The Bogoliubov dispersion relation for the elementary excitations of the weakly-interacting Bose gas is shown to hold for the case of the weakly-interacting photon gas (the "photon fluid") in a nonlinear Fabry-Perot cavity. The chemical potential of a photon in the 2D photon fluid does not vanish. The Bogoliubov relation, which is also derived by means of a linearized fluctuation analysis in classical nonlinear optics, implies the possibility of a new, superfluid state of light. The theory underlying an experiment in progress to observe sound waves in the photon fluid is described, and another experiment to measure the critical velocity of this superfluid is proposed.

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We show the existence of a region in the parameter space that defines the field dynamics in a Fabry-Pérot cylindrical cavity, where three output stable stationary states of the light are possible for a given localized incident field. Two of these states do not preserve the bilateral (i.e., left-right) symmetry of the entire system. These broken-symmetry states are the high-transmission nonlinear modes of the system. We also discuss how to excite these states.

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A new type of transverse instability in dispersively nonlinear optical cavities, called the optical whistle, is discussed. This instability occurs in the mean field, soliton forming limit when the cavity is driven with a finite width Gaussian beam, and gives rise to oscillation, period doubling, and chaos. It is also seen that bistability is strongly affected due to the oscillation within the upper transmission branch. The phenomenon is interpreted as a mode mismatch in the soliton formation process and is believed to have broad applicability.