A Schrodinger formulation for paraxial light beam propagation and its application to propagation through nonlinear parabolic-index media

The Helmholtz equation is reduced to the Schrodinger-like equation and then the quantities representing the gross features for a paraxial optical beam , such as the width, divergence, radius of curvature of the wave front, com plex beam parameter, beam quality factor, and the potential function repres enting beam propagation stability, are studied by using the quantum mechani cal methods. The results derived in other ways previously are rederived by our formulation in a more systematical and explicit fashion analytically, a nd some new results are demonstrated. The general equations for the evoluti on of these quantities, i.e., the first- and second-order differential equa tions with respect to the propagation distance, such as the universal formu la for the width and curvature radius, the general formula for the first de rivative of the complex beam parameter with respect to the axial coordinate , the general formula for the second derivative of the width with respect t o the axial coordinate, and some general criteria for the conservation of t he beam quality factor and the existence of a potential well of the potenti al function, are derived. We also discuss the application of our formulatio n to nonlinear parabolic-index media.