Wolf effect of partially coherent light fields in two-dimensional curved space

Wolf effect refers to a spectral shift of light during its propagation even in free space, which results from the fluctuating (or correlation) nature of light sources. In conventional optics, the propagation laws of light are usually considered in flat space. However, optical phenomena are fascinating in the presence of space curvature. Here the problem of spectral changes of light during its propagation is addressed in a two-dimensional (2D) curved space, and the influence of space curvature on the Wolf effect is revealed. The propagation expression for a partially coherent polychromatic light beam is analytically derived for propagating inside 2D curved surfaces of revolution with constant Gaussian curvature under a linear paraxial approximation. It shows that the curved spaces with larger positive curvature accelerate and enhance the spectral shifts (blue- and redshifts) of light during their propagation, and the spaces with larger negative curvature may decelerate and suppress the spectral shifts. Furthermore, different correlation lengths of light sources also affect the behaviors of spectral shifts of light in such curved surfaces of revolution. Our result provides a method to measure the curvature of curved space by measuring the spectral shift of light during its propagation in curved space, like the cases of light propagating in practical gravitational space.