Diffraction limit of light in curved space

Abstract

Overcoming the diffraction limit is crucial for obtaining high-resolution images and observing fine microstructures. With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with gravitational fields in recent years, how spatial curvature affects the diffraction limit is an attractive and important question. Here we investigate the issue of the diffraction limit and optical resolution on two-dimensional curved space—surfaces of revolution (SORs) with constant or variable spatial curvature. We show that the diffraction limit decreases and the resolution is improved on SORs with positive Gaussian curvature, opening a new avenue to super-resolution. The diffraction limit is also influenced by the propagation direction, as well as the propagation distance in curved space with variable spatial curvature. These results provide a possible method to control the optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of the nonuniform strong gravitational effect by probing locally the optical resolution.