Spectral Properties of THz Quantum-Cascade Lasers: Frequency Noise, Phase-Locking and Absolute...

Spectral Properties of THz Quantum-CascadeLasers: Frequency Noise, Phase-Locking and AbsoluteFrequency Measurement

Marco Ravaro & Vishal Jagtap & Christophe Manquest &Pierre Gellie & Giorgio Santarelli & Carlo Sirtori &Suraj P. Khanna & Edmund H. Linfield &Stefano Barbieri

Received: 10 December 2012 /Accepted: 29 April 2013 /Published online: 25 May 2013# Springer Science+Business Media New York 2013

Abstract Quantum cascade lasers combine desirable features, namely high optical powerand compactness, as no other coherent source in the field of THz generation. While theirmaximum operating temperature is progressively increasing, getting close to the rangeaccessible by Peltier cooling, their range of application is expanding into new fields, suchus molecular spectroscopy and their use as local oscillators. These applications wouldbenefit from the investigation and improvement of the laser coherence properties. In thiscontribution we report the exploitation of electro-optic coherent detection based on a near-IRfrequency comb to measure the frequency noise of a free running 2.5 THz quantum cascadelaser. An intrinsic linewidth quantum limit of ~230 Hz has been measured, in goodagreement with the Schawlow-Townes theoretical prediction. The same detection schemeis then exploited to phase-lock the quantum cascade laser line to a multiple of the comb toothspacing, while a second comb allows to precisely measure the THz frequency. Such a dual

J Infrared Milli Terahz Waves (2013) 34:342356DOI 10.1007/s10762-013-9981-7

M. Ravaro (*) : V. Jagtap : C. Manquest : P. Gellie : C. Sirtori : S. BarbieriLaboratoire Matriaux et Phnomnes Quantiques, Universit Paris Diderot and CNRS (UMR 7162),10 rue A. Domont et L. Duquet, 75205 Paris, Francee-mail: [email protected]

G. SantarelliLaboratoire Photonique, Numrique et Nanosciences, UMR 5298 Universit de Bordeaux 1, InstitutdOptique and CNRS, 351 cours de la Libration, 33405 Talence, France

S. P. Khanna : E. H. LinfieldSchool of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, UK

Present Address:M. RavaroCNR-Istituto Nazionale di Ottica, Via Carrara 1, 50019 Sesto Fiorentino, Italy

Present Address:S. P. KhannaNational Physical Laboratory, Dr. K. S. Krishna Marg, New Delhi 110012, India

frequency comb experimental setup thus yields a narrow line THz emission traceable to amicrowave frequency standard.

Keywords Quantumcascade lasers . THz generation . THz detection . Coherence . Frequencymetrology

1 Introduction

Owing to output powers in themWrange and covering of the whole spectral region between 1.2and 4.9 THz, with operating temperatures up to 189 K in pulsed mode and 120 K in continuouswave (CW), quantum cascade lasers are promising CW sources for several applications in theTHz range, namely imaging, molecular spectroscopy, and astronomy [15]. In addition, recentdemonstrations of active mode-locking operation and optical seeding are paving the way fortheir employment in applications based on THz broadband pulses [6, 7].

Concerning the CW regime, in many cases applications require a precise knowledge andimprovement of the QCL spectral purity. The frequency stability of THz QCLswas first studiedthrough the use of mixing techniques [8, 9], which have pointed out a linewidth of the order of~MHz (~10 kHz) on a s (ms) timescale, limited by temperature and driving current fluctuations.On the other hand, due to a small expected linewidth enhancement factor (LEF) arising fromtheir symmetric gain spectrum, THz QCLs should exhibit intrinsic linewidths in the sub-kHzrange [10]. Such features were experimentally demonstrated: first, by measuring the LEF of a2.6 THz QCL, using a self-mixing technique, which lead to an estimated LEF of ~0.5 [11];more recently, by measuring the frequency noise power spectral density (FNSD) of a 2.5 THzQCL, using two alternative techniques: one based on the slope of the absorption profile of amolecular transition as frequency discriminator [12]; the other based on the mixing between theQCL emission frequency and a near-IR frequency comb [13].

In the first part of this work we will review this last technique, which, more specifically,relies on an electro-optic heterodyne detection scheme, where a multiple of the tooth spacing ofa near-IR frequency comb is exploited as local oscillator (LO). Due to the low frequency noiseof the latter, the QCL FNSD can be obtained by measuring the frequency noise of theintermediate frequency beat note, in the tens ofMHz range. Compared to the use of a moleculartransition as frequency discriminator, this approach is intrinsically broadband, i.e. it can be usedto measure the FNSD of THz QCLs at virtually any frequency demonstrated to date [14].

The low frequency noise of THz QCLs is favorable to active linewidth reduction throughboth frequency- and phase-locking techniques [15]. Indeed, several demonstrations offrequency stabilization have been reported so far, with the aim of obtaining a high power,metrological grade THz source, possibly referenced to a microwave standard. Such a sourcewould overcome the power limits of current, microwave-traceable, THz generation tech-niques such as i) photomixing of CW NIR lasers referenced to a frequency comb [16], or ii)high-order multiplication of microwave frequencies [17]. Initial improvements of the QCLlinewidth were obtained through the use of a FIR laser line as LO reference and a Schottkydiode mixer [18]. Nevertheless, such approach can be exploited only in narrow spectralwindows around discrete gas laser lines. A similar constraint holds for frequency locking toa molecular absorption line [19]. Thanks to the progress of microwave frequency multipli-cation techniques, THz QCL frequency-locking was later demonstrated using a microwavereference up-converted in the THz range [20, 21]. Whereas this scheme allows directlyreferencing to a microwave frequency standard, potentially giving access to ultra-narrowQCL emission, on the other hand it offers a limited tuning range (~10 %) and requires the

J Infrared Milli Terahz Waves (2013) 34:342356 343

use of a hot-electron bolometer (HEB) mixer, due to the low power available from thereference source.

These limitations were recently overcome by exploiting a NIR frequency comb asreference in combination with room temperature detection schemes such as electro-opticsampling and photo-switching in a GaAs photo-conductor [2224]. In both cases, by feedingthe resulting intermediate frequency beat-note into phase-lock electronics controlling theQCL injected current, the high signal to noise ratio lead to sub-hertz beat-note linewidths.This approach is intrinsically broad-band, as the reference is an effective multi-frequencyLO, covering a few THz wide spectrum composed of dense lines spaced by ~100 MHz.On the other hand, it is not possible to know a priori which multiple of the comb toothspacing is involved in the beat-note generation, which leaves the absolute THz frequencyundetermined. In the second part of this work we will describe the phase-locking of a THzQCL through electro-optic sampling based on a dual NIR frequency comb setup. Besidesresulting in narrow-line THz emission, this approach allows determining the order of therepetition rate harmonic used as reference, thus making the stabilized QCL frequencytraceable to a radio frequency standard [25].

2 Frequency Noise of a THz QCL

The approach that we have developed to measure the FNSD of a THz QCL, is based on twosteps: i) down conversion of the QCL spectrum into the radio frequency range through THzelectro-optic sampling, and ii) measurement of the FNSD of the down-converted QCL line. On

ZnTe /4 /2WP

QCL

lead-acidbattery

QCL

THz

fbeat

RF

EO amplitude modulator

VCO+ tracking circuit

BPfilter

fVCO

near-IRcomb

LPfilter

FFTAnalyzer

fbeat-fVCO

VOUT

fVCO

RF

SpectrumAnalyzer

wire-grid polariserquartz /4 waveplate

RF mixer

RF

balanced detection

HETERODYNEDETECTION

Discriminator

FNSD MEASUREMENT

fRF

RF

Fig. 1 Experimental setup toacquire the FNSD of a THz QCL.The QCL operating temperature isstabilized at 20 K and the laser isdriven in continuous wave using alead-acid battery for minimumnoise. The THz beam is collimat-ed and then focused onto theZnTe crystal with a pair of f1off-axis parabolic mirrors. Backreflections into the QCL cavityare attenuated by a simple homebuilt optical isolator, composedby a quartz quarter-wave plateplus a grid polarizer. At the outputof the heterodyne detection fbeat isof the order of a few tens of MHz.Before the band pass filter(labeled BP) fbeat is summed tothe frequency of an RF synthe-sizer (not shown) in order to bringit close to 140 MHz, the centraloperation frequency of the VCO

344 J Infrared Milli Terahz Waves (2013) 34:342356

the one hand, this approach allows the exploitation of techniques developed in the RF range forthe measurement of the FNSD. On the other hand, it can be used to study the FNSD of THzQCLs at any emission frequency demonstrated to date. This is because the heterodyne down-conversion process is exploitable in the whole THz region covered by QCLs.

2.1 Experimental Setup

In Fig. 1 the full experimental setup is schematized in two sections, each performing one ofthe two functions just mentioned. The heterodyne detection unit is based on a frequencydoubled fs fiber laser emitting at 780 nm with a repetition rate frep ~250 MHz, which acts aslocal oscillator. Such near-IR comb is injected into an electro-optic amplitude modulatordriven by the THz field emitted by the QCL and consisting of a 2 mm-thick ZnTe crystal, apair of /4 and /2 wave plates, and a polarizing beam splitter. The QCL modulates therefractive index of the ZnTe crystal, and the resulting modulation of the comb polarization atthe QCL frequency, QCL, is converted into an amplitude modulation by the subsequentpolarization optics.

At the modulator output (Fig. 2) the near-IR comb exhibits two AM sidebands, spaced byQCL from the carrier. Such sideband combs overlap with the carrier comb and generate a setof beatnotes, with the lowest lying at the frequency

f beat t QCL t n f rep 1

with n = Int(QCL(t)/frep) ~104 and fbeat(t) < frep/2 [26]. fbeat is finally detected using a shot-

noise limited balanced detection unit based on a pair of Si-photodiodes [22]. A direct linkfrom the THz to the tens of MHz range is thus obtained, resulting in a beating signal thatcarries information on the amplitude and the phase of the QCL emission. It should be notedthat in Eq. (1) fbeat and QCL have been explicitly written as time functions, contrary to frep,

f0+jfrep

f0+ QCL+kfrep

frep

f0+(j+1)frep

QCL

0

BW

f

opta

b

f0+ QCL+(k+1)frep

fbeat

Fig. 2 a Schematic of the spec-tral envelope of the amplitude-modulated NIR beam. Red solidand blue dashed curves represent,respectively, the carrier comb andthe sidebands combs at +/QCL, all of bandwidth BW.b Enlargement of the (a) panelshowing the individual combteeth of the optical carrier and ofthe upper terahertz sideband. Hereopt is the optical carrier frequen-cy, f0 is the carrier offsetfrequency, j and k integernumbers, and fbeat the lowestlying beat-note


which can be considered as a constant (see Ref. [13] for details). Under this assumption, thefrequency noise of fbeat(t) reproduces that of the QCL emission line.

The so-obtained fbeat(t) is injected in the FNSD measurement unit where it is firstlypassed through a 10 MHz-wide band-pass filter. Then it is compared, using an RF mixer, tothe frequency of a fast-tuning voltage controlled oscillator (VCO), with a frequency, fVCO(t),tunable from ~5 to ~10 MHz around 140 MHz. By acting on its control voltage, labeledVout(t), fVCO(t) is phase-locked to fbeat(t), with a slope Vout/fbeat = (3.8 MHz/V)

-1 and acontrol bandwidth of 1 to 3 MHz. By tracking fbeat(t), the VCO thus acts as a frequencydiscriminator, with Vout(t) representing the fbeat(t) frequency noise for Fourier frequenciesbelow the locking bandwidth (~1-3 MHz). At the same time, a fraction of Vout(t) is used tofrequency control the QCL current through a slow control loop, with a bandwidth below1 kHz. This is necessary to eliminate the QCL low Fourier frequency noise and consequentfrequency drift (few MHz/s) produced by thermal and mechanical fluctuations, and thusmaintain fbeat(t) within the VCO tuning range. The power spectrum of Vout(t) is thenmeasured using a fast-Fourier transform analyzer (FFT in Fig. 1), and the FNSD of theQCL is finally derived through the above VCO slope.

The QCL used in our experiment oscillates at 2.5 THz and is based on a standard 2.5 mm-long, 240 m-wide ridge-waveguide Fabry-Perot cavity [27]. It was kept at a constanttemperature of 20 K in a Helium flow cryostat and driven in CW at a current of 1.3 A.The red dashed curve in Fig. 3 is an example of measured FNSD, in the 300 Hz-10 MHzFourier frequency range. In the spectrum we can clearly distinguish three different trends: i)up to 10 kHz the QCL frequency is affected by technical noise, that can be ascribed tomechanical vibrations and/or temperature/current fluctuations [28], with a resulting sloperoughly proportional to 1/f2; ii) in the range 10 kHz-100 kHz we observe a flat plateauat ~75 Hz2/Hz that we identify as the quantum noise limit of the QCL FNSD; iii) above100 kHz, the frequency noise power grows as f2, up to the bandwidth of the tracking circuit(~1 MHz). Such behavior arises from the fbeat(t) signal white phase-noise floor introduced bythe shot-noise limited balanced detection, which results in a limited Signal-to-Noise RatioSNR (or phase-noise power density to carrier ratio), of 89 dB/Hz in this case [13].

To experimentally verify this point, we tested our measurement system by replacingfbeat with the signal generated by an RF synthesizer (labeled RF in Fig. 1), with anoutput power yielding the same SNR of +89 dB/Hz. Starting from 300 kHz, the so-obtained blue dotted curve perfectly overlaps with the computed thin, black, solid line

1k 10k 100k 1M 10M10-1

100

101

102

103

104

105

106

1/f 2

SNR =

80dB

110d

B

100d

B

a. QCL from FFT b. RF generator from FFT c. (a-b)

S(f

) (Hz

/Hz)

Frequency (Hz)

89dB

Fig. 3 FNSD S(f) traces of theQCL (red dashed) and the RFgenerator (blue dotted). (note thatbelow ~10 kHz the red dashedcurve is hidden by the identicalblack solid one). The black solidcurve is obtained by dividing thered curve by the blue curve. Thethin black lines represent thecalculated FNSD resulting from alimited SNR (phase- noise powerdensity to carrier ratio),S(f) = (2/SNR) f

2, for SNRsof 80, 89, 100, and 110 dB in1 Hz bandwidth


S(f) = 2/108.9f2, as well as with the red dashed curve. The effect of the finite SNR

on the recorded QCL FNSD can be partially removed by normalizing the latter to thesynthesizer trace. This is shown by the black solid trace in Fig. 3, i.e. the ratiobetween the dashed and the dotted curve, where the white frequency noise plateau ofthe QCL extends up to ~300 kHz.

2.2 Intrinsic Linewidth and Impact of the Optical Feedback

While allowing fast spectral acquisition with high sensitivity and high resolution, theelectro-optic modulator produces an unwanted optical feedback into the QCL cavity, dueto the auto-collimated back reflection from the high refractive index ZnTe crystal. The latterforms an effective 25 cm-long external cavity coupled with the 2.5 mm long QCL cavity,and the resulting change in the Q factor affects the QCL frequency noise. With respect to theQCL intrinsic linewidth 0, the linewidth with feedback can be written as [2931]:

01

1 2H

pKcos 4QCLLext

.c

tg1H

h in o2 2where K is the feedback coupling coefficient, defined as

K 1RQCL RZnTe

RQCL

sLext

LQCLneff3

Here RQCL (0.3) and RZnTe (0.3) are the reflectivities of the QCL facet and ZnTe crystal; His the Henry alpha-factor; neff = 3.5 is the effective index of the QCL lasing mode; Lext = 25 cmand LQCL = 2.5 mm are respectively the length of the external cavity and of the QCL ridge, andthe coupling parameter takes into account all additional attenuation factors, including thefraction of the reflected field that couples back into the lasing mode [30]. This formulaessentially translates the fact that, depending on the phase of the feedback light, the externalmirror can either increase or decrease the Q factor of the cavity, resulting in a linewidthnarrower or larger than its intrinsic value, with a modulation depth determined by K.

As shown in Fig. 1, in order to establish the effect of feedback on the QCL frequencynoise we used a wire grid polarizer followed by a quartz quarter-wave plate to realize asimple optical isolator [13]. The so-obtained reduction of the feedback coupling coefficientwas inferred by investigating the frequency pulling associated with the optical feedback.

-0.75 -0.50 -0.25 0.00 0.25 0.50 0.75

-150

-100

-50

0

50

100

150

200

K=2K=0.1

QCL-

0 (M

Hz)

Lext (1/ )

Fig. 4 Calculated frequencypulling due to the optical feed-back vs. external cavity length. Inthe low feedback regime, K

Assuming that the free running QCL oscillates on a single mode of frequency 0, the lattercan be expressed as follows [30, 31]:

QCL 0 cK4Lext sin 4QCLLext.c

Hcos 4QCLLext

.c

h i4

Depending on the value of the feedback coefficient K, the frequency pulling can exhibittwo different behaviors: in the low feedback regime (K1Eq. (4) has more than one solution, in a number increasing with K, with a frequency spacing~c/(4Lext). At the frontier between these two regimes, for K slightly larger than one, the QCLcan switch from oscillation on a single mode, when the feedback is in phase with the QCLintracavity field, to a multimode regime, when the feedback is out of phase (see Fig. 4).

We found experimentally that when the isolation was set to minimum the QCL passedperiodically from single- to multi-mode operation while moving longitudinally the ZnTecrystal, indicating a feedback coefficient K>1. As shown in the example reported in Fig. 5,in the multi-mode regime we could observe two resonances of the external cavity (FreeSpectral Range ~100 MHz), one of them selecting a set of seven modes of the QCL ridge(Free Spectral Range ~15 GHz). Instead, when the isolation was maximized, when movingthe ZnTe crystal single-mode operation was preserved and fbeat oscillated with a peak-to-peak amplitude of 10 MHz over a period of 60 m, i.e. equal to half the emissionwavelength of the QCL. From the pulling amplitude of 5 MHz, from Eq. (4) (withH=0) we calculate a feedback coupling coefficient K~0.05 (=2.610

-3). Still under theassumption that H=0, from Eq. (2) we have that for K~0.05 then 0.9

black solid curve of Fig. 3). From the 7540 Hz2/Hz white frequency noise level we obtain anintrinsic linewidth 0=75 Hz~235 Hz. This result is in fair agreement with that reported inRef.[12], 0=90 Hz for P=3.3 mW, acquired with a completely different technique. The bluedashed curve was recorded with, minimum isolation, the same output power used for the blackone, andwith the feedback phase delay set so that the QCLwas oscillating on a singlemode.Withrespect to the solid curve, above ~10 kHz the white frequency noise level is reduced byapproximately a factor of 7. From this finding and assuming H=0, using Eq. (2) we calculateK1.65 (0.08), which is consistent with the coexistence of single- and multi-mode operationshown in Fig. 5.

The experimental intrinsic linewidth of 0 ~235 Hz can be compared with the theoret-ical Henrys linewidth of a semiconductor laser [32]:

0 cn0eff

2 hQCLtm 1 2H 8P

5

where n'eff=3.75 is the measured effective group refractive index [33], t=10 cm-1 and

m=5 cm-1 are the QCL calculated total and radiative losses, and P=2 mW is the output power

from one facet. With such values, from Eq. 5 we calculate 0=105 Hz, i.e. approximately afactor of 2 below the linewidth inferred from the experimental FNSD. Such discrepancy could i)suggest thatH is actually non-negligible but rather close to 1, or ii) be ascribed to an additionalbroadening due thermal photons, as formulated in a recent theoretical proposal [34].Nevertheless, due to the experimental uncertainty of our results, systematic measurements ondifferent devices should be performed in order to validate both or one of these hypotheses.

3 Phase Locking to a Frequency Comb and Frequency Referencing of a THz QCL

Starting from the FNSD, the laser line shape can be either calculated numerically, or, in someparticular case, expressed analytically [35]. With respect to our experimental FNSD traces, itshould be noted that while the intrinsic linewidth is a fundamental limit, the actual QCLlinewidth, observed on a reasonable time scale, is strongly broadened by the low-frequencytechnical noise [8, 9]. As shown in Fig. 7, the low Fourier frequency part of the spectrum is

1k 10k 100k100

101

102

103

104

105

maximum isolation minimum isolation

S(f)

(Hz/

Hz)

Frequency (Hz)

75 Hz/Hz

10 Hz/Hz

Fig. 6 Experimental FNSDtraces for an output powerP=2 mW with maximum (blacksolid curve) and minimumisolation (blue dashed curve).The black solid trace is the sameas in Fig. 3


entirely dominated by the 1/f2 noise contribution, which thus determines the QCL linewidth[15]. On the contrary, the white frequency noise emerges at higher frequencies, thereforecontributing just to the onset of line wings. For metrological applications requiring kHzresolution, the QCL spectral purity can be improved by locking the laser frequency to astable reference, with a feedback bandwidth sufficient to completely suppress the formerfrequency noise contribution. In addition, the recourse to such technique can allow a preciseknowledge of the stabilized frequency, depending on the type of reference employed.

3.1 Phase-Locking to a NIR Frequency Comb

The frequency stabilization technique that we describe here is based on the same heterodynedetection scheme introduced in Section 2.1, and exploits the so-obtained down-convertedRF beating to feedback on the QCL injected current. Figure 8 shows the experimental setupfor the phase-locking of a THz QCL to a NIR frequency comb, including a second detectionunit dedicated to the QCL frequency measurement. The QCL output is divided into twobeams by a GaAs beam-splitter and drives two identical electro-optic modulators based onZnTe crystals and on commercial fs-fiber lasers. In the phase-locking unit the lowest lyingbeating fbeat is amplified and compared using a RF mixer to a reference signal fRF generatedby a frequency synthesizer. The error signal, oscillating at fbeat-fRF, is fed into fast phase-lockelectronics and used to control a small fraction of the terahertz QCL bias current.

Figure 9 illustrates the results of phase-locking of a 2.5 THz bound-to-continuum QCLemitting ~3 mWon a single longitudinal mode: in panel (a), the RF spectrum acquired with aresolution bandwidth RBW = 1 MHz shows the free running fbeat, with a signal-to-noiseratio SNR = 30 dB; panels (b) and (c) show the same beat-note after closing the feedbackloop, with RBWs of 100 kHz and 1 Hz, respectively.

As expected, the SNR scales linearly with RBWdown to 1Hz, indicating that approximately100% of the QCL power is locked to n frep in such bandwidth. Given the QCL emitted power,the obtained SNR of 90 dB/Hz corresponds to a NEP of few pW/Hz. The noise bumps inFig. 9b indicate that the phase-lock bandwidth, not limited by the electronic circuit, isof ~1.1 MHz. As discussed above (Fig. 7), the use of a low-noise current driver and an opticalisolator would allow a narrower control bandwidth, thus reducing the minimum QCL powerrequired for the phase-locking. With a locking bandwidth of 100 kHz, given the above NEP, a

1k 10k 100k100

101

102

103

104

105

106

Fast frequency modulationSlow frequency

modulation

fBWFourier Frequency (Hz)

FNSD

(Hz2 /

Hz)

8ln(2)f/

2

Fig. 7 QCL slow and fast fre-quency noise contributions as sin-gled out by the line S(f) = 8ln(2)f/2. The former contribution deter-mines the laser linewidth while thelatter only gives rise to line wings[15]. The interception frequencyfBW thus loosely indicates theminimum feedback bandwidth re-quired to efficiently reduce theQCL linewidth. We remind that theFNSD trace shown here was ac-quired using an optical isolator anddriving the QCL with a lead acidbattery. Otherwise, the controlbandwidth required can be signifi-cantly higher


QCL power of 10 W would yield a signal-to-noise ratio of 15 dB in the locking bandwidth,which is still sufficient to perform the phase-lock with an acceptable cycle slip rate [36].

3.2 Measurement of the n-Factor

With respect to phase-locking to a THz master laser or to a multiplied microwave reference,the main drawback of frequency-comb based phase-locking lies in the lack of knowledge ofthe absolute stabilization frequency. Indeed, the NIR comb provides a multi-frequency LOthat covers a few THz broad spectrum with dense lines. As a consequence, determiningwhich multiple of the comb tooth spacing (the n factor in Eq. (1)) is involved in the fbeatgeneration would require an a priori knowledge of the QCL frequency with accuracy betterthan frep, which is not achievable with standard FTIRs.

On the other hand, as it appears in Eq. (1), the n factor is simply equal tothe derivative dfbeat/dfrep and can in principle be determined by increasing the toothspacing by a sufficient amount frep and by calculating the corresponding ratiofbeat/frep = n. It is important to note that the accuracy required on n, given byn=n|(fbeat)/fbeat|+n|(frep)/frep|

exploited by Yokohama and coworkers to measure the exact output frequency of a100 GHz multiplier chain [25]. Due to the narrow line of the latter (~1 Hz), then~1200 could be measured by changing the repetition rate by only frep=100 Hz. Inthe case of a free running THz QCL, since the n factor is ~104 and (fbeat) ~10 MHz(due to the intrinsic fluctuations of the free running QCL frequency), fbeat should beshifted by fbeat > n (fbeat) ~100 GHz in order to have n

was stable and narrower than 1 Hz (see Fig. 9 panel (c)), fbeat = QCLn frep coulddrift by ~10 kHz/s and its linewidth, LW(fbeat), was limited by those of both f rep and f rep :

LW fbeat f nLW frep 2 nLW frep 2g0:5e10 kHz on 1 s timescale. The mini-

mum tuning necessary to get nn f beat en10 kHze100 MHz,i.e. frep=fbeat/n>10 kHz, well below the maximum frep tuning range. In practice (seebelow), frep was changed by ~1 MHz, corresponding to a total shift of the beatnotefbeat~10 GHz. This results in a change of the n factor, n, during the measurement(see Fig. 10), which had to be monitored and taken into account for the exactdetermination of n.

Fig. 10 Schematic of the n-factor measurement: result of the frep1frep2 tuning in the RF frequencydomain (panels 1a, 2a) and in the optical frequency domain (panels 1b, 2b). With respect to Eq. (1), herefbeat1=n1 frep1-QCL and fbeat2=n2 frep2-QCL. Accordingly, assuming that QCL is constant,f beat1 f beat2 n1 f rep1n2 f rep2 n1f rep n f rep2, with frep=frep1-frep2 and n=n1-n2. This isillustrated in panels 1b-2b, where the red and blue thick arrows describe the total shift of fbeat, fbeat = n1 frep, equal to the difference between n frep2 (grey dashed arrow) and fbeat1-fbeat2. If QCL is notconstant during the measurement (see text), this can be taken into account in the same equation, whichbecomes fbeat1-fbeat2=n1 frep + n frep2-QCL, with QCL = QCL1-QCL2

gascellgas

llQCL

QCL

mixer

near-IR combEO detection

phase-lockelectronics

SA

frep

frequencystandard

RF

near-IR combEO detection

frepRF

RF

fbeat

fRF

fbeat

clock

Fig. 11 Schematic of high resolution spectroscopy experimental setup based on a THz QCL. As in Fig. 8, thesetup includes a NIR frequency comb for the QCL phase-locking, and a second one, which allows measuringthe QCL absolute frequency thanks to the recourse to a frequency standard. In addition, the latter unit cansimultaneously be exploited for spectroscopic measurements, e.g. on a gas cell


The experimental setup was tested with a 2.5 THz QCL similar to that described inSection 3.1, kept at a temperature of 20 K and driven at moderate current so that itoscillated on a single longitudinal mode. After phase-locking fbeat = QCL-n frep tofRF=20 MHz in the phase-locking unit, we measured the repetition rate frep1 and thebeating frequency fbeat1 with the n-factor measurement unit. Then frep was reduced byabout 1 MHz, resulting in an increase of the n-factor n2-n1=n=41, before mea-suring the final frep2 and fbeat2. The measured values are summarized in the followingtable

fbeat frep n

1 62 0815 kHz 250 529 634100 Hz n12 49 7415 kHz 249 482 721100 Hz n1+41

1-2 12 34010 kHz 1 046 9131 Hz 41

During the measurement we also took into account the drift of the repetition rate(not stabilized) in the phase locking unit frep=frep1-frep2=81 Hz, producing a change ofthe QCL frequencyQCL=nfrep~(QCL/frep)frep~(2.5 1012/(96.5 106))frep=20.2 105Hz. On the basis of the above values we finally calculated the n1 factor

n1 f beat1 f beat2n f rep2QCL

f rep1 f rep2 9782:02 0:05 6

With QCL staying locked to n frep, the experiment was found to be reproducible, andalways returned integer n values within the measurement accuracy of 0.05. The phase-lockedQCL frequency can finally be expressed as QCL n1 f rep1 f beat1 n2 f rep2 f beat2 2:450681 THz 1 MHz, with an accuracy limited only by the free running repetition rate ofthe two frequency combs. It is important to stress that a much better accuracy, ~10-11, couldbe achieved by locking frep to a frequency standard, of which we could not dispose duringthe experiments. In this context, Fig. 11 shows an example of possible experimental setup,including a phase-locking unit and a frequency measurement unit, both based on frequencycombs referenced to a microwave frequency standard.

4 Conclusion

This contribution points out that, besides the high emitted power and compactness, THzQCLs exhibit desirable features specifically for spectroscopic and metrological applications.Thanks to the development of an original experimental setup we have measured the FNSDof a 2.5 THz QCL using a NIR fiber frequency comb. Our experimental spectra demonstratethat the previously reported free running MHz linewidth of THz QCLs [8, 9], sufficientlynarrow for former Doppler limited spectroscopy and heterodyning experiments [35], islimited by technical frequency noise arising from temperature and driving currentfluctuations, and environmental instability. In perspective, the development of specificlow noise current drivers and ultra-stable laser heads, as those currently designed forcommercial visible and NIR laser diodes, would result in an improved degree ofcoherence, closer to the intrinsic limit set by quantum noise, which lies in the subkHz range.


On the other hand, for applications requiring a superior spectral purity, the spectralfeatures pointed out by the experimental FNSD are favorable for a radical linewidthreduction through phase-locking. Due to the reasonable feed-back bandwidth necessary toefficiently suppress the low-frequency technical noise, phase-locking has been demonstratedexploiting several experimental schemes based on different types of reference [1824]. Herewe have described phase-locking of THz QCLs based on a dual NIR frequency comb setup.With respect to our former results on frequency comb-based phase-locking [23, 24], the useof a second comb allows exactly determining which multiple of the comb tooth spacing isused as reference, making the QCL emission traceable to a microwave frequency standard.This paves the way to frequency metrology experiments combining the high THz power ofQCLs with the outstanding spectral properties of NIR combs.

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Spectral Properties of THz Quantum-Cascade Lasers: Frequency Noise, Phase-Locking and Absolute Frequency MeasurementAbstractIntroductionFrequency Noise of a THz QCLExperimental SetupIntrinsic Linewidth and Impact of the Optical Feedback

Phase Locking to a Frequency Comb and Frequency Referencing of a THz QCLPhase-Locking to a NIR Frequency CombMeasurement of the n-Factor

ConclusionReferences

Spectral Properties of THz Quantum-Cascade Lasers: Frequency Noise, Phase-Locking and Absolute...

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