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International Conference on Optoelectronic Science and Engineering '90

Study of switching in dispersive optical bistability

Dejin Yu

Published Dec 4, 2017• 0 citations
Publisher

Abstract

The semiclassical theory is used to study the switching in the dispersive optical bistability. In the mean-field approximation, the equations of OB system are solved numerically. It is shown that the dispersion has remarkable influence on the output intensity and the risetime of switching. In the "bad cavity case', it is more striking. Under the different cavity conditions, the dispersive spectra of switching output are given.

DOI
10.1117/12.2294903

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The semiclassical theory is used to study the switching in the dispersive optical bistability. In the mean-field approximation, the equations of OB system are solved numerically. It is shown that the dispersion has remarkable influence on the output intensity and the risetime of switching. In the "bad cavity case', it is more striking. Under the different cavity conditions, the dispersive spectra of switching output are given.
Long-time behavior of transmitted and reflected field amplitude of optical bistability by a cavity including an absorptive resonant medium from an initial to a final steady state on switching the incident field is investigated by solving numerically the semiclassical dynamical equations without the mean-field approximation. The transmitted field amplitude as a function of time is monotonic as a whole, and an oscillatory character is seen on it in a shorter period. The dynamical character such as the oscillation amplitude and the duration of a whole process depend strongly on two parameters included in the equations.
The problem of dispersive optical bistability has so far been treated only in the mean-field approximation. A rigorous justification of the mean-field theory can only be obtained from exact solutions of the steadystate Maxwell-Bloch equations which retain the spatial dependence of the field. In this paper exact analytic solutions are presented for these equations. The authors demonstrate that the mean-field equation connecting the input and the output fields follows naturally from these solutions in the limits $T\ensuremath{\rightarrow}0$, ${\ensuremath{\delta}}_{F}\ensuremath{\rightarrow}0$, and $\ensuremath{\alpha}L\ensuremath{\rightarrow}0$ for the mirror transmission coefficient, the detuning of the field from the cavity resonance, and the linear absorption, respectively, with $\frac{\ensuremath{\alpha}L}{2T}$ and $\frac{{\ensuremath{\delta}}_{F}L}{2cT}$ remaining finite. The results are illustrated with the help of graphs showing the output versus input intensity for different values of the relevant parameters. The effect of these parameters on the phase shift of the output field is also displayed.
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.
We study the semiclassical mean-field theory of single-mode dispersive optical bistability in the limit of a fully developed hysteresis cycle (i.e., in the limit of large values of the bistability parameter C) and when all decay rates have comparable magnitude. We locate (i) on the upper branch instabilities leading to time periodic regimes, (ii) on the lower branch instabilities leading to a switching before the limit point is reached. None of these instabilities are observed in the case of purely absorptive optical bistability.
Static and dynamic properties of dispersive optical bistability (OB) in semiconductor lasers biased from below to above threshold has been investigated both theoretically and experimentally. The OB result is found to be varied continuously from below to above threshold. Although conventionally the OB switch-off time in dispersive semiconductor laser amplifiers is limited by the effective carrier lifetime, a much faster OB switch-off can be obtained when a laser diode operates well above threshold in the injection-locked condition.>
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.