Theory of propagation effects in time-resolved four-wave mixing

Schillak, P.; Balslev, I.

doi:10.1103/physrevb.48.9426

Cited by 18 publications

(9 citation statements)

References 8 publications

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“…The propagation of coherent laser pulses resonant with exciton transition energy in bulk crystals and heterostructure semiconductors have been intensively studied. Ulbrich and Fehrenbach have shown the first experimental observation of the propagation delay of the light pulses transmit-ted through the thick GaAs films due to the dispersion of group velocity [2], and Schillak and Balslev have reported the variation of the temporal profile of excitonic nonlinear response theoretically [3]. Moreover, the polariton beats [4] and the change of the temporal profiles caused by an increase of the excitation power [5,6], which are induced by the polariton propagation, have been reported.…”

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confidence: 99%

Transient reflectivity response with negative time delay caused by femtosecond pulse propagation in GaAs thin films

Watanabe

Kojima

Wada

et al. 2009

Phys. Status Solidi (c)

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We have investigated the propagation effects on the transient response of confined excitons in GaAs thin films by a reflection‐type pump‐probe technique. The spectrally integrated signal demonstrated slower rise than the pulse width in the negative time region. Moreover, reflectivity change spectra indicate that the response in the negative time region originates from the effect of the confined excitons and that the signal rise time at each exciton state is different. The propagation velocities estimated from the rise times and the film thickness correspond to the group velocities of the exciton polariton in bulk crystals. Therefore, the origin of the responses in the negative time region is the pulse modulation caused by the propagation effect of exciton polariton. In addition, it was confirmed that this propagation disappears with an increase in temperature due to the spatial decoherence of excitons. These results demonstrate that the propagation effect of exciton polariton on optical response in femtosecond time scale has a considerable influence in the realization of ultrafast optical devices. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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confidence: 99%

Transient reflectivity response with negative time delay caused by femtosecond pulse propagation in GaAs thin films

Watanabe

Kojima

Wada

et al. 2009

Phys. Status Solidi (c)

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“…In the presence of the optical ringing, the configuration of two intersected beams was also considered in investigations of the resonant four-wave mixing in atomic [21,22] and solid-state media [20,23,24,25]. In these works, the collective oscillations of the field were obtained in the time-resolved and time-integrated studies of a new diffracted pulse.…”

Section: Nonlinear Pump-probe Interactionmentioning

confidence: 99%

“…In the presence of the optical ringing, the interaction of two intersected probe and pump beams (this configuration is also used in the present work) was considered for the cases of atomic media [21,22] and solids [20,23,24,25]. Most of the results of these studies are related to the time-integrated and time-resolved properties of the diffracted four-wave mixing signal.…”

Section: Introductionmentioning

confidence: 99%

Coherent interaction of laser pulses in a resonant optically dense extended medium under the regime of strong field-matter coupling

et al. 2004

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Nonstationary pump-probe interaction between short laser pulses propagating in a resonant optically dense coherent medium is considered. A special attention is paid to the case, where the density of two-level particles is high enough that a considerable part of the energy of relatively weak external laser-fields can be coherently absorbed and reemitted by the medium. Thus, the field of medium reaction plays a key role in the interaction processes, which leads to the collective behavior of an atomic ensemble in the strongly coupled light-matter system. Such behavior results in the fast excitation interchanges between the field and a medium in the form of the optical ringing, which is analogous to polariton beating in the solid-state optics. This collective oscillating response, which can be treated as successive beats between light wave-packets of different group velocities, is shown to significantly affect propagation and amplification of the probe field under its nonlinear interaction with a nearly copropagating pump pulse. Depending on the probe-pump time delay, the probe transmission spectra show the appearance of either specific doublet or coherent dip. The widths of these features are determined by the density-dependent field-matter coupling coefficient and increase during the propagation. Besides that, the widths of the coherent features, which appear close to the resonance in the broadband probe-spectrum, exceed the absorption-line width, since, under the strong-coupling regime, the frequency of the optical ringing exceeds the rate of incoherent relaxation. Contrary to the stationary strong-field effects, the density-and coordinate-dependent transmission spectra of the probe manifest the importance of the collective oscillations and cannot be obtained in the framework of the single-atom model.

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“…This corresponds to dephasing times of 2.5 and 0.3 ps for the A n -\ and A n =2 excitons, respectively. The details of the calculations and an analysis of the approximations assumed will be published separately [15].…”

Section: Co-0) T N-i(y2n-y\n) Co ~ 0) Tn + Iy 2nmentioning

confidence: 99%

Nonlinear quantum beats of propagating polaritons

et al. 1993

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We observe nonequidistant oscillations in the correlation trace of the nonlinear signal in a four-wave mixing experiment when exciting the upper polariton branch between the A n = \ and the A n =2 excitons in CdSe. The quantum beats are described qualitatively and quantitatively taking into account propagation interference effects on the third-order nonlinear polarization, and the homogeneous dampings of the exciton polaritons are determined. 42.50.Md, 78.47.+p The investigation of quantum beats have been introduced in the early sixties as an ultrahigh resolution spectroscopy in atomic and molecular physics [1]. When two or more levels of atoms or molecules are excited by a short light pulse, a modulation of the fluorescence is observed, with the beat frequency v=AE/h, where AE is the level splitting.In solids the appearance of quantum beats resulting from the interference of extended electronic states is impeded by the occurrence of energy bands rather than discrete levels. However, the Coulomb interaction between electrons and holes infer the presence of exciton resonances just below the band edge. These levels can give rise to observation of quantum beats in linear resonance fluorescence measurements [2-4] as well as in nonlinear four-wave mixing [5-10] and induced magnetoabsorption [11]. The quantum beat measurements give information about energy splittings, oscillator strengths, dephasing times, etc.Strong coupling between photons and free excitons results in the formation of polaritons that are propagating modes conserving the polarization over macroscopic distances. This was recently demonstrated by Frohlich et al.[ 12] in a time-resolved experiment, where they performed linear transmission of a light pulse in the region of the \S exciton polariton in CU2O. The observed nonequidistant oscillations of the transmitted signal were explained as resulting from quantum beats between the lower and upper branches of the \S polariton, i.e., between propagating modes in a strongly dispersive medium.In the present Letter, we report the first observation of propagation interference effects on the third-order nonlinear polarization as measured in a coherent four-wave mixing experiment. As a model we have chosen the upper polariton branch in CdSe between the A" = \ and A n -2 exciton resonances. We observe nonequidistant oscillations in the correlation trace of the nonlinear signal that can be understood as quantum beats between continuously distributed propagating polaritons within the same strongly dispersive branch.We perform degenerate four-wave mixing in a selfdiffraction geometry. Two laser pulses with wave vectors k| and k2 create a grating, which diffracts photons from pulse 2 in the direction 2k2~-kj [13]. The laser source in the experiments is a mode-locked argon-ion laser which pumps synchronously a tunable dye laser (DCM) with a repetition rate of 82 MHz. The pulse duration (FWHM) is about 7 ps, but the time resolution in the coherent four-wave mixing is only limited by the coherence time of the laser pu...

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Theory of propagation effects in time-resolved four-wave mixing

Cited by 18 publications

References 8 publications

Transient reflectivity response with negative time delay caused by femtosecond pulse propagation in GaAs thin films

Transient reflectivity response with negative time delay caused by femtosecond pulse propagation in GaAs thin films

Coherent interaction of laser pulses in a resonant optically dense extended medium under the regime of strong field-matter coupling

Nonlinear quantum beats of propagating polaritons

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