  Acting as analog models of curved spacetime, surfaces of revolution employed
for exploring novel optical effects are followed with great interest nowadays
to enhance our comprehension of the universe. It is of general interest to
understand the spectral effect of light propagating through a long distance in
the universe. Here, we address the issue on how curved space affects the
phenomenon of spectral switches, a spectral sudden change during propagation
caused by a finite size of a light source. By using the point spread function
of curved space under the paraxial approximation, the expression of the on-axis
output spectrum is derived and calculated numerically. A theoretical way to
find on-axis spectral switches is also derived, which interprets the effect of
spatial curvature of surfaces on spectral switches as a modification of
effective Fresnel number. We find that the spectral switches on surfaces with
positive Gaussian curvature are closer to the source, compared with the flat
surface case, while the effect is opposite on surfaces with negative Gaussian
curvature. We also find that the spectral switches farther away from the light
source are more sensitive to the change in Gaussian curvature. This work
deepens our understanding of the properties of fully and partially coherent
lights propagating on two-dimensional curved space.
