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Physical Review Research

Self-pulsing in Fabry-Perot lasers: An analytic scenario

Luigi A. Lugiato, Franco Prati

Published Dec 2, 2019• 9 citations
Publisher

Abstract

In this paper the authors demonstrate that in a Fabry-Perot laser under the condition of adiabatic elimination of the atomic polarization the multimode instability can arise very close to threshold, and the instability condition is given by a simple formula.
DOI
10.1103/physrevresearch.1.032029

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We start from the Maxwell-Bloch equations that govern the dynamics of Fabry-Perot lasers and, considering a doubled cavity, generalize our traveling wave formalism to the case in which the two-level medium does not fill the cavity but occupies only a portion of it. We linearize these equations and focus on the adiabatic elimination of both atomic fluctuations. Next, we restrict our attention to free running lasers under resonant conditions and analyze amplitude and phase instabilities. The examination of the unstable domain leads to the conclusion that the multimode Fabry-Perot instability arises near threshold only when the ratio of the longitudinal to the transverse atomic relaxation rate is substantially smaller than unity. This result agrees with our previous study in the limit of adiabatic elimination of the atomic polarization fluctuations only. We describe the self-pulsing behavior that arises from the multimode instability, and exhibits hysteretic behavior when the pump parameter is swept forward and backward. Finally, we investigate the single-mode instability and show that in the Fabry-Perot case there is no longer the correspondence between single-mode and multimode instabilities that is well known in the case of ring lasers. We confirm that in the case of resonant Fabry-Perot lasers the single-mode amplitude instability arises very far from threshold.
The transmission characteristics of a Fabry-Perot cavity containing a resonant absorber are described analytically and graphically for internal fields of arbitrary intensity. The multimode instability considered by Bonifacio and Lugiato [Opt. Commun. 19 , 72 (1976)] for the unidirectional ring laser is treated for the standing-wave cavity. In particular, an instability may exist when the medium is located at one of the ends of the cavity, but not if the medium fills the cavity. The results are explained in terms of induced side-mode gain and spatial hole burning.
This tutorial paper is based on lectures delivered by G M Stéphan at PELS'97. The idea was to tell the students about the methodology used by the authors to understand and to quantitatively compute the flips observed between two polarization states in a single-frequency He-Ne laser. The study is limited to this phenomenon. Contents are: introduction, quasi-isotropic lasers and polarization flips; the passive Fabry-Perot interferometer, an illustrative example; a vectorial description of a two energy-level system with magnetic degeneracy; two useful tools: adiabatic elimination of fast variables and use of Lyapunov exponents to study the stability of a solution; medium polarization in the adiabatic approximation; the laser equations for the field. These contents are organized for people coming into the field: rather than being too general, we have preferred to focus on limited and well defined examples from which other cases can be studied.
Self-pulsing of a single-mode laser has been studied with the use of the inhomogeneously broadened 3.51-\ensuremath{\mu}m transition in xenon. Time-averaged intensity power spectra, average power output, and real-time observations of intensity fluctuations have been recorded for various detunings of the Fabry-Perot cavity. Two forms of self-pulsing have been observed, both of which can be explained in terms of the phase locking of several frequencies which simultaneously exist in the same spatial mode, made possible by the rapid variations of the index of refraction in the high-gain medium. One form of such mode splitting occurs in the wings of the atomic response due to the variations in the inhomogeneously broadened anomalous dispersion. The second form can occur anywhere in the tuning range of the laser as it is caused by distortions induced in the dispersion by the hole-burning effects of the oscillating mode. The pulsation frequency of this induced mode splitting varies with cavity tuning, shows a dip at the atomic line center, and may be absent for detuning of one or two homogeneous linewidths away from center. The instabilities have shown subharmonic bifurcations of the pulsation frequencies. Both high-QQQ pulsation frequencies and broad bands of frequencies in the power spectra have been observed for various operating conditions.