The hollow Gaussian beam propagation on curved surface based on matrix optics method

TL;DR

This paper introduces a matrix optics approach to study hollow Gaussian beam propagation on curved surfaces with constant Gaussian curvature, revealing unique properties and potential applications in beam control and optics.

Contribution

It is the first to apply ABCD matrix method to analyze light transmission on curved surfaces and derives an analytical propagation formula for hollow Gaussian beams in this context.

Findings

Propagation characteristics include dark spot size change and ray splitting.

HGBs exhibit periodicity and diffraction properties on curved surfaces.

Beam parameters and surface shape control the dark region area.

Abstract

In this paper, ABCD matrix is introduced to study the paraxial transmission of light on a constant gaussian curvature surface (CGCS), which is the first time to our knowledge. It is also proved that the curved surface can be used as the implementation of fractional Fourier transform, we further generalize that we can obtain the transfer matrix of an arbitrary surface with gently varying curvature by matrix optics. As a beam propagation example, based on the Collins integral, an analytical propagation formula for the hollow Gaussian beams (HGBs) on the CGCS is derived. The propagation characteristics of HGBs on one CGCS are illustrated graphically in detail, including the change of dark spots size and splitting rays. Besides its propagation periodicity and diffraction properties, a criterion for convergence and divergence of the spot size is proposed. The area of the dark region of the HGBs can easily be controlled by proper choice of the beam parameters and the shape of CGCS. In addition, we also study the special propagation properties of the hollow beam with a fractional order. Compared with HGBs in flat space, these novel characteristics of HGBs propagation on curved surface may further expand the application range of hollow beam.