Accurate semiclassical analysis of light propagation on tilted hyperplanes

Patrick Gioia; San Vu Ngoc

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arXiv · 2504.13485

Accurate semiclassical analysis of light propagation on tilted hyperplanes

Patrick Gioia·San Vu Ngoc

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Abstract

In the scalar light model given by Helmholtz' equation in R^{1+d} , we consider the transformation of an initial scene (a hologram) in {0}xR^d by an arbitrary affine transformation (which can be viewed as a propagation into a tilted hyperplane). In the high frequency regime, we use microlocal and semiclassical analysis to describe the propagator as a semiclassical Fourier integral operator, thus generalising the well-known Angular Spectrum formula from optics. We then prove new precise Egorov theorems, including subprincipal terms, which indicate how to take into account the propagation along rays of geometric optics.

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Patrick Gioia, San Vu Ngoc. 2025-04-18. Accurate semiclassical analysis of light propagation on tilted hyperplanes. https://arxiv.org/abs/2504.13485

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