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Setup for measuring the linewidth enhancement factor based on the mixing of a high-frequency modulated distributed feedback quantum cascade laser (QCL-2) with a reference distributed feedback quantum cascade laser (QCL-1). The beams are superimposed using a ZnSe beam splitter and mixed onto a high-speed HgCdTe detector connected to a spectrum analyzer.
Spectra with the same modulation index of are reported for three different modulation frequencies: (a) 500, (b) 80, and (c) . The spectra are normalized to the amplitude of the unmodulated beat note signal.
(a) Amplitude of the central line (circles) and the average of the first sideband peak amplitudes (squares) for a modulation frequency of . Solid and dashed lines correspond to the calculated spectral amplitudes of the central line and the average of the first sideband peaks, respectively. The calculated linewidth enhancement factor is . Typical error bars for a measurement with an amplitude modulation of are reported. (b) Measurements for higher frequency modulations: (circles), (squares), and (crosses). Calculated amplitudes for different values of linewidth enhancement factor are reported for both central line (solid lines) and average of sideband peak amplitudes (dashed lines) for comparison.
Linewidth enhancement factor is plotted as a function of modulation frequency. The first measurement is obtained from the measurement of the ratio of the average of the first sideband to the central peak amplitudes (circles) and the second measurement corresponds to the measurement of the difference of first sideband amplitudes (square). The solid line corresponds to a simple thermal model considering the thermal chirping which is in agreement with the experimental values.
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