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Physical Review A

Behavior of sodium atomic vapor in optical cavities below the threshold for bistability

W. Schulz, W. R. MacGillivray, M. C. Standage

Published Aug 1, 1987• 2 citations
Publisher

Abstract

A study is presented of the transmission characteristics of low-finesse ring and Fabry-Perot optical cavities containing sodium vapor and operated below the threshold for optical bistability. Novel features are observed in the transmission signals obtained as the laser light frequency is swept through resonance with a sodium D transition. The ring cavity transmission peaks display a broad absorption profile except for the peak which is tuned to the center of the profile which is almost completely transmitted. A similarly tuned cavity transmission peak in the Fabry-Perot \'etalon is split into three, with the central peak being very narrow. A theoretical description for each cavity is developed in terms of a \ensuremath{\Lambda}-type, three-state model for the atomic energy levels associated with the transition. Using parameter values based on the experimental conditions, theoretical transmission signals for the linear cavity are obtained which are in good detailed agreement with the experimental results. For the ring cavity, agreement is also good except for the degree of absorption of the central peak.

DOI
10.1103/physreva.36.1316

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Journal of the Optical Society of America B•May 1, 1988•7 citations
A study is presented of the transmission characteristics of low-finesse ring and Fabry-Perot optical cavities containing sodium vapor and operated below the threshold for optical bistability. Novel features are observed in the transmission signals obtained as the laser light frequency is swept through resonance with a sodium D transition. The ring cavity transmission peaks display a broad absorption profile except for the peak which is tuned to the center of the profile which is almost completely transmitted. A similarly tuned cavity transmission peak in the Fabry-Perot 'etalon is split into three, with the central peak being very narrow. A theoretical description for each cavity is developed in terms of a \ensuremath{\Lambda}-type, three-state model for the atomic energy levels associated with the transition. Using parameter values based on the experimental conditions, theoretical transmission signals for the linear cavity are obtained which are in good detailed agreement with the experimental results. For the ring cavity, agreement is also good except for the degree of absorption of the central peak.
Experiments were performed on a bistable system consisting of a low finesse cavity and sodium atoms as the nonlinear medium. The atoms were excited by a dye laser system tuned to the D lines. Both ring and Fabry-Perot configurations were employed, and steady-state as well as transient behaviour was investigated. Flat mirrors of approximately 93% reflectivity were used in all experiments. With sodium vapour as the medium, experiments were performed in steady state, and a marked difference was observed in the behaviour of the Fabry-Perot cavity as compared to the ring set-up. This discrepancy could be explained when the sodium transition was modelled as a three - level lambda -type system, where the Doppler width is of the same order of magnitude as the ground state splitting. In this case the atoms with a Doppler shift close to half the ground state splitting have a major influence on the macroscopic refractive index. Extensive computer simulations were performed using this three -level model, and good qualitative agreement between experiment and theory was obtained for both types of cavity. A vacuum system containing a multiple atomic beam apparatus was constructed in order to reduce the Doppler width. Both the ring and the Fabry-Perot configuration could be set up inside the vacuum chamber.. The steady-state experiments displayed bistability when the laser intensity, laser frequency or cavity frequency were cycled. At higher atomic densities the system showed instabilities and multiple switching.
We report experimental observations of dispersive- and absorptive-optical bistability due to saturation of the D1{D}_{1}D1​ line of atomic sodium in a tight-focused Fabry-Perot cavity. Under the conditions of large optical power broadening and substantial collisional broadening by argon buffer gas used for part of the data, the sodium very nearly behaves as a two-level homogeneously broadened absorber. It thus yields a test of the two-level mean-field optical-bistability model. That model, including homogeneous broadening, fails to account quantitatively for the power levels and power dependencies of the cavity transmission. In particular, this model predicts too rapid an onset of atomic saturation with cavity power. In contrast, predictions of a two-level Gaussian-field optical-bistability model for the dependence of transmitted power as a function of laser power and frequency are confirmed by the experimental data. However, there is a remaining discrepancy in the absolute value of the cavity power.
A bistable system consisting of an optical cavity with a medium of sodium atomic beams has been subjected to square pulses of light resonant with a D transition. The lifetimes of the field in the cavity and of the atomic medium are approximately equal. The system transmission data recorded has been compared with simulated data calculated from a theoretical model which treats the atomic energy configuration associated with the D lines as a three-level, lambda-type. Good qualitative agreement is obtained showing the system switching on to the high transmission branch. In particular, as the intensity of the input pulse ends, from the high intensity side, to the low to high branch transition threshold, switching is delayed by a time which is more than one order of magnitude longer than the field and atomic lifetimes.
Abstract We report on the observation of a novel manifestation of saturation-induced optical bistability in a resonantly pumped optical ring cavity interacting strongly with a cloud of atoms via a narrow atomic transition. The bistability emerges, above a critical pump rate, as an additional peak in the cavity’s normal mode spectrum close to atomic resonance. This third transmission peak is usually suppressed due to strong resonant absorption, but in our experiment it is visible because of the linewidth of the atomic transition being much smaller than that of the cavity, which sets the experiment into the bad-cavity regime. Relying on complete saturation of the transition, this bistability has a quantum origin and cannot be mimicked by a classical material presenting a nonlinear refraction index. The appearance of the central peak in addition to the normal modes is predicted by a semi-classical model derived from the Tavis–Cummings Hamiltonian from which we derive a bistability phase diagram that connects our observations with former work on optical bistability in the good cavity regime. The phase diagram reveals several so far unexplored bistable phases.
We report on the observation of a novel manifestation of saturation-induced optical bistability in a resonantly pumped optical ring cavity interacting strongly with a cloud of atoms via a narrow atomic transition. The bistability emerges, above a critical pump rate, as an additional peak in the cavity's normal mode spectrum close to atomic resonance. This third transmission peak is usually suppressed due to strong resonant absorption, but in our experiment it is visible because of the linewidth of the atomic transition being much smaller than that of the cavity, which sets the experiment into the bad-cavity regime. Relying on complete saturation of the transition, this bistability has a quantum origin and cannot be mimicked by a classical material presenting a nonlinear refraction index. The appearance of the central peak in addition to the normal modes is predicted by a semi-classical model derived from the Tavis-Cummings Hamiltonian from which we derive a bistability phase diagram that connects our observations with former work on optical bistability in the good cavity regime. The phase diagram reveals several so far unexplored bistable phases.
We report on the static and dynamic behavior of the intensity and polarization of the light transmitted by a Fabry–Perot cavity filled with sodium vapor without a buffer gas. The light beam is resonant with the D1 transition, and the behavior can be traced back to the simultaneous presence of Zeeman pumping and hyperfine pumping in the sodium ground state, combined with velocity-selective hole-burning effects. Together with optical bistability, tristability, and pitchfork bifurcation, the system displays intrinsic oscillations in the absence of a magnetic field. We discuss the features of these phenomena, particularly the appearance of Hopf bifurcations, and the ways they are affected by the experimental control parameters. We also report evidence of period doubling and of more-complex dynamics in the presence of a magnetic field.