Laser Photonics Rev., 1–8 (2016)/ DOI 10.1002/lpor.201600003 LASER & PHOTONICS REVIEWS ORIGINAL PAPER Abstract Optical frequency combs generated by quantum cascade lasers have recently been demonstrated in the mid and far infrared, but a detailed analysis of the possibility of a fine control of the emission to use them for high-resolution spectroscopy and metrology applications is still missing. In this manuscript the attempt of frequency stabilizing a mid-infrared quantum cascade laser comb (QCL-comb) against a metro- logical mid-infrared intracavity-difference-frequency-generated comb through a single phase-locking chain acting on the driv- ing current is presented. Following a brief derivation, simple relations between the QCL-comb frequency parameters and optical quantities such as the refractive index have been found and used to observe how the locking affects the physics of the system. The conclusion is that the current locking essentially acts on the effective refractive index to reduce the offset fluctu- ations (common noise), but does not sensitively affect the group refractive index and the mode spacing. Nonetheless, the over- all single QCL-comb tooth linewidth is reduced from 500 kHz down to values ranging from 1 to 23 kHz on a 40 ms time scale. Frequency stability characterization of a quantum cascade laser frequency comb Francesco Cappelli 1,∗ , Giulio Campo 1 , Iacopo Galli 1 , Giovanni Giusfredi 1 , Saverio Bartalini 1 , Davide Mazzotti 1 , Pablo Cancio 1 , Simone Borri 1 , Borislav Hinkov 2 ,J´ er ˆ ome Faist 2 , and Paolo De Natale 1 1. Introduction Optical frequency combs (OFCs) [1, 2] are nowadays es- sential equipment for ultra-broadband coherent communi- cations [3], and for visible/near-infrared spectroscopy and metrology [4–7]. Since the molecular fingerprint region, characterized by the fundamental ro-vibrational transitions of simple molecules, falls in the mid infrared (MIR), there is a strong demand for OFCs operating in this spectral region (MIR-combs). The most recent and compact techniques to generate MIR-combs employs high- Q microresonators [8–10] and quantum cascade lasers. Quantum cascade lasers (QCLs) [11] are quantum-well semiconductor lasers, emitting MIR or terahertz radiation. The laser transition takes place between two sublevels of the conduction band. Single-frequency QCLs are characterized by a linewidth of the order of 1 MHz on a 100 ms time scale [12, 13]. Many efforts have been done in order to reduce this linewidth together with an absolute control of 1 CNR-INO – Istituto Nazionale di Ottica, Largo Enrico Fermi 6, 50125 Firenze FI, Italy & LENS – European Laboratory for Non-Linear Spectroscopy, Via Nello Carrara 1, 50019, Sesto Fiorentino FI, Italy 2 Institute for Quantum Electronics, ETH Zurich, 8093, Z ¨ urich, Switzerland ∗ Corresponding author: e-mail: [email protected]the frequency [14–17]. The most straightforward approach used to control the emitted frequency consists in modulating the driving current, thus changing the temperature and, as a consequence, the refractive index of the waveguide. Comb emission can be obtained with QCLs designed to have low group velocity dispersion [18,19], where the four- wave mixing process [20] correlates the longitudinal modes of the laser cavity. For MIR-operating devices the upper state lifetime is shorter than the round-trip time, therefore the accumulation of energy during the round trip is not possible and a pulsed passive mode-locked regime cannot be achieved [18, 21–23]. The first characterization of quantum cascade laser fre- quency combs (QCL-combs) focused on the intermode beat note at the cavity round-trip frequency [18]. Then, taking advantage of a dual-comb spectroscopy setup, a mode equidistance fractional accuracy of 7.5 × 10 −16 rel- ative to the carrier (optical frequency) was demonstrated [24]. Moreover, using a high-finesse cavity as multimode C 2016 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Transcript
Laser Photonics Rev., 1–8 (2016) / DOI 10.1002/lpor.201600003
LASER& PHOTONICSREVIEWS
ORIGINAL
PAPER
Abstract Optical frequency combs generated by quantumcascade lasers have recently been demonstrated in the midand far infrared, but a detailed analysis of the possibility ofa fine control of the emission to use them for high-resolutionspectroscopy and metrology applications is still missing. In thismanuscript the attempt of frequency stabilizing a mid-infraredquantum cascade laser comb (QCL-comb) against a metro-logical mid-infrared intracavity-difference-frequency-generatedcomb through a single phase-locking chain acting on the driv-ing current is presented. Following a brief derivation, simplerelations between the QCL-comb frequency parameters andoptical quantities such as the refractive index have been foundand used to observe how the locking affects the physics of thesystem. The conclusion is that the current locking essentiallyacts on the effective refractive index to reduce the offset fluctu-ations (common noise), but does not sensitively affect the grouprefractive index and the mode spacing. Nonetheless, the over-all single QCL-comb tooth linewidth is reduced from 500 kHzdown to values ranging from 1 to 23 kHz on a 40 ms time scale.
Frequency stability characterization of a quantum cascadelaser frequency comb
Francesco Cappelli1,∗, Giulio Campo1, Iacopo Galli1, Giovanni Giusfredi1, Saverio Bartalini1,Davide Mazzotti1, Pablo Cancio1, Simone Borri1, Borislav Hinkov2, Jerome Faist2,and Paolo De Natale1
1. Introduction
Optical frequency combs (OFCs) [1, 2] are nowadays es-sential equipment for ultra-broadband coherent communi-cations [3], and for visible/near-infrared spectroscopy andmetrology [4–7]. Since the molecular fingerprint region,characterized by the fundamental ro-vibrational transitionsof simple molecules, falls in the mid infrared (MIR), there isa strong demand for OFCs operating in this spectral region(MIR-combs). The most recent and compact techniquesto generate MIR-combs employs high-Q microresonators[8–10] and quantum cascade lasers.
Quantum cascade lasers (QCLs) [11] are quantum-wellsemiconductor lasers, emitting MIR or terahertz radiation.The laser transition takes place between two sublevels of theconduction band. Single-frequency QCLs are characterizedby a linewidth of the order of 1 MHz on a 100 ms timescale [12, 13]. Many efforts have been done in order toreduce this linewidth together with an absolute control of
1 CNR-INO – Istituto Nazionale di Ottica, Largo Enrico Fermi 6, 50125 Firenze FI, Italy & LENS – European Laboratory for Non-Linear Spectroscopy,Via Nello Carrara 1, 50019, Sesto Fiorentino FI, Italy2 Institute for Quantum Electronics, ETH Zurich, 8093, Zurich, Switzerland∗Corresponding author: e-mail: [email protected]
the frequency [14–17]. The most straightforward approachused to control the emitted frequency consists in modulatingthe driving current, thus changing the temperature and, asa consequence, the refractive index of the waveguide.
Comb emission can be obtained with QCLs designed tohave low group velocity dispersion [18,19], where the four-wave mixing process [20] correlates the longitudinal modesof the laser cavity. For MIR-operating devices the upperstate lifetime is shorter than the round-trip time, thereforethe accumulation of energy during the round trip is notpossible and a pulsed passive mode-locked regime cannotbe achieved [18, 21–23].
The first characterization of quantum cascade laser fre-quency combs (QCL-combs) focused on the intermodebeat note at the cavity round-trip frequency [18]. Then,taking advantage of a dual-comb spectroscopy setup, amode equidistance fractional accuracy of 7.5 × 10−16 rel-ative to the carrier (optical frequency) was demonstrated[24]. Moreover, using a high-finesse cavity as multimode
2 F. Cappelli et al.: Frequency stability characterization of a quantum cascade laser frequency comb
frequency-to-amplitude converter, the frequency noisepower spectral density of such a device was measured downto the Schawlow-Townes limit [25], proving that the modesare correlated till the quantum limit.
As for early-stage classical femtosecond-lasers fre-quency combs [26], it is worth to study the coherenceproperties of the QCL-combs emission together with thestrategies to control the main optical parameters [27]. Inthis manuscript we investigate the comb properties of themultimodal QCL emission, using an intracavity-difference-frequency-generated metrological comb (IC-DFG-comb)[28] as reference in a dual-comb-like setup. This character-ization is essential for controlling QCL-combs and for mostof the subsequent applications. Basically we phase-lock aQCL-comb tooth to an IC-DFG-comb one and we study thecollective effect on the other QCL-comb teeth. The resultsare interpreted within the framework of frequency combsin terms of offset and spacing frequencies, relating theseparameters and their fluctuations to primary physical quan-tities such as the effective waveguide refractive index andthe group refractive index.
2. Experimental setup
In fig. 1 the experimental setup is shown. The QCL-combis a broad-gain Fabry-Perot device, emitting continuous-wave radiation around 4.70 μm. The spacing ( fs) betweenthe longitudinal modes (QCL-comb teeth) is about 7 GHz.The laser working temperature is 16.5◦C and the currentis 735 mA, with an emitted power of 60 mW on a sin-gle transverse mode. In fig. 2 the laser spectrum measuredwith an FTIR spectrometer is shown. The IC-DFG-combis essentially used to convert the MIR QCL-comb spec-trum down to the radio frequencies (RF). It is generated
Figure 1 Experimental setup used for the beat-note detection.λ/2: half-wave plate to adjust the polarization; BS: asymmet-ric non-polarizing beam splitter (transmission 99%, reflection1%); BP: RF band pass filter (in figure the center frequencyis reported); LP: low pass filter; MIX: RF mixer; PLL: phase-locked-loop electronics. Each frequency synthesizer in the setup(including the ones in spectrum analyzers) is referenced to ahigh-stability Rb/GPS disciplined 10-MHz quartz oscillator.
63000 63500 64000 6450010-4
10-3
10-2
10-1
100
inte
nsity
(a.
u.)
frequency (GHz)
Figure 2 QCL-comb spectrum measured with an FTIR spec-trometer. The resolution is 7 GHz, therefore the laser modescannot be resolved. Considering that the spectrum is 700-GHzwide, and the mode spacing is 7 GHz, an overall number of about100 modes is deduced.
by injecting the radiation emitted by a commercial near-infrared frequency comb (NIR-comb) into a Ti:sapphire(Ti:Sa) laser cavity [28]. There, a non-linear crystal mixesthe Ti:Sa continuous-wave intracavity radiation with theNIR-comb radiation, generating a MIR-comb. Since theTi:Sa is referenced to the same NIR-comb through a lock-ing chain which uses the direct-digital-synthesis (DDS) offrequencies [29, 30], the frequency noise of the IC-DFG-comb (single tooth linewidth) is particularly low (2 kHz in a1-s time scale). Moreover, the long-term frequency stabilityand frequency accuracy of the NIR-comb is transferred tothe MIR-comb in a straightforward way. The average per-tooth power is 1 μW and the repetition rate ( fr ) is 1 GHz.The emitted spectrum is about 300-GHz wide [31].
As shown in fig. 1, the QCL-comb beam (about 1 mW ofpower) is superimposed to the IC-DFG-comb beam (about0.5 mW of power), sending them to a HgCdTe photodetec-tor (200-MHz bandwidth). The recorded heterodyne beat-note signal (HBNS) is used for further analysis of the phasenoise and frequency control of the QCL-comb. A fractionof the HBNS is recorded by an RF spectrum analyzer (spec-trum analyzer 1). When the frequency spacing between theQCL-comb modes and the IC-DFG-comb ones falls withinthe bandwidth of the detector, the obtained RF spectrumis made of several peaks, each of them resulting from thebeating between a QCL-comb tooth and an IC-DFG-combtooth (in a ratio of one every seven). The spacing betweenthese peaks is | fs − 7 fr | (about 10 MHz). This differencecan be positive or negative, and in a HBNS both casescan occur at the same time. The RF peaks coming from apositive difference are named direct, the others are namedfolded.
The HBNS is also used in two RF chains. As representedon the left, the signal is filtered at 30 MHz just to select onlyone peak (with all the parameters chosen to have the bet-ter signal-to-noise ratio). Then it is sent to a home-made
hybrid analog/digital phase-locked-loop (PLL) electronics.The obtained correction signal is then sent to the currentmodulator. The modulator consists of a control circuitryplaced in parallel to the QCL, based on a field-effect tran-sistor (FET) [13]. In particular, the processed error signalis fed to the gate of the FET, which acts by proportionallydecreasing the current flowing through the laser. In orderto reduce the amplitude of the frequency fluctuations from500 kHz down to few kilohertz, the amplitude of the currentmodulation is of the order of 1.3 μA. Thanks to this chainthe filtered HBNS is locked to the 30 MHz local oscillator.In this way the involved QCL-comb tooth is phase lockedto the related IC-DFG-comb tooth.
On the right, the chain to remove the offset is depicted.The HBNS is filtered at 30 MHz to select only one peak,summed in an RF mixer to a 100 MHz signal and then sub-tracted in another mixer to the original HBNS. In this way,spectrum analyzer 2 shows the HBNS where one peak hasbeen subtracted from all the others, therefore any commonfrequency (noise) contribution (namely, the offset contribu-tion) is canceled out.
3. Results
When the QCL-comb operates in free-running regime, thepeaks in the HBNS (observed with spectrum analyzer 1)are about 500-kHz wide (see fig. 4b). As a first step, theperformance of the loop has been tested. The loop has beenclosed and the PLL parameters optimized. Then the HBNShas been acquired with spectrum analyzer 1 in real-timemode. Each acquisition is made of 20 frames. Each framecontains the HBNS in time domain over a 2-ms time in-terval sampled at 75 MHz. Afterwards, for each frame theFourier transform of the signal (amplitude and phase) hasbeen computed. All the 20 obtained amplitude spectra ofan acquisition are reported in fig. 3. In fig. 4 a zoom ofthe locked peak (the one filtered to be used in the lockingchain) is shown. On a frequency span of 2 MHz (fig. 4a) thetypical shape of locked signals is evident, with the bumpsgiven by the electronic bandwidths. On a span of 12 kHz(fig. 4c) the peak is still resolution-bandwidth-limited anda perfect stability over the whole acquisition time is ob-served. In fig. 4c the phase of the signal around the lockedpeak is also reported. The phase is clearly stable over thewhole acquisition, in particular the phase value at peakis (−10.0 ± 0.4)◦ in 40 ms, sampled every 2 ms. Now, forstudying the collective effect of the locking, we concentrateour attention on the other peaks, in particular on the firstneighbor (see fig. 3). On a span of 2 MHz the peak shows ashape very close to the one of the locked peak (see fig. 4a),but on a span of 12 kHz frequency fluctuations are evident(fig. 4d). Nonetheless, they are strongly reduced comparedto the free-running regime. We can estimate a linewidth ofa few kHz against 500 kHz (see fig. 4b).
To be more quantitative, a time tracking (frame-by-frame) of the center frequencies of the peaks has been car-ried out. Each peak in every frame has been fitted with a
Figure 3 FFT amplitude of the 20 frames of an acquisition of theHBNS acquired using spectrum analyzer 1. Each color is relatedto a specific frame. The QCL-comb operates in locking condition.Each frame contains the HBNS in time domain over a 2-ms timeinterval sampled at 75 MHz.
Gaussian function and the center frequency has been ob-tained. In fig. 5 the results are shown (for the labeling ofthe peaks refer to fig. 6). Observing the trend of the redlines frame-by-frame, considering that the fourth peak is thelocked one, the elastic effect typical of frequency-comb sys-tems [29] shows up. In particular the frequency-fluctuationsamplitude increases proportionally to the distance from thefixed peak. This confirms the coherence among the modes.Afterwards, the 20 amplitude spectra have been averaged,yielding the spectrum shown in fig. 6. All the peaks havebeen fitted with a Gaussian function (see fig. 7 for an ex-ample). The obtained widths (σ ) have been plotted againstthe peak number and fitted with the following function:
σ (m) =√
σ 20 (m − m0)2 + RBW 2 (1)
where m numbers the peaks in the HBNS, m0 denotes thelocked peak, and RBW is the instrumental resolution band-width. The use of this function comes from the assumptionthat both the shape of the instrumental function and the dis-tribution of the frequency fluctuations are Gaussian, and itis justified by the fact that the function fits well the acquireddata. σ0 represents the mean square root value of the fre-quency fluctuations of the spacing between the laser modes(� fs) contributing to the HBNS peaks together with theinstrumental resolution. It can be interpreted as the widthof the first-neighbor peak (compared to the locked one) ex-cluding the instrumental resolution. We remark that σ0 doesnot represent a strict estimation of the coherence among themodes, since coherent frequency fluctuations affecting allthe modes do contribute to this width, and this fact is ev-ident from the measurements reported in fig. 5 where theelastic effect is emphasized. Repeating this procedure with
4 F. Cappelli et al.: Frequency stability characterization of a quantum cascade laser frequency comb
Figure 4 a, c) Zoom of the locked peak (see fig. 3): amplitude ona wider (a) and on a narrower span (c), and phase (c). Even on thenarrower span (c) a perfect stability both of the peak amplitudeand phase can be observed. In particular the phase value at peakis (−10.0 ± 0.4)◦ in 40 ms, sampled every 2 ms. d) Zoom of thefirst-neighbor peak in locking operation (see fig. 3). On this narrowspan the presence of frequency fluctuations is evident. b) Peakin free-running operation. The linewidth on a 40-ms time scale is515 kHz.
few different acquisitions (sets of 20 frames) and averagingover the obtained values, yields
σ0 lock = (450 ± 40) Hz (2)
21 3 4 65 7 1098 1211 13 14 1615 17 201918
frame #fr
eque
ncy
(2 k
Hz/
div)
1
2
3
4
5
6
7
8
9
10
11
12
peak #
Figure 5 Time tracking (frame-by-frame) of the center frequen-cies of the peaks in locking operating regime (see fig. 3). Eachpeak in every frame has been fitted with a Gaussian function andthe center frequency has been obtained. For the labeling of thepeaks refer to fig. 6. The errors given by the fit are negligibleon the shown scale. Observing the trend of the red lines frame-by-frame, considering that the fourth peak is the locked one, theelastic effect typical of frequency-comb systems shows up.
0 10 20 30 40 50 60 7010-7
10-6
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average FFTGaussian fit - direct peaksGaussian fit - folded peaks
1211
109
87
6
5
4
32
ampl
itude
(a.
u.)
frequency (MHz)
1
locked peak
Figure 6 Average over the 20 amplitude spectra of an acquisitionin locking operating regime (see fig. 3). Each peak has been fittedwith a Gaussian function (see fig. 7, top for a zoomed view) andlabeled with an integer number m. For the direct peaks the relativeQCL-comb mode has a higher frequency compared to the relativeDFG-comb mode. For the folded peaks the opposite holds.
Since the QCL-comb modes are 100, and considering thatwe phase-lock the central one (or one nearby), the accumu-lated residual frequency noise on the modes on the sides ofthe spectrum is
Figure 7 Top: zoom of the first-neighbor averaged peak (number3 in fig. 6) fitted with a Gaussian function. Bottom: fit of the peakswidths in locking operating regime using eq. 1.
Since the linewidth of the IC-DFG-comb (the reference) is�νDFG = (750 ± 200) Hz (on a 20 ms time scale) [28], wecan state that the overall single QCL-comb mode linewidthis reduced from 500 kHz to values ranging from 1 to 23 kHzon a 40 ms time scale.
Afterwards, in order to study the dynamics of the laser infree-running operation, the locking chain has been opened,and the HBNS has been acquired downstream the chainremoving the offset fluctuations (common noise). The ac-quisitions and the time tracking of the center frequencies ofthe peaks have been obtained in the same manner. In fig. 8the results are shown (for the labeling of the peaks refer tofig. 9). Observing the trend of the red lines frame-by-frame,considering that the third peak is the one used for the off-set subtraction (therefore frequency-fluctuations-free), theelastic effect typical of frequency-comb systems shows upagain, confirming the coherence among the modes even inthis case. A comparison between fig. 5 and 8 shows thatthe locking does not affect the coherence among the combmodes. Then the 20 amplitude spectra have been averaged,giving the spectrum shown in fig. 9. All the peaks have been
21 3 4 65 7 1098 1211 13 14 1615 17 201918frame #
freq
uenc
y (2
kH
z/di
v)
1
2
3
4
5
6
7
8
9
peak #
Figure 8 Time tracking (frame-by-frame) of the center frequen-cies of the peaks in free-running operating regime with the offsetcanceled. Each peak in every frame has been fitted with a Gaus-sian function and the center frequency has been obtained. Forthe labeling of the peaks refer to fig. 9. The errors given by the fitare negligible on the shown scale. Observing the trend of the redlines frame-by-frame, considering that the third peak is the oneused for the offset subtraction (therefore frequency-fluctuations-free), the elastic effect typical of frequency-comb systems showsup.
10-7
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3
average FFT
Gaussian fit - direct peaks
ampl
itude
(a.
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frequency (5 MHz/div)
reference
12
Figure 9 Average over the 20 amplitude spectra of an acqui-sition in free-running operating regime with the offset canceled,acquired using spectrum analyzer 2. The reference peak usedfor the offset subtraction has been pointed out. Each peak hasbeen fitted with a Gaussian function and labeled with an integernumber m. The offset cancellation works for direct peaks.
fitted with a Gaussian function (see fig. 10 for an example).The obtained σ have been plotted against the peak numberand fitted again with eq. 1. The value obtained averagingover few different acquisitions is
σ0 free run. = (343 ± 12) Hz (4)
We remark here that despite the widths of the peaks inthe HBNS are very similar in free running and in lock-ing regime, this is not the case in the optical domain (at
6 F. Cappelli et al.: Frequency stability characterization of a quantum cascade laser frequency comb
10-7
10-6
10-5
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average FFTGaussian fit
sigma = (500.8 ± 3.0) Hz
ampl
itude
(a.
u.)
frequency (2 kHz/div)
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800
1000
1200
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1600
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2000
2200
2400
σ0
= (343 ± 11) Hz
sigm
a (H
z)
peak number
Figure 10 Top: zoom of the first-neighbor averaged peak (num-ber 4 in fig. 9) fitted with a Gaussian function. Bottom: fit of thepeaks widths in free-running operating regime using eq. 1. De-spite the widths of the peaks in the HBNS is very similar in freerunning and in locking regime (see fig. 7), this is not the case inthe optical domain (at 64 THz). In free-running regime the peakslook so narrow (few kilohertz of width) just thanks to the sub-traction of the offset, operation made by the acquisition chain anduseful just for comparing the two combs. In the optical domain thecomb modes in free running operation are broad (about 500 kHz– see fig. 4b).
64 THz). In free-running regime the peaks look so narrow(few kilohertz of width) just thanks to the subtraction ofthe offset, operation made by the acquisition chain and use-ful just for comparing the two combs. In the optical domainthe comb modes are stable in frequency, therefore useful forhigh-resolution spectroscopy applications, only in lockingconditions.
In order to interpret these results in terms of the twomain optical quantities characterizing the laser waveguide– the effective and the group refractive index (nc and ng ,respectively) – a specific discussion is needed (see Sup-plemental material). The frequencies of a reference mode(whose frequency and order are νc and N , respectively) andof its first neighbor are expressed in terms of the effective
Table 1 Measured widths (frequency fluctuations) in free-running and locked operation. The reported values are referredto a 40 ms time scale.
free running locked
� fs (343 ± 12) Hz (450 ± 40) Hz
�νc (500 ± 50) kHz (750 ± 200) Hz
and the group refractive index. Subsequently, the OFC off-set ( fo) and spacing ( fs) parameters and their fluctuationsare derived. The obtained relations for the fluctuations are(see eq. 30 and 31 in Supplemental material)
�nc
nc= −�νc
1
N
2nc L
c(5a)
�ng
ng= −� fs
2ng L
c(5b)
where L = (6.40 ± 0.05) mm is the physical length of thewaveguide, nc = (3.175 ± 0.005), ng = (3.320 ± 0.025),and N = 9030 (computed as the ratio between the opti-cal frequency and the spacing fs).
In table 1 the measured values are collected (refer toeq. 2 and 4). All the reported values are referred to a40 ms time scale. We remark here that the given valuesfor � fs are not a strict estimation of the coherence amongthe modes, since coherent frequency fluctuations affectingall the modes do contribute to this width (see fig. 5 and8 where the elastic effect is emphasized). In order to un-derstand the impact of the locking on the laser parameters,the ratios between the values in locking conditions and infree-running conditions are computed, yielding
�nc
nc
∣∣∣∣lock
= 0.0015 · �nc
nc
∣∣∣∣free
(6a)
�ng
ng
∣∣∣∣lock
= 1.3 · �ng
ng
∣∣∣∣free
(6b)
The main phenomenon that gives the tunability of theemitted frequency in QCLs is the variation of the refractiveindex with temperature (the contribution of the variationof the physical length of the laser cavity due to thermalexpansion is one order of magnitude smaller – see ref. [32]page 178). In phase-locking conditions the driving currentis used to control the temperature of the waveguide throughthe Joule effect. The ratios given in eq. 6 clearly show thatthe loop acts essentially on the effective refractive index nc
reducing its fluctuations in order to stabilize the emission(satisfying �νc = �νDFG). On the other hand �ng/ng isalmost unaffected. This means that the contribution givenby the term related to �nc in �ng is negligible compared
to the one related to the dispersion dn/dν (see eq. 23 givenin Supplemental material). In other words we can state thatthe current control (through temperature) effectively actson the effective refractive index but does not significantlyaffect the dispersion.
4. Conclusion and Outlook
With this work we have thoroughly studied, both exper-imentally and theoretically, how to frequency stabilize aMIR QCL-comb. To this purpose, a metrological MIR IC-DFG-comb has been used as reference. Through a singlephase-locking chain acting on the driving current, one QCL-comb mode has been locked to an IC-DFG-comb mode,and the behavior of the other QCL-comb modes has beenstudied. The locked QCL-comb mode shows a perfectlystable phase difference related to the IC-DFG-comb one –(−10.0 ± 0.4)◦ in 40 ms, sampled every 2 ms –, while theother QCL-comb modes show a reduced linewidth from500 kHz down to values ranging from 1 to 23 kHz ona 40 ms time scale, depending on the distance from thelocked mode. Following a brief derivation, simple relationsbetween the QCL-comb parameters ( fs and fo) and the ef-fective and the group refractive index have been found andused to observe how the locking affects the physics of thelaser. The conclusion is that the current locking essentiallyacts on the effective refractive index n to reduce the off-set fluctuations (common noise), but does not significantlyaffect the group refractive index ng and the mode spacing.This preliminary study paves the way to a full control ofthis type of sources. Several approaches will be tried in or-der to control the mode spacing, like optical feedback andtemperature control independent of current such as irradi-ation of the waveguide using an external laser [15]. Thefull frequency control will dramatically widen the appli-cability of such miniaturized comb sources as broadbandhigh-resolution spectrometers both in dual-comb setups andcoupled to high-finesse cavities.
Supporting Information
Additional supporting information may be found in the online ver-sion of this article at the publisher’s website.
Acknowledgments. We thank Gustavo Villares for useful scien-tific discussions. We gratefully acknowledge funding from ESFRIRoadmap – Extreme Light Infrastructure (ELI) project, Italian Min-istry of Foreign Affairs – “Broadcon” Italy-Israel bilateral project,and EU 7th Framework Program, Laserlab-Europe – grant agree-ment 284464.
Received: 5 January 2016, Revised: 21 April 2016,Accepted: 10 May 2016
Published online: 7 June 2016
Key words: frequency comb, quantum cascade laser, laser sta-bilization.
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