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Optics Express

Separation of coherent and incoherent nonlinearities in a heterodyne pump-probe experiment

Paola Borri, F. Romstad, W. Langbein, Anthony E. Kelly, Jesper Mørk, J. M. Hvam

Published Jul 31, 2000• 26 citations
Publisher

Abstract

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.

DOI
10.1364/oe.7.000107

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Journal of the Optical Society of America B•Aug 1, 2000•2 citations
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.
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.
We give the first analysis of heterodyne experiments that includes the propagation along the waveguide. Under the assumption that the material polarization is adiabatically eliminated we derive simple analytic expressions for the coherent coupling term, exact for Gaussian pulses and a good approximation for other shapes. We find that the measured signal does not display any phase dependence close to zero pump–probe delay. A four-wave mixing band is identified in the heterodyne signal, and a new class of experiments is proposed by analogy with the spatial case.
A heterodyne detection scheme was applied to micro-pump–probe spectroscopy to study the transient response of an exciton in a single semiconductor quantum dot. The elimination of the pump pulse in the frequency domain provided us a direct probing of the energy relaxation process of the quantum state excited by the pump pulse. The excitonic Rabi oscillations were also monitored by this technique, even in the presence of a strong pump pulse. This spectroscopic technique is suitable for the observation of the optical response and coherent manipulation of a semiconductor quantum dot.
The nonlinear signal in a degenerate four-wave mixing experiment as a result of diffraction of a spatially distributed third-order nonlinearity is studied theoretically. The approach has been applied for the case of monochromatic and ultrashort pulses. As a consequence, the degenerate four-wave mixing signal is found to be independent of light-coherence parameters and cannot be explained as a product of diffraction on a dynamic grating. In this model only the fast component of the signal (the coherent artifact) is related directly to third-order nonlinear processes. The main features (the origins, temporal shapes, dependencies of pump intensity, and modulation effects) of the coherent artifact and a slow-decay component are discussed theoretically and experimentally.