Universal dynamical properties of three-mode Fabry-Perot lasers

We present an asymptotic study of a three-mode Fabry-Perot laser with arbitrary relative modal gains in the rate equation limit. Dynamical modes are defined as the eigenvectors of the stability or Jacobian matrix. The associated eigenvalues are the decay rates and the relaxation oscillation frequencies. We show that if the modal gains are not equal, the ratio of the relaxation oscillation frequencies may display rational ratios which will lead to resonances. We classify the various states of the modal field intensities as in-phase, partial and perfect antiphase and find universal relations between the peak heights in the power spectra of the total and of the modal intensities at each of the relaxation oscillation frequencies. Our theoretical results are confirmed by numerical computation using the full rate equations. Experimental results obtained for the noise spectrum of an LNP microchip laser fully support our theoretical results. We also conjecture some properties of lasers operating in an arbitrary N-mode regime.