SPECTRAL-ANALYSIS OF THE DEGENERATE OPTICAL PARAMETRIC OSCILLATOR AS A NOISELESS AMPLIFIER

We consider a degenerate optical parametric oscillator driven by a stationary field of frequency 2OMEGA and by a modulated field of frequency OMEGA with a small modulation (signal) of frequency omega' much less than OMEGA. By using the eigenvectors of an appropriate matrix we identify the conditions to obtain maximum ampliFIcation when a single quadrature component is modulated; the amplification coefficient is calculated analytically as a function of the frequency omega' and of the parameters. Using a method of quantum Langevin equations, we express in analytic form the noise spectrum for a generic quadrature component of the field of frequency OMEGA. By combining the results concerning amplification and noise we compare the signal-to-noise ratio in the output with that in the input, and determine the range of parameters in which the performance of the system is better than that of the phase-insensitive linear amplifier. In particular we identify the cases in which noiseless amplification is possible. The approach developed in this paper can be applied to a generic cavity-based phase-sensitive amplifier.