequency wave propagation, including smooth and cusped caustics, whispering gallery and creeping waves, and tangent ray diffraction by a smooth boundary. We also study a subclass of solutions exhibiting localisation near a cubic parabola, and discuss their possible relevance to the study of the canonical inflection point problem governing the transition from whispering gallery waves to creeping waves.

This talk is part of the Isaac Newton Institute Seminar Series series.

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