Quantum X-Waves and Applications in Nonlinear Optics

This chapter describes a formulation for 3D optical field quantization based on X-waves, and discusses its application to nonlinear optical parametric amplification (OPA) and Kerr media. All the machinery is based on the paraxial and slowly varying envelope approximation (SVEA), with reference to vacuum and to a normally dispersive medium. The chapter reports on a quantum theory of nonlinear X-waves and some of its corollaries; in particular the possibility of generating a very exotic and, intriguing for many applications, state of light-the progressive undistorted squeezed vacuum. Quantum nonlinear X-waves turn out to have the same properties of quantum fiber solitons. They can propagate with a well-defined photon number, thus enabling sequential measurements on the same quantum state; all the applications of quantum fiber solitons may be translated in the quantum X-waves world, with the non trivial benefits of a 3D space.