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Topical Meeting on Optical Bistability (OB)

Transverse Traveling Pulses in Bistable Interferometers with Competing Nonlinearities

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

Published Jan 1, 1988• 0 citations
Publisher

Abstract

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/.

DOI
10.1364/obi.1988.thd.3

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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/.
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 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 multiple interferometer is proposed and stimulated Raman radiation, stimulated Mandel’stam–Brillouin radiation, and Cerenkov-type optical parametric oscillation are considered in this interferometer, which is excited by an external light beam. An extremely low threshold intensity of the exciting beam is noted. Optical bistability and hysteresis, self-pulsing of the radiation intensities, amplification of amplitude-phase deviations in the incident pumping beam, limitation of the intensity of the beam transmitted by the interferometer, and nonlinear reflection of the beam from the multiple interferometer are predicted and discussed. It is also noted that the threshold for generation of the second Stokes component of stimulated Raman radiation and stimulated Mandel’stam–Brillouin radiation under the conditions discussed is usually not achieved, even for high excess of the exciting beam intensity over the threshold for generation of the first Stokes component.
A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input, i.e., it depends crucially upon the radial variations in the input. Such bistabilities are characterized by much more pronounced changes in transverse profiles than in total transmission. An optical cavity is not required, making such systems good candidates for continuous wave studies of delayed-feedback instabilities which require a round-trip time longer than the medium response time. Trapping bistability and diffraction-free-encoding bistability are two limiting cases of transverse optical bistabilities. Trapping bistability occurs only for a long self-focusing nonlinear medium and arises from self-trapping of a single beam with a single feedback mirror or from cross trapping of two counterpropagating beams. In the diffraction-free-encoding case, diffraction is negligible through the portion of the nonlinear medium performing the encoding, but it is significant through any remaining medium and in the free-space propagation to the mirror and back. This paper is organized as follows: The physics of transverse optical bistabilities is summarized in Section I. Theoretical models are presented in Section II. A thin-sample-encoding (TSE) rings model is defined and shown not only to predict transverse bistability but also to account for the interference rings observed to accompany TSE bistability; it also yields delayed-feedback instabilities with a rich bifurcation sequence. Transverse bistability using a short length of sodium vapor is reported under TSE and DFE conditions in Section III. Recently it was discovered that TSE bistability has been seen only when the feedback beam is displaced from the input by about one beam diameter at the sodium. It remains to be determined just how much the nonconcentric feedback assists the concentric bistability predicted by the TSE rings model. A delayed-feedback instability with a period of twice the round-trip time is also seen.
Of the Lorenz-type instabilities expected in optical systems, the single-mode instability in optical bistability has been the subject of detailed theoretical and experimental work by our groups. A treatment employing the plane-wave and mean-field limits of the Maxwell-Bloch equations predicts a rich variety of higher-order bifurcations including period doublings and intermittency.1 An extension of this work to include the transverse dependence of the intracavity field reveals no significant qualitative differences between the plane-wave theory and the Gaussian beam theory as regards the stability boundaries obtained from a linearized analysis.2 The instability persists in the presence of a Gaussian transverse profile and the boundaries are not radically modified compared with those obtained from the plane-wave theory. However, numerical integration of the Maxwell-Bloch equations in the single transverse mode approximation does not show the wealth of higher-order dynamic states present in the plane-wave case. An experimental investigation of optical bistability for two-level atoms in a single transverse, single longitudinal mode cavity exhibits limit cycle oscillation with stability boundaries that agree well with the boundaries obtained from the work in Ref. 2. However, for the range of values C < 300, |Δ| < 5, |θ| < 50, X ~ 102, the experimental results do not show the diversity of higher dynamic states expected from the plane-wave theory, in agreement with our numerical results. In addition the measurements support the existence of a single transverse mode oscillation. The sum of our theoretical and experimental work provides a quantitative statement for the role of the transverse effects in optical instabilities.
The possibility of formation of a basic (stationary) and an additional (moving) high-absorption domain in an optically bistable system, based on high absorption, is demonstrated. A semiconductor with the absorption coefficient dependent on the concentration of free charge carriers in the conduction band is considered as a nonlinear medium. Under certain conditions, an optical beam passing through the stationary high-absorption domain acquires an annular profile and, after traveling a certain distance, transforms into a Gaussian beam with an intensity on the axis sufficient to switch the medium-beam system to the upper state. This moving domain periodically disappears and reappears due to diffusion processes.