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Review of Scientific Instruments

Separating the coherent and incoherent effects in optical correlation experiments on semiconductors and other saturable absorbers

Abner F. Bello, David J. Erskine, Harry B. Radousky

Published Feb 1, 1996• 5 citations
Publisher

Abstract

In some pump–probe optical correlation experiments, the measured signal versus delay between pulses generally consists of two components: the convolution of the pulse autocorrelation with the sample impulse response, and a coherent artifact. The latter can obscure the first component near zero delay where fast time scale processes will be manifest. We present a mathematical description of the relative shapes and sizes of the two components, so that a fitting process can separate them. This can yield both the dephasing and relaxation times of saturable absorbers such as semiconductors. The method is particularly appropriate when the orientational dephasing and relaxation times are of the same time scale as the laser pulse width.

DOI
10.1063/1.1146629

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In some pump–probe optical correlation experiments, the measured signal versus delay between pulses generally consists of two components: the convolution of the pulse autocorrelation with the sample impulse response, and a coherent artifact. The latter can obscure the first component near zero delay where fast time scale processes will be manifest. We present a mathematical description of the relative shapes and sizes of the two components, so that a fitting process can separate them. This can yield both the dephasing and relaxation times of saturable absorbers such as semiconductors. The method is particularly appropriate when the orientational dephasing and relaxation times are of the same time scale as the laser pulse width.
When pump-probe measurements are performed using pulses originating from the same laser, it is necessary to consider the coherent interaction between the two pulses in determining any material relaxation rates on the time scale of the laser pulse.1-5 For pump and probe beams crossing at an angle, the source of the coherent artifact can be understood in the following manner.1 When the two beams are simultaneously present in the sample, they interfere to produce a spatial modulation of the dielectric constant. Light from the pump beam then scatters from this induced grating into the probe direction. This model has led to the suggestion that for the collinear, copropagating beams, where the spatial grating disappears, the coherent artifact should vanish.3 While the spatial modulation is eliminated by choosing this geometry, we demonstrate here that the coherent artifact, which results directly from the nonlinear polarizability of the material, still remains. We have, however, been able to develop a general method for isolating the incoherent response, thus permitting the material relaxation to be extracted without any knowledge of the coherence properties of the pulse.
We demonstrate that the transient coherent nonlinearity (coherent artifact) affecting the pump-probe response of semiconductor optical amplifiers can be experimentally separated from the incoherent transient. The technique is based on measuring the mirror component of the coherent artifact which is a background-free four--wave mixing signal at a different frequency with respect to the transmitted probe in a heterodyne detection scheme. Measurements on amplifiers of different length reveal strong deviations from the commonly expected symmetric shape of the coherent artifact in case of long waveguides.
A recently proposed collisional time-correlation function method for resonance laser–target interactions in molecular targets is modified and extended to include time-delayed multiphoton processes in the dynamics. The explicitly time-dependent laser and target dynamics in this method is separated into laser electric field and molecular target dipole/susceptibility correlation functions. The first and second order laser field correlation functions, also known as Glauber field correlation functions, are evaluated in a continuum mode description of photon number representation for both resonance and time-delayed multiphoton processes. We show that such a description allows for the incorporation of laser pulse shape and phase coherence in the formalism, while the laser–target interaction dynamics is still described similarly to the resonance single- and multiphoton processes. As an example, the transition rates for a two-photon Gaussian pump–probe dynamics are derived in which we show that the phase coherence between the Gaussian pump and probe pulses can be incorporated and controlled through a single delay-time-dependent parameter.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.
Measurements of the relaxation times T1 and T2 of a two-level system by nonlinear transient spectroscopic methods are discussed, where delayed incident pulses are assumed to have correlation times much shorter than T1 or T2 but varied widths. In particular, a delayed degenerate four-wave mixing (photon echoe) and apump-and-probe type transmission measurement with incoherent long pulses are considered in detail, and a principle of their use for ultrafast spectroscopy is clarified. If the field is steady and T1>>T2, the time resolutionof T2measurement by the delayed four-wave mixlng is determined by the field correlation, therefore by the spectral width of the incident light irrespective of the pulse width. The time resoution of the T1 measurement by the pump-and-probe method is determined by the intensity correlation of the incident light, whereasthe one by the delayed four-wave mixing by a higher order correlation.