Intensity phase coherence in three-mode Fabry-Perot lasers

We study analytically the intensity phase coherence in a three-mode Fabrey-Perot laser. We consider in detail the case of a central mode with maximum gain and two side modes with smaller but equal gains. This laser is characterized by three relaxation oscillation frequencies Omega ''(R)>Omega ''(L1)>Omega ''(L2). In the framework of a linearized theory, the laser dynamics is, respectively, inphased and perfectly antiphased at Omega ''(R) and Omega ''(L2), irrespective of the modal gains. At Omega ''(L1) the antiphase is only partial if the side mode gains are smaller than the central mode gain. Analytic gain- and pump-dependent relations between the three frequencies and between the heights of the peaks in the power spectra at these frequencies are established. We also derive universal relations between the peaks of the power spectra of the modal and the total intensities at the same frequencies that do not involve any parameter at all.