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Physical Review A

Optical bistability by an atomic vapor in a focusing Fabry-Perot cavity

Weston J. Sandle, Alan C. Gallagher

Published Oct 1, 1981• 53 citations
Publisher

Abstract

We report experimental observations of dispersive- and absorptive-optical bistability due to saturation of the ${D}_{1}$ 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.

DOI
10.1103/physreva.24.2017

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Physical Review A•Sep 1, 1993•19 citations
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 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.
A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.
We report the observation of transverse optical bistability (TOB) in a sodium-filled Fabry-P\'erot resonator, pumped by circularly polarized light, nearly resonant with the D1{\mathit{D}}_{1}D1​ line, in the presence of a buffer gas, for low vapor density. A sequence of circularly symmetric patterns, ascribable to superpositions of resonator modes, is obtained. The appearance of TOB can be explained in terms of a self-induced intensity-dependent lens formed in the medium by the interaction with the laser light. A simple model that considers the transverse diffusion of the atoms inside the cell provides predictions in good qualitative agreement with the observations.
We report on studies on optical bistability from coherently driven $\ensuremath{\Lambda}$-type three-level atoms in a Fabry-Perot resonator. The nonlinear mechanism relies on transverse optical pumping and is due to population trapping in a coherent superposition of the ground-state sublevels. If, under appropriate conditions, a zero-field level-crossing resonance (Hanle resonance) occurs in the atomic system, the optical device is shown to display dispersive or absorptive bistability. Our theoretical studies are based on numerical solutions of the corresponding three-level Bloch equations in the presence of optical feedback. Experiments are performed on the D1{D}_{1}D1​ line in a sodium-filled Fabry-Perot resonator using transverse optical Zeeman pumping of the 2S12^{2}S_{\frac{1}{2}}2S21​​ ground state. The measurements are found to be in fair agreement with the theoretical predictions from our simple model.
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 on instabilities in the transmitted polarization of a laser beam crossing a planar Fabry-P\'erot resonator filled with sodium vapor, at a null magnetic field, when the input field is linearly polarized and tuned near the center of the D1 line. We have measured bifurcation diagrams in the input-power--cavity-detuning parameter space at various angles of incidence. The system shows monostability, bistability, and limit cycles in the transmitted polarization. Oscillations appear only when the angle of incidence is different from zero and the oscillation phase changes with the position on the transverse profile. The observed dynamics is explained by a simplified model which accounts for Zeeman and hyperfine pumpings, focusing and defocusing effects, and atomic motion. By means of this model, we have determined the codimensionality of the system within a theory of the dynamical systems.