Paraxial light and atom optics: The optical Schrodinger equation and beyond

Paraxial light and atom optics are compared. To lowest order the slowly varying amplitude of a light field in a dielectric medium with a spatially dependent refractive index satisfies an equation which has the form of a Schrodinger equation: the ''optical Schrodinger equation.'' The unsystematic procedure of neglecting certain second-order derivatives is replaced by a systematic expansion which allows the calculation of consecutive corrections. The general theory is applied to harmonic motion in a graded index fiber and to tunneling between coupled fibers. The physical relations between wave evolution of massive particles and paraxially propagating waves are elucidated.