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Natl. Bur. Stand. (U.S.), Spec. Publ.; (United States)

Nonlinear optical susceptibilities of semiconductors and optical bistability

H. M. Gibbs, S. L. McCall, Thirumalai Venkatesan, A. Passner, Arthur C. Gossard, W. Wiegmann

Published May 1, 1980• 1 citation
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Abstract

The transmission of 500 ns pulses through GaAs-AlGaAs heterostructures has been studied as a function of light intensity and wavelength. The intrinsic exciton absorption can be modeled by the sum of a small unsaturable background and a dominant term which saturates as a Bloch resonance. Corrections for the Gaussian transverse spatial profile and finite optical thickness lead to 150 W/cm/sup 2/ for the uniform-plane-wave saturation intensity for an optically thin GaAs exciton transition. The nearly Bloch-like saturation curve does not imply that the free exciton transition is a simple saturable two-level system, but does suggest that it saturates as a homogeneously broadened line.

Related papers

Mechanisms of the low density nonlinear optical response of excitons in gallium arsenide and the study of exciton transport.

A. C. Schaefer

The study of the nonlinear optical response of excitons in semiconductors is important for both scientific and technological applications. Although the nonlinear optical properties of bulk semiconductors and heterostructures have been studied for almost three decades, with most of the research focusing on heterostructures, the mechanisms leading to the nonlinearities in these systems are not completely understood. Determining these mechanisms and developing a theoretical picture which describes the most dominant effects remains a challenge and an active area of study. Although optical interactions in semiconductors is a genuine many-body problem, a description of this system similar to the optical Bloch equations used in atomic studies has shown some success, but more work is needed to make this model complete. Experimental work, particularly in the bulk system uncomplicated by the interface disorder present in heterostructures, will provide the guidance to extend this formalism. In this dissertation, the frequency domain resonant nonlinear optical response of excitons in bulk gallium arsenide at low density is studied to gain insight into the dominant mechanisms leading to the response, as well as the dynamics of the nominally three-dimensional excitonic system. Specifically, the nonlinear response was probed with differential transmission (DT) and four-wave mixing (FWM) experiments, which measure to lowest order the third-order susceptibility, $\chi\sp{(3)}.$ Using these various tools, three specific areas were studied and the results will be presented. First, the role of the biexciton, the state of two bound excitons, in determining the bulk nonlinear response was explored. The observation of a red-shifted nonlinear resonance suggests the importance of this state at moderate densities. Second, a new response, characterized by a resonant increase in exciton absorption induced by optical pumping with initial superlinear growth and a transition to behavior described by simple line broadening with increased pump intensity, was studied in detail. A model considering increased polariton absorption with increased exciton-exciton interactions explains these effects. Finally, nonlinear optical spectroscopy was used to study exciton transport, where near-ballistic behavior was revealed. The effect of exciton transport, thermalization and radiative recombination on the nonlinear optical response was explored.

•Jan 1, 1996•0 citations

Origin of the nonlinear index saturation in the band tail absorption region of GaAs/AlGaAs multiple quantum wells

Bruno G. Sfez, J. L. Oudar, Robert Kuszelewicz +1 more

The saturation behavior of the nonlinear index δnNL in the band tail of GaAs/AlGaAs multiple quantum wells is experimentally studied in quasi-steady state and in a low absorption region (below 300 cm−1), where dispersive optical bistability is observed. Measurements at different detunings from the exciton resonance allow us to study the absorption dependence of the saturation parameters. The saturation intensity IS is found inversely proportional to the linear absorption coefficient, while the saturating nonlinear index δnS is approximately constant. This evidences that the nonlinear index saturation is due to a saturation of the carrier density versus light intensity, due to the saturation of the band tail absorption itself.

Applied Physics Letters•Mar 9, 1992•10 citations

Contributions to optical absorption in GaAs/AlGaAs multiple quantum wells

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An examination of the contribution of excitons, compared to the continuum states, to the optical properties of GaAs/AlGaAs multiple quantum wells illuminates the mechanisms underlying nonlinear absorption and nonlinear refraction and yields information which is useful for optimizing devices which incorporate these materials. We have measured the absorption as a function of intensity at three different wavelengths—above the band edge, on the excitonic resonance, and far below the band edge—to separate the effects. We find that different well thicknesses have different saturation intensities both for excitonic and continuum absorption.

Annual Meeting Optical Society of America•Jan 1, 1987•1 citation

Optical nonlinearity, bistability, and signal processing in semiconductors

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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.

Journal of the Optical Society of America B•Jul 1, 1985•69 citations

Optical Bistability in Semiconductors

Chi C. Sung, C. M. Bowden

There are two different models to explain the observed optical bistability (OB) in GaAs. Haken and Goll1 use the saturation of the two-level (electron and hole) atoms as the mechanism of OB, whereas the Stark shift of excitons is the dominant factor in the work by Koch and Haug.2 We analyze both models, including the local field effect.3 It is shown that the validity of each model depends very much upon the parameters involved. We also give a similar analysis for CuCℓ where the biexcitons are important. In contrast to the earlier work by Abram and Maruani,4 we find by careful analysis, including the origin of the background dielectric constant, that the local field correction is not important in this case. The contribution of the exciton and biexciton interaction, however, can be important and should be included in the calculation of OB given by Haug.5 The changes in the numerical results of Ref. 5, by including the exciton-biexciton interaction and the local field correction are to be represented.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•1 citation

Self-Induced Transmission on a Free Exciton Resonance in a Semiconductor

Harald W. Giessen, A. Knorr, S. Haas +6 more

We observe coherent long-distance propagation of an optical pulse in resonance with the free exciton at high light intensities in an optically thick semiconductor. The experiments show pulse reshaping, pulse breakup, and a high degree of transmission. Microscopic calculations using the semiconductor Maxwell-Bloch equations yield good agreement with the experimental data.

Physical Review Letters•Nov 9, 1998•107 citations
The transmission of 500 ns pulses through GaAs-AlGaAs heterostructures has been studied as a function of light intensity and wavelength. The intrinsic exciton absorption can be modeled by the sum of a small unsaturable background and a dominant term which saturates as a Bloch resonance. Corrections for the Gaussian transverse spatial profile and finite optical thickness lead to 150 W/cm/sup 2/ for the uniform-plane-wave saturation intensity for an optically thin GaAs exciton transition. The nearly Bloch-like saturation curve does not imply that the free exciton transition is a simple saturable two-level system, but does suggest that it saturates as a homogeneously broadened line.
The study of the nonlinear optical response of excitons in semiconductors is important for both scientific and technological applications. Although the nonlinear optical properties of bulk semiconductors and heterostructures have been studied for almost three decades, with most of the research focusing on heterostructures, the mechanisms leading to the nonlinearities in these systems are not completely understood. Determining these mechanisms and developing a theoretical picture which describes the most dominant effects remains a challenge and an active area of study. Although optical interactions in semiconductors is a genuine many-body problem, a description of this system similar to the optical Bloch equations used in atomic studies has shown some success, but more work is needed to make this model complete. Experimental work, particularly in the bulk system uncomplicated by the interface disorder present in heterostructures, will provide the guidance to extend this formalism. In this dissertation, the frequency domain resonant nonlinear optical response of excitons in bulk gallium arsenide at low density is studied to gain insight into the dominant mechanisms leading to the response, as well as the dynamics of the nominally three-dimensional excitonic system. Specifically, the nonlinear response was probed with differential transmission (DT) and four-wave mixing (FWM) experiments, which measure to lowest order the third-order susceptibility, $\chi\sp{(3)}.$ Using these various tools, three specific areas were studied and the results will be presented. First, the role of the biexciton, the state of two bound excitons, in determining the bulk nonlinear response was explored. The observation of a red-shifted nonlinear resonance suggests the importance of this state at moderate densities. Second, a new response, characterized by a resonant increase in exciton absorption induced by optical pumping with initial superlinear growth and a transition to behavior described by simple line broadening with increased pump intensity, was studied in detail. A model considering increased polariton absorption with increased exciton-exciton interactions explains these effects. Finally, nonlinear optical spectroscopy was used to study exciton transport, where near-ballistic behavior was revealed. The effect of exciton transport, thermalization and radiative recombination on the nonlinear optical response was explored.
The saturation behavior of the nonlinear index δnNL in the band tail of GaAs/AlGaAs multiple quantum wells is experimentally studied in quasi-steady state and in a low absorption region (below 300 cm−1), where dispersive optical bistability is observed. Measurements at different detunings from the exciton resonance allow us to study the absorption dependence of the saturation parameters. The saturation intensity IS is found inversely proportional to the linear absorption coefficient, while the saturating nonlinear index δnS is approximately constant. This evidences that the nonlinear index saturation is due to a saturation of the carrier density versus light intensity, due to the saturation of the band tail absorption itself.
An examination of the contribution of excitons, compared to the continuum states, to the optical properties of GaAs/AlGaAs multiple quantum wells illuminates the mechanisms underlying nonlinear absorption and nonlinear refraction and yields information which is useful for optimizing devices which incorporate these materials. We have measured the absorption as a function of intensity at three different wavelengths—above the band edge, on the excitonic resonance, and far below the band edge—to separate the effects. We find that different well thicknesses have different saturation intensities both for excitonic and continuum absorption.
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.
There are two different models to explain the observed optical bistability (OB) in GaAs. Haken and Goll1 use the saturation of the two-level (electron and hole) atoms as the mechanism of OB, whereas the Stark shift of excitons is the dominant factor in the work by Koch and Haug.2 We analyze both models, including the local field effect.3 It is shown that the validity of each model depends very much upon the parameters involved. We also give a similar analysis for CuCℓ where the biexcitons are important. In contrast to the earlier work by Abram and Maruani,4 we find by careful analysis, including the origin of the background dielectric constant, that the local field correction is not important in this case. The contribution of the exciton and biexciton interaction, however, can be important and should be included in the calculation of OB given by Haug.5 The changes in the numerical results of Ref. 5, by including the exciton-biexciton interaction and the local field correction are to be represented.