  We theoretically address squeezed light generation through the spontaneous
breaking of the rotational invariance occuring in a type I degenerate optical
parametric oscillator (DOPO) pumped above threshold. We show that a DOPO with
spherical mirrors, in which the signal and idler fields correspond to first
order Laguerre-Gauss modes, produces a perfectly squeezed vacuum with the shape
of a Hermite-Gauss mode, within the linearized theory. This occurs at any
pumping level above threshold, hence the phenomenon is non-critical.
Imperfections of the rotational symmetry, due e.g. to cavity anisotropy, are
shown to have a small impact, hence the result is not singular.
