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Soviet Journal of Quantum Electronics

Spontaneous oscillations, single pulses, and transient processes in multistage interferometers with competing nonlinearities

A V Grigor'yants, Yu. A. Rzhanov, Yu. I. Balkareǐ, Matvey I. Elinson

Published Oct 31, 1987• 2 citations
Publisher

Abstract

A numerical investigation was made of a mathematical model describing the dynamics of a semiconductor Fabry–Perot interferometer with competing carrier-density and thermal mechanisms of nonlinear refraction and with absorption that increases on increase in temperature. The first-ever investigations were made of the following topics: spontaneous oscillations of the transmission near various equilibrium conditions and switching from one limit cycle to another; generation of single pulses in response to weak additional illumination in the case of a monostable optical multivibrator; nonmonotonic transient processes during switching. The proposed model made it possible to study the transition of a dispersive optical bistability to spontaneous oscillations and then to an absorptive bistability (breakdown) as a result of variation of the parameters of the system.

DOI
10.1070/qe1987v017n10abeh010745

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A numerical investigation was made of a mathematical model describing the dynamics of a semiconductor Fabry–Perot interferometer with competing carrier-density and thermal mechanisms of nonlinear refraction and with absorption that increases on increase in temperature. The first-ever investigations were made of the following topics: spontaneous oscillations of the transmission near various equilibrium conditions and switching from one limit cycle to another; generation of single pulses in response to weak additional illumination in the case of a monostable optical multivibrator; nonmonotonic transient processes during switching. The proposed model made it possible to study the transition of a dispersive optical bistability to spontaneous oscillations and then to an absorptive bistability (breakdown) as a result of variation of the parameters of the system.
We have numerically investigated the dynamics of initiation and propagation of traveling pulses (TP) in the semiconductor interferometer with two competing mechanisms of nonlinear refraction, connected with interband free carriers photogeneration and semiconductor heating. The possibility of existence of TP, which represent the novel type of transverse effects in optical bistability, have been predicted in our recent work /1/. TP are realized under pumping intensity close to the threshold of originating of McCall’s type regenerative oscillations (RO) /1,2/, when interferometer responds to a weak additional signal by single optical pulse with standard shape (regime of single-shot multivibrator /1,3/ ). If transverse dimentions of the interferometer are large enough, then under constant plane-wave pumping and additional local lighting the optical- carrier density TP arises. TP has sharp forward and backward fronts and moves across pumping beam with constant velocity due to carrier diffusion. After the passage of traveling pulse the system returns back to initial homogeneous steady state. Changing parameters of the interferometer or pumping intensity, we can obtain TP with increased or decreased transmission (direct or inverted TP), each of them can be initiated by lokal increasing or decreasing of input intensity. If interferometer is pumped by beam with Gaussian profile, the thentral - intensive part of the beam can corresponds to RO while the beam periphery- to the single--shot regime. In this case the central part of the beam serves as a periodic source of TP, moving towards beam periphery. The contraversal situation is possible, when the periphery of Gaussian beam corresponds to the RO, while the central part - to the single-shot regime. In this case TP are periodically spontaneously initiated at the beam periphery and move to the beam center. Two TP annihilate after collision. In the both cases profile of transmitted beam periodically changes. All regimes described above have been found by numerical simulation using interferometer parameters close to InSb /4/.
The dynamic properties of a Fabry–Perot interferometer filled with a material exhibiting second-order dispersive nonlinearity are studied both theoretically and experimentally. The response of the medium is described by an intensity dependent phase constant as derived from self-action effects. Considering two relaxation times, that of the material and that of the cavity, the basic relations for the stability analysis and for the numerical calculations are obtained. Bistability and self-pulsing effects are predicted. Moreover, the transient behavior is characterized by anomalous switching properties like overshoot and alternate switching. The corresponding experiments performed on a nonlinear transmission line resonator confirm the theoretical results. In a final discussion, the relations to the field of nonlinear optics are outlined.
We consider semiconductor Fabry-Perot interferometer (FBI) where interband free carriers photogeneration and heating due to recombination make a different sign contribution to the refractive index and temperature shift of band edge results in induced absorption. Such situation is realized in a number of semiconductors which demonstrate optical bistability (OB). Using the parameters of InSb /1,2/ we have numerically investigated transformation of steady input-output characteristic IO(Iin) under variation of initial detuning δo of FPI. Different δo leads to the following characteristics: dispersive-absorptive hysteresis of "butterfly"-type /3/; "butterfly"-type hysteresis with unstable regions corresponding to McCall’s regenerative oscillations (RO) /4/; single-valued characteristic with region of RO; as well as characteristic containing region of RO and absorptive OB with sharp decreasing of output intensity IO at forward switching. The limits of changing of input intensity Iin, δo and characteristic thermal time are found, where RO and OB of dispersive and absorptive type are exist.
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 noise on an optical bistable system in the vicinity of one of the bifurcation points is investigated by studying the transient response to a step input of light. The experiment is performed under absorptive conditions in a sodium-filled nonlinear Fabry-Perot in the bad cavity limit. Alternatively, a bistable electronic circuit (Schmitt trigger) is shown to exhibit the same type of behavior while admitting more detailed studies. On the monostable side of the bifurcation point, we observe a transient bimodality as well as a shift of the average switching delay to shorter times with increasing noise. Both results are in accord with a recent prediction by Broggi and Lugiato. We also present indications that the average switching time is smoothly connected with the lifetime of the metastable state on the bistable side of the bifurcation point.