Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2304.07530 · Physical Review A

Single-photon optical bistability in a small nonlinear cavity

Игорь Евгеньевич Проценко, Alexander V. Uskov

Published Aug 23, 2023• 6 citations
arXivHTMLPDF

Abstract

We theoretically investigated the bistability in a small Fabry-Perot interferometer (FPI) with the optical wavelength size cavity, the nonlinear Kerr medium, and only a few photons, on average, excited by the external quantum field. Analytical expressions for the stationary mean photon number, the bistability domain, the field, and the photon number fluctuation spectra are obtained. Multiple stationary states of the FPI cavity field with different spectra are possible at realistic conditions, for example, in the FPI with the photonic crystal cavity and the semiconductor-doped glass nonlinear medium.

DOI
10.1103/physreva.108.023724

Related papers

Single beam two-photon optical bistability in a submicron size Fabry-Perot cavity

Nitin C. Kothari, T. Kobayashi

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.

IEEE Journal of Quantum Electronics•Apr 1, 1984•29 citations

Theory of two-photon double-beam optical bistability

Govind Prasad Agrawal, Christos Flytzanis

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.

Physical Review A•Dec 1, 1981•18 citations

Bistable transmission by a Fabry—Perot interferometer filled by a medium characterised by active and reactive nonlinearities

Sergey M. Zakharov

A phenomenological approach and the third-order nonlinear optical susceptibility are used in an analysis of the transmission of coherent light through a Fabry—Perot interferometer filled by a medium with active and reactive nonlinearities. The mean-field approximation is used to demonstrate analytically the feasibility of optical bistability. The conditions for appearance of this bistability are discussed.

Quantum Electronics•Jan 31, 1994•2 citations

TWO-PHOTON OPTICAL MULTISTABILITY THEORY

Li Fu-Li, 中国科学技术大学物理系

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.

Acta Physica Sinica•Jan 1, 1983•2 citations

Absorption optical bistability in an interferometer with light-induced relaxation of the nonlinearity

Vladimir Yu. Bazhenov, M. S. Soskin

A theoretical investigation is made of an optical absorption bistability in a Fabry–Perot interferometer filled with a nonlinear medium exhibiting reversible optical bleaching due to interaction with radiations with two different wavelengths. It is shown that the optical feedback efficiency can be enhanced, which makes it possible to reduce significantly the requirements in respect of the level of the residual absorption by the nonlinear medium.

Soviet Journal of Quantum Electronics•Mar 31, 1990•0 citations

Nonlinear All-Photonic Crystal Fabry-Pérot Resonator

Rumen Iliew, F. Lederer, Christoph Etrich +2 more

We study the bistability behavior of the transmitted field in dependence on the pump for an allphotonic crystal Fabry-Pérot resonator with Kerr nonlinearity. Finite-difference time-domain calculations are used to obtain the hysteresis for different detunings.

•Jan 1, 2007•0 citations
We theoretically investigated the bistability in a small Fabry-Perot interferometer (FPI) with the optical wavelength size cavity, the nonlinear Kerr medium, and only a few photons, on average, excited by the external quantum field. Analytical expressions for the stationary mean photon number, the bistability domain, the field, and the photon number fluctuation spectra are obtained. Multiple stationary states of the FPI cavity field with different spectra are possible at realistic conditions, for example, in the FPI with the photonic crystal cavity and the semiconductor-doped glass nonlinear medium.
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.
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.
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.