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

We consider a degenerate optical parametric oscillator driven by a sta tionary field of frequency 2OMEGA and by a modulated field of frequenc y OMEGA with a small modulation (signal) of frequency omega' much less than OMEGA. By using the eigenvectors of an appropriate matrix we ide ntify the conditions to obtain maximum ampliFIcation when a single qua drature component is modulated; the amplification coefficient is calcu lated analytically as a function of the frequency omega' and of the pa rameters. 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 amp lification and noise we compare the signal-to-noise ratio in the outpu t with that in the input, and determine the range of parameters in whi ch the performance of the system is better than that of the phase-inse nsitive linear amplifier. In particular we identify the cases in which noiseless amplification is possible. The approach developed in this p aper can be applied to a generic cavity-based phase-sensitive amplifie r.