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Optics Express

A filtering procedure for systematic removal of pump-perturbed polarization artifacts

Thomas Polack

Published Jun 12, 2006• 11 citations
Publisher

Abstract

In time-dependent optical spectra, fast dynamics of narrow transitions give rise to artifacts consisting of spectral oscillations. In contrast with spectrally-integrated experiments, the interpretation of spectrally-resolved pump-probe experiments is thus far from straightforward in regimes where such coherent effects dominate, i.e., when the timescales of pump-induced processes are shorter than the medium dephasing times. Analyzing the two-dimensional Fourier transform of the time-dependent spectrum, we identify the components responsible for these artifacts and we introduce a simple Fourier-filtering procedure for their systematic removal. This technique is theoretically demonstrated on the time-dependent spectrum of a transition undergoing a frequency shift. The technique is also shown to have the additional benefit of efficient noise filtering of time-dependent spectra.

DOI
10.1364/oe.14.005823

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In time-dependent optical spectra, fast dynamics of narrow transitions give rise to artifacts consisting of spectral oscillations. In contrast with spectrally-integrated experiments, the interpretation of spectrally-resolved pump-probe experiments is thus far from straightforward in regimes where such coherent effects dominate, i.e., when the timescales of pump-induced processes are shorter than the medium dephasing times. Analyzing the two-dimensional Fourier transform of the time-dependent spectrum, we identify the components responsible for these artifacts and we introduce a simple Fourier-filtering procedure for their systematic removal. This technique is theoretically demonstrated on the time-dependent spectrum of a transition undergoing a frequency shift. The technique is also shown to have the additional benefit of efficient noise filtering of time-dependent spectra.
A model calculation is presented that describes the features of spectral-hole burning measurements performed under conditions of femtosecond transient excitation and probing. Pump-induced changes in the spectrum of probe transmittance arise not only from changes in level population (hole burning), but also from the presence of pump polarization during the probe, and from perturbations of the decay of the probe polarization. These latter effects give rise to oscillating differential transmittance spectra when the (shorter) probe pulse arrives prior to the peak of the pump noise. Only when the probe pulse follows the bulk of the pump pulse does the level population effect dominate the spectrum, so that one can observe dynamic hole-burning effects without distortion.>
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Exciton Rabi oscillations and Rabi splitting differ significantly from their atomic counterparts in part because Coulomb interactions between excitons strongly influence the exciton Rabi frequency.' While both exciton Rabi oscillations and Rabi splitting were demonstrated recently in quantum wells (QWs),'.l experimental investigation of how exciton-exciton interactions affect these coherent optical Q~OCCSS~S has been hindered bya number of complications. In time-domain studies, the Rabi frequencyvaries with time due to the changing electric field strength. In typ ical spectral domain studies, a spectrally-broad probe pulse is spectrally resolved after its transmission through the sample. The resulting pump-probe spectra are difficult to interpret due to the presence of coherent spectral oscillations and a sensitive dependence on the pump-probe delay. In this paper we report studies of exciton Rabi splitting where spectrally narrow pump and probe pulses were used. In this case, coherent spectral oscillations in pump-probe spectra can be avoided by tuning the central frequency of the probe pulse. The intensity dependence of the Rabi splitting obtained from these studies reveals a distinctly nonlinear relationship between the Rabi frequency and the applied electric field, in contrast to the linear dependence expected from mean-field bed theoretical models.' Pump-probe experiments were performed on a 130 A GaAs1AlGa.k multiple QW sample at 10 K. Figure I shows results of pump-probe meas
Time - dependent behaviors of molecular coherence in resonant multiphotoni onization spectra of molecules are theoretically investigated . An expression for the transition probability of time-resolved two-photon ionization processes via coherently excited resonant intermediate states is derived in the perturbative density matrix formalism. Model calculations of the probability of ionization are performed to predict appearance of quantum beats in pump-probe two-photon ionization experiments. The quantum beat signals in the time-resolved ionization spectra are compared with those in time-resolved total photon emission spectra.
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 employed the Tavis-Cummings model to study the pump-probe spectra of molecular polaritons. To describe the dissipative effects caused by the environment, the population decays of the photon mode and the two level states (TLSs), as well as the fast component of the dephasing of TLSs, are described by using the Lindblad equation. The effect of static disorder in the TLS transition frequency is incorporated into the equation of motion of the density matrix. The pump-probe spectra of the model system are calculated using the optical response function approach. Pronounced Rabi oscillations are observed in the pump-probe spectra, which are signatures of the strong light-matter coupling between the cavity mode and the collective bright state of the TLSs. To help understand the pump-probe spectra, we also simulate the laser pulse induced dynamics of the bright state of the molecular polaritons. The results show that the bright state lifetime is primarily determined by the dephasing time of the TLSs, consistent with the fast decay of the Rabi oscillations observed in the pump-probe spectra. Once the coherence decays, the long-time pump-probe response is dominated by the excited state population of the dark state manifold.