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IEEE Journal of Quantum Electronics

Transient reflection of light near excitonic resonances

Jaak Aaviksoo, J. Kühl

Published Jan 1, 1989• 15 citations
Publisher

Abstract

The authors present an experimental analysis of the temporal structure of picosecond light pulses reflected from GaAs crystals near the lowest excitonic resonance at normal and Brewster angle incidence. The reflected pulses exhibit nonexponentially decaying tails, measured over five orders of magnitude, which follow the dynamics of the coherent polarization in the reflecting layer. Model calculations, including spatial dispersion effects and dead layer effects, provide a general understanding of the data. The numerical fit, however, fails to describe the fast initial decay observed experimentally. The latter can be explained by taking into account an inhomogeneous transition layer with a depth-dependent damping constant. Strong intensity dependence of the transients is observed.>

DOI
10.1109/3.40637

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The authors present an experimental analysis of the temporal structure of picosecond light pulses reflected from GaAs crystals near the lowest excitonic resonance at normal and Brewster angle incidence. The reflected pulses exhibit nonexponentially decaying tails, measured over five orders of magnitude, which follow the dynamics of the coherent polarization in the reflecting layer. Model calculations, including spatial dispersion effects and dead layer effects, provide a general understanding of the data. The numerical fit, however, fails to describe the fast initial decay observed experimentally. The latter can be explained by taking into account an inhomogeneous transition layer with a depth-dependent damping constant. Strong intensity dependence of the transients is observed.>
The coherent emission process at excitonic resonance was first investigated in short-period ZnSe/ZnSxSe1-x (x equals 0.18) superlattices with one period of 50 A/50 A and 19 A/19 A by observing a temporal profile with subpicosecond time resolution, of reflected pulses in the Brewster-angle configuration. As a result, an almost background-free signal with nonresonant contribution reduced greatly, was observed reflecting free induction decay (FID) of coherently driven exciton polarization. In particular, a beat signal of FID was clearly observed for the first time, which arises from interference effect between a few split spectral lines of the relevant exciton. Further, it was confirmed that the decay spread of FID becomes faster as the power density of incident pulse was increased for the SL sample with a thicker well. The results may be explained qualitatively by a simple model with the knowledge of the exciton structure as well as a preliminary data of the phase relaxation time obtained by four- wave-mixing measurement. The present results have provided a basis for that the transient Brewster-angle reflection spectroscopy serves as a powerful tool for exploring coherent interaction of exciton with light.
Time-resolved photoluminescence (PL) of excitonic molecules in GaAs quantum wells (QW's) reveals an initial transient characterized by a finite rise and an extremely fast nonexponential decay [H. Wang, J. Shah, and T. C. Damen et al., Solid State Commun. 98, 807 (1996)]. The transient is attributed to coherent quantum evolution towards the molecule ground state of two optically correlated excitons, ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}},$ which undergo the Coulombic attraction. In the present paper, we develop a theory of the transient PL and fit the experimental data. The radiative decay of a quasi-two-dimensional (2D) excitonic molecule is analyzed with the giant oscillator strength model adapted to QW's and with the bipolariton model. Within the 2D bipolariton model, the main ``hidden'' channel of the radiative decay of an excitonic molecule is the resonant dissociation into two outgoing interface (surface) polaritons rather than the observable decay into the bulk radiative modes. We conclude that quasi-2D molecules dissociate already within the initial transient of PL, while the following exponential decay of the molecule-mediated PL is due to the escape of secondary interface polaritons into the bulk modes. According to the 2D bipolariton model, the sequence ``two incoming $\mathrm{photons}\ensuremath{\rightarrow}\mathrm{two}$ virtual $\mathrm{excitons}\ensuremath{\rightarrow}2\mathrm{D}$ $\mathrm{molecule}\ensuremath{\rightarrow}\mathrm{two}$ outgoing interface polaritons'' is a completely coherent process. The fit of the time-resolved molecule-mediated PL provides us with numerical estimates of the exciton-photon coupling in GaAs QW's.
We investigate the temporal evolution of the instantaneous frequency of ultrashort-pulse four-wave mixing in GaAs/Gax{\mathrm{Ga}}_{\mathit{x}}Gax​${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum-well structures. We find that the coherent light emitted by excitons exhibits a complex phase behavior which depends critically on the density of excitons and the central frequency of the exciting pulses. Depending on the excitation conditions, we observe nonlinear shifts of the instantaneous frequency within one ultrashort pulsed emission or quantum beats. In the latter case we determine that the beat \ensuremath{\pi}-phase shift is very fast, only 40% above the fundamental quantum limit. We also present elaborate numerical simulations of the experiments based on a six-band generalization of the semiconductor Bloch equations. This formalism takes into account Coulomb many-body interactions and Pauli exclusion. It reproduces the salient features of the experimental data. It fails to account for important details revealed by the very sensitive phase measurements. The discrepancies can be traced back to two approximations in the theory: the statical treatment of screening, and the Lorentzian description of dephasing. In both cases, this indicates the need for theoretical refinements requiring a microscopic description of Coulomb scattering and dephasing processes in a non-Markovian theory.
We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small +ve+ve+ve $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large +ve+ve+ve $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small +ve+ve+ve delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.
The coherent emission from excitons corresponding to different subband transitions in a 500 Åbroad GaAs/AlGaAs quantum well is studied by spectrally resolved transient four-wave mixing (FWM). For the simultaneous excitation of several subband transitions, the dephasing times of the lowest exciton and higher- order exciton transitions are determined from the width of the resonances in the FWM spectrum. The decay of the spectrally integrated FWM signal as a function of the time delay between the excitation laser pulses does not reflect the dephasing times but is determined by the laser pulse width for multi-subband excitation. This is indicative of quantum interference between exciton and continuum transitions. Many-body Coulomb effects have to be included in a theoretical treatment of these experimental observations.