Intermediate Models in Nonlinear Optics

Intermediate Models in Nonlinear Optics

In this paper, new models are derived for laser propagation in a nonlinear medium. These models are intermediate between nonlinear Maxwell systems and nonlinear Schrödinger equations and are exact in linear cases. We prove rigorous error estimates for a generic class of systems. In the last section, we perform numerical tests in order to investigate the numerical effectivity of the bounds given...

Intermediate model for spatial evolution in nonlinear optics

This paper follows the work of Colin-Gallice-Laurioux [5] in which a new model generalising the Schrödinger model of the diffractive optics is derived for the laser propagation in nonlinear media. In particular, it provides good approximate solutions of the MaxwellLorentz system for highly oscillating initial data with broad spectrum. In real situations one is given boundary data. We propose to...

Quasi - exactly solvable models in nonlinear optics

We study a large class of models with an arbitrary (finite) number of degrees of freedom, described by Hamiltonians which are polynomial in bosonic creation and annihilation operators, and including as particular cases n-th harmonic generation and photon cascades. For each model, we construct a complete set of commuting integrals of motion of the Hamiltonian, fully characterize the common eigen...

On the Models of Nonlocal Nonlinear Optics. *

where D is a certain function of the electric field. For derivation of such type of equation see [1, 2]. Recent theoretical and experimental results highlight a very interesting phenomenology, such as “accessible solitons”, collapse arrest, optical vortices (see e.g. [3−6] and references therein), associated with so-called nonlocal nonlinear media. Most of the models studied before are not inte...

Nonlinear Optics Basics: Kramers-Krönig Relations in Nonlinear Optics