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IEEE Journal of Quantum Electronics

Two-photon optical bistability in polar molecules: vibrational coupling effects

M. A. Antón, Isabel Gonzalo

Published Jun 1, 1995• 12 citations
Publisher

Abstract

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.>

DOI
10.1109/3.387047

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Motivation. Polyatomic molecules can be described by a two–level system represented by two crossed harmonic potential curves (including vibrational levels) in order to study their nonlinear signal response. The variation of the coupling parameter has an important influence on the behavior of the dipole moments and, consequently, on the polarization on the new coupled–state basis. Method. The calculation method employed is based on the Liouville formalism for the density matrix, where the conventional optical Bloch equations are solved in Fourier space to obtain the density matrix elements associated to the polarization of the system. Changes in the coupling parameters V0 (energetic difference between the minima of the potential curves), S (height to which the vibronic coupling occurs) and v (coupling parameter) produce modifications in the behavior of the dipole moments and Polarization on the coupled system. In this communication, two studies are presented: (a) variation of the parameters S and v, while keeping V0 constant and, (b) variation of S and V0, while keeping v constant. In order to study the effects of these changes, the rotating–wave approximation is neglected, which permits us to analyze the processes that occur out of the resonance region. Moreover, the permanent dipole moments of the states in the uncoupled basis are included. Results. First case (variation of S and v): an important increment of dipole moments and polarization magnitude values were observed for low values of v and high values of S. Second case (variation of S and V0): an abruptly increment in the polarization magnitude were found at high values of S and low values of V0. Conclusions. The observed changes in the nonlinear response are associated to modifications in the overlap integral and consequently to the dipole moments of the states in the new coupled basis.

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Zeeman Coherence Effects in Absorptive Polarization Bistability

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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

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•1 citation
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 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.
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.
Optical bistability (OB) in a unidirectional ring cavity with a three-level Λ-type molecular system with nonzero permanent dipole moments is discussed. We found that in the (2+2)-transition processes, the permanent dipole moments induced new quantum coherence effects which lead to controlling the OB behavior of the system. Moreover, we showed that the group velocity can be switched from slow to fast or vice versa under specific conditions of difference in permanent dipole moments of the probe transition.
Degenerate four-wave-mixing phase conjugation is analyzed in the case of two-photon transitions between levels having unequal dipole moments. The theoretical treatment is based upon a nonperturbative solution of the density matrix and does not require the rotating-wave approximation. We give an analytical expression for the polarization component oscillating at the field frequency for a medium excited by stationary waves. In the weak-probe-beam limit, the contributions in the direction of the probe and conjugated beams are evaluated. For instance, by using this two-photon process, instead of the usual single-photon one which is independent of the permanent dipole moments even in the strong-field limit, it is shown that lower intensities are sufficient to reach higher reflectivities. The influences of the permanent dipole moments, relaxation rates, and field frequency are also discussed.
Motivation. Polyatomic molecules can be described by a two–level system represented by two crossed harmonic potential curves (including vibrational levels) in order to study their nonlinear signal response. The variation of the coupling parameter has an important influence on the behavior of the dipole moments and, consequently, on the polarization on the new coupled–state basis. Method. The calculation method employed is based on the Liouville formalism for the density matrix, where the conventional optical Bloch equations are solved in Fourier space to obtain the density matrix elements associated to the polarization of the system. Changes in the coupling parameters V0 (energetic difference between the minima of the potential curves), S (height to which the vibronic coupling occurs) and v (coupling parameter) produce modifications in the behavior of the dipole moments and Polarization on the coupled system. In this communication, two studies are presented: (a) variation of the parameters S and v, while keeping V0 constant and, (b) variation of S and V0, while keeping v constant. In order to study the effects of these changes, the rotating–wave approximation is neglected, which permits us to analyze the processes that occur out of the resonance region. Moreover, the permanent dipole moments of the states in the uncoupled basis are included. Results. First case (variation of S and v): an important increment of dipole moments and polarization magnitude values were observed for low values of v and high values of S. Second case (variation of S and V0): an abruptly increment in the polarization magnitude were found at high values of S and low values of V0. Conclusions. The observed changes in the nonlinear response are associated to modifications in the overlap integral and consequently to the dipole moments of the states in the new coupled basis.
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