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The Bogoliubov dispersion relation for the elementary excitations of theweakly-interacting Bose gas is shown to hold for the case of theweakly-interacting photon gas (the ``photon fluid'') in a nonlinear Fabry-Perotcavity. This relation, which is also derived by means of a linearizedfluctuation analysis in classical nonlinear optics, implies the possibility ofa new superfluid state of light. The theory underlying an experiment inprogress to measure this dispersion relation is described, and anotherexperiment to test the prediction of the superfluidity of this state of lightis proposed.Comment: 11 pages, 4 figures, REVTEX style, to be published in PRA, Nov. 1,  199

Bogoliubov dispersion relation and the possibility of superfluidity for weakly interacting photons in a two-dimensional photon fluid