For an optical bistable two-level system in a Fabry-Perot cavity we analyze the dependence of the transmitted field amplitude on three experimental parameters: the frequency of the incident radiation, the transition atomic frequency, and the length of the F.P. cavity. In each case the remaining parameters (including the input amplitude) are assumed to be fixed. Both absorptive and dispersive contributions are included, and in the mean-field approximation a cubic state equation should be solved. An explicit analytical expression for the transmitted intensity as a function of all physical parameters is obtained. Typical results are presented in graphical form. The main characteristic features of the optical hysteresis cycles are described and new possibilities for optical device design are examined. Use of the above explicit solution for stability analyses is briefly discussed.
For an optical bistable two-level system in a Fabry-Perot cavity we analyze the dependence of the transmitted field amplitude on three experimental parameters: the frequency of the incident radiation, the transition atomic frequency, and the length of the F.P. cavity. In each case the remaining parameters (including the input amplitude) are assumed to be fixed. Both absorptive and dispersive contributions are included, and in the mean-field approximation a cubic state equation should be solved. An explicit analytical expression for the transmitted intensity as a function of all physical parameters is obtained. Typical results are presented in graphical form. The main characteristic features of the optical hysteresis cycles are described and new possibilities for optical device design are examined. Use of the above explicit solution for stability analyses is briefly discussed.
A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.
When the output parameter of an optical device could be a multivalued function of the input parameter, this device can be working in an optical bistable status. The most typical optical bistable device is a Fabry–Perot cavity containing a nonlinear optical medium, the refractive index of which depends on the light intensity. Upon the action of an intense input optical beam, the transmitted (or reflected) intensity of this device may exhibit a nonlinear response to the incident light intensity variation and, especially under appropriate working conditions, the characteristic output/input curve may manifest a single (or multiple) hysteresis loop(s). Such type of optical bistable device can be used as an optical differential amplifier, optical switch, optical limiter, optical clipper, optical discriminator, or an optical memory element, depending on the chosen nonlinear medium and operation conditions.
A semiclassical theoretical model is described under the plane-wave and mean-field approximations on the transmission characteristics of a system of two-level atoms with large permanent dipole moments contained in a Fabry-Perot cavity and driven by two coherent two-photon resonant fields. In the steady-state situation, the coupled field equations are solved by eliminating one of the field variables to obtain the state equation. This state equation is numerically analyzed in detail, thus providing the regions on two-dimensional maps corresponding to one, three, and five stationary states of the system. The linear stability analysis is also carried out for the case when the length of the cavity is such that the medium-relaxation times are much shorter than the cavity-photon life times for both the waves. The simple stability criterion that the negative-slope regions of the transmission curves are unstable holds, but only the lowest positive-slope branches show stability in all of the cases we tested numerically.
In this work a theoretical model treating the optical bistability in a two state dissipative atomic medium inside a Fabry-Perot cavity is presented.The model is based on a semiclassical point of view to explain the field-matter interaction.The atoms of the medium are described by the "quantum polarization equation of motion" while the field is described by the "classical Maxwell's field equations".Applying the boundary conditions to the fields inside the Fabry-Perot cavity, the occurrence of optical bistability is deduced between the incident field intensity and both the intracavity and transmitted field intensities.Also the effect of building standing and nonstanding waves inside the cavity on bistability is discussed.
Within the framework of the theories of absorptive bistability recently proposed by various authors, the different sets of coupled differential equations describing the steady-state fields inside the Fabry-Perot cavity are solved analytically. Expressions are obtained for the bistability equation, which links the incident and transmitted fields, for different ranges of the mirror transmission coefficient. Comparison is made with the mean-field theory of Bonifacio and Lugiato. Conditions for stationary points in the bistability curve are derived.
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.