On canonical pairs in 2-transverse-mode DOPOs

In ref. [1] we analyzed the properties of a Degenerate Optical Parametric Oscillator (DOPO) tuned to the first transverse mode family at the signal frequency. Above threshold, a Hermite-Gauss mode with an arbitrary orientation in the transverse plane is emitted, and thus the rotational invariance of the system is broken. When quantum effects were taken into account, it was found on the one hand, that quantum noise is able to induce a random rotation on this classically emitted mode. On the other hand, the analysis of a balanced homodyne detection in which the local oscillator (LO) was orthogonal to the excited mode at any time, showed that squeezing in the quadrature selected by the LO was found for every phase of this one, squeezing being perfect for a pi/2 phase. This last fact revealed an apparent paradox: If all quadratures are below shot noise level, the uncertainty principle seems to be violated. In [1] we stated that the explanation behind this paradox is that the quadratures of the rotating orthogonal mode do not form a canonical pair, and the extra noise is transferred to the diffusing orientation. Thes notes are devoted to prove this claim.

Non-critically squeezed light via spontaneous rotational symmetry breaking

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.

Cavity solitons in bidirectional lasers

We show theoretically that a broad area bidirectional laser with slightly different cavity losses for the two counterpropagating fields sustains cavity solitons (CSs). These structures are complementary, i.e., there is a bright (dark) CS in the field with more (less) losses. Interestingly, the CSs can be written/erased by injecting suitable pulses in any of the two counterpropagating fields.