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Physical Review A

Nonlinear dynamics of a multimode microchip laser due to enhanced stimulated absorption

Gregory Kozyreff, Paul Mandel

Published Feb 15, 2000• 6 citations
Publisher

Abstract

We study the dynamics of a laser oscillating on L optical transitions connecting a common upper level and L lower sublevels. Each transition is single mode. The minimal generalization of the rate equations to explain the experimental observations includes the low-frequency coherence dynamics [Europhys. Lett. 45, 307 (1999)]. These equations are studied analytically. We prove that such a laser has a low intensity self-pulsing threshold corresponding to the destabilization of the lowest of the relaxation oscillation frequencies. It also displays antiphased dynamics in the time-periodic regime, resulting in a vanishingly small oscillation amplitude of the total intensity while modal intensities have finite amplitude oscillations. The physical origin of this behavior is found to be the enhancement of stimulated absorption by quantum interference.

DOI
10.1103/physreva.61.033813

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We study the dynamics of a laser oscillating on L optical transitions connecting a common upper level and L lower sublevels. Each transition is single mode. The minimal generalization of the rate equations to explain the experimental observations includes the low-frequency coherence dynamics [Europhys. Lett. 45, 307 (1999)]. These equations are studied analytically. We prove that such a laser has a low intensity self-pulsing threshold corresponding to the destabilization of the lowest of the relaxation oscillation frequencies. It also displays antiphased dynamics in the time-periodic regime, resulting in a vanishingly small oscillation amplitude of the total intensity while modal intensities have finite amplitude oscillations. The physical origin of this behavior is found to be the enhancement of stimulated absorption by quantum interference.
In a LiNdP 4 O 12 microchip laser pumped by a diode laser, atomic interference arise due to the simultaneous oscillation on two transitions forming a Λ configuration. For a microchip laser, the low-frequency coherence is an important dynamical variable. It is coupled to the low spatial frequency of the population inversion grating. This results in modal intensities which are self-pulsing while the total intensity remains nearly constant. In addition, the modal power spectra display combinations of the relaxation oscillation frequencies which are absent in the power spectrum of the total output power.
We study a Nd-doped microchip glass laser that emits in two polarizations and in many longitudinal modes. Saturation of the inversion by standing waves causes spatial inhomogeneity of both the longitudinal and azimuthal distributions of the laser gain. These nonlinear inhomogeneities couple the modes and result in low-frequency oscillations (10--500 kHz) of the light flux in the individual laser modes. These oscillations are steadily driven by quantum noise and appear as 15% fluctuations of the power in each mode. In-phase fluctuations in the laser modes appear at the frequency of the main relaxation oscillation of the total laser power. Antiphase fluctuations appear at other frequencies in individual longitudinal and polarization laser modes only. The dominant frequency of these fluctuations is determined by the light power in the mode. Numerical simulations of rate equations, including Langevin forces, satisfactorily reproduce the experimental results. These phenomena must be taken into account when lasers are applied as stable coherent optical light sources, and also with sensitive absorption measurements in the laser cavity.
We analyze the intensity fluctuation of multimode lasers by extending the linear-response theory of McCumber for single-mode lasers. In the two-mode case, we prove analytically that the rate equations allow for an additional dynamical oscillation frequency associated with the antiphase motion. This explains the self-organized collective behavior of two-mode lasers, i.e., that the total output behaves just like a single-mode laser. The linear stability predicts the scaling law for this time scale, which results quite generally through cross-saturation dynamics of population inversion. Experimental results in two different laser systems confirm these predictions.
We study analytically the intensity phase coherence in a three-mode Fabry-P\'erot 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 ${\mathrm{\ensuremath{\Omega}}}_{\mathit{R}}^{\mathrm{\ensuremath{''}}}$\ensuremath{\gtrsim}${\mathrm{\ensuremath{\Omega}}}_{\mathit{L}1}^{\mathrm{\ensuremath{''}}}$\ensuremath{\gtrsim}${\mathrm{\ensuremath{\Omega}}}_{\mathit{L}2}^{\mathrm{\ensuremath{''}}}$. In the framework of a linearized theory, the laser dynamics is, respectively, inphased and perfectly antiphased at ${\mathrm{\ensuremath{\Omega}}}_{\mathit{R}}^{\mathrm{\ensuremath{''}}}$ and ${\mathrm{\ensuremath{\Omega}}}_{\mathit{L}2}^{\mathrm{\ensuremath{''}}}$, irrespective of the modal gains. At ${\mathrm{\ensuremath{\Omega}}}_{\mathit{L}1}^{\mathrm{\ensuremath{''}}}$ 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. \textcopyright{} 1996 The American Physical Society.
Summary form only given. Quantum interference in a three-level atomic system with two fields operating in a /spl Lambda/ or V scheme has attracted much attention as a mechanism for the mediation of interactions between light and matter. Amplification and even laser-behavior without a population inversion can be produced by such a system. Kozyreff and Pandel have recently shown analytically and numerically that atomic interference in a microchip laser with a population inversion operating on a /spl Lambda/-transition should result in antiphase pulsations in the vicinity of the Hopf bifurcation point. The phenomenon has been observed in a LiNdP/sub 4/O/sub 12/ (LNP) laser operating on a /spl Lambda/-scheme consisting of /sup 4/F/sub 3/2/(1)/spl rarr//sup 4/I/sub 11/2/(2,3) transitions in a limited pump power region. This paper outlines our demonstration of peculiar large-amplitude periodic pulsations in an intracavity frequency-doubled microchip LNP laser operating on a /spl Lambda/-transition and contains a theoretical confirmation of the mechanism for these pulsations.
Self-action of a frequency-modulated laser beam, propagating through a two-level saturable absorber, is modeled numerically basing of the direct solution of Maxwell-Bloch equations. Following the common idea of spectroscopy, we plot the output intensity versus the input laser frequency that periodically changes in time. At modulation frequencies comparable with the relaxation rates the hysteresis loop is observed, i.e. the dependence of the transmitted intensity upon the instantaneous frequency depends on the direction of the frequency change. At large amplitudes of modulation coherent transient oscillations of the output intensity are observed.