Diffraction limit of light in curved space

TL;DR

This paper explores how spatial curvature in curved spaces affects the diffraction limit and optical resolution, revealing that positive curvature can enhance resolution and suggesting new methods for super-resolution imaging and gravitational detection.

Contribution

It demonstrates that spatial curvature influences diffraction limits, with positive curvature improving resolution, and introduces potential applications in super-resolution imaging and gravitational field detection.

Findings

Diffraction limit decreases on surfaces with positive Gaussian curvature.

Optical resolution is affected by propagation direction and distance in curved space.

Curved space can be used to control optical resolution and detect gravitational effects.

Abstract

Overcoming diffraction limit is crucial for obtaining high-resolution image and observing fine microstructure. 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 affect the diffraction limit is an attractive and important question. Here we investigate the issue of diffraction limit and optical resolution on two-dimensional curved spaces - surfaces of revolution (SORs) with constant or variable spatial curvature. We show that the diffraction limit decreases and resolution is improved on SORs with positive Gaussian curvature, opening a new avenue to super-resolution. The diffraction limit is also influenced by propagation direction, as well as the propagation distance in curved space with variable spatial curvature. These results provide a possible method to control optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of non-uniform strong gravitational effect by probing locally the optical resolution.