Diffractive Nonlinear Geometric Optics *
نویسندگان
چکیده
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.
منابع مشابه
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...
متن کاملDiffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide
The propagation of modulated light in a 2d nonlinear photonic waveguide is investigated in the framework of diffractive optics. It is shown that the dynamics obeys a nonlinear Schrödinger equation at leading order. We compute the first and second corrector and show that the latter may describe some dispersive radiation through the structure. We prove the validity of the approximation in the int...
متن کاملMathematik in den Naturwissenschaften Leipzig Diffractive geometric optics for Bloch wave packets
We study, for times of order 1/ε, solutions of wave equations which are O(ε2) modulations of an ε periodic wave equation. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order ε. We construct accurate approximate solutions of three scale WKB type. The leading profile is both transported at the group velocity and dispersed by a Schrödinger equatio...
متن کاملNonlinear Diffractive Optics with Curved Phases: Beam Dispersion and Transition between Light and Shadow
We give asymptotic descriptions of smooth oscillating solutions of hyperbolic systems with variable coefficients, in the weakly nonlinear diffractive optics regime. The dependence of the coefficients of the system in the space-time variable (corresponding to propagation in a non-homogeneous medium) implies that the rays are not parallel lines –the same occurs with non-planar initial phases. App...
متن کاملWavelength tuning of femtosecond pulses generated in nonlinear crystals by using diffractive lenses.
We demonstrate that diffractive lenses (DLs) can be used as a simple method to tune the central wavelength of femtosecond pulses generated from second-order nonlinear optical processes in birefringent crystals. The wavelength tunability is achieved by changing the relative distance between the nonlinear crystal and the DL, which acts in a focusing configuration. Besides the many practical appli...
متن کامل