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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nonlinear dynamics and chaos of excitonic optical bistability system

Tingwan Wu, Fa Ou, Fu‐Gen Wu

Published Oct 28, 1992• 0 citations
Publisher

Abstract

Some results of probing to the common properties, including bistability, transient behavior, and instability of the excitonic optical nonlinear dynamic systems, such as interaction of light field with carrier in semiconductor, or anharmonic vibration of lattice in ionic crystal, are presented. Since the excitonic optical bistability (EOB) was found, it has garnered much attention for its advantage in properties and application prospects. Some models have been proposed for different kinds of OB. However, so far as we know, there has been relatively less concern given to the common dynamic characteristics of these systems, which are significant for applications. On the other hand, the instability of the EOB device certainly has the same importance, the study for which is not ample yet. In this paper we study the increasing absorptive OB, the behaviors of responding to inject signal, also the self-pulsing and chaotic phenomena in the excitonic OB systems.

DOI
10.1117/12.130432

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Some results of probing to the common properties, including bistability, transient behavior, and instability of the excitonic optical nonlinear dynamic systems, such as interaction of light field with carrier in semiconductor, or anharmonic vibration of lattice in ionic crystal, are presented. Since the excitonic optical bistability (EOB) was found, it has garnered much attention for its advantage in properties and application prospects. Some models have been proposed for different kinds of OB. However, so far as we know, there has been relatively less concern given to the common dynamic characteristics of these systems, which are significant for applications. On the other hand, the instability of the EOB device certainly has the same importance, the study for which is not ample yet. In this paper we study the increasing absorptive OB, the behaviors of responding to inject signal, also the self-pulsing and chaotic phenomena in the excitonic OB systems.
In this paper, some new results of the study on the bistability and the instability of semiconductor optical amplifier are presented, which may be expected to be available to a class of excitonic optical bistable and amplifying systems. For these systems, both saturation and increasing absorptive bistability will product, depending on the competition among the interactions in the medium, especially the nonlinear couplings, and the lasing conditions. Particularly, the output curve appears a novel feature of optical hysteresis, with amplifying effect as well. On the other hand, the instability of the stationary states is investigated by linear stability analyzing. Some new phenomena of 'critical slowing down' are discovered near the relevant critical points, in the dynamic responding course.
Turbulence and chaos in a semiconductor crystal? These are just some of the intriguing predictions of nonlinear optics with coherent excitons. In this chapter we discuss some aspects of nonlinear coherent optics with the participation of the excitons, photons, and biexcitons. As in many nonlinear systems, these effects arise because of feedback mechanisms, i.e., the light impinging on the system affects the electronic states, which in turn affect the dielectric constant of the medium through which the light passes. These effects are closely related to the phenomena of self-organization [1-8] and optical bistability [7-10] and self-pulsations and the appearance of chaos [2-6]. The cooperative nonlinear coherent processes in optical systems have recently attracted much attention [7-20]. These investigations have stimulated the development of new mathematical methods [21-31] and have opened up possibilities for many new applications. The theoretical and the experimental investigations in these directions give rise to the theory of solitons [32∧2] and lead to the new developments in the optics of ultrashort pulses [43-58]. Ultrafast phenomena such as self-induced transparency and nutation are related to the propagation of solitons and pulse trains, whereas the transient stages of the ultrashort lightpulse penetration in the media are described by area theorems. These coherent ultrafast phenomena typically take place during intervals of time less than the relaxation time, i.e., femtoseconds to picoseconds in typical solids. Collisions and incoherent scattering processes destroy the coherent evolution of the excited particles. But if coherent macroscopic states of the excitons, photons, and biexcitons have been formed because of spontaneous or induced BEC, in this case one can consider their time evolution over intervals of time much greater than the relaxation time.
This paper presents an approach to the intracavity interaction of electromagnetic waves with anharmonic lattice vibrations of ionic crystals. The nonlinear lattice dynamics and an expression for the nonlinear polarization are derived in terms of optical phonon modes. In the rotating-wave approximation the total coherent Hamiltonian of the system is derived. Using the corresponding equation of steady states, the increasing absorption optical bistability (IAOB), as a nonlinear effect, is demonstrated. The results show that optical nonlinearities due to the interaction of photons with various elementary excitations of bosonic type such as phonons and excitons may be the origin of IAOB, which is consistent with our previous works.
Abstract The Hurwitz criteria are used for a stability analysis of the steady state excitonic optical bistability curves in a semiconductor pumped by an exter- nal laser resonant with the exciton level. Besides the middle branch of the bistability curves which is unstable in the sense of the linear stability theory, we have found other domains of instability in the upper and lower branches of the steady state curves. Numerical results show that a possible route to chaos in the photon-exciton system is period-doubling self- oscillation process. The influence of the presence of free carriers that coexist with the excitons is also discussed. 1. Introduction Stability and instability are two sides of matter which are by no means independent but closely related. For example, in case the system state curve develops three branches, it is the unstable behaviour of the middle branch that causes a jumping up or down to the upper or lower branches thus generating the effect of bistability. Bistable devices them- selves may in turn manifest a rich variety of instabilities leading to spontaneous pulsations of both regular and irregular nature. Since 1987 a fully new direction of research dealing with optical self-pulsing and chaos has been orient- ed by the original works of McCall [l], Bonifacio and Lugiato
Physical reasons for the development of spatial and temporal instabilities realizing in optical bistability (OB) cavity- free systems are analyzed. It is shown that there are certain types of instability. We describe diffraction instability of light beams due to its propagation through a boundary on a high absorption domain. We consider instability generated by nonlinear dependence of a relaxation time of excited states of atoms (molecules) on vibration temperature or on room temperature under the condition of presence (or absence) of nonlinear absorption. We investigate instability due to an influence of laser- induced electric field and instability caused by the delay in a scheme with additional lateral feedback and instability in a scheme with mirror having a hole at its axis caused by dynamical lenses.
A system of nonlinear differential equations describing the dynamic evolution of coherent excitons, photons, and biexcitons is derived in the geometry of a ring cavity. Nonlinearity is caused by the direct binding of two excitons in a biexciton as a result of their Coulomb interaction, which was first predicted by Ivanov, Keldysh, and Panashchenko. The equation of state of the theory of optical bistability is obtained for the stationary case. The stability of stationary states is studied, and the switching times between the branches of the optical bistability curve are determined. It is shown that the appearance of nonlinear periodic and chaotic self-pulsations with the creation of a system of limit cycles and strange attractors in phase space is possible in the unstable portions of the equation of state. Dynamic optical bistability is studied, and the possibility of experimentally detecting the phenomena studied is discussed.