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Physics of the Solid State

Optical bistability, switching, and self-pulsing in direct-gap semiconductors upon the binding of two excitons in a biexciton

A. Kh. Rotaru, V. Z. Tronchu

Published Oct 1, 1998• 2 citations
Publisher

Abstract

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.

DOI
10.1134/1.1130624

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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.
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.
A theory is developed for regular and chaotic self fluctuations in crystal CuCl for a ring resonator geometry. A system of nonlinear differential equations is derived for the dynamic evolution of coherent excitons, photons, and biexcitons. It is shown that, in the unstable portions of the optical bistability curves, nonlinear periodic and chaotic self fluctuations can develop with the creation of limit cycles and strange attractors in the phase space of the system. A computer simulation is used to determine the parameters for which reliable switching takes place in the system and the parameter ranges are found within which the system undergoes a transition from strange attractor to limit cycle. The possibility of experimentally observing the phenomena studied here is discussed.
An investigation is reported of static and dynamic optical bistability and optical switching in a system of coherent excitons and biexcitons in semiconductors subject to the exciton-photon interaction and optical conversion of excitons into biexcitons. The Heisenberg equations of motion for excitons and biexcitons and the wave equation for the field are used to derive a system of nonlinear differential equations describing the dynamic evolution of such a system. The equation of state for a theory of optical bistability is derived for the static case. A study is made of the stability of stationary optical bistability states. A computer experiment is used in an investigation of the switching times between the branches
Much attention is being paid of late to the study of cooperative processes in the exciton region of the spectrum. Previously, using generalized Keldysh equations that describe coherent excitons and photons that are weakly nonhomogeneous in space and in time, the theory of optical bistability (OB) was developed in the exciton region of the spectrum, and optical switchover between branches of optical-bistability loop was investigated. The paper presents a theoretical investigation of regular and chaotic self-pulsations in a CuCl crystal with the participation of coherent excitons and biexcitons. We proposed the method of chaotic self-pulsation breakdown in the system of coherent excitons and biexcitons. The method consists in action of external periodical turbulence (Y/spl tilde/=Y+/spl alpha/ sin(/spl omega//spl tau/)) upon a stochastic system. The range of amplitude values and frequencies of an external harmonic pump were found at which the chaotic oscillation regime becomes nonlinear periodic by transformation of strange attractor into a limit cycle.