Coherent states and nonparaxial propagation of light in graded-index media

A study is made of the trajectories and widths of coherent states in nonparaxial propagation of light in a medium with a refractive index which differs slightly from a quadratic profile. Explicit expressions are obtained for the trajectories and widths and it is shown that they generally depend on the wavelength of light. In the limit of wavelengths tending to zero the expressions for the trajectories reduce to the corresponding expressions in ray optics and the ray widths decrease to zero. The coherent states thus make it possible to generalize the concept of a geometric ray and to allow for the wave properties of light in solutions obtained by ray optics methods.