Multiscale Approach to Parabolic Equations Derivation: Beyond the Linear Theory

The concept of the iterative parabolic approximation based on the multiscale technique is discussed. This approach is compared with the traditional ways to derive the wide-angle parabolic equation. While the latter fail in the nonlinear case, the multiscale derivation technique leading to iterative parabolic equations can be easily adapted to handle it. The nonlinear iterative parabolic approximations for the wave propagation in Kerr media are presented. An example demonstrating the capability of iterative parabolic equations to take nonparaxial propagation effects in Kerr media into account is considered.