A complete system of solutions of the equation describing the parametric excitation of an oscillator is presented. This system makes it possible to take into account losses in a parametrically excited oscillator in terms of the perturbation theory. It is shown that, although the oscillator losses are small (the relative spectral width of a typical laser cavity is 10 −8 ), they limit the achievable squeezing coefficients by values on the order of ten. At present, the progress in resonator technique allows one to achieve relative spectral widths on the order of 10 −11 –10 −12 . Therefore, it can be expected to achieve squeezing coefficients on the order of 10 3 .
The quantum aspects of parametric excitation of two electromagnetic modes are considered. It is shown that a Gaussian wave packet, evolving in the two-dimensional space of these modes, is the exact solution of the Schroedinger equation. Equations are derived for describing evolution of the packet parameters with time. Perturbation theory is used to obtain explicit expressions for these parameters at low parametric excitation rates. It is found that the variance of the sum of the fields of these modes oscillates at the pump frequency. In contrast to parametric excitation of one mode, the minimum and maximum variance both increase with time. The increase in the minimum variance accounts for the small squeezing coefficients obtained experimentally for optical parametric oscillators. The effect is described by two squeezing coefficients.