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

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