Accurate semiclassical analysis of light propagation on tilted hyperplanes

2025/04/18 by Gioia, Patrick, Ngoc, San Vu
#Analysis of PDEs (math.AP) #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Signal Processing (eess.SP) #Symplectic Geometry (math.SG) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2504.13485

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 0xR^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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