Generation of Coherent and Spatially Squeezed States of an Electromagnetic Beam in a Planar Inhomogeneous Dielectric Waveguide

We use slow-varying amplitude approximation (SVA) for the wave equation to study both analytically and numerically propagation of an electromagnetic beam in the waveguide structure with parabolic susceptibility spatial dependence. Such a structure is similar to the harmonic oscillator in quantum mechanics. We analyze this structure as a single mode guide and introduce the notion of number of “photons” in the mode. In particular, we pay special attention to the possibility of effective build-up of the coherent and spatially squeezed vacuum states of the mode that can be of interest for a number of practical applications. The way to provide these types of mode excitation is suggested. Several applications for controlling the mode composition of an electromagnetic wave in the parabolic index-gradient waveguide for various frequency ranges are considered.