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Journal of the Optical Society of America B

Analysis of dispersive and absorptive bistability in a four-level system typical of organic media

Ying Hua Ji, Fucheng Lin, Hua Xia, Michelle Lynn Stone

Published May 1, 1997• 1 citation
Publisher

Abstract

We investigate a general theory of optical bistability for a four-level system with single and triple states. Both absorptive and dispersive mechanisms are included. By solving the stable-state equation of a density matrix and using the mean-field approximation, we derive the state equation of bistability. The bistabilities with dispersion and absorption of single and triplet states, including pure dispersion and pure absorption, are numerically studied. The effects of cooperative parameters, resonant transition detuning, and cavity detuning parameters on bistable behavior are analyzed. We find that the absorption of triplet states is beneficial to dispersive bistability but is detrimental to absorptive bistability. The detuning of the resonant transition between single states is detrimental to bistability, whereas that between triplet states is beneficial to bistability. The structure of four levels with single and triplet states is a typicality of organic media. Our analysis is helpful for research into bistability devices of organic media.

DOI
10.1364/josab.14.001109

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We investigate a general theory of optical bistability for a four-level system with single and triple states. Both absorptive and dispersive mechanisms are included. By solving the stable-state equation of a density matrix and using the mean-field approximation, we derive the state equation of bistability. The bistabilities with dispersion and absorption of single and triplet states, including pure dispersion and pure absorption, are numerically studied. The effects of cooperative parameters, resonant transition detuning, and cavity detuning parameters on bistable behavior are analyzed. We find that the absorption of triplet states is beneficial to dispersive bistability but is detrimental to absorptive bistability. The detuning of the resonant transition between single states is detrimental to bistability, whereas that between triplet states is beneficial to bistability. The structure of four levels with single and triplet states is a typicality of organic media. Our analysis is helpful for research into bistability devices of organic media.
The optical bistability of a four-level system with triplet-state absorption typical of organic media is studied. We derive the state equation of optical bistability with triplet-state absorption. Different bistabilities with resonant absorption or dispersion of the triplet state are numerically discussed. The effects of the cooperativity parameter and the atomic- and cavity-detuning parameters on optical bistable behavior are analyzed. It is found that the hysteresis loops decrease with an increase of both the cooperativity parameter and the atomic-detuning parameter of the triplet state and that under some conditions reverse saturable-absorptive media can display bistability.
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.
The influence of transverse effects on optical bistability in Fabry-Perot cavity filled with saturable absorber was numerically investigated. A simple model of singlet absorption was used on numerically solving the relationships between the input and output light fields. The proposed model corresponds well to organic compounds considered as novel optical materials with third-order optical nonlinearities. The proposed optically bistable systems were demonstrated for two organic dyes of fluorescein and rhodamine 6G dispersed in transparent solid matrices. Their optically bistable behaviour was anticipated considering the homogeneous and Gaussian distribution of light energy in the radial direction. Most notable cases are discussed related to the changes of the Gaussian beam radii, positive feedback conditions in the Fabry-Perot cavity and considering linear and nonlinear absorption parameters of the organic media. The simulation results enabled us to establish numerically thresholds of Fabry-Perot mirror reflectance and Gaussian beam radius for both nonlinear organic materials, above which absorptive optical bistability can occur. The results can be helpful in design of optical switches for all-optical communication networks.
We theoretically analyze the behavior of single optical bistability (OB), double OB, and tristability (OT) in a three-level V-type atomic system confined in a unidirectional optical ring cavity. The physics behind the emergence of various bistable and tristable states, and switching from the absorptive to the dispersive characteristics, are explored. The role of probe- and control-field detunings on the input-output characteristics is probed. Further, it is found that the switching between various bistable phenomena is defined by the ratio between the absolute peak values of the parameters describing dispersion and absorption, respectively. This ratio sets a criterion for obtaining absorptive OB, OT, double OB, and dispersive OB. The role of control-field intensity and detuning as well as the cooperation parameter on the input-output characteristics are explored. Finally, a scheme is discussed to control the width of the middle branch of double OB and OT as well as single OB.
We analyze instabilities in mixed absorptive and dispersive optical bistability in the rate-equation approximation and the mean-field and good-cavity limits. Our starting point is a set of multimode equations derived from the Maxwell-Bloch equations for ring-cavity boundary conditions. We obtain analytic expressions for the instability conditions. In a plane-wave analysis, we find that a portion of the lower transmission branch can be unstable in addition to the upper-branch instability found in purely absorptive bistability. Also, a new disconnected region of instability can exist on the upper branch. Our analysis becomes particularly simple for equal and opposite cavity detunings and we explore this case in detail. We extend our treatment to include a Gaussian transverse intensity profile and show that the instabilities remain in the presence of Gaussian averaging. We also show that many of the results obtained in the rate-equation approximation hold when the atomic linewidth and atomic decay rate are of the same order.