Abstract

We have studied quantum effects in a system governed by the spatial nonlinear Schrödinger equation derived for a two beams interaction in a quadratic nonlinear material. For a quadratic nonlinear material it has recently been demonstrated [1, 2, 3] that under suitable conditions in the interaction between the fundamental and the second harmonic field the fundamental field propagation can be described as a solution of a nonlinear Schroedinger equation. In this work we are interested at the quantum properties of the fundamental beam in this kind of interaction. We use a quantum field description [1] where the spatial variable of propagation z plays the role of time in the standard quantum theory, and we apply it to the ease of a strong plane wave that can be described as a classical field propagating through the nonlinear medium in lite z-direction. We assume. TE polarizations for all the monocrohmatics fields involved into the interaction in a type I material. The quantum description of the field can be performed introducing the corresponding quantum operators, which fulfill the following equation, obtained from the classical one [41: where normalized units have been used and α is a parameter linked to the material properties. The quantum character is supposed to be given by small quantum fluctuations This procedure is valid only if the spatial perturbation is slowly varing in the transverse coordinate, as discussed in ref. [4]. A comparison with the solutions obtained starting from the linearized system of equations describing the intraction process in a quadratic nonlinear material, is also presented.

© 1996 IEEE