Mode-locking of a terahertz laser by direct phase
Jean Maysonnave, Kenneth Maussang, Nathan Jukam, Joshua R. Freeman,
Julien Mad´ eo, P. Cavali´ e, Rakchanok Rungsawang, Suraj Khanna, Edmund
Linfield, Alexander Giles Davies, et al.
To cite this version:
Jean Maysonnave, Kenneth Maussang, Nathan Jukam, Joshua R. Freeman, Julien Mad´ eo, et
al.. Mode-locking of a terahertz laser by direct phase synchronization. Optics Express, Optical
Society of America, 2012, 20, pp.16662. <hal-00740637>
HAL Id: hal-00740637
Submitted on 10 Oct 2012
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Mode-locking of a terahertz laser by direct phase
J. Maysonnave,1 K. Maussang,1,* N. Jukam,1 J. R. Freeman1, J. Madéo,1 P. Cavalié,1 R.
Rungsawang,1 S.P. Khanna,2 E.H. Linfield,2 A.G. Davies,2 H.E. Beere,3 D.A. Ritchie,3
S.S. Dhillon,1 and J. Tignon1
1Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS (UMR 8551),
Université P. et M. Curie, Université D. Diderot , 75231 Paris Cedex 05 , France
2School of Electronic and Electrical Engineering, University of Leeds, Leeds LS9 2JT, UK
3 University of Cambridge, Cavendish Lab, Cambridge CB3 0HE, UK
Abstract: A novel scheme to achieve mode-locking of a multimode laser is
demonstrated. Traditional methods to produce ultrashort laser pulses are
based on modulating the cavity gain or losses at the cavity roundtrip
frequency, favoring the pulsed emission. Here, we rather directly act on the
phases of the modes, resulting in constructive interference for the
appropriated phase relationship. This was performed on a terahertz quantum
cascade laser by multimode injection seeding with an external terahertz
pulse, resulting in phase mode-locked terahertz laser pulses of 9ps duration,
characterized unambiguously in the time domain.
2012 Optical Society of America
OCIS codes: (140.3520) Lasers, injection-locked; (140.4050) Mode-locked lasers; (140.5965)
Semiconductor lasers, quantum cascade; (300.6495) Spectroscopy : Spectroscopy, teraherz.
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Ultrashort pulses of light have attracted great interest for decades [1-4], resulting in major
fundamental and technological advances, from metrology  to industrial applications .
They result from the temporal interference between modes that are equally spaced in the
frequency domain by the free spectral range (FSR) of a cavity (Fig.1a). For N modes with a
random phase relationship, the combined intensity is random as well, with mean amplitude
scaling as N (Fig.1b, green curve). If, however, the phase difference between consecutive
modes is fixed and constant in time, the laser is described as modelocked. The interference is
then constructive, leading to the formation of a pulse train with peak intensity scaling as N2
and period T given by the round trip time (Fig.1b, blue curve). The experimental realization of
mode-locking is based on two key elements : first, a broadband gain medium that provides
a large number of lasing modes leading to shorter pulses (~T/N); second, a mechanism that
fixes the phase relationship between lasing modes. This is usually performed through internal
modulation of the cavity, either active (e.g. using an acousto-optic modulator) or passive (e.g.
the optical Kerr effect). Additionally, the fixed phase relationship may also be disrupted by
the group velocity dispersion (GVD) of the medium. This can be compensated to achieve
mode-locking by, for example, using an anomalous dispersive element.
Since the original demonstration of mode-locking , there has been a constant effort to
realize similar schemes in various regions of the electromagnetic spectrum. The terahertz
(THz) frequency domain, corresponding to energies in the milli-electronvolt range, has
enormous potential for the exploration of intersubband physics in semiconductors,
superconductors, imaging, gas analysis or biological applications [7, 8]. In 2002, quantum
cascade lasers (QCL) emerge as compact, powerful and efficient sources of THz radiation .
Over the past decade, QCL performance has steadily increased to give a far greater range of
operating frequencies and higher operating temperatures. More recently, advanced
functionalities have been investigated, including pulse amplification , phase-control [11,
12], and mode-locking [13, 14] offering the possibility of using QCLs as a powerful and
versatile source for time-domain spectroscopy (TDS). Only one realization of mode-locking
has been reported in the terahertz spectral range, with an active scheme based on frequency
feedback  but, without direct control over the individual phases.
In the present work, thanks to the unprecedented control over the phase in the THz
domain, we demonstrate a novel approach for mode-locking, where the phase of the laser
longitudinal modes is directly imprinted using multimode injection seeding . We apply
this technique to a 2.75THz quantum cascade laser (QCL), leading to the formation of 9ps
THz laser pulses. The unique ability of Time Domain Spectroscopy  (TDS) and coherent
electro-optic detection [16, 17] to give access to both the amplitude and phase allows to fully
characterize the locked phase relationship between the modes, as well as the initial transient
Fig. 1. a) Frequency domain representation for N=12 modes with equal amplitude. b)
Corresponding time domain intensity profile. A given amplitude spectrum results in different
behaviors in the time domain depending on the phase relationship between modes. The case of
mode-locking, where all modes have the same phase, is illustrated in blue, whereas the case of
a random phase distribution is shown in green.
2. Phase synchronization by multimode injection seeding
The principle of our experiment is schematically depicted in Fig.2 and satisfies the two key
requirements cited above. First, we use a QCL with a 350GHz gain bandwidth, able to sustain
about 11 lasing modes. Second, the phase of the QCL lasing modes is initially fixed by an
external seed with a known phase rather than set randomly by the inherent spontaneous
emission . For this, the QCL is switched-on periodically and synchronously injected with
broadband phase-locked THz seed pulses that have a constant phase over the QCL gain
bandwidth . This multimode injection seeding induces the formation of multiple
longitudinal modes lasing with the fixed phase relationship of the seed. As a result, after a
brief linear amplification regime, the gain is clamped to the losses, leading to the formation of
a train of THz laser pulses with constant amplitude (Fig.2a). Moreover, the QCL is
periodically switched on and off, on a nanosecond timescale so that, as it will be demonstrated
below, the dispersion remains negligible. This periodic switching is performed synchronously
with the seeding, leading to a series of pulse trains, synchronized and phase-locked to each
Fig. 2. a) Time domain: the QCL is gated at low frequency compared to the roundtrip time.
When the laser is switched on, a seeding pulse is injected in the cavity with a field Eseed(t).
After a brief transient regime, the laser gain g(t) is saturated and matches the losses, leading to
an output field Eout(t) consisting in a constant amplitude laser pulse train. b) Frequency domain:
the terahertz seed pulses consist in a frequency comb with spacing frep and no frequency offset
(green full lines). The free running QCL modes have linewidths smaller than frep (blue full
lines) and a priori do not match the excitation comb frequencies. When the laser is gated for
Tgate< 1/frep, lines are broaden up to 1/Tgate with overlap over several frequencies of the
excitation comb (blue dashed lines). If the laser is gated periodically at frep frequency, an inner
comb structure appears, with frep spacing and no frequency offset (red full lines). Each
component of the periodically gated QCL spectrum is then excited by a component of the
excitation terahertz frequency comb, imprinting its phase.
The periodic switching also plays an important role for the resonant injection of the QCL
laser modes, as can be understood in the frequency domain (Fig.2b). The seed field consists in
a series of identical THz pulses with a repetition rate frep (76MHz). As a result, the seed
spectrum is a frequency comb, with spacing frep (Fig.2c , green lines) and no frequency offset
since the carrier phase shift is null . The free-running QCL spectrum displays several
modes, spaced by the FSR, with a linewidth in the MHz range  (blue solid lines).
Consequently, the seed pulse frequency components are a priori not resonant with the free-
running QCL modes. However, when the QCL is turned-on for a time Tgate<1/frep, each QCL
mode broadens to a linewidth Tgate (blue dashed lines), larger than the excitation comb
frequency spacing. Last, since the QCL is periodically turned-on with a gate synchronized to
seeding pulses, the spectrum of the broadened QCL is structured into a comb with spacing frep
and no frequency offset (red lines). Therefore each component of the periodically gated QCL
spectrum is resonantly excited by a component of the seeding terahertz frequency comb,
imprinting its own phase and permitting multi-mode injection seeding.
3. Experimental setup
A schematic diagram of the experiment is shown in Fig.3. The QCL is an AlGaAs/GaAs
bound-to-continuum design with a plasmon waveguide that lases at 2.75THz. The QCL is
cleaved to a length of 1.5mm and soldered with indium onto a copper heat sink which is
maintained at a temperature of 10K. An upper limit of the GVD was estimated to be 4?10-2
ps2/mm at 3THz. Thus, a gaussian pulse of 10ps FWHM broadens by one cycle (333fs) only
after 3ns of propagation. Consequently, the QCL is switched-on for less than 1ns to avoid any
Fig. 3. a) The seed THz pulses are produced by illuminating an interdigited photo-conductive
antenna with near infrared femtosecond laser pulses. After a THz seed pulse enters the QCL, a
square RF pulse synchronized to the femtosecond laser pulse biases the QCL above lasing
threshold. The THz beam emitted and a split-off beam from the femtosecond beam are then
focused onto a ZnTe crystal for the electro-optic sampling detection. b) Detection of the
emitted field, with a quarter wave electro-optic sampling geometry. The signal is proportional
to the amplitude of THz field emitted by the QCL.
A square shape RF is generated by illuminating a photodiode with a Ti:Sapphire
femtosecond laser, with pulse duration of typically 100fs and a repetition rate of 76MHz. This
periodically pulses biases the QCL above lasing threshold , when added to a quasi-DC
bias (25% duty cycle at kHz frequencies) with a bias tee. The RF pulse rise time is typically
400ps with duration of 600ps. A 50Ω RF switch modulates this bias for lock-in detection. The
THz seed pulses are generated with a photo-conductive antenna [19, 20], excited by the same
laser, and are coupled into the facet of the QCL with parabolic mirrors (not shown). An
electronic delay on the RF pulse permits synchronization with the seeding pulse. The antenna
is biased periodically at frequency 2f with a constant polarity. The QCL is modulated at
frequency f=10kHz, whilst the lock-in reference is f, so that in this configuration only the field
emitted by the QCL is detected. The THz beam emitted and a split-off beam from the
femtosecond beam are then focused onto a 200 µm ZnTe crystal for the electro-optic sampling
detection  (Fig.3b): the THz electric field induces a small birefringence and a polarization
rotation of the femtosecond beam, measured in a balanced photodiode scheme. It results in a
direct measurement of the field amplitude and phase, including any transient dynamics.
Fig. 4. a) Amplitude and phase resolved measurements of the emitted electric field, for a THz
seed pulse generated with 4V applied to the photo-conductive antenna, and a DC bias of
120A/cm2 and 7.5W RF pulse applied to the QCL. The seeding pulse is injected in the QCL at
t=-24ps. Inset: expanded view of the TDS measurement between t=526ps and t=528ps. b)
Instantaneous emitted intensity, calculated from the TDS field measurement. A train of pulses,
separated by the cavity round trip (35ps), is clearly visible, with a FWHM of 9ps in intensity. c)
Pulse width (blue square, right axis) and spectrum width (red circle, left axis) as a function of
the number of round trip in the QCL. d) Fourier transform of the measured electrical field in
the steady state regime. Several modes are visible, separated by the cavity free spectral range
(29GHz). A spectrum of the QCL, obtained by Fourier transform infrared spectroscopy (FTIR),
has been superimposed. Both are renormalized to their maximum value and are resolution
Figure 4a shows the amplitude of electrical field E(t) emitted by the QCL, and demonstrates
unambiguously the formation of ultrashort THz laser pulses. At early times (t<300ps), the
frequency components of the seed pulse corresponding to the QCL gain bandwidth are
amplified, whilst the rest undergo losses and rapidly vanish, resulting in a spectral narrowing
(blue squares in Fig.4c). In the time domain, this results in pulse width broadening (red circles
in Fig.4c). After this transient regime of about 300ps, a quasi-constant amplitude train of
pulses is clearly visible, with a FWHM of about 9ps in intensity, as illustrated more clearly by
Fig.4b which shows the square of the electric field E2(t). Figure 4d shows the spectrum
obtained by Fourier transform of the signal measured in the steady state region (red curve). It
is obtained by weighting the signal with a hamming window of 500ps centered at t0=550ps,
and the FFT routine of MATLAB is used to compute the spectrum. It consists of an ensemble
of discrete modes, equally spaced by the QCL FSR (29GHz). The resolution of the
measurement is limited by the length of the mechanical delay line (800ps) that does not allow
the resolution of the underlying QCL frequency comb discussed above. The spectrum of the
free-running QCL (i.e. without seeding and RF modulation), which cannot be determined
using electro-optic sampling, was measured with a commercial FTIR and is also shown in
Fig.4d (resolution limited). Whilst the center frequencies have similar relative amplitudes, the
spectrum of the injected QCL presents additional lasing side-modes, interpreted as a signature
of mode-locking .
Fig. 5. a) The phase of each laser mode (in blue) is obtained from the argument of the complex
FFT of the field measured in the steady state region (t>300ps). Similarly, a measurement of the
seeding pulse field provide after FFT the spectral phase of the seeding pulse (green line). In the
inset, an expanded view for clarity, around the laser modes’ frequencies, showing
unambiguously that the phases are identical. The spectral phase of the seeding pulse has
negligible variation over the frequency bandwidth of the laser (2π×6?10-3 rad standard
deviation). b) Reconstructed field from the measured amplitudes and phases.
The spectral phase of the field can be obtained from the argument of the complex
spectrum at the corresponding frequency, but for a window of 400ps only, centered at
t0=550ps. Error bars are estimated by measuring the phase with the same procedure but for
different values of t0 from 500ps to 600ps. Then, the phase of each mode can be extracted
(Fig.5a, blue dots) and compared to the spectral phase of the seeding pulse (Fig.5a, green
line). They are measured to be almost identical within the error bars. This clearly
demonstrates that (i) there is a fixed phase relationship between all the modes, imprinted by
the seeding, and (ii) the phase difference between the modes is constant, providing optimal
contrast for the interference and hence Fourier-transform limited pulses . As a last
demonstration of the completeness of the measurement, we show in Fig.5b the field calculated
from the measured amplitudes and phases (t>300ps), showing excellent agreement with the
measured field (Fig.4a).
5. Conclusion and outlook Download full-text
In this current work, 9ps THz pulses are generated, limited by the number of modes i.e. the
spectral gain of the laser. This can be easily increased using broadband QCLs  that have
shown bandwidths greater than 1THz. Further, new THz phase-modulation techniques 
could be used to finely adjust the individual phases of the mode phases with on-demand
values. This would provide an integrated pulse shaper, whereas in optics, pulse shaping is a
subsequent . In conclusion, we have shown that mode-locking can be achieved by directly
imprinting the desired phase relationship onto the laser modes of a THz QCL by multimode
phase-locked injection seeding, directly characterized with phase resolved electro-optic
detection. This could lead to experimental investigations of pulse formation dynamics and
stability in QCLs [24-27], and ultimately the generation of ultrashort and intense THz pulses.
Such devices would also be powerful tools for use in THz-TDS, molecular spectroscopy or
coherent control with phase-shaped pulses [23, 28].
We thank Louis-Anne de Vaulchier and François-Régis Jasnot, who performed the FTIR
measurement. We acknowledge funding from ANR (FR), EPSRC (UK) and European
Research Council grants “TOSCA” and “NOTES”.