Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis

Journal name:
Nature Photonics
Year published:
Published online


Terahertz quantum cascade lasers are compact, electrically pumped semiconductor laser sources that are capable of delivering tens of milliwatts of power in continuous wave. Here, we demonstrate that these devices can be operated in a regime of active mode-locking by modulating their bias current with a radiofrequency synthesizer. Detection of the emitted pulse train is made possible by phase-locking the quantum cascade laser repetition rate and carrier frequency to a harmonic of the repetition rate of a mode-locked femtosecond fibre laser. This technique allows coherent sampling of the terahertz electric field, showing that the terahertz pulses are transform-limited. In addition, our technique allows control of the carrier-envelope phase shift of the quantum cascade laser.

At a glance


  1. Schematic diagram showing sampling of the terahertz QCL emission by a femtosecond laser in the time domain (left) and frequency domain (right).
    Figure 1: Schematic diagram showing sampling of the terahertz QCL emission by a femtosecond laser in the time domain (left) and frequency domain (right).

    a, Original terahertz pulse train electric field amplitude (green curve). The black curve represents the pulse envelope and the red dots indicate the sampled points. d, Fourier transform of the original pulse train. b, Sampled terahertz pulse train by the femtosecond laser pulse train (see equation (2)). The sampling time step is given by Δts = 1/  − k/ , where k = int( / ). In the example in the figure Δts is equal to 0.5 THz cycles. One in every k QCL pulses is sampled by the femtosecond laser. e, Fourier transform of the sampled terahertz pulse train. Following equation (4), the spectrum is composed of replicas of the Fourier transform of Ed(t), centred at n ×  , where n is an integer. The shaded area indicates the modes selected by low-pass filtering (see text). c, Down-converted terahertz pulse train after the low-pass filtering process. The repetition rate is Δf =   − k ×  . f, Fourier transform of the down-converted terahertz pulse train. The new carrier frequency is η = νQCL − r ×  , where r = int (νQCL/ ). In d and f, the vertical dashed lines are integer multiples of and Δf respectively, and δTHz and δMHz indicate the corresponding carrier-envelope frequency offsets31 of the original terahertz QCL and of the down-converted comb. Note that, in general, these will be different, resulting in different pulse-to-pulse phase shifts.

  2. Electrical and optical characteristics of the terahertz QCL operated in continuous wave at a heat-sink temperature of 20 K.
    Figure 2: Electrical and optical characteristics of the terahertz QCL operated in continuous wave at a heat-sink temperature of 20 K.

    a, Voltage/current (black line) and output power/current (green line) characteristics. b, Emission spectrum measured at a drive current of 1.24 A (red circle in a). The spectrum is single mode. The linewidth is limited by the 7.5 GHz resolution of the FTIR spectrometer. c, Emission spectrum measured at a drive current of 1.35 A (red square in a). The separation between the longitudinal modes is ~26.6 GHz (equal to twice ). d, Emission spectrum measured at a drive current of 1.35 A. In this case, the current of the QCL was modulated by RF-1 with +10 dBm of RF power at a frequency of 13.315 GHz (see set-up of Fig. 3).

  3. Experimental set-up.
    Figure 3: Experimental set-up.

    The terahertz QCL is driven in continuous wave with a commercial power supply. Synthesizer RF-1 is connected to the QCL through a bias-T with a bandwidth of 15 GHz. Synthesizer RF-2 is used to control the repetition rate of the femtosecond laser,  = 96.513 MHz. The frequency-doubled (775 nm) power output of the femtosecond laser (1,550 nm wavelength, 100 fs pulsewidth, 96 MHz repetition rate) is ~50 mW. The ZnTe crystal is 2 mm thick, and is followed by λ/4 and λ/2 waveplates, a polarizing beamsplitter (PBO), and a fast balanced photodetector (see Methods). The output of the balanced detector, after being amplified and filtered with a lowpass filter of ~50 MHz bandwidth, is phase-compared using an RF mixer to the signal generated by synthesizer RF-3. RF-1, RF-2 and RF-3 share a common 10 MHz clock. The dashed arrows indicate the active controls of the QCL carrier frequency and of the fs-laser repetition rate.

  4. RF spectra of the sampled THz waveform.
    Figure 4: RF spectra of the sampled THz waveform.

    a, Single-shot trace of the down-converted terahertz QCL spectrum recorded with a RBW of 100 kHz, and a sweep time of 5.5 ms. The QCL is driven at a current of 1.35 A (Fig. 2d) and is modulated with +10 dBm of RF power, and frequency fRF1 = 13.321794 GHz Δf = 3 MHz is the frequency interval between the lines. In this spectrum, the loop that controls vQCL is left open. b, Spectrum collected with the Max–Hold function of the spectrum analyser switched ON for ~1 s. In this case, fRF1 = 13.322794 GHz Δf = 4 MHz. As in a, the loop that controls vQCL is left open. c, Spectrum collected with a RBW of 100 kHz and 100 video averages. Here, fRF1 = 13.315794 GHz Δf = 3 MHz. In this spectrum, fRF3 = 21.3 MHz, which allows phase-locking of the sixth line from the left (labelled L0) to . The wings indicated by the red arrows on both sides of L0 show that the bandwidth of the phase-locked loop is ~1.5 MHz (ref. 29). Compared to panels a and b, the signal was amplified by a further 30 dB.

  5. Mode-locked operation of the terahertz QCL under simultaneous injection- and phase-locking for an increasing number of longitudinal modes.
    Figure 5: Mode-locked operation of the terahertz QCL under simultaneous injection- and phase-locking for an increasing number of longitudinal modes.

    Left column: RF experimental spectra in linear scale with = 96.513 MHz,  = 13.315894 GHz and Δf = 2.9 MHz. Central column: corresponding experimental waveforms (dots), and calculated waveforms assuming (red lines) that all modes have equal phases (Δφ = 0). The bottom axis shows the effective measured timescale on the oscilloscope (Fig. 1c). The top axis shows the original timescale (Fig. 1c) obtained by rescaling the measured timescale by the factor (Δf/ ). The sampling step is Δts  2.3 ps, that is, equal to approximately six optical cycles at 2.5 THz. Note that all the measured pulses are identical. Indeed, the waveforms were obtained by setting fRF3 = 7 × Δf = 20.3 MHz, so that η = 0, which gives a null carrier-envelope phase shift for the sampled terahertz pulse train (see equation (4), expression within brackets). Right column: computed pulse intensity in the terahertz range obtained from equation (1) with φm = 0, m, and using the measured values of Em (Fig. 1c) and vQCL (2.5 THz; see Fig. 2). a,d,g, 1,240 mA drive current, +4 dBm RF power. b,e,h, 1,326 mA drive current, +9 dBm RF power. c,f,i, 1,346 mA drive current, +10 dBm RF power.

  6. Spectra of the phase-locked lines labeled L0 to L5 in Fig. 4c, measured with a RBW of 1 Hz, and 30 video averages.
    Figure 6: Spectra of the phase-locked lines labeled L0 to L5 in Fig. 4c, measured with a RBW of 1 Hz, and 30 video averages.

    The frequency of each line was offset to zero, and its intensity normalized to 1 (0 dB). Inset: relative phase-noise increment from L1 as a function of line index, obtained from the spectra in the main figure at 30 Hz from the carrier frequency (black dots). The red line represents the expected noise increment, given by 10 × log (n2), where n is the line index.


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Author information


  1. Laboratoire Matériaux et Phénomènes Quantiques, Université Paris 7 and CNRS UMR 7162, 10 rue A. Domont et L. Duquet, 75205 Paris, France

    • Stefano Barbieri,
    • Marco Ravaro,
    • Pierre Gellie,
    • Christophe Manquest &
    • Carlo Sirtori
  2. LNE-SYRTE, CNRS, UPMC, Observatoire de Paris, 61 avenue de l'Observatoire, 75014 Paris, France

    • Giorgio Santarelli
  3. School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom

    • Suraj P. Khanna,
    • Edmund H. Linfield &
    • A. Giles Davies


S.B. conceived and performed the experiment, analysed data and wrote the paper. M.R. performed the experiment, analysed data and contributed to manuscript preparation. P.G. performed the experiment and analysed the data. G.S. conceived and performed the experiment, analysed data and contributed to manuscript preparation. C.M. fabricated the quantum cascade laser. C.S. analysed the data and contributed to manuscript preparation. S.P.K. grew the quantum cascade laser material used for this work, under the supervision of E.H.L. and A.G.D.

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