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International Meeting on Instabilities and Dynamics of Lasers and Nonlinear Optical Systems

Instrinsic Dynamical Instability in Optical Bistability with Two-Level Atoms

Albert T. Rosenberger, Luis A. Orozco, Harry J. Kimble

Published Jan 1, 1985• 1 citation
Publisher

Abstract

Self pulsing due to the single-mode instability has been observed in optical bistability.1 This self-pulsing instability has its roots in corresponding instabilities first analyzed for the homogeneously broadened laser. It shares a common physical origin in the intrinsic mechanism by which a strong intracavity field alters the absorption profile of the intracavity medium to produce amplification at frequencies offset from that of the strong field.

DOI
10.1364/idlnos.1985.wa2

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Intrinsic Dynamical Instability in Optical Bistability with Two-Level Atoms

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Physical Review A•Sep 1, 1981•73 citations
Self pulsing due to the single-mode instability has been observed in optical bistability.1 This self-pulsing instability has its roots in corresponding instabilities first analyzed for the homogeneously broadened laser. It shares a common physical origin in the intrinsic mechanism by which a strong intracavity field alters the absorption profile of the intracavity medium to produce amplification at frequencies offset from that of the strong field.
Beams of homogeneously broadened two-state sodium atoms in a confocal ring resonator have been employed to investigate the steady-state characteristics of absorptive [1] and dispersive optical bistability. Also studied in the same system is the dynamical behavior due to the intrinsic single-longitudinal-mode instability [2] originating in the alteration of the atomic absorption profile by a strong field as in the Lorenz-type instability in the homogeneously broadened laser. All experimental parameters are carefully measured and corrected for transit broadening, finite absorption, and residual Doppler broadening in order to be able to make an absolute comparison with the single-Gaussian-transverse-mode theory [3-6]. Despite the frequency degeneracy of the transverse modes of the resonator, the agreement with this theory for absorptive bistability is remarkably good. The dispersive bistability data are more difficult to interpret, but they seem to be in reasonable agreement with the theory; the same can be said of the results for the domain and oscillation frequency of the instability, at least within a certain region of parameter space. Outside this region, multiple unstable states appear for various intracavity intensities; recent observations suggest that these may be due in part to instabilities involving higher-order transverse modes of the resonator.
We have recently observed a sinewave self-pulsing in the beam transmitted by a passive cavity containing 2-level molecules, driven by a continuous wave. In this experiment made at a wavelength λ ≅ 3.5 mm, the intracavity Rabi frequency is comparable to the free spectral range ( 830 kHz ) of the very long cavity used (l =182 m) {1} and much larger than the collisional linewidth (≅ 25 kHz) .The medium is then strongly saturated by the driving field ( saturation parameter > 1000) so that its absorption , heavy in the linear regime (αl > 100), is in fact quite moderate. We claim that the self-pulsing observed in these conditions is the first experimental evidence of the multimode instability, predicted a long time ago by Bonifacio and Lugiato {2} but not yet observed. This instability is the multimode counterpart of the single mode instability, recently observed by Orozco et al {3}.
The effect of transverse intensity variation on the various instabilities associated with optical bistability seems to be catastrophic in the case of pure absorptive bistability1,2 but benign in the mixed absorptive-dispersive case.2,3 In particular, recent results of Lugiato et al.2 indicate that the mean-field single-mode instability is not destroyed by the assumption of a Gaussian transverse intensity profile, and that it should be observable for experimentally accessible parameter values. Stimulated by these results, we have looked for and observed self-pulsing due to the single-mode instability in the predicted region of parameter space.
We report the observation of an instability in a bistable optical system with a homogeneously broadened two-level medium involving the onset of the cavity side mode that is two modes away from the source frequency and three modes away from the molecular resonance frequency. These measurements extend the range of a recent report [Phys. Rev. A 39, 703 (1989)] of observations of the multimode instability in optical bistability predicted by Lugiato and Bonifacio [Lett. Nuovo Cimento 21, 505 (1978); 21, 510 (1978)], with the key difference being that the experimental observations in the previous report were limited to instabilities of the side mode adjacent to the source frequency.
We review and extend the theory of instabilities in absorptive optical bistability for ring cavities containing homogeneously broadened two-level media. The instabilities occur in the high-transmission branch and result in either a precipitation to the low-transmission branch or in pulsed multimode operation. Two numerical approaches are used to predict operation away from the simple mean-field limit. First, an iterative method is used to solve the general field eigenvalue equation for cavity modes with frequencies displaced from the input frequency. This work shows that the instability region decreases in size as the mirror transmission increases. These calculations are confirmed by the second numerical technique, consisting of direct integrations of the coupled Maxwell-Bloch equations. This second approach also provides time histories of the instability evolutions, and divides the instability range into a precipitation regime and a self-pulsing regime. The results are discussed in terms of first- and second-order phase transitions, and agree with the analytical results obtained within the dressed-mode description of optical bistability. They show that when the incident field is adiabatically decreased along the high-transmission branch, the spiking behavior always appears abruptly. By further decreasing the incident intensity, the self-pulsing disappears either continuously if the system remains in the high-transmission branch, or discontinuously if the system precipitates to the low-transmission branch. Connection is made with induced probe gain known in the saturation spectroscopy of absorbers (uninverted media), in which population pulsations transfer energy from a saturating wave to the probe waves. The very close relationship with multimode operation in homogeneously broadened unidirectional ring lasers is also established.