Spatial behavior of light in second-harmonic generation

Abstract

We investigate the spatial behavior of nonclassical light produced by type I second-harmonic generation in the traveling-wave configuration. An input-output transformation for the system of fundamental and secondharmonic field is derived in the framework of a linearization approach and used to investigate the properties of an optical system, which consists of a crystal with a quadratic nonlinearity pumped at frequency v and enclosed in a two-lens telescopic system. If a faint input image at frequency 2v is injected into this device, for a sufficiently large interaction length, the output displays a pair of symmetric amplified versions of the input image at both fundamental and second-harmonic frequency. The analysis of the quantum fluctuations in the output images shows that under certain conditions, this optical device operates noiselessly with respect to the output at frequency v, whereas the output images at frequency 2v are affected by a slight degradation of the signal-to-noise ratio.