  As an analog model of general relativity, optics on some two-dimensional (2D)
curved surfaces has been increasingly paid attention to in the past decade.
Here, in light of Huygens-Fresnel principle, we propose a theoretical frame to
study light propagation along arbitrary geodesics on any 2D curved surfaces.
This theory not only enables us to solve the enigma of "infinite intensity"
existed previously at artificial singularities on surfaces of revolution, but
also makes it possible to study light propagation on arbitrary 2D curved
surfaces. Based on this theory, we investigate the effects of light propagation
on a typical surface of revolution, Flamm's paraboloid, as an example, from
which one can understand the behavior of light in the curved geometry of
Schwarzschild black holes. Our theory provides a convenient and powerful tool
for investigations of radiation in curved space.
