Quantum fluctuations in a continuous vectorial Kerr medium model

We consider a model for a Kerr medium in a planar resonator, which
takes into account the vectorial character of the radiation field.
We analyze the spatial behavior of quantum fluctuations around a
steady state, with a roll-pattern configuration in the beam
cross-section, using a Langevin treatment based on the Wigner
representation. The spatial distribution of the quantum
fluctuations around the roll-pattern is dominated by the neutral
(or Goldstone) mode, corresponding to rigid spatial displacements
of the pattern. The spatial configuration of the field immediately
outside the cavity input/output mirror depends on the time window
over which fluctuations are averaged: only when the time window is
on the order of the cavity lifetime the output field fluctuations
are qualitatively similar to that of the intracavity field. The
quantum correlations among the fields in play, as described by the
full multimode model, turn out to be in good agreement with those
predicted by a simple three-mode model.