Floquet theory of intracavity laser frequency modulation

The theory of laser oscillation with an intracavity sinusoidal modulation o f the optical frequency is revisited and analyzed in the framework of gener al principles governing the properties of time-dependent periodic systems. It is shown that the two traditional and complementary descriptions of freq uency modulation (FM) laser oscillation and pulsed FM mode-locking [S.E. Ha rris and O.P. McDuff, IEEE J. Quantum Electron. QE-1, 245 (1965); D.J. Kuiz enga and A.E. Siegman, ibid. QE-6, 694 (1970)] can be unified by means of a more general approach based on a Floquet analysis of the laser equations i n presence of a periodic phase perturbation. Starting from a spatially exte nded model of intracavity laser frequency modulation for a homogeneously br oadened two-level ring laser, the relevant Floquet modes and corresponding Floquet exponents governing the stability properties of the nonlasing state are derived as solutions of a nonlinear eigenvalue problem. Resonance phen omena, which occur when the modulation frequency is made close to an intege r multiple of the cavity axial mode separation, explain the onset of FM las er oscillation and the transition to the pulsed FM mode lockings closer to the synchronous modulation. In particular, the transition from FM laser osc illation to the pulsed FM mode locking is shown to be sharp and due to a cr ossing of the threshold curves of two distinct Floquet modes. The role of c avity dispersion on the transition is also investigated. [S1050-2947(99)066 10-X].