Intensity autocorrelation measurements of frequency combs in the terahertz range

We report on direct measurements of the emission character of quantum cascade laser based frequency combs, using intensity autocorrelation. Our implementation is based on fast electro-optic sampling, with a detection spectral bandwidth matching the emission bandwidth of the comb laser, around 2.5 THz. We find the output of these frequency combs to be continuous even in the locked regime, but accompanied by a strong intensity modulation. Moreover, with our record temporal resolution of only few hundreds of femtoseconds, we can resolve correlated intensity modulation occurring on time scales as short as the gain recovery time, about 4 ps. By direct comparison with pulsed terahertz light originating from a photoconductive emitter, we demonstrate the peculiar emission pattern of these lasers. The measurement technique is self-referenced and ultrafast, and requires no reconstruction. It will be of significant importance in future measurements of ultrashort pulses from quantum cascade lasers.

Figure 1

Measurement setup and detector bandwidth. (a) Time-domain correlation setup based on two-probe electro-optic sampling. The two probes sample the THz radiation of a QCL based frequency comb at two mutually delayed points in time. The probe pulse length is 146 fs. A fast acquisition module records the two sampled values and a further real-time routine computes from here the instantaneous intensity, and the two-point electric field and intensity product. When averaged over time and normalized, this gives the autocorrelation functions $g^{\left(1\right)}\left(\tau \right)$ and $g^{\left(2\right)}\left(\tau \right)$. (b) Calculated coherence length of the THz detection in a (110)-oriented ZnTe, and a probe center wavelength of 775 nm (full line), together with measured absorption in ZnTe at 300 K (dashed line). The detectivity is matched to the laser comb emission, which is marked for when the investigated laser is operating in a narrow beat-note regime, 2.2–2.8 THz (light gray), and dispersed regime, 1.6–3.3 THz (dark gray).

Figure 2

First- and second-order autocorrelation measurements of a 2-mm-long THz laser comb operating in the narrow beat-note regime [(a), (b)] and the dispersed regime [(c), (d)]. Insets show a zoom-in into the $g^{\left(2\right)}\left(\tau \right)$ around $\tau =0$ to evidentiate the subcycle intensity resolution of the technique. (a) $g^{\left(1\right)}\left(\tau \right)$ measurement of laser emission in the narrow beat-note regime, at 906 mA and $T=23$ K. Inset: beat note at 900 mA. (b) $g^{\left(2\right)}\left(\tau \right)$ in the narrow beat-note regime. For long time delays, the intensity decays to 1, and therefore uncorrelated but continuous-wave-like. (c) $g^{\left(1\right)}\left(\tau \right)$ measurement of laser emission in the dispersed regime, at 1010 mA and $T=23$ K. Inset: beat note at 1000 mA. (d) $g^{\left(2\right)}\left(\tau \right)$ measurement of laser emission in the dispersed regime. For long time delays, the intensity becomes uncorrelated, and decays again to a value of 1. Light (blue) lines represent few-cycle average of the $g^{\left(2\right)}\left(\tau \right)$, to filter the subcycle resolution of the intensity autocorrelation (window averaging 5 ps).

Figure 3

Spectral analysis of the QCL based frequency comb when operated in the narrow beat-note and dispersed regime, using electro-optic correlations. (a) Low-resolution amplitude spectra from the Fourier transformation of $g^{\left(1\right)}\left(\tau \right)$ [gray (full squares) and blue (empty squares)], shown together with coherence length computations for ZnTe and a center probe wavelength of 775 nm. (b) Transfer function of the detection based on ZnTe under these conditions, where absorption at room temperature has been taken into account (blue full line) shown together with the transfer function of electro-optic sampling (blue dotted-dashed line). (c) Emitted THz power spectrum from electro-optic sampling (using the transfer function of the crystal in (b)] when the laser is operated in comb regime compared to a low-resolution FTIR measurement. (d) Emitted THz power spectrum from electro-optic sampling (using the transfer function in (b)] when the laser is operated in the dispersed regime compared to a low-resolution FTIR measurement [15, 17].

Figure 4

Results of first- and second-order autocorrelation of a pulsed THz comb based on optical rectification in a photoconductive emitter, using the same correlation technique. (a) $g^{\left(1\right)}\left(\tau \right)$ of the THz pulse with an electric field profile as shown in the inset. We compare the measurement to a simulated pulse with Gaussian spectrum and find qualitatively good agreement. (b) $g^{\left(2\right)}\left(\tau \right)$ of the pulsed radiation, normalized to the average intensity within a time window of 13 ps. Characteristic to pulsed radiation is the decay of the intensity autocorrelation function to a value of 0, which is a clear indicator for the pulsed emission and the value at zero path delay of 6.59.