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Physica Scripta

Optical Nonlinearities and Instabilities in Semiconductors

H. Haug, Stephan W. Koch, Markus Lindberg

Published Jan 1, 1986• 247 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/1986/t13/030

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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.
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
Semiconductors exhibit large optical nonlinearities near the band edge because of resonance enhancement. Optical bistability occurs when the optical nonlinearities are coupled with feedback. In bulk GaAs and GaAs–AlGaAs multiple-quantum-well superlattices, the nonlinearity arising from the presence of the free-exciton resonance has produced room-temperature optical bistability with a few milliwatts of power. The formation of biexcitons in CuCl, the saturation of the bound exciton on CdS, and band-filling effects in InSb, InAs, and HgCdTe lead to observation of bistability in these materials. A bistable etalon can be operated in an optical-gate mode to generate optical analogs of electronic gates such as and, or, and nor. It has been demonstrated that a GaAs optical NOR gate responds in ∼1 psec, using only ≲3 pJ of energy. However, because of the carrier lifetime of a few nanoseconds, the repetition rate of the NOR gate is now limited to a few hundred megahertz.
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.
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.