Floquet theory of intracavity laser frequency modulation

Abstract

The theory of laser oscillation with an intracavity sinusoidal modulation of the optical frequency is revisited and analyzed in the framework of general principles governing the properties of time-dependent periodic systems. It is shown that the two traditional and complementary descriptions of frequency modulation ͑FM͒ laser oscillation and pulsed FM mode-locking ͓S.E. Harris and O.P. McDuff, IEEE J. Quantum Electron. QE-1, 245 ͑1965͒; D.J. Kuizenga and A.E. Siegman, ibid. QE-6, 694 ͑1970͔͒ can be unified by means of a more general approach based on a Floquet analysis of the laser equations in presence of a periodic phase perturbation. Starting from a spatially extended model of intracavity laser frequency modulation for a homogeneously broadened 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 phenomena, which occur when the modulation frequency is made close to an integer multiple of the cavity axial mode separation, explain the onset of FM laser oscillation and the transition to the pulsed FM mode locking closer to the synchronous modulation. In particular, the transition from FM laser oscillation to the pulsed FM mode locking is shown to be sharp and due to a crossing of the threshold curves of two distinct Floquet modes. The role of cavity dispersion on the transition is also investigated.

On the stability & phase locking to a system reference of an optoelectronic oscillator with large delay

“…A more sophisticated Floquet analysis of the dynamical system describing the full complex amplitude of a laser with intra-cavity phase modulation [18] predicts a solution identical to Equation 19 except at near zero detuning where a pulsed mode-locked solution emerges. Close to zero detuning the peak phase excursion of the phase modulated oscillation can become so great that the sidebands of the Bessel super mode reach the edge of the RF-selection filter passband which results in dissipation of their energy.…”

Photonic Floquet media with a complex time-periodic permittivity

“…for realizing time modulation [37][38][39][40][41][42][43][44]. Owing to the growing interests in the time Floquet photonic system, sustainable time modulation on the permittivity with very high modulation frequency can be feasible in the near future [24].…”

Nonstationary Casimir Effect and Analytical Solutions for Quantum Fields in Cavities with Moving Boundaries

“…It was extensively studied in many experiments, devoted, in particular, to such problems as the generation of optical pulses [24,25], phase locking of laser modes (where the frequencies of the mirror oscillations varied from 50 Hz [26] to 500 KHz [27,28] and 1 MHz [29,30], see the review in [31]), or modulation of the laser radiation [32,33] (in [33] the frequencies varied from 17 to 70 KHz). The theory of these phenomena was considered, e.g., in [34][35][36].…”