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Topical Meeting on Optical Bistability (OB)

Zeeman Coherence Effects in Absorptive Polarization Bistability

Govind Prasad Agrawal

Published Jan 1, 1983• 1 citation
Publisher

Abstract

The phenomenon of optical bistability is usually treated within the framework of a single optical mode interacting with a two-level system. Recently, a number of authors1-5 have considered the two-mode case where the mode coupling gives rise to new interesting features such as optical tristability.2 In a specific case of particular interest, the coupling between orthogonally circular polarized modes arises from a two-photon resonance of the Zeeman sublevels.2,5 Bistability or tristability is then observed in the polarization characteristics of a single optical beam. Although Zeeman coherence effects are expected to play an important role, these have usually been neglected in a theoretical description of polarization bistability.2,4

DOI
10.1364/obi.1983.thb13

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The phenomenon of optical bistability is usually treated within the framework of a single optical mode interacting with a two-level system. Recently, a number of authors1-5 have considered the two-mode case where the mode coupling gives rise to new interesting features such as optical tristability.2 In a specific case of particular interest, the coupling between orthogonally circular polarized modes arises from a two-photon resonance of the Zeeman sublevels.2,5 Bistability or tristability is then observed in the polarization characteristics of a single optical beam. Although Zeeman coherence effects are expected to play an important role, these have usually been neglected in a theoretical description of polarization bistability.2,4
Since the first observation of optical bistability in 1976 (1), a large number of investigations of this phenomenon have appeared in the literature (2). Of particular theoretical interest has been the bistable system composed of "two-level" atoms within an optical resonator. While the theory in this case is well-advanced, only recently have experimental results been obtained (3,4). The work that we report is for absorptive bistability with an intracavity medium that approximates a collection of two-level atoms.
Single-beam two-photon optical bistability in a two-level system where the levels have unequal electric dipole moments is analyzed theoretically. By means of unitary transformations the system is transformed into a two-level nonpolar system with a field-dependent effective transition dipole moment. Two-photon optical bistability is found to be favored as the difference between the dipole moments grows. When the excited electronic system is coupled to a vibrational normal mode of the nuclei, the susceptibility becomes three-valued and consequently a different type of optical bistability appears, which can coexists with the previous one.>
We study a theoretical model that describes an optically pumped Fabry–Perot cavity filled with sodium vapor as a nonlinear absorptive medium. The nonlinear medium is subjected to a static magnetic field. A difference of population is built up between Zeeman sublevels of the ground state when the pump exceeds a threshold. This gives rise to a nonsymmetrical absorption of the two circularly polarized components of the incident light. The emphasis of this paper is on the derivation of analytic results. We show that the system can exhibit a self-pulsing behavior and that in a suitable domain of parameters the system has two or more steady states. This is known as optical bistability or optical multistability.
A two-photon optical bistability equation is derived for a three-level V-type atom in a cavity. We consider the bistable states of the purely absorptive type and investigate the influence of the phase difference of the two cavity field modes on bistability characteristics due to the nonlinear coupling between atomic transitions and fields. Very different results are found for the three cases of phase difference we considered. The bistability is found to diminish when the two modes are in phase, in contrast to the two-level case. In addition, we also discuss the effect of longitudinal and transverse relaxation times on the bistability and how the bistability operation characteristics of one mode can be controlled by adjusting the other.
Absolute quantitative comparisons between experiment and theory are reported for the steady-state characteristics of optical bistability with two-state atoms in ring and in standing-wave resonators. The case treated here is the absorptive one, with both atoms and cavity resonant with the field. The experiment is designed to realize as closely as possible a standard theoretical model of two-state atoms interacting with a single mode of the electromagnetic field in a resonator and is described in detail. A detailed explanation is also given of the extensions to the standard theory that are needed to account for unavoidable experimental limitations such as transit broadening and the nonideal nature of the resonator. The good agreement observed between experiment and theory provides a foundation for quantitative investigation of nonlinear dynamics and quantum phenomena in this nonequilibrium optical system.
A novel mechanism is proposed for optical bistability by utilizing the effect of interference which occurs when two levels are coupled by a one-photon resonance and by a two-photon resonance. The resulting bistability does not require atomic saturation, so the bistability can be observed at relatively low incident intensities, and the mechanism is essentially Doppler free, since it occurs by a two-photon process involving absorption of counterpropagating beams of the same frequency. A significant feature is that two-photon bistability can be controlled not only by the magnitude of the field of the one-photon resonance but also by its phase, and an oscillation or amplification of the field of the two-photon resonance can be observed under certain conditions by the mechanism of the parametric interaction of the field of the one-photon resonance and the field of the two-photon resonance through a nonlinear medium.