On Mathematical Problems in Geometric Optics

Institute for Mathematical Physics Semilinear Geometric Optics for Generalized Solutions Semilinear Geometric Optics for Generalized Solutions

This paper is devoted to the study of nonlinear geometric optics in Colombeau algebras of generalized functions in the case of Cauchy problems for semilinear hyperbolic systems in one space variable. Extending classical results, we establish a generalized variant of nonlinear geometric optics. As an application, a nonlinear superposition principle is obtained when distributional initial data ar...

REFRACTION PROBLEMS IN GEOMETRIC OPTICS April 22, 2013

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.

Two-photon geometric optics.

We report two-photon correlation experiments using spontaneous parametric down-conversion under a severe manipulation of the input pump field. Considering the case of passing the laser beam through a focusing lens before the down-conversion crystal, theoretical calculations and a series of imaging experiments demonstrate two-photon geometric optics effects. In particular, the imaging in coincid...

Dispersive nonlinear geometric optics

We construct infinitely accurate approximate solutions to systems of hyperbolic partial differential equations which model short wavelength dispersive nonlinear phenomena. The principal themes are the following. ~1! The natural framework for the study of dispersion is wavelength e solutions of systems of partial differential operators in e]. The natural e-characteristic equation and e-eikonal e...