Generalization of Wolf effect of light on arbitrary two-dimensional surface of revolution

Investigation of physics on two-dimensional curved surface has significant meaning in study of general relativity, inasmuch as its realizability in experimental analogy and verification of faint gravitational effects in laboratory. Several phenomena about dynamics of particles and electromagnetic waves have been explored on curved surfaces. Here we consider Wolf effect, a phenomenon of spectral shift due to the fluctuating nature of light fields, on an arbitrary surface of revolution (SOR). The general expression of the propagation of partially coherent beams propagating on arbitrary SOR is derived and the corresponding evolution of light spectrum is also obtained. We investigate the extra influence of surface topology on spectral shift by defining two quantities, effective propagation distance and effective transverse distance, and compare them with longitudinal and transverse proper lengths. Spectral shift is accelerated when the defined effective quantities are greater than real proper lengths, and vice versa. We also employ some typical SORs, cylindrical surfaces, conical surfaces, SORs generated by power function and periodic peanut-shell shapes, as examples to provide concrete analyses. This work generalizes the research of Wolf effect to arbitrary SORs, and provides a universal method for analyzing properties of propagation compared with that in flat space for any SOR whose topology is known.