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NASA STI/Recon Technical Report N

Excitonic Bistabilities, Instabilities and Chaos in Laser-pumped Semiconductors

Nguyen Ba An, Dan Trung Nguyen, Hoang Xuan Nguten

Published Jul 1, 1992• 0 citations
OpenAlex

Abstract

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

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Vasile Tronciu, Anatol Rotaru

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physica status solidi (b)•Apr 1, 1999•0 citations
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 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.
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.
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.
The main mechanisms for the observed large optical nonlinearities in semiconductors are briefly discussed and illustrated for the example of the exciton ionization by plasma screening. These nonlinearities cause various types of optical bistability, either of intrinsic nature or evoked by an additional resonator feedback. Under certain operation conditions also higher instabilities such as oscillations and chaos can be obtained. As an example, the self-pulsing of an induced absorber in a ring cavity is treated. The resulting locked oscillations are shown to follow a Farey-tree scenarium.
The theory of dynamic optical bistability and self-pulsations in condensed media is elaborated. The nonlinearity is due to a process in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. A computer experiment is used to study the switching times between the optical bistability branches. The scenario for the transition to the dynamical chaos mode is found. The action of external periodical force upon the system is investigated and the range of amplitude values and frequencies of external harmonic pump were found at which the chaotic regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. Finally, we discuss the possibility of detecting these phenomena in experiments.
The theory of dynamic optical bistability and self-pulsations in condensed media is elaborated. The nonlinearity is due to a process in which two excitons are bound into a biexciton by virtue of their Coulomb interaction. A computer experiment is used to study the switching times between the optical bistability branches. The scenario for the transition to the dynamical chaos mode is found. The action of external periodical force upon the system is investigated and the range of amplitude values and frequencies of external harmonic pump were found at which the chaotic regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle. Finally, we discuss the possibility of detecting these phenomena in experiments.