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Acta Physica Sinica

TWO-PHOTON OPTICAL MULTISTABILITY THEORY

Li Fu-Li, 中国科学技术大学物理系

Published Jan 1, 1983• 2 citations

Abstract

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.

DOI: 10.7498/aps.32.71

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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.

Transmission characteristics of a nonlinear Fabry-Perot interferometer with two independent optical beams are considered under steady-state conditions. The sum frequency of two beams is taken to be near a two-photon resonance of the nonlinear medium. Two beams are coupled through the intensity-dependent susceptibility and influence propagation of each other in a mutual way. A set of two coupled-state equations is derived and it incorporates saturated absorption and dispersion as well as the effect of optical Stark shift. The system is found to have as many as seven stationary states, and at most, three are stable among them. The degenerate case of a single beam in two-photon resonance with the medium is also considered with particular emphasis on the effect of the optical Stark shift on optical bistability.

We describe a semiclassical theoretical model on two-photon optical bistability in a nonlinear Fabry-Perot cavity filled with molecules having large permanent dipole moments under the plane wave and mean field approximations. The mathematical analysis follows with the assumption of a two-level system with large permanent dipoles. In the steady state situation, field equation is shown to provide the bistable behavior of the nonlinear cavity when resonant with two-photon excitation under certain conditions. It is shown that for a large difference in permanent dipole moment\mu_{0} = (\mu_{aa}-\mu_{bb})/2between levels|a\rangleand|b\rangle, (\mu_{0}^{2}/|\mu_{ba}|^{2}\gg1, where μbais the transition dipole moment), the two-photon optical bistability can result in a submicron size Fabry-Perot cavity.

We have studied the case of optical multistability in a four-level system interacting with two coherent fields. The system, shown in fig. 1, consists of two pairs of energy levels, 1, 2, and 3, 4, absorption occurs between levels 1- 4 and emission takes place from 3-2. The 'intra-band' transitions, 4-3 and 2- 1 are assumed non-radiative and extremely fast. The system is irradiated by two beams, one tuned to the absorption spectrum, the other to the emission spectrum, in a Fabry-Perot cavity. Solution of the optical Bloch equations following [1] enables us to write the input-output equations, la and lb, in the form where Yi, Xi, are the appropriately scaled input and output fields, Ci the 'bistability' parameter, and Δi, ϕi, the atomic and cavity detuning respectively, of field i.