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Physical Review A

Light-shift-induced level crossing and resonatorless optical bistability in sodium vapor

T. Ackemann, A. Heuer, Yu. A. Logvin, Wulfhard K. Lange

Published Sep 1, 1997• 43 citations
Publisher

Abstract

It is demonstrated experimentally and theoretically that a light-shift-induced level crossing in an oblique magnetic field results in a nonmonotonous dependency of the transmission of a sodium vapor cell on the input power. If feedback by a single plane mirror is added, bistability of the transmission and of the beam profile (resonatorless transverse optical bistability) is observed. The origin of the bistable behavior and the parameter dependencies is explained by the properties of the homogeneous solution. Numerical simulations with a Gaussian incident beam reproduce well the switching behavior of the beam profile found in the experiment.

DOI
10.1103/physreva.56.2321

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It is demonstrated experimentally and theoretically that a light-shift-induced level crossing in an oblique magnetic field results in a nonmonotonous dependency of the transmission of a sodium vapor cell on the input power. If feedback by a single plane mirror is added, bistability of the transmission and of the beam profile (resonatorless transverse optical bistability) is observed. The origin of the bistable behavior and the parameter dependencies is explained by the properties of the homogeneous solution. Numerical simulations with a Gaussian incident beam reproduce well the switching behavior of the beam profile found in the experiment.
We present here instabilities observed in the transverse profile of a continuous-wave light beam that crosses a sample of sodium vapor twice by means of a feedback mirror. The wave front and the intensity of the beam are spatially modulated by the intensity-dependent dispersive and absorptive action of the vapor. Experimental evidence indicates that the vapor acts as a phase-conjugate mirror, thus providing an active cavity when it is coupled with the feedback mirror. The instabilities develop as a consequence of sideband generation at the resonant modes of this cavity. The transverse-mode profiles of these sidebands are analyzed experimentally.
A transverse optical bistability would not occur with a plane-wave input; it is characterized by pronounced changes in transverse profiles, but not in total transmission.1 The systems studied here consist of a single feedback mirror and a nonlinear medium (Na vapor) sufficiently thin that diffraction is negligible during the nonlinear radially dependent phase encoding. With the input focused beyond (before) the Na and the mirror center of curvature on the input (output) side of the Na, self-defocusing (self-focusing) optical bistability is seen--but only when the feedback is nonconcentric, i.e., the feedback beam is displaced off-axis relative to the input beam. If cylindrical lenses are used to form an elongated focus in the Na, bistability is still seen. This suggests that one-transverse-dimension (ID) theories may be adequate to describe the system's steady-state and transient behavior. ID numerical simulations with nonconcentric feedback are under way.
A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input; it is characterized by pronounced changes in transverse profiles, but not in total transmission.1-5 In order to use transverse bistabilities to study instabilities of the type first studied by Ikeda6 for a ring cavity, one needs a medium response time τM less than the round-trip time tR between the medium and the feedback mirror. Here instabilities are studied experimentally using a short length of sodium vapor and a far-field mirror (Fig. 1).7,8 This system has advantages over previous9,10 all-optical passive systems for studying instabilities: its input is cw, permitting the study of slowly evolving waveforms; it has little sensitivity to laser frequency shifts, because it has no cavity; its optical nonlinearity arises from a vapor of one-electron atoms, giving hope for a detailed quantitative comparison of experiments and calculations.
This paper gives a detailed description of the plane-wave Gaussian models of optical bistability and of the experimental investigations of the single-mode instability induced on a beam of sodium atoms in a cavity by an external driving field. Our goal is to provide a careful comparison of the theoretical and experimental results. We focus on the shape of the instability domain, the nature and behavior of the spontaneous output oscillations produced by the instability, and their frequency dependence on the control parameters. We carry out this comparison using both the plane-wave and Gaussian models. Our analysis shows that the latter is in good quantitative agreement with the experimental results. We investigate in detail the main assumption of the Gaussian model, namely, that the internal cavity field retains the same radial profile as the input field.
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.
The absorption profiles of left-hand and right-hand circularly polarized laser light propagating through sodium vapor are asymmetric and considerably frequency shifted if small static magnetic fields are present. Using an analytical model we show how optical pumping ``enhances'' the laser-induced light shift from the kilohertz to the gigahertz range. We compare the analytical results with experimental data obtained from the homogeneously broadened Na D1{\mathit{D}}_{1}D1​ transition.