hv photonics

Article Frequency Tuning and Modulation of a Quantum Cascade with an Integrated Resistive Heater

Kutan Gürel 1, Stéphane Schilt 1,*, Alfredo Bismuto 2, Yves Bidaux 2, Camille Tardy 2, Stéphane Blaser 2, Tobias Gresch 2 and Thomas Südmeyer 1

1 Laboratoire Temps-Fréquence, Institut de Physique, Université de Neuchâtel, CH-2000 Neuchâtel, Switzerland; [email protected] (K.G.); [email protected] (T.S.) 2 Alpes SA, CH-2072 Saint-Blaise, Switzerland; [email protected] (A.B.); [email protected] (Y.B.); [email protected] (C.T.); [email protected] (S.B.); [email protected] (T.G.) * Correspondence: [email protected]; Tel.: +41-032-718-2917

Received: 23 June 2016; Accepted: 26 July 2016; Published: 30 July 2016

Abstract: We present a detailed experimental investigation of the use of a novel actuator for frequency tuning and modulation in a quantum cascade laser (QCL) based on a resistive integrated heater (IH) placed close to the active region. This new actuator is attractive for molecular spectroscopy applications as it enables fast tuning of the QCL wavelength with a minor influence on the optical output power, and is electrically-controlled. Using a spectroscopic setup comprising a low-pressure gas cell, we measured the tuning and modulation properties of a QCL emitting at 7.8 µm as a function of the active region and IH currents. We show that a current step applied to the IH enables the laser frequency to be switched by 500 MHz in a few milliseconds, as fast as for a step of the current in the active region, and limited by heat dissipation towards the laser sub-mount. The QCL optical frequency can be modulated up to ~100 kHz with the IH current, which is one order of magnitude slower than for the QCL current, but sufficient for many spectroscopic applications. We discuss the experimental results using a thermal model of the heat transfer in terms of cascaded low-pass filters and extract the respective cut-off frequencies. Finally, we present a proof-of-principle experiment of wavelength modulation spectroscopy of a N2O transition performed with a modulation of the IH current and show some potential benefits in comparison to QCL current modulation, which results from the reduced associated amplitude modulation.

Keywords: quantum cascade laser; frequency tuning; modulation spectroscopy

1. Introduction Quantum cascade lasers (QCLs) [1] are widely used in high resolution molecular spectroscopy and trace gas sensing applications in the mid- spectral region owing to their unique spectral and wavelength tuning properties. QCLs can be designed to emit in a broad wavelength region ranging from below 4 µm to more than 10 µm based on the mature InP material. Singlemode operation with output powers reaching more than 100 mW is routinely achieved nowadays at room temperature using a distributed feedback (DFB) grating [2], or by placing the QCL chip in an external cavity configuration [3]. QCLs can be continuously tuned in wavelength through their temperature or injection current. Temperature tuning is rather slow as the QCL temperature is generally controlled with a thermo-electrical cooler (TEC) through a fairly massive sub-mount. However, with a typical temperature-tuning coefficient of (∆ν/ν)/T « 10´4 K´1 corresponding to ~3 GHz/K in the wavelength range of 8 µm, a large tuning range can be achieved by varying the QCL temperature with a moderate change of the optical output power. Temperature tuning is, thus, mainly used for large but slow frequency sweeping. On the other hand, the QCL wavelength can

Photonics 2016, 3, 47; doi:10.3390/photonics3030047 www.mdpi.com/journal/photonics Photonics 2016, 3, 47 2 of 12 be rapidly changed with the injection current, at frequencies exceeding 100 kHz [4]. However, the tuning range is limited and current modulation induces a significant change of the emitted optical power. QCL current modulation is widely used in sensitive spectroscopic techniques for trace gas sensing like wavelength/frequency modulation spectroscopy (WMS/FMS) [5,6] or photoacoustic spectroscopy (PAS) [7]. Each of these techniques involves a modulation of the laser wavelength and a harmonic demodulation of the output signal detected after light-gas interaction (optical signal in WMS or acoustic signal in PAS). A derivative-like signal of the gas absorption feature is thus obtained, which is used to quantify the gas concentration. However, the strong variation in the optical power induced by the QCL current modulation leads to residual amplitude modulation (RAM). This RAM can distort the harmonic signals of a gas absorption line, in particular by inducing an offset in the first harmonic signal (1f detection) that can be detrimental in some applications, for instance when using this signal as an error signal in a feedback loop to stabilize a laser at the center of a molecular or atomic transition. RAM also results in an asymmetry of the second harmonic signal (2f detection) of a gas absorption line. A novel tuning actuator in QCLs was recently developed by Alpes Lasers. It consists of a small heating element incorporated next to the active region of DFB QCLs [8]. This integrated heater (IH) is a resistive element driven by an electrical current, which heats the laser via Joule’s dissipation. This novel design allows the temperature of the active region to be varied much faster than by direct temperature control with a TEC, with a reduced associated change in optical power compared to QCL current modulation. These properties make this new tuning actuator attractive for gas phase spectroscopy applications. The IH current also constitutes a novel channel to apply fast corrections for frequency stabilization and noise reduction in a QCL. Electrical feedback applied to the QCL current is the standard approach to stabilize a QCL to an optical reference, such as a molecular transition or the resonance of an , where an error signal proportional to the QCL frequency fluctuations is generated. However, other methods have been demonstrated for frequency noise reduction in QCLs that circumvent the use of an optical reference by exploiting the correlation observed between fluctuations of the optical frequency and of the voltage between the QCL terminals [9]. Using the QCL voltage noise as an error signal to reduce the frequency noise requires another actuator that enables fast internal temperature corrections to be applied to the QCL. The reason is that temperature variations were identified to be the major contribution in the conversion of the terminal voltage noise into frequency noise in QCLs [9]. Such a correction signal cannot be applied directly to the QCL current, as it would simply transpose the QCL voltage noise into current noise without significantly changing the fluctuations of the electrical power dissipated in the laser that are responsible for the frequency noise. Therefore, a fast control of the internal temperature of a QCL for noise reduction was implemented by Tombez et al. by illuminating the top surface of the QCL with a near-infrared laser radiation that could be quickly modulated [10]. A feedback bandwidth in the range of 300 kHz was, thus, obtained. Another approach reported by Sergachev et al., consisted of driving the QCL at constant electrical power instead of constant current, which was realized using fast signal processing of the measured voltage noise [11]. The novel actuator based on an IH is attractive for the realization of such noise reduction loops in a significantly simpler and more compact implementation. However, prior to this, a first step consists in properly characterizing the properties of this new IH actuator. In this article, we present a detailed characterization of the modulation properties of such new IH in a QCL emitting at 7.8 µm. The reported characterization includes the tuning coefficients, frequency modulation transfer function, as well as the step response. As an example of applications that can benefit from this new actuator, we present a proof-of-principle experiment of WMS of N2O using a modulation of the IH current, and compare it to the standard approach of injection current modulation. Photonics 2016, 3, 47 3 of 12 Photonics 2016, 3, 47 3 of 12

2.2. Materials Materials and and Methods Methods The QCL QCL manufactured manufacture byd by Alpes Alpes Lasers Lasers incorporates incorporates an integrated an integrated resistive resistive heater, as heater described, as bydescribed Bismuto by et Bismuto al. [8]. The et al. laser [8] is. The a buried-heterostructure laser is a buried-heterostructure DFB-QCL with DFB a- widthQCL with of the a activewidth regionof the ofactive 10.3 regionµm and of a10.3 length m and of 2.25 a length mm. of The 2.25 integrated mm. The heaterintegrated has heater a thickness has a ofthickness 2 µm and of 2 a  widthm and of a 8widthµm, andof 8 ism, located and is at located a distance at a ofdistance ~1 µm of from ~1  them from active the region. active The region. QCL The emits QCL in emits the spectral in the ´1 ˝ ˝ rangespectral between range between 1273 and 1273 1278 and cm 1278within cm−1 within a temperature a temperature range ofrange 0 C of to 0 45°C toC and45 °C delivers and deliver up tos 80up mWto 80of mW output of output power. power. It was It mountedwas mounted on a on copper a copper sub-mount sub-mount housed house ind ain modified a modified version version of theof the laser laser laboratory laboratory housing housing (LLH) (LLH of) of Alpes Alpes Lasers, Lasers, which which accommodated accommodated thethe additionaladditional electricalelectrical connections to drive the IH. The laser and the IH share a commoncommon electrical potential at the laser cathode,cathode, as shown in Figure1 1a,a, andand wereweredriven driven by by twotwoseparate separate home-made home-made low-noise low-noise current current sourcessources [[9]9].. TheseThese driversdrivers can can deliver deliver a a current current up up to to 1 A1 andA and have have a noise a noise spectral spectral density density lower lower than 1/2 1than nA/Hz 1 nA/Hzat1/2 Fourier at Fourier frequencies frequencies higher higher than than 1 kHz. 1 kHz This. This feature feature generally generally enables enables accessing accessing the frequencythe frequency noise noise inherent inherent to a QCLto a itself,QCL itself without, without technical technical limitation limitation resulting resulting from the from QCL the current QCL sourcecurrent [ 12 source]. The [12] IH. hasThe a IH nearly has ohmica nearly response, ohmic response as shown, as in shown Figure 1inb, Figure with an 1 assessedb, with an resistance assessed ofresistance ~9 Ω that of is~9 almost Ω that independentis almost independent of temperature. of temperature The QCL. The temperature QCL temperature was regulated was regulated at the mK at levelthe mK with level a double-stage with a double TEC and-stage a negative TEC and thermal a negative coefficient thermal (NTC) coefficient resistor as temperature (NTC) resistor sensor, as controlledtemperature by sensor, a home-made controlled temperature by a home regulator.-made temperature regulator.

Figure 1.1. (a) Electrical connection scheme of the QCL with IH with their respective current source source;; (b) current-voltagecurrent-voltage responseresponse of of the the IH IH at at a sub-mounta sub-mount temperature temperature of 25 of˝ C.25 The°C. dataThe data points points (light (light blue) areblue) well are approximated well approximated by the by pure the ohmicpure ohmic response response described described by the by dashed the dashed dark blue dark line. blue line.

The frequency tuning, impulse response and modulation transfer function of the laser were The frequency tuning, impulse response and modulation transfer function of the laser were measured using a spectroscopic set-up that involved a 10-cm long low-pressure gas cell filled with a measured using a spectroscopic set-up that involved a 10-cm long low-pressure gas cell filled with nominal pressure of 10 mbar of pure N2O. However, the imperfect tightness of the cell induced a a nominal pressure of 10 mbar of pure N O. However, the imperfect tightness of the cell induced contamination by air at a total pressure2 of ~70 mbar (see Section 3.1), which broadened the a contamination by air at a total pressure of ~70 mbar (see Section 3.1), which broadened the absorption absorption lines. The tuning coefficients as a function of temperature, injection current and IH lines. The tuning coefficients as a function of temperature, injection current and IH current were current were obtained by performing a large frequency scan with each actuator and comparing the obtained by performing a large frequency scan with each actuator and comparing the position of position of several N2O absorption lines to their reference frequency extracted from the HITRAN several N O absorption lines to their reference frequency extracted from the HITRAN database [13]. database 2[13]. The frequency modulation (FM) response of the QCL was measured by tuning the The frequency modulation (FM) response of the QCL was measured by tuning the laser to the side of laser to the side of an absorption line used as a frequency discriminator that linearly converted the an absorption line used as a frequency discriminator that linearly converted the frequency modulation frequency modulation of the laser (induced by a small modulation of the injection current or of the of the laser (induced by a small modulation of the injection current or of the IH current) into intensity IH current) into intensity modulation that was detected with a photodiode (PVI-4TE-5 from Vigo, modulation that was detected with a photodiode (PVI-4TE-5 from Vigo, Ozarow Mazowiecki, Poland, Ozarow Mazowiecki, Poland, with a bandwidth of 100 MHz). The resulting intensity modulation with a bandwidth of 100 MHz). The resulting intensity modulation was measured in amplitude and was measured in amplitude and phase using a lock-in amplifier and converted into frequency phase using a lock-in amplifier and converted into frequency modulation using the measured slope of modulation using the measured slope of the absorption line (see Figure 2). the absorption line (see Figure2). Finally, the applicability of the IH for spectroscopy applications was evaluated by the Finally, the applicability of the IH for spectroscopy applications was evaluated by the measurement of the first harmonic WMS signal of a N2O transition obtained by modulating either measurement of the first harmonic WMS signal of a N O transition obtained by modulating either the the IH current or the QCL current at the same frequency2 of 25 kHz and at different IH or QCL currents. IH current or the QCL current at the same frequency of 25 kHz and at different IH or QCL currents.

Photonics 2016, 3, 47 4 of 12 Photonics 2016, 3, 47 4 of 12 Photonics 2016, 3, 47 4 of 12

FigureFigure 2. 2Example. Example of of N N2O2O absorption absorption line line used used as a frequency discriminator discriminator to to measure measure the the FM FM Figure 2. Example of N2O absorption line used as a frequency discriminator to measure the FM −1 responseresponse of ofthe the QCL. QCL. The The P11e P11e line line of of the the vibrationalvibrational band νν11 ofof NN2O2O located located at at 1275.5 1275.5 cm cm´ −was1 was used used response of the QCL. The P11e line of the vibrational band ν1 of N2O located at 1275.5 cm was used in this case and is shown here. The absorption spectrum was measured by tuning the QCL or IH in thisthis casecase and and is is shown shown here. here. The The absorption absorption spectrum spectrum was was measured measured by tuning by tuning the QCL the or QCL IH current or IH current and recording the voltage of the photodiode at the output of the reference gas cell. The andcurrent recording and recording the voltage the of voltage the photodiode of the photodiode at the output at of the the outputreference of gas the cell. reference The current gas cell. axis wasThe current axis was converted into a relative frequency using the separately measured tuning convertedcurrent axis into was a relative converted frequency into using a relative the separately frequency measured using the tuning separately coefficient. measured The operating tuning coefficient. The operating point is shown by the red circle and the linear range by the red line with a pointcoefficient. is shown The byoperating the red circlepoint andis shown the linear by the range red bycircl thee and red the line linear with arange slope byD .the red line with a slope D. slope D. 3.3 Results. Results 3. Results 3.1.3.1. Tuning Tuning Coefficients Coefficients 3.1. Tuning Coefficients The static tuning coefficients of the QCL were determined from the position of various N O The static tuning coefficients of the QCL were determined from the position of various N2O2 absorptionabsorptionThe static lines lines tuning measured measured coefficients during during of aa scanscanthe QCL (see(see Figurewere determined33a)a) andand plotted from as as thea a function function position of of ofthe the various reference reference N2 O frequencyabsorptionfrequency extracted lines extracted measured from from the theduring HITRAN HITRAN a scan database database (see Figure [[13]13] forfor 3a) temperaturetemperature and plotted ( (T as),), injection injectiona function current current of the (I (QCL IreferenceQCL) and) and IHfrequencyIH current current extracted (IIH (IIH) tuning,) tuning, from respectively. respectively the HITRAN. database [13] for temperature (T), injection current (IQCL) and IH current (IIH) tuning, respectively.

Figure 3. (a) N2O absorption spectrum measured by tuning the QCL with the electrical power Figure 3. (a)N2O absorption spectrum measured by tuning the QCL with the electrical power dissipated in the IH (bottom spectrum obtained at T = 25 ˝°C and IQCL = 450 mA) and corresponding dissipatedFigure 3. ( ina) theN2O IH absorption (bottom spectrum spectrum obtained measured at T = by 25 tuningC and theIQCL QCL= 450 with mA) the and electrical corresponding power N2O absorption spectrum calculated from HITRAN database [13] for a N2O pressure of 10 mbar Ndissipated2O absorption in the spectrum IH (bottom calculated spectrum from obtained HITRAN at databaseT = 25 °C [13 and] for IQCL a N =2 O450 pressure mA) and of 10corresponding mbar diluted diluted in air (total pressure of 70 mbar) over a pathlength of 10 cm (upper spectrum). The reference in air (total pressure of 70 mbar) over a pathlength of 10 cm (upper spectrum). The reference spectrum N2Ospectrum absorption is inverted spectrum for the calculated clarity of fromthe figure HITRAN. The total database pressure [13] in for the areference N2O pressure cell that of resulted 10 mbar is inverted for the clarity of the figure. The total pressure in the reference cell that resulted from air dilutedfrom inair aircontamination (total pressure arising of 70 from mbar) the ove imperfectr a pathlength cell tightness of 10 wascm (upperestimated spectrum). to be ~70 The mbar reference from contamination arising from the imperfect cell tightness was estimated to be ~70 mbar from comparisons spectrumcomparisons is inverted between for measuredthe clarity and of the calculated figure. Thespectra total; ( bpressure) corresponding in the reference static tuning cell thatcurve resulted as a between measured and calculated spectra; (b) corresponding static tuning curve as a function of the IH fromfunction air contamination of the IH current arising (green from markers: the imperfect experimental cell tightness points; redwas dashed estimated line: to quadratic be ~70 mbar fit) and from currentcomparisonsassociated (green variationbetween markers: ofmeasured experimentalthe optical and power calculated points; (blue red marker spectra dasheds:; Experimental line:(b) corresponding quadratic points; fit) ands taticblue associated dashedtuning curveline: variation 3 rdas a offunction theorder optical polynomialof the power IH current fit) (blue. The markers:(green experimental markers: Experimental data experimental of the points; optical bluepoints; power dashed werered dashed line:extracted 3rd line: orderfrom quadratic the polynomial measured fit) and fit).

Theassociatedtransmission experimental variation through data of of thethe the opticalN optical2O cell; power power the gaps (blue were in extractedmarkerthe datas: result fromExperimental thefrom measured the presencepoints; transmission blue of N dashed2O absorption through line: 3 the rd Norder2linesO cell; polynomial that the have gaps been fit) in the. removed.The data experimental result from thedata presence of the optical of N2O power absorption were linesextracted that havefrom beenthe measured removed.

transmission through the N2O cell; the gaps in the data result from the presence of N2O absorption TuninglinesTuning that of have the of theQCLbeen QCL removed. injection injection current current or sub-mount or sub-mount temperature temperature results results in a nearly in a linearnearly frequency linear sweep.frequency On the sweep other. hand,On the the other frequency hand, tunes the frequency quadratically tunes with quadratically the IH current with as the shown IH current in Figure as3 b, resultingshownTuning fromin Figure of the the Ohm’s3 b, QCL resulting law injection dependence. from currentthe Ohm The or’s law quadraticsub depende-mount response ncetemperature. The also quadratic shows results response that in the a IHnearlyalso affects shows linear the frequency sweep. On the other hand, the frequency tunes quadratically with the IH current as shown in Figure 3b, resulting from the Ohm’s law dependence. The quadratic response also shows

Photonics 2016, 3, 47 5 of 12 Photonics 2016, 3, 47 5 of 12 that the IH affects the QCL frequency purely thermally through Joule’s dissipation. This leads to a QCLlinearPhotonics frequency response 2016, 3of purely, 47 the laser thermally frequency through as a function Joule’s dissipation. of the electrical This power leads todissipated a linear responsein the5 IHof 12 that of the is displayed in Figure 4 in comparison with the temperature and QCL-current tuning curves. The laserthat frequency the IH affects as a function the QCL of frequency the electrical purely power thermally dissipated through in Joule’s the IH dissipation. that is displayed This leads in Figure to a 4 in assessed tuning coefficients are −2.9 GHz/K (vs temperature), −37 GHz/W (vs dissipated power in the comparisonlinear response with the of the temperature laser frequency and as QCL-current a function of tuningthe electrical curves. power The dissipated assessed in tuning the IH coefficientsthat is areactive´displayed2.9 region GHz/K from in Figure (vs the temperature), QCL 4 in current) comparison ´and37 with− GHz/W29 GHz/W the temperature (vs (vs dissipated. dissipated and power QCL power-current in in the the tuning active IH), respectively. curves.region fromThe The the QCLpowerassessed current) tuning tuning coefficient and ´coefficients29 GHz/W for the are IH − (vs.2.9 is GHz/K slightly dissipated (vs lower temperature), power than infor the− the37 IH),GHz/W QCL respectively. current, (vs dissipated as the The power heat power dissipationin the tuning coefficientoccursactive at a region forslightly the from IHlarger the is QCL slightly distance current) lower from and thanthe −29 activeGHz/W for the area, (vs QCL. dissipatedthus current, resulting power as in the in a the heatlower IH), dissipation respectively.heating of this occursThe latter at aregion. slightlypower The larger tuning corresponding distance coefficient from thermalfor the the IH activeresistance is slightly area, Rlowerth thus associated than resulting for thewith in QCL athe lower current, heating heating as of the the ofheat laser this dissipation active latter region.region by theoccurs dissipated at a slightly power larger P distancewas determined from the active from area, the thus ratio resulting of the in power a lower and heating temperature of this latter tuning The corresponding thermal resistance Rth associated with the heating of the laser active region by the region. The corresponding thermal resistance Rth associated with the heating of the laser active region dissipatedcoefficients, power Rth =P (wasΔν/Δ determinedP)/(Δν/ΔT). from It amounts the ratio to of R theth, QCLpower = 12.8 and temperature(K/W) and R tuningth, IH =coefficients, 10 (K/W), respectively,by the dissipated for the heat power sources P was resulting determined from from the the QCL ratio current of the and power IH andcurrent. temperature tuning Rth = (∆ν/∆P)/(∆ν/∆T). It amounts to Rth, QCL = 12.8 (K/W) and Rth, IH = 10 (K/W), respectively, coefficients, Rth = (Δν/ΔP)/(Δν/ΔT). It amounts to Rth, QCL = 12.8 (K/W) and Rth, IH = 10 (K/W), for therespectively, heat sources for the resulting heat sources from resulting the QCL from current the QCL and IHcurrent current. and IH current.

FigureFigure 4. Static4. Static tuning tuning coefficients coefficients of of the the QCL measured measured for for temperature, temperature, QCL QCL-current-current and and Figure 4. Static tuning coefficients of the QCL measured for temperature, QCL-current and IH-current IH-currentIH-current tuning, tuning, respectively respectively (markers: (markers: ExperimentalExperimental points; points; lines: lines: Linear Linear fits) fits). . tuning, respectively (markers: Experimental points; lines: Linear fits). 3.2. Tuning3.2. Tuning Speed Speed 3.2. Tuning Speed The The tuning tuning speed speed of of the the QCL QCL has has been been determined from from the the frequency frequency step step response response to a to a change of the injection current, IH current, and temperature, respectively. For this measurement, the changeThe of tuning the injection speed ofcurrent, the QCL IH hascurrent, been and determined temperature, from therespectively. frequency For step this response measurement, to a change the of thelaser injection was tuned current, to the IH side current, of a N and2O temperature,absorption line respectively., as illustrated For in thisFigure measurement, 5. The optical the power laser was laser was tuned to the side of a N2O absorption line, as illustrated in Figure 5. The optical power transmitted through the gas absorption cell was monitored on an oscilloscope using a fast tuned to the side of a N2O absorption line, as illustrated in Figure5. The optical power transmitted transmittedphotodiode. through A small the step gas of current absorption (1.2 mA cell for wasthe QCLmonitored or 6.6 mA on for an the oscilloscope IH) or of temperature using a fast through the gas absorption cell was monitored on an oscilloscope using a fast photodiode. A small step photodiode.(0.16 K) wasA small applied, step producingof current a (1.2 frequency mA for change the QCL of approximately or 6.6 mA for 500 the MHz. IH) or The of temporal temperature of current (1.2 mA for the QCL or 6.6 mA for the IH) or of temperature (0.16 K) was applied, producing (0.16evolution K) was ofapplied, the QCL producing frequency a was frequency linearly converted change of into approximately a change of the 500 transmitted MHz. The optical temporal aevolution frequencypower ofin change t thehe side QCL ofof approximatelythe frequency absorption was line. 500 linearly MHz. converted The temporal into evolution a change of of the the QCL transmitted frequency optical was linearlypower in converted the side of into the a absorption change of theline. transmitted optical power in the side of the absorption line.

Figure 5. (a) Experimental principle of the QCL frequency step response measurement using an

absorption line of N2O; (b) the side of the absorption profile (blue curve) corresponding to the P11e

line of N2O at 1275.5 cm−1 acts as a frequency discriminator (dashed red line) that linearly converts FigureFigure 5.5. (a(a) )Experimental Experimental principle principle of of the the QCL QCL frequency frequency step step response response measurement measurement using using an the change of the laser frequency into a change of the transmitted optical power detected by a anabsorption absorption line line of ofN2 NO; O;(b) ( bthe) the side side of ofthe the absorption absorption profile profile (blue (blue curve) curve) corresponding corresponding to to the P11e photodiode. A current2 step of the QCL, IH or TEC was applied (from I1 to I2, see inset) to produce an line of N2O at 1275.5 cm´−11 acts as a frequency discriminator (dashed red line) that linearly converts line ofexponential N2O at 1275.5 frequency cm changeacts as (schematized a frequency by discriminator the green line) (dashed of approximately red line) that 500 linearly MHz that converts was the the change of the laser frequency into a change of the transmitted optical power detected by a changerecorded of the by laser an oscilloscope. frequency into a change of the transmitted optical power detected by a photodiode. photodiode. A current step of the QCL, IH or TEC was applied (from I1 to I2, see inset) to produce an A current step of the QCL, IH or TEC was applied (from I1 to I2, see inset) to produce an exponential exponential frequency change (schematized by the green line) of approximately 500 MHz that was frequency change (schematized by the green line) of approximately 500 MHz that was recorded by anrecorded oscilloscope. by an oscilloscope.

Photonics 2016, 3, 47 6 of 12 Photonics 2016, 3, 47 6 of 12

PhotonicsThe 2016 monitored, 3, 47 signals were recorded on the oscilloscope and are displayed in Figure 6 (for6 of 12a The monitored signals were recorded on the oscilloscope and are displayed in Figure6 (for temperature step) and in Figure 7 (for a step of the QCL or IH current). Here, the frequency change a temperature step) and in Figure7 (for a step of the QCL or IH current). Here, the frequency resultingThe monitored from a step signals of the were IH currentrecorded is on nearly the oscilloscope as fast as for and a are step displayed of the injection in Figure current: 6 (for a change resulting from a step of the IH current is nearly as fast as for a step of the injection current: frequencytemperature step step) of 500and MHz in Figure is achieved 7 (for a in step a similar of the QCLtimescale or IH of current). a few milliseconds. Here, the frequency In comparison, change a frequency step of 500 MHz is achieved in a similar timescale of a few milliseconds. In comparison, theresulting temperature from a control step of withthe IH the current TEC is is approximately nearly as fast as four for orders a step of of magnitude the injection slower current:. The a thetemporalfrequency temperature responsestep control of 500 observed withMHz theis achieved forTEC a is temperature approximately in a similar steptimescale four applied orders of a oftofew magnitude the milliseconds. QCL sub slower.- mountIn comparison, The is temporal well responseapproximatedthe temperature observed by controlfor a single a temperature with exponential the TEC step decay is applied approximately with to a longthe QCL time four sub-mount constant orders of of magnitude is ~100 well s approximated (dashed slower line. The inby a singleFiguretemporal exponential 6). response decay observed with a for long a time temperature constant step of ~100 applied s (dashed to the line QCL in Figure sub-mount6). is well approximated by a single exponential decay with a long time constant of ~100 s (dashed line in Figure 6).

Figure 6. Temporal evolution of the QCL optical frequency measured for a step change of the TEC Figure 6. Temporal evolution of the QCL optical frequency measured for a step change of the TEC temperature of ~0.16 K, displayed in a semi-log scale. The inset shows a linear representation. The temperature of ~0.16 K, displayed in a semi-log scale. The inset shows a linear representation. experimentalFigure 6. Temporal data are evolution well approximated of the QCL by optical a single frequency exponential measured decay withfor a a step time change constant of ofthe ~100 TEC s The experimental data are well approximated by a single exponential decay with a time constant (dashedtemperature-dotted of ~0.16line). K, displayed in a semi-log scale. The inset shows a linear representation. The of ~100experimental s (dashed-dotted data are well line). approximated by a single exponential decay with a time constant of ~100 s In(dashed contrast,-dotted the line). temporal response to a step of the QCL or IH current shows a very different behaviorIn contrast, (Figure the 7) temporalcharacterized response by a strong to a step deviation of the from QCL a or single IH current exponential shows response a very, differentwhich behaviorindicatesIn (Figurecontrast, that different7) the characterized temporal thermal response time by a constants strong to a step deviation are of involved the fromQCL in aor single theIH system.current exponential showsFor a stepa response, very of thedifferent QCL which behavior (Figure 7) characterized by a strong deviation from a single exponential response, which indicatescurrent, that a very different fast change thermal of the time optical constants frequency are involvedis first observed in the with system. a time For constant a step ofτ1 < the 1 μ QCLs, indicates that different thermal time constants are involved in the system. For a step of the QCL current,which ais very not completely fast change resolved of the optical in the plot. frequency This very is first short observed time constant with ais time attributed constant to theτ1

Figure 7. Temporal evolution of the QCL optical frequency measured for a step change of the QCL

current (a) and IH current (b), displayed in a semi-log scale. The insets show a linear representation Figure 7. Temporal evolution of the QCL optical frequency measured for a step change of the QCL Figureof the 7. initialTemporal 0.5-ms evolution decay. The of temporal the QCL response optical frequencydoes not correspond measured to for a single a step exponential change of thedecay QCL current (a) and IH current (b), displayed in a semi-log scale. The insets show a linear representation currentof time (a )constant and IH currentτ2 (dashed (b),-dotted displayed lines), in but a semi-log is modelled scale. by The the insets sum showof four a decaying linear representation exponential of of the initial 0.5-ms decay. The temporal response does not correspond to a single exponential decay theterms initial (dashed 0.5-ms lines). decay. The temporal response does not correspond to a single exponential decay of of time constant τ2 (dashed-dotted lines), but is modelled by the sum of four decaying exponential time constant τ (dashed-dotted lines), but is modelled by the sum of four decaying exponential terms terms (dashed2 lines). (dashed lines).

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Photonics 2016, 3, 47 7 of 12 For a change of the IH current, a similar temporal response is observed (Figure7b), which is For a change of the IH current, a similar temporal response is observed (Figure 7b), which is dominated by the time constants τ3 « 0.8 ms and τ4 « 4 ms that are close to the case of the QCL dominated by the time constants τ3 ≈ 0.8 ms and τ4 ≈ 4 ms that are close to the case of the QCL current. However, the first two time constants are not as short (τ1 « 8 µs and τ2 « 50 µs, respectively). Thiscurrent. results However, from the the fact first that two the heattime isconstants not directly are generatednot as short in ( theτ1 ≈ active8 μs and region, τ2 ≈ 5 but0 s at, respectively). some distance fromThis it, results and some from time the isfact needed that the until heat the is dissipated not directly heat generated reaches thein the active active region. region, but at some distance from it, and some time is needed until the dissipated heat reaches the active region. The cut-off frequency f i = 1/(2πτi) associated to each of these time constants will be better The cut-off frequency fi = 1/(2πτi) associated to each of these time constants will be better identified in the measurement of the frequency modulation (FM) transfer functions of the laser identified in the measurement of the frequency modulation (FM) transfer functions of the laser presented in Section 3.3. presented in Section 3.3. 3.3. Frequency Modulation Response 3.3. Frequency Modulation Response The FM transfer functions obtained for a modulation of the QCL injection current or IH current The FM transfer functions obtained for a modulation of the QCL injection current or IH current are displayed in Figure8 (in amplitude and phase) for different average IH currents. The FM response are displayed in Figure 8 (in amplitude and phase) for different average IH currents. The FM with respect to the QCL injection current modulation is independent of the IH current. For IH response with respect to the QCL injection current modulation is independent of the IH current. For current modulation, the FM response (in terms of frequency tuning coefficient per unit of IH current, IH current modulation, the FM response (in terms of frequency tuning coefficient per unit of IH in GHz/mA) scales almost linearly with the average IH current as a result of the quadratic thermal current, in GHz/mA) scales almost linearly with the average IH current as a result of the quadratic response of the heater, previously shown in Figure3b. If expressed per unit of dissipated electrical thermal response of the heater, previously shown in Figure 3b. If expressed per unit of dissipated power (in GHz/W), the tuning coefficient for the IH at low modulation frequency becomes nearly electrical power (in GHz/W), the tuning coefficient for the IH at low modulation frequency becomes independent of the average IH current, on the order of 20 GHz/W that is in good agreement with the nearly independent of the average IH current, on the order of 20 GHz/W that is in good agreement valuewith previouslythe value previously obtained forobtained the DC for tuning the DC coefficient. tuning coefficient. The FM The response FM response for QCL for injection QCL injection current showscurrent a bandwidth shows a bandwidth of ~1 MHz, of corresponding~1 MHz, corresponding to a drop to of a 10 drop dB inof amplitude10 dB in amplitude and to an and associated to an ˝ phaseassociated shift of phase´90 shift, a value of −90 that°, a is value acceptable that is inacceptable a feedback in loopa feedback to stabilize loop to the stabilize frequency the offrequency a QCL to anof optical a QCL reference.to an optical For reference. a modulation For a ofmodulation the IH current, of the aIH bandwidth current, a bandwidth of around 100of around kHz is 100 typically kHz achieved,is typically defined achieved, in the def sameined wayin the as same for the way QCL as for current the QCL modulation. current modulation.

Figure 8. FM transfer function in amplitude (a) and phase (b) obtained for a modulation of the Figure 8. FM transfer function in amplitude (a) and phase (b) obtained for a modulation of the QCL-current (blue lines) and IH-current (red lines), both at different IH currents IIH. QCL-current (blue lines) and IH-current (red lines), both at different IH currents IIH. In order to investigate more quantitatively these FM transfer functions and get a deeper understandingIn order to of investigate the observed more dynamic quantitatively responses these, we modelled FM transfer the thermal functions response and get R( af) deeperof the understandingQCL (obtained of by the normalizing observed dynamic the dynamic responses, FM responsewe modelled by its the value thermal at 1 response Hz) by Rcascaded(f ) of the QCLfirst (obtained-order low by-pass normalizing filters that the describe dynamic the FM heat response extraction by itsin different value at 1parts Hz) byof the cascaded laser following first-order low-passthe model filters previously that describe used by the Tombez heat extraction et al. [4] in. By different considering parts that of the the laser output following frequency the of model the previouslylaser is mainly used by determined Tombez et by al. the [4]. average By considering temperature that the in the output active frequency region and of the that laser the isapplied mainly determinedcurrent modulation by the average (to the temperature heater or active in the region) active induces region anda proportional that the applied variation current of the modulation electrical (topower the heater dissipated or active in the region) device, induces the measured a proportional FM response variations, thus of, the also electrical represent power the laser dissipated thermal in theresp device,onse R the(f):measured FM responses, thus, also represent the laser thermal response R(f ):

TT RRi R()() f∆ f  i (1) Rp f q “ Pp f q “ 1 j f f (1) ∆P i 1 ` j f { ifi ÿi In this equation, the Ri represent the thermal resistances and the fi the characteristic frequencies (thermal cut-off frequencies) associated to the different parts of the laser, which also depend on the corresponding thermal capacities Ci:

Photonics 2016, 3, 47 8 of 12

PhotonicsIn this 2016 equation,, 3, 47 the Ri represent the thermal resistances and the f i the characteristic frequencies8 of 12 (thermal cut-off frequencies) associated to the different parts of the laser, which also depend on the corresponding thermal capacities Ci: 1 f  1 (2) fi i“ 2 RC (2) 2πRiiiCi ThisThis simple simple model model was was used used to simultaneously to simultaneously fit the fit theexperimental experimental data data in magnitude in magnitude and phase and tophase determine to determine the different the different time constants. time constants. In contrast In to contrast the model to the used model in Reference used in [4 Ref], whicherence made [4], usewhich of three made different use of low-pass three different filters, low we- addedpass filters, here a we 4th added filter with here a a low 4th cut-off filter with frequency a lowf 4 cutto- takeoff intofrequency account f the4 to longest take into time account constant theτ4 longestpreviously time observed constant in τ the4 previously step response observed shown in in the Figure step7 . Asresponse this 4th shown filter was in Figure not clearly 7. Asapparent this 4th filter in the was measured not clearl transfery apparent functions, in the its measured cut-off frequency transfer f 4functions,= 1/(2πτ 4its) was cut- directlyoff frequency determined f4 = 1/(2 fromπτ4) thewas slow directly decay determined observed infrom the stepthe slow response decay and observed was not consideredin the step as response a free parameter and was innot the considered fit. We also as extracteda free parameter the relative in the contribution fit. We alsori extractedof the thermal the resistancerelative contribution of each part ofri theof the QCL thermal structure resistance to the total of each thermal part resistance: of the QCL structure to the total thermal resistance: Ri ri “ R (3) r  Ri i i (3) i Ri ři The fitted model is plotted along with the measured frequency modulation responses in Figure9 The fitted model is plotted along with the measured frequency modulation responses in Figure 9 and shows a very good agreement in terms of amplitude and phase. The cut-off frequencies f i retrieved and shows a very good agreement in terms of amplitude and phase. The cut-off frequencies fi fromretrieved the fit from for thethe modulationfit for the modulation of the QCL of andthe QCL IH currents and IH arecurrents listed are in listed Table 1in together Table 1 t withogether the relative weight r of each filter. These frequencies were used in the modeled step responses displayed with the relativei weight ri of each filter. These frequencies were used in the modeled step responses indisplayed Figure7, whichin Figure were 7, which also in were good also agreement in good agreement with the experimentalwith the experimental data. For data. the For QCL the current QCL modulation,current modulation, the highest the cut-off highest frequency cut-off frequency is ~220 kHz, is ~220 whereas kHz, whereas it is one orderit is one of order magnitude of magnitude lower for IHlower modulation. for IH modulation. This results This from results the fact from that the the fact heat that is the generated heat is generated at some distance at some fromdistance the from active regionthe active with region the IH, with and thethe temperatureIH, and the temp of theer activeature of region the active cannot region be changed cannot asbe fast changed as with as a fast change as ofwith the QCLa change current of the that QCL acts current directly that onto acts the directly active onto region. the active region.

FigureFigure 9. 9Relative. Relative FM FMresponse response ofof thethe QCLQCL obtained under direct modulation modulation of of the the injection injection current current (blue(blue points) points or) or IH IH current current (red (red points) points) and and fitted fitted model model (solid (solid lines). lines Both). Both amplitude amplitude (a )(a and) and phase phase (b ) responses(b) responses are shown. are shown. A global A global phase phase shift shift of 180 of ˝180was° was added added to allto all phase phase plots. plots.

Table 1. Cut-off frequencies fi and relative weights ri of the different low-pass filters obtained from Table 1. Cut-off frequencies f i and relative weights ri of the different low-pass filters obtained from the the fit of the transfer functions for QCL and IH current modulation. The frequency f4 was fixed from fit of the transfer functions for QCL and IH current modulation. The frequency f 4 was fixed from the the longest time constant τ4 observed in the step response of Figure 7. longest time constant τ4 observed in the step response of Figure7. Modulation f1 (kHz) r1 f2 (kHz) r2 f3 (Hz) r3 f4 (Hz) r4 QCLModulation current f 1 (kHz)220 r1 0.27f 2 (kHz) 8.3 r2 0.20f 3 (Hz) 230 r3 0.36f 4 (Hz) 42 r4 0.17 IH current 19.6 0.18 3.2 0.16 200 0.46 40 0.20 QCL current 220 0.27 8.3 0.20 230 0.36 42 0.17 IH current 19.6 0.18 3.2 0.16 200 0.46 40 0.20 3.4. Preliminary Application in WMS The IH offers an alternative channel to modulate the emission frequency of the QCL at a relatively high speed. A benefit of this actuator is the capability to act directly on the internal temperature of the active region, thus offering new possibilities to reduce the frequency noise of a QCL in an all-electrical configuration using the voltage noise measured between the QCL terminals

Photonics 2016, 3, 47 9 of 12

3.4. Preliminary Application in WMS The IH offers an alternative channel to modulate the emission frequency of the QCL at a relatively high speed. A benefit of this actuator is the capability to act directly on the internal temperature of the active region, thus offering new possibilities to reduce the frequency noise of a QCL in an all-electrical configuration using the voltage noise measured between the QCL terminals as an error signal [10]. Another potential benefit of modulating the QCL frequency through the IH current is the reduced associated RAM that can be achieved in some conditions in comparison to the modulation of the QCL injection current. This property is attractive when using the first harmonic (1f ) signal of a molecular or atomic absorption line obtained in WMS to frequency-stabilize a QCL. In this case, the RAM constitutes an undesired spurious effect that generally degrades the stabilization performance as a result of the background offset present in the 1f signal. The importance of this offset depends on several parameters, such as the ratio between the FM and AM indices of the laser, but also on the phase shift between AM and FM, and on the phase of the 1f demodulation. The traditional injection current modulation used to modulate the frequency of a QCL is naturally accompanied by some RAM as the optical power scales linearly with the injection current. This RAM produces the background offset in the 1f signal of an absorption line, whose amplitude depends on the phase of the 1f demodulation. This phase can be adjusted to cancel out the offset component due to RAM [14], but this can lead at the same time to a strong reduction of the amplitude of the 1f signal of the absorption line (induced by the laser FM), depending on the phase shift between AM and FM. Modulating the IH current to generate a WMS signal is an alternative method that can present some advantages in terms of RAM. In contrast to the QCL injection current that directly influences the output power by changing the of the medium, the IH current has only an indirect effect on the output power via the induced temperature change. The resulting variation of the optical power is thus weaker and can reduce the RAM impact in WMS. To illustrate the attractiveness of the IH current modulation for WMS, we present here a proof-of-principle experiment performed on a N2O absorption line with a modulation of the IH current and we compare the results with the standard approach of injection current modulation. For this purpose, we modulated the QCL frequency with a 25-kHz sine wave signal applied either to the QCL injection current or to the IH current and we demodulated the photodiode signal detected at the output of the gas cell at the modulation frequency using a lock-in amplifier. In addition, the laser current was slowly swept with a triangular signal at 10 Hz to scan through the absorption line and the 1f signal was recorded on an oscilloscope during this sweep. Both the modulation depth and the phase of the lock-in detection were adjusted to maximize the amplitude of the 1f signal of the gas absorption line. The first harmonic WMS signals obtained for a modulation of the QCL injection current and of the IH current are shown in Figure 10a. Both curves were obtained for a QCL injection current of ~420 mA at a laser sub-mount temperature of ~20 ˝C. In the case of injection current modulation, no current was applied to the IH. For IH current modulation, a DC bias current of ~170 mA was applied on top of the modulation and the QCL temperature was slightly decreased by ~2 K to compensate for the resulting frequency shift of ~6 GHz and to keep the laser on the N2O transition. The derivative signal of the absorption line sits on a background offset that directly results from the intensity modulation of the emitted light. This offset is large in the case of a modulation of the QCL injection current, as it directly modulates the laser gain and therefore the optical power. However, the relative importance of the RAM, and thus the magnitude of the background offset in the WMS 1f signal, has a significant dependence on the average QCL current: the relative magnitude of the offset decreases when the QCL injection current increases, as the relative power modulation is reduced accordingly, whereas the FM tuning coefficient has only a minor dependence. This relative reduction of the RAM is illustrated in Figure 10b, which shows the ratio between the background offset (arising from RAM) and the peak-to-peak amplitude of the spectroscopic component of the N2O absorption line (arising from FM) in the detected 1f signal obtained for QCL and IH current modulation at different QCL (respectively Photonics 2016, 3, 47 10 of 12

IH) currents. For a modulation of the IH current, the offset in the 1f signal is tiny as the optical power varies only due to the resulting temperature change. The offset has also an opposite sign compared to the QCL current modulation, as the optical power decreases with increasing IH current as illustrated in Figure3b, whereas it increases with the injection current. Furthermore, the relative magnitude of the background offset in the WMS 1f signal (and thus the importance of RAM) remains almost constant at any IH current, which illustrates the good decoupling between frequency and amplitude modulation whenPhotonics modulating 2016, 3, 47 the IH current. 10 of 12

Figure 10. (a) Comparison of the first harmonic WMS signal of a N2O line obtained for QCL injection Figure 10. (a) Comparison of the first harmonic WMS signal of a N2O line obtained for QCL injection current and IH current modulation (at T ≈ 20 ˝°C and IQCL ≈ 420 mA), showing the strongly reduced current and IH current modulation (at T « 20 C and IQCL « 420 mA), showing the strongly reduced backgroundbackground offset offset obtained obtained for for IH current IH current modulation; modulation (b) ratio; (b) betweenratio between the offset the and offset the amplitudeand the ofamplitude the 1f signal of the obtained 1f signal for obtained QCL and for IH QCLmodulation and IH at modulation different QCL at different (IH) currents, QCL converted(IH) current intos, aconverted corresponding into a frequency corresponding detuning. frequency For each detuning. value of For the each QCL value (IH) of current, the QCL the (IH) laser current, temperature the laser was temperature was slightly varied to keep the laser frequency around the considered N2O transition. slightly varied to keep the laser frequency around the considered N2O transition. At each DC current, At each DC current, the amplitude of the applied modulation was adjusted to maximize the the amplitude of the applied modulation was adjusted to maximize the peak-to-peak amplitude of the peak-to-peak amplitude of the 1f signal. 1f signal.

4. Conclusions and Outlook 4. Conclusions and Outlook In conclusion, we have characterized in detail a new frequency tuning actuator in a QCL In conclusion, we have characterized in detail a new frequency tuning actuator in a QCL emitting emitting at 7.8 μm. A resistive IH placed in the vicinity of the active region can be electrically at 7.8 µm. A resistive IH placed in the vicinity of the active region can be electrically controlled, controlled, enabling fast changes of the internal temperature of the laser to be applied, which results enabling fast changes of the internal temperature of the laser to be applied, which results in a fast in a fast control of the emission frequency. The laser output frequency has a linear dependence on controlthe electrical of the emissionpower dissipated frequency. in Thethe resistive laser output heater frequency and this has frequency a linear tuning dependence occurs on with the a electrical minor powerchange dissipated of the emitted in the optical resistive power. heater The and impulse this frequency response tuning of the occurslaser frequency with a minor to a changecurrent ofstep the emittedapplied opticalto the IH power. is as fast The as impulse for a step response change of of the the laserQCL frequencycurrent and to a a frequency current step change applied of 500 to theMHz IH iswas as fastachieved as for in a stepa few change milliseconds, of the QCL limited current by the and head a frequency dissipation change out of of the 500 active MHz region was achieved towards in athe few laser milliseconds, sub-mount. limited For a by sine the modulation, head dissipation the QCL out ofcurrent the active remains region approximatively towards the laser one sub-mount. order of Formagnitude a sine modulation, faster and the enables QCL frequency current remains-modulating approximatively the QCL radiation one order with of magnitude a bandwidth faster in the and enablesMHz range frequency-modulating (corresponding to thea drop QCL in radiation amplitude with of a~10 bandwidth dB and an in associated the MHz rangephase (corresponding shift of −90°), ˝ towhereas a drop inthe amplitude bandwidth of is ~10 limited dB and to ~100 an associated kHz when phase modulating shift of the´90 IH), current. whereas A the thermal bandwidth model is limitedwas presented to ~100 kHzto describe when modulatingthe transfer functions the IH current. experimentally A thermal measured model was for presenteda modulation to describe of the theQCL transfer current functions and IH experimentallycurrent. Four different measured time for constants a modulation were ofdetermined the QCL current and identified and IH current.to the Fourheat differentdissipation time in constantsdifferent parts were of determined the device. and The identified shortest time to the constant heat dissipation is one order in of different magnitude parts ofshorter the device. in the The case shortest of QCL time current constant modulation, is one order corresponding of magnitude to shorter a cut-off in the frequency case of higherQCL current than modulation,200 kHz, compared corresponding to ~20 kHz to afor cut-off IH current frequency modulation. higher than 200 kHz, compared to ~20 kHz for IH currentNevertheless, modulation. the modulation bandwidth achieved with the IH is sufficient for most spectroscNevertheless,opic applications the modulation of QCLs, bandwidth such as achieved WMS for with trace the IH gas is sufficientsensing or for laser most stabilization. spectroscopic applicationsModulating ofthe QCLs, IH current such asalso WMS has the for further trace gas advantage sensing orof lasera reduced stabilization. RAM compared Modulating to a direct the IH currentmodulation also hasof the the QCL further current advantage in some of conditions. a reduced We RAM showed compared a proof to-of a- directprinciple modulation demonstration of the QCLof the current benefit in of some this decoupled conditions. frequency/amplitude We showed a proof-of-principle modulation in demonstration the case of the of 1 thef signal benefit of a of N this2O absorption line, where the spectroscopic signal was almost free of background offset for a modulation of the IH current, whereas a higher offset was observed when modulating the QCL current. In this latter case, the relative magnitude of the background offset could be reduced by adjusting the phase of the demodulation, or by operating the QCL at a higher current. However, the first solution might also lead to a decrease of the amplitude of the absorption signal depending on the phase shift between AM and FM induced by the current modulation. For the modulation of the IH current, the relative background offset is fairly independent of the DC current, as both the optical frequency and output power of the QCL have a similar dependence on the IH current. Finally, the new IH provides an additional channel to apply fast frequency corrections to a QCL for frequency stabilization and noise reduction. This is attractive to reduce the short-term linewidth

Photonics 2016, 3, 47 11 of 12

decoupled frequency/amplitude modulation in the case of the 1f signal of a N2O absorption line, where the spectroscopic signal was almost free of background offset for a modulation of the IH current, whereas a higher offset was observed when modulating the QCL current. In this latter case, the relative magnitude of the background offset could be reduced by adjusting the phase of the demodulation, or by operating the QCL at a higher current. However, the first solution might also lead to a decrease of the amplitude of the absorption signal depending on the phase shift between AM and FM induced by the current modulation. For the modulation of the IH current, the relative background offset is fairly independent of the DC current, as both the optical frequency and output power of the QCL have a similar dependence on the IH current. Finally, the new IH provides an additional channel to apply fast frequency corrections to a QCL for frequency stabilization and noise reduction. This is attractive to reduce the short-term linewidth of a QCL without using an optical reference such as a molecular transition, by directly exploiting the noise on the voltage between the QCL terminals, as previously demonstrated [10,11]. Whereas a former implementation used an external near-infrared shining on the top surface of a QCL for fast control of the QCL internal temperature, the new IH provides a much more compact all-electrical solution that we will investigate in the future.

Acknowledgments: The authors from the University of Neuchâtel would like to acknowledge the financial support from the Swiss National Science Foundation (SNSF) and by the Swiss Confederation Program Nano-Tera.ch, scientifically evaluated by the SNSF. Author Contributions: A.B. and Y.B. designed the laser used in this work. T.G. and S.B. processed it and tested it. C.T. contributed to the initial characterization of QCLs with integrated heaters. S.S. conceived and supported the characterization experiments. K.G. performed the measurements. K.G. and S.S. analyzed the data. K.G., S.S., A.B. and Y.B. discussed the experimental data. T.S. oversaw the work. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations The following abbreviations are used in this manuscript: AM Amplitude modulation DFB Distributed feedback FM Frequency modulation FMS Frequency modulation spectroscopy IH Integrated heater LLH Laser laboratory housing PAS Photoacoustic spectroscopy QCL Quantum cascade laser RAM Residual amplitude modulation TEC Thermo-electrical cooler WMS Wavelength modulation spectroscopy

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