  Nonlinear optical cavities are crucial both in classical and quantum optics;
in particular, nowadays optical parametric oscillators are one of the most
versatile and tunable sources of coherent light, as well as the sources of the
highest quality quantum-correlated light in the continuous variable regime.
Being nonlinear systems, they can be driven through critical points in which a
solution ceases to exist in favour of a new one, and it is close to these
points where quantum correlations are the strongest. The simplest description
of such systems consists in writing the quantum fields as the classical part
plus some quantum fluctuations, linearizing then the dynamical equations with
respect to the latter; however, such an approach breaks down close to critical
points, where it provides unphysical predictions such as infinite photon
numbers. On the other hand, techniques going beyond the simple linear
description become too complicated especially regarding the evaluation of
two-time correlators, which are of major importance to compute observables
outside the cavity. In this article we provide a regularized linear description
of nonlinear cavities, that is, a linearization procedure yielding physical
results, taking the degenerate optical parametric oscillator as the guiding
example. The method, which we call self-consistent linearization, is shown to
be equivalent to a general Gaussian ansatz for the state of the system, and we
compare its predictions with those obtained with available exact (or
quasi-exact) methods.
