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...

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...

We present recent works on the construction of high-frequency solutions to Einstein vacuum equations in general relativity, based [Tou22b, Tou23]. In these articles, author shows existence a family spacetimes (g λ ) λ∈(0,1] generalised wave gauge oscillating at frequency -1 and defined by geometric optics ansatz. this survey, we first review Cauchy theory for gauge, Burnett’s conjecture relativ...

Abstract We derive a general solution based on geometric optics that describes the light propagation properties in multimode optical fibers with inverted refractive index profiles. Using this solution, we classify rays according to their and calculate analytical expressions of ray trajectories inside these under different launching conditions. In addition, discuss most suitable conditions maxim...