We consider nonlinear dynamics of a system of interacting photons and excitons driven by a resonantly exciting light field. Using the linear stability analysis for nonlinear coupled equations of photon and exciton operators we investigated that, besides the usual unstable domain which is a negative slope branch, there are other unstable ones in the leftmost and rightmost sides of the lower and upper branches of the frequency-density bistable curves. Numerical study shows that the system has very rich information on the instability nature and a self-oscillation process leading to chaos can occur in these unstable domains.
We consider nonlinear dynamics of a system of interacting photons and excitons driven by a resonantly exciting light field. Using the linear stability analysis for nonlinear coupled equations of photon and exciton operators we investigated that, besides the usual unstable domain which is a negative slope branch, there are other unstable ones in the leftmost and rightmost sides of the lower and upper branches of the frequency-density bistable curves. Numerical study shows that the system has very rich information on the instability nature and a self-oscillation process leading to chaos can occur in these unstable domains.
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
The dynamical behavior of counterpropagating light waves interacting with a nonlinear medium is studied numerically. It is found that the wave and the medium form a system that becomes unstable under certain conditions and exhibits self-oscillation. Because the interacting medium is modeled by an ensemble of two-level systems, we recognize the self-oscillation frequency as the Rabi-frequency of the constituent systems. The physical mechanisms responsible for this self-oscillation are the gain and the distributed feedback of the combined lightwave-medium system. When the environment changes, in particular when the intensity is increased, this system becomes more unstable and we find that the oscillation exhibits more complex behavior, including quasi-periodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are also calculated. A physical interpretation of the quasiperiodic motion is given by an exact calculation of the absorption spectrum of our two-level medium. The negative absorption (gain) peaks are found at the frequencies of the quasi-periodic motions, thus implying that the gain of the combined light-medium system is responsible at least in part for the observed complex behavior. In addition, we investigate the stability of the propagating plane wave when a transverse wave is added to the system as a perturbation. Instabilities are analyzed by linearizing the nonlinear equations which model the lightwave-medium system. The results show that the instability is highly-correlated with the four-wave mixing phase conjugation.
The Hurwitz criteria are used for a stability analysis of the steady state excitonic optical bistability curves in a semiconductor pumped by an external 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.
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.
We study a new class of nonlinear cooperative phenomena that occur when light propagates in direct-gap semiconductors. The nonlinearity here is due to a process, first discussed by A. L. Ivanov, L. V. Keldysh, and V. V. Panashchenko, in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. For the geometry of a ring cavity, we derive a system of nonlinear differential equations describing the dynamical evolution of coherent excitons, photons, and biexcitons. For the time-independent case we arrive at the equation of state of optical bistability theory, and this equation is found to differ considerably from the equations of state in the two-level atom model and in the exciton region of the spectrum. We examine the stability of the steady states and determine the switchover times between the optical bistability branches. We also show that in the unstable sections of the equation of state, nonlinear periodic and chaotic self-pulsations may arise, with limit cycles and strange attractors being created in the phase space of the system. The scenario for the transition to the dynamical chaos mode is found. A computer experiment is used to study the dynamic optical bistability. Finally, we discuss the possibility of detecting these phenomena in experiments.
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.