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physica status solidi (b)

Speckle Analysis of Resonant Secondary Emission

W. Langbein

Published Nov 1, 2002• 5 citations
Publisher

Abstract

The technique of the speckle analysis of resonant secondary emission is reviewed. It is a novel, linear optical technique to measure the microscopic intensity and polarization dynamics in inhomogeneously broadened ensembles, that represents an alternative for established non-linear optical techniques such as photon-echo or spectral hole burning. Both time-resolved and spectrally resolved variants of the speckle analysis are discussed. Experimental results obtained on semiconductor quantum wells using both techniques are presented.

DOI
10.1002/1521-3951(200211)234:1<84::aid-pssb84>3.0.co;2-y

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The technique of the speckle analysis of resonant secondary emission is reviewed. It is a novel, linear optical technique to measure the microscopic intensity and polarization dynamics in inhomogeneously broadened ensembles, that represents an alternative for established non-linear optical techniques such as photon-echo or spectral hole burning. Both time-resolved and spectrally resolved variants of the speckle analysis are discussed. Experimental results obtained on semiconductor quantum wells using both techniques are presented.
A linear optical method to measure coherence and dephasing of excitations in solids is presented. The spectrally resolved degree of coherence of resonantly scattered light is deduced from the intensity fluctuations over its emission directions (speckles). The spectral intensity correlation gives a direct measure of the dephasing rate within the inhomogeneously broadened ensemble. For localized excitons in semiconductor quantum wells, the combination of static disorder, phonon scattering, and radiative decay leads to a spectral dependence of the emission coherence and the dephasing rate, which is well described by model calculations.
A new method to measure the coherence of inhomogeneously broadened optical excitations in semiconductor nanostructures is presented. The secondary emission of excitons in semiconductor quantum wells is investigated. The spectrally-resolved coherence degree of resonantly-excited light emission is deduced from the intensity fluctuations over the emission directions (speckles). The spectral correlations of the speckles give direct access to the homogeneous line width as function of spectral position within the inhomogeneously broadened ensemble. The combination of static disorder and phonon scattering leads to a partially coherent emission. The temperature dependence of the homogeneous line width is well explained by phonon scattering.
A new method to measure the time-dependent coherence of both homogeneously and inhomogeneously broadened optical excitations in solids is presented. The coherence degree of resonantly excited light emission is deduced from the intensity fluctuations over the emission directions (speckles). This method determines the decays of intensity and coherence separately, thus distinguishing lifetime from pure dephasing. The secondary emission of excitons in semiconductor quantum wells is investigated. Here the combination of static disorder and inelastic scattering leads to a partially coherent emission. The temperature dependence is well explained by phonon scattering.
Quantitative analysis of speckle distributions, i.e., intensity fluctuations, in resonant secondary emission is a powerful tool to study quantum coherence in a wide range of optically excited systems. Finite directional or temporal resolution and any instability in the setup will necessarily reduce the fluctuations which would be misinterpreted as loss of coherence. We discuss the consequences of this averaging and show how the amount of averaging can be extracted from histograms of the speckle intensity and how it can be corrected for. Using functional integration methods, analytic expressions for the intensity distribution in experiments with finite directional or temporal resolution are derived. These should help to make the quantitative speckle analysis a widely used technique for measuring quantum coherence optically.
The excitonic coherence in semiconductor quantum wells is measured by time-resolved speckle analysis and four-wave mixing. It is found that in the case of single GaAs quantum wells, the results of both methods are in agreement, and can be understood in the framework of an inhomogeneously broadened distribution of localized excitons which are subject to phonon-scattering and radiative recombination. The speckle analysis gives the additional distinction between recombination and pure dephasing processes. In multiple quantum wells, the radiative coupling between the quantum wells leads to a pronounced change of the observed dynamics. In the secondary emission, a strong coherent component with an oscillating time-structure is observed for small scattering angles. This is attributed to the beating of the radiative eigenstates of the stacked structure.
We have performed spectral interferometry with Rayleigh scattered light coming from a single speckle and emitted after resonant creation of excitons in GaAs quantum wells. The experiment confirms the coherence of the secondary emission at early times, regardless of sample parameters, but underlines the stochastic nature of a single speckle. The scattered electric field is calculated, correctly accounting for the center-of-mass quantization in the disordered potential. We find that the amplitudes of the electric fields emitted by different excitons are uncorrelated, so that the well-known Poisson distribution for speckle intensities applies.