Gaussian beams and caustic avoidance in gravitational optics

Abstract

In this study, we consider a beam summation method adapted from the semiclassical regime of quantum mechanics to study the classical properties of thin light bundles in gravity. In Newtonian paraxial optics, this method has been shown to encapsulate the wave properties of the light beams. In our case, the wave function assigned to the light bundle can be viewed as a coarse-grained description that captures information about the dynamics of superposed bundles within the geometric optics regime. We investigate two solutions of the null bundle wave function that differ by their origin: (i) a point source and (ii) a finite source. It is shown that while the wave function in the point source case contains the same information as the standard thin null bundle framework, the finite source case corresponds to a Gaussian beam. The novel aspect of this work arises from our geometric construction of covariant Gaussian beams, which can be applied in any spacetime. Additionally, the effects of a finite source on cosmological distances are discussed. With this framework, one can model light propagation from coherent sources while avoiding the mathematical singularities of the standard thin null bundle formalism. We explicitly demonstrate the caustic-avoidance property of Gaussian beams in the analytically tractable example of a Barriola-Vilenkin monopole spacetime.

arXiv commentv3: Published version. Journal reference and DOI added. 68 pages, 6 figures, 3 appendices

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