  Analogous coherent states are deduced from classical optical fields on curved
surface in this paper. The Gaussian laser beam, as a fundamental mode, cannot
be adequately simulated by coherent states due to their inherent diffraction in
flat space. But things will be different when it propagates on a surface with
uniform curvature called the constant Gaussian curvature surface (CGCS). By
generalizing the method of Feynman path integral, an equivalent coherent states
solution is demonstrated here to describe the beam propagation. The temporal
evolution of the Schrodinger equation is analogously translated into a spatial
transmission in this derivation, we obtain the expression of quantized momentum
transmitted on curved surface, which is proportional to the square root of the
Gaussian curvature $K$. In addition, we build a beam propagation picture
identical to the squeezed state. We hope this research can give a new view on
the quantum field in curved space.
