a mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎the method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎the problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical met...

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.

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...

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...

We give an idea of the evolution of mathematical nonlinear geometric optics from its foundation by Lax in 1957, and present applications in various fields of mathematics and physics.

Nonlinear geometric optics with various frequencies for entropy solutions only in L∞ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and L–stability. New multidimensional features are recognized, especially including nonlinear propagations of oscilla...