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International Conference on Ultrafast Phenomena

An Analysis of Coherence Effects in Pump-Probe Measurements

Stephen L. Palfrey, Tony F. Heinz, Kenneth B. Eisenthal

Published Jan 1, 1984• 0 citations
Publisher

Abstract

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.

DOI
10.1364/up.1984.thd2

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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 the existence of coherent coupling effects in pump-probe measurements with collinear, copropagating beams, despite the absence of any induced spatial gratings in this geometry. The coherent interaction, which is found to be similar but not identical to that for crossed beams, must be taken into account in analyzing relaxation processes occurring on the time scale of the laser pulse. These coherent effects cannot generally be eliminated by detecting the total change in energy in both the pump and probe beams.
We show that in order to describe completely the coherent coupling between the pump and probe pulses in a pump– probe measurement of transient absorption, the influence of induced phase gratings must be included. The importance of phase gratings is demonstrated experimentally for the case of a bleachable dye and analyzed in terms of transient four-wave mixing. These results are relevant to the interpretation of pump–probe measurements on all time scales performed with pulses from a single laser, particularly when the pulse duration is comparable with the material response time.
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.
A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.