Diffractive optics in nonlinear media with periodic structure

Periodic Multiphase Nonlinear Diffractive Optics with Curved Phases

We describe diffraction for rapidly oscillating, periodically modulated nonlinear waves. This phenomenon arises for example when considering long-time propagation, or through perturbation of initial oscillations. We show existence and stability of solutions to variable coefficient, nonlinear hyperbolic systems, together with 3-scales multiphase infinite-order WKB asymptotics: the fast scale is ...

Diffractive Nonlinear Geometric Optics *

Contents. x1. The origin and nature of Schrr odinger type approximations. x2. Formulating the ansatz. x3. Equations for the prooles. x4. Solvability of the the proole equations. x5. Convergence towards exact solutions. x6. The quasilinear case.

Diffractive Nonlinear Geometric Optics with Rectification

This paper studies high frequency solutions of nonlinear hyperbolic equations for time scales at which diiractive eeects and nonlinear eeects are both present in the leading term of approximate solutions. The key innovation is the analysis of rectiication eeects, that is the interaction of the nonoscillatory local mean eld with the rapidly oscillating elds. The main results prove that in the li...

Diffractive Nonlinear Geometric Optics for Short Pulses

This paper considers the behavior of pulse-like solutions of length ε 1 to semilinear systems of hyperbolic partial differential equations on the time scale t = O(1/ε) of diffractive geometric optics. The amplitude is chosen so that nonlinear effects influence the leading term in the asymptotics. For pulses of larger amplitude so that the nonlinear effects are pertinent for times t = O(1), accu...

Polarization Optics of Periodic Media