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Physical Review A

Theory of two-photon optical tristability

J.A. Hermann, Daniel F. Walls

Published Oct 1, 1982• 11 citations
Publisher

Abstract

An intracavity two-photon absorber interacting with two coherently driven cavity modes is studied. The possible stable output configurations of the cavity-mode amplitudes are determined for both the absorptive and dispersive cases. Under certain conditions this system is shown to display optical bi- and tristability.
DOI
10.1103/physreva.26.2085

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The analysis presented in part I of this paper is applied to the two-photon interaction of a cavity field mode with N three-level atoms in a Lambda configuration instead. Reduction of the three-level two-photon model to an effective two-level two-photon model leads to a given effective interaction Hamiltonian, which incorporates the optical Stark effect. Using the technique developed by Collett, Cardinear, Collett and Walls, the authors calculate the squeezing spectra for the output field for different Stark shift in the good cavity limit. For the same driving field strength, the inclusion of Stark shift changes the transmission strength.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 28, 1992•0 citations
We consider an intracavity nonlinear medium interacting with two modes of the electromagnetic field via a two-photon process. The cavity is coherently driven at the frequencies of the two modes. We consider as the intracavity medium (a) a two-photon absorber, and (b) NNN three-level atoms. These systems display a new class of bifurcations, and, in the case of the two-photon absorber, optical tristability is possible.
The theory of the optical multistability by two-photon resonant interaction is investigated. The nonlinear medium inside a Fabry-Perot cavity is in two-photon resonance with the laser beam. The two-photon equation of state including dynamical Stark shift and relaxation parameters is obtained and studied under mean-field approximation. The equations for both Fabry-Perot cavity and ring cavity take basically the same form. The physics mechanisms resulting in optical multistability are also studied. It has been shown that the combined effects of Kerr switching and saturation absorption switching can lead to two-photon optical double-bistability, tristability as well as bistability. Furthermore, the criterion conditions under which double-bistability or tristability can occur are given and discussed. Finally, the phase-conjugated reflectivity by two-photon four-wave mixing is also shown to exhibit multistability as well as hysteresis.
We consider a new class of bifurcations that may arise in multiphoton processes inside a coherently driven optical cavity involving more than one mode of the radiation field. For a non-saturable, non-linear medium, a single bifurcation point exists where the symmetric solution bifurcates into a number of non-symmetric solutions. The nature of the bifurcation ranges from a simple pitchfork bifurcation, in the case of four-wave mixing, to more complicated phenomena in higher-order processes. A saturable non-linear medium exhibits similar behaviour for low-input intensities; however, as the input intensity is increased the medium saturates, and at a second bifurcation point the symmetric branch regains its stability. The presence of fluctuations assures the accessibility of the symmetric branch. Thus, for example, for a two-photon absorbing medium we have the possibility of optical tristability involving one symmetric solution and two non-symmetric solutions.
The analysis presented in part I of this paper is applied to the two-photon interaction of a cavity field mode with N three-level atoms in a Lambda configuration instead. Reduction of the three-level two-photon model to an effective two-level two-photon model leads to a given effective interaction Hamiltonian, which incorporates the optical Stark effect. Using the technique developed by Collett, Cardinear, Collett and Walls, the authors calculate the squeezing spectra for the output field for different Stark shift in the good cavity limit. For the same driving field strength, the inclusion of Stark shift changes the transmission strength.