Interferometric cross correlation with a numerical lock-in: Nonlinear polariton pulse propagation through GaAs

Abstract

We present a ultrasensitive method for measuring the ultrafast optical response of a sample with respect to its amplitude and phase. Combining interferometric crosscorrelation, a wavemeter and a numerical lock-in technique, the method is distinguished by its dynamic range (7 orders of magnitude in the intensity) and phase resolution ( A @ /~T = 1/50). Time resolution depends on residual dispersion ofthe set-up but is limited to -40 fs by the width of the input pulses. We demonstrate, as an example, high precision measurements of nonlinear Is-exciton-polariton propagation through GaAs.Most experiments in ultrafast spectroscopy involve two pulses, an input and an output pulse. If the input pulse can be characterized in a separate set-up, linear correlation techniques can be used to determine the optical response function &(t,t'). The advantages of linear techniques are their potential high sensitivity regarding minimum average power and dynamic range. Our method consist of two parts, the optical set-up and a numerical evaluation algorithm. Three signals are measured in the same Mach-Zehnder interferometer simultaneously ( Fig. 1): i) a linear crosscorrelation signal using both exit interference patterns that is proportional to the optical response function of the sample, ii) an autocorrelation of the pulses to determine the power spectrum of the pulses used, and ii) the autocorrelation of a HeNe laser that represents a reference with which mechanical or thermal drifts of the interferometer can be removed. The amplitude and phase of all signals are determined by a numerical lock-in technique.To demonstrate the performance of the I &h".