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 second-harmonic 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 $\ensuremath{\omega}$ and enclosed in a two-lens telescopic system. If a faint input image at frequency $2\ensuremath{\omega}$ 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 $\ensuremath{\omega},$ whereas the output images at frequency $2\ensuremath{\omega}$ are affected by a slight degradation of the signal-to-noise ratio.
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