Theoretical and Experimental Study of Heterodyne Phase-Sensitive Dispersion Spectroscopy with an Injection-Current-Modulated Quantum Cascade Laser

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Letter Theoretical and Experimental Study of Heterodyne Phase-Sensitive Dispersion Spectroscopy with an Injection-Current-Modulated Quantum Cascade Laser

Zhen Wang 1,2, Kin-Pang Cheong 3, Mingsheng Li 4, Qiang Wang 5 and Wei Ren 1,2,*

1 Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, New Territories, Hong Kong SAR, China; [email protected] 2 Shenzhen Research Institute, The Chinese University of Hong Kong, New Territories, Hong Kong SAR, China 3 School of Aeronautics and Astronautics, Sichuan University, Chengdu 610017, China; [email protected] 4 Department of Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, China; [email protected] 5 State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China; [email protected] * Correspondence: [email protected]

Received: 28 September 2020; Accepted: 28 October 2020; Published: 29 October 2020

Abstract: We report the theoretical and experimental study of calibration-free heterodyne phase-sensitive dispersion spectroscopy (HPSDS) in the mid-infrared using a direct current modulated mid-infrared quantum cascade laser (QCL). The modulation of QCL current at several hundred MHz or higher generates the synchronous frequency and intensity modulation of the QCL emission. An analytical model of the phase of the beat note signal in HPSDS is derived by considering the absorption and dispersion processes and incorporating the QCL modulation parameters. In the experiment, a 4.5 µm QCL modulated at 350 MHz was used to measure N2O at 200 Torr in a 10 cm gas cell. The N2O concentrations inferred from the analytical model were compared with the nominal values to show good agreement over the concentration range of 189 805 ppm with a standard − deviation <3%. When the QCL wavelength was locked at the line-center of the molecular transition, it was of interest to ﬁnd that the theoretical model was simpliﬁed to that used for near-infrared HPSDS with an electro-optical modulator for laser modulation.

Keywords: laser dispersion spectroscopy; quantum cascade laser; heterodyne detection; frequency modulation

1. Introduction Molecular dispersion spectroscopy has received more attention in the recent decade by measuring the refractive index in the vicinity of a molecular resonance [1–4]. Compared with absorption spectroscopy, it provides the advantages of inherent immunity to laser power ﬂuctuations and large dynamic range [5]. Dispersion spectroscopy has been used in many applications such as remote open-path gas sensing [6–8], isotope analysis [9], and combustion diagnostics [10,11]. Representative detection schemes adopted for laser dispersion spectroscopy include chirped laser dispersion spectroscopy (CLaDS) [1], heterodyne phase-sensitive dispersion spectroscopy (HPSDS) [2], and multi-heterodyne dispersion spectroscopy [12,13]. Additionally, dispersion spectroscopy enhanced by using a high-ﬁnesse optical cavity, known as noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy (NICE-OHMS), has achieved a sensitivity of 5 10 13 of integrated × − absorption [4]. Among these detection schemes, HPSDS is an attractive technique that features a simpler

Sensors 2020, 20, 6176; doi:10.3390/s20216176 www.mdpi.com/journal/sensors Sensors 2020, 20, 6176 2 of 9 optical configuration and signal processing. In the previous studies of near-infrared HPSDS, a two- or three-color laser beam was generated by modulating laser intensity using commercial electro-optical modulators (EOMs). The refractive index of gas medium is then measured by phase-sensitive detection using a lock-in amplifier. The spectroscopic principle, theoretical model, and experimental setup for near-infrared HPSDS were well documented elsewhere [2,5]. Besides that, the MEMS-based vertical-cavity surface-emitting laser (VCSEL) was also applied in HPSDS for multispecies detection due to the mode-hop-free broadband wavelength tunability of the MEMS-VCSEL [3]. Compared with near-infrared gas sensing, a higher sensitivity could be achieved in the mid-infrared domain where most gas molecules have the fundamental absorption bands. However, commercial EOMs are not always available in the mid-infrared that limits the further application of HPSDS. Martín-Mateos et al. reported a HPSDS-based gas sensor using a mid-infrared light source based on the difference frequency generation (DFG) [14]. The sidebands of the mid-infrared light could be generated by modulating the pump laser using EOMs. However, the DFG system is complex due to the use of a high power pump laser and the phase matching associated with the nonlinear crystal. Later on, the mid-infrared HPSDS was performed using a directly modulated quantum cascade laser (QCL) for the successful CO detection at 4.59 µm [15]. As opposed to the near-infrared intensity modulation with an EOM, the injection current of the QCL was directly modulated using a radio frequency (RF) signal generator at a modulation frequency of hundreds of MHz. Note that the current modulation of QCL at such a high frequency generates the synchronous intensity modulation (IM) and frequency modulation (FM) [16–18]. Additionally, HPSDS measurements are also affected by the sideband ratio associated with the laser modulation frequencies and intrinsic properties of QCLs. Thus, a reliable spectroscopic model is required for QCL-based HPSDS towards the realization of calibration-free measurements of gas concentrations. Hangauer et al. [18,19] conducted a relatively comprehensive investigation of the E-field emission of the directly current-modulated QCL for CLaDS. Instead of performing frequency demodulation of the beat note signal in CLaDS, the HPSDS technique measures the phase of the beat note signal after the frequency down-conversion. In this work, we introduce a calibration-free model for HPSDS using QCLs in the mid-infrared. The model construction starts with the E-field emission reported for CLaDS [18,19] because both dispersion techniques use the high-frequency injection-current-modulated QCL. The new model only contains the specific modulation characteristics of the laser source, the spectroscopic parameters obtained from the HITRAN database [20], and the gas properties to be determined. As a proof-of-principle, we experimentally performed the HPSDS detection of N2O using a distributed-feedback (DFB) QCL near 4.5 µm. The theoretical model can be further simplified to the model used for near-infrared HPSDS with an EOM when the QCL wavelength is locked to the line-center of the molecular transition.

2. Model In QCL-based dispersion spectroscopy, a three-color laser beam is generated by directly modulating (angular frequency Ω) the injection current of the laser. Here we adopted the identical symbols and expressions to represent the QCL emission as those used in the references [18,19]. The IM index m (defined as the amplitude of IM divided by the total laser intensity) and the FM index β (defined as the amplitude of FM divided by the modulation frequency) are both assumed to be small enough (m « 1, β « 1). Thus, the QCL emission has the carrier (E0) centered at the optical angular frequency ω and two modulation sidebands (E1 and E 1) at ω Ω. The E-fields can be expressed by the following − ± time-domain forms: p E0 = P0 cos(ωt), (1) ( ) m p 2β E = P cos[(ω + Ω)t] + cos[(ω + Ω)t θ] , (2) 1 4 0 m − Sensors 2020, 20, 6176 3 of 9

( ) m p 2β E 1 = P0 cos[(ω Ω)t] cos[(ω Ω)t + θ] , (3) − 4 − − m − where P0 is the laser intensity, and θ is the FM–IM phase shift. The laser beam is then transmitted through the gas sample where each wavelength component experiences the corresponding phase shift and attenuation because of the molecular dispersion and absorption. After passing through the gas medium with a path length of L, the transmitted beam can be expressed as E0 = A cos(ωt ψ ), (4) 0 0 − 0 ( ) 2β E0 = A cos[(ω + Ω)t ψ ] + cos[(ω + Ω)t θ ψ ] , (5) 1 1 − 1 m − − 1 ( ) 2β E0 1 = A 1 cos[(ω Ω)t ψ 1] cos[(ω Ω)t + θ ψ 1] , (6) − − − − − − m − − − where ( + ) k α ω kΩ L m | | p (ω + kΩ)L A = e− 2 P , ψ = [n(ω + kΩ) 1], k 4 0 k c − and the coefficient k = 1, 0, 1; n(ω) and α(ω) are the refractive index and absorption coefficient, − respectively; c is the speed of light in vacuum. The transmitted laser beam is detected by a square-law photodetector. 2 I E0 + E10 + E0 1 . (7) ∝ − The beat note signal between the carrier and two sidebands can be obtained by the first harmonic detection. The dispersion information is encoded in the phase of the beat note signal. The refractive index and absorption coefficient obey the Kramers–Kronig relation [21].

Z + c ∞ α(ω0) n(ω) = 1 + ℘ dω0, (8) 2 2 π 0 ω ω 0 − where the symbol ℘ denotes the Cauchy principal value, which is determined by the pole of the integrand for numerical calculation. Here we assume a Voigt line-shape for calculating the absorption proﬁle [22,23]. Finally, the measured phase of the beat note signal can be expressed as

1 ϕ = tan− [2Fβ sin(ψ0 ψ1 θ) 2Gβ sin(ψ 1 ψ0 θ)+ − − − − − − Fm sin(ψ0 ψ1) + Gm sin(ψ 1 ψ0)]/ − − − (9) [2Fβ cos(ψ0 ψ1 θ) 2Gβ cos(ψ 1 ψ0 θ)+ − − − − − − Fm cos(ψ0 ψ1) + Gm cos(ψ 1 ψ0)] − − − where the coefficient F = exp[ α(ω + Ω)L α(ω)L] and G = exp[ α(ω Ω)L α(ω)L]. It should be − − − − − noted that laser characterization is required to obtain β, m, and θ. Though the analytical expression is somewhat complex, it clearly shows the contribution from FM sidebands and IM sidebands, respectively. As the laser characterization process is not so straightforward, it is of interest to investigate the possible methods to obtain a simpler analytical expression. Here we assume the frequency (ω) of the laser carrier (E0) matches the line-center (ωc) of the gas molecule, as shown in Figure1. Then the two pairs of sidebands induced by FM and IM have the equal frequency difference relative to the line-center of the molecular transition. Considering the symmetric line-shape of the absorption profile, both pairs of sidebands are attenuated equally so that A1 = A 1 in Equations (5) and (6), whereas the − carrier experiences a larger attenuation. Thus the parameter F equals to parameter G in Equation (9). Considering the antisymmetric line-shape of the refractive index shown in Figure1, the left sideband Sensors 2020, 20, 6176 4 of 9

(E10) and right sideband (E 10) have the same modulus but an opposite phase shift, Ψ1 Ψ 1. Sensors 2020, 20, 6176 − ≈ −4 of− 9 The following is assumed here:

(ω+kLkΩ)L ωLL ψk =[nn(ω +  kΩ ) 11 ]  [ nn( ω + k kΩ ) 1 1 , ] ,(10 (10)) k ccc− ≈ c −  becausebecause ω ≫ ΩΩ [2,5].[2,5]. The The carrier carrier has has no no extra extra phase phase shift shift induced induced by by the the target target molecule; thus, Ψ0 == 0.0. 0

FigureFigure 1. 1. SchematicSchematic of of the the laser laser transmission transmission through through a gas sample a gas sampledue to the due simultaneous to the simultaneous absorption absorptionand dispersion. and Red dispersion. arrows: intensity Red arrows: modulation intensity (IM) sidebands; modulation green (IM) arrows: sideban frequencyds; green modulation arrows: frequency(FM) sidebands. modulation (FM) sidebands.

Referring to the theoretical model, at the resonant frequency of the molecule, Equation (9) Referring to the theoretical model, at the resonant frequency of the molecule, Equation (9) is is simpliﬁed to the following expression: simplified to the following expression:  L ωccL  ϕ=[nn(ωcc +  Ω) 1.1]. (11 (11)) c − Hence,Hence, the the HPSDS HPSDS phase phase signal signal at at the the resonant resonant frequency frequency of of the the gas gas molecule molecule is is only only relevant relevant to to thethe gas gas properties, properties, such such as as refractive refractive index, but independent of laser parameters such as β,, m,, and θ.. WeWe analyzed that such a simplification simpliﬁcation was mainly caused by the fact fact that that FM FM sidebands sidebands are are out out ofof phase and IM sidebands are in phase, as shown in Equations (2) and (3). After experiencing the the equalequal phase shiftshift butbut withwith opposite opposite signs, signs, the the beat beat notes notes between between the the carrier carrier (Equation (Equation (4)) (4)) and and the twothe twoFM sidebandsFM sidebands (the (t latterhe latter parts parts of Equations of Equations (5) and (5) (6))and cancel(6)) cancel each each other. other. The modelThe model becomes becomes a pure a pureintensity intensity modulation modulation that isthat similar is similar to the to near-infrared the near-infrared HPSDS HPSDS using using an EOM, an EOM, because because only only the beat the beatnotes notes between between carrier carrier and theand two the IMtwo sidebands IM sidebands remain remain in the in model. the model. WeWe can further verify this hypothesis by by comparing comparing the the result result with with the the near near-infrared-infrared HPSDS. HPSDS. The measured phase of of the the beat note note signal signal for for the the EOM EOM-based-based near near-infrared-infrared HPSDS HPSDS is is given given by by the the followingfollowing equation equation [2]: [2]: ωL ϕ=[nnn(ω +  Ω) n( ω Ω )]. .(12 (12)) 2c − − When ω = ωc, there exists the following relationship: When ω = ωc, there exists the following relationship:  n(nnωc +ccΩ ) 111 = [n(ωc  Ω)  1 ] (13(13)) − − − − As a result, both HPSDS models converge to the same equation when the laser frequency is fixed at the line-center of the target absorption line. The HPSDS detection at the line-center provides a possible method to measure gas concentrations without the need for laser characterization.

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As a result, both HPSDS models converge to the same equation when the laser frequency is fixed atSensors the 2020 line-center, 20, 6176 of the target absorption line. The HPSDS detection at the line-center provides5 of a9 possible method to measure gas concentrations without the need for laser characterization. 3. Experimental 3. Experimental To verify the theoretical model, a QCL-based HPSDS system was built with the configuration shownTo in verify Figure the 2. theoretical A continuous model,-wave a QCL-basedQCL (Alpes HPSDSLasers SA, system St-Blaise was builtin Switzerland with the configuration) was used to shown in Figure2. A continuous-wave QCL (Alpes Lasers SA, St-Blaise in Switzerland) was used exploit the R(18) line of N2O centered at 2238.36 cm−1. The QCL wavelength was scanned across the to exploit the R(18) line of N O centered at 2238.36 cm 1. The QCL wavelength was scanned across N2O absorption profile with2 a slow bias current ramp− generated by a low-noise laser controller the(Newport, N2O absorption Irvine, CA, profile USA, with ILX LDC a slow-3736). bias currentA high frequency ramp generated (Ω/2π by= 350 a low-noise MHz) modulation laser controller signal (Newport,from one channel Irvine, CA,of an USA, RF generator ILX LDC-3736). (Stanford A highResearch frequency System (Ω, /Sunnyvale,2π = 350 MHz) CA, modulationUSA, SG 382) signal was fromsuperimposed one channel with of the an bias RF current generator via (Stanforda bias-tee Researchcircuit, which System, was Sunnyvale,then injected CA, to the USA, QCL. SG Note 382) wasthat superimposeda power splitter with was theused bias to currentsplit thevia RF asignal bias-tee into circuit, two channels which waswith then the same injected frequency to the QCL. and Noteinitial that phase. a power Hence, splitter a three was-color used beam to split was the generated RF signal by into modulating two channels the QCL with injection the same current frequency at a andhigh initial modulation phase. frequency. Hence, a three-color beam was generated by modulating the QCL injection current at a high modulation frequency.

Figure 2. Schematic of the heterodyne phase-sensitive dispersion spectroscopy (HPSDS) gas sensing Figure 2. Schematic of the heterodyne phase-sensitive dispersion spectroscopy (HPSDS) gas sensing system. QCL, quantum cascade laser; LC, laser controller; RSG, RF signal generator; LIA, system. QCL, quantum cascade laser; LC, laser controller; RSG, RF signal generator; LIA, lock-in lock-in ampliﬁer; PS, power splitter; PD, photodetector; CM, concave mirror; MFC, mass ﬂow amplifier; PS, power splitter; PD, photodetector; CM, concave mirror; MFC, mass flow controller; PM, controller; PM, pressure meter. pressure meter.

The three-color beam was directed through a 10-cm gas cell filled with N2O/N2 mixtures at a fixed pressureThe ofthree 200- Torrcolor monitored beam was by directed a pressure through meter. a The 10- transmittedcm gas cell QCLfilled beam with impingedN2O/N2 mixtures on a mercury at a cadmiumfixed pressure telluride of 200 (MCT) Torr photodetector monitored by (VIGO a pressure Systems, meter. O˙zar Theów transmitted Mazowiecki QCL in Poland, beam PVI-4TE-10.6)impinged on witha mercury 800 MHz cadmium bandwidth telluride to generate(MCT) photodetector the heterodyne (VIGO beat Systems, note signal. Ożarów The detectedMazowiecki electrical in Poland, beat notePVI-4TE signal-10.6) (350 with MHz) 800 was MHz then bandwidth mixed with to agenerate sinusoidal the waveform heterodyne with beat a slightly note signal. different The frequency detected (electricalΩ/2π = 349.9 beat MHz)note signal generated (350 byMHz) another was RFthen signal mixed generator. with a sinusoidal Thus, the frequencywaveform ofwith the a beat slightly note signaldifferent was frequency downshifted (Ω to/2π 100 = kHz, 349.9 which MHz) falls generated in the operation by another range RF of a signal commercial generator. lock-in Thus, amplifier the (Signalfrequency Recovery, of the beat Oak note Ridge, signal TN, USA,was downshifted Model 7265). to Finally, 100 kHz, the whi dispersionch falls informationin the operation was encodedrange of ina commercial the phase of lock the- frequencyin amplifier downshifted (Signal Recovery, electrical Oak signal Ridge that, TN, could USA, be retrieved Model 7265). using Finally, the lock-in the amplifier.dispersion To information improve the was measurement encoded in precision,the phase theof the outputs frequency of the downshifted two RF generators electrical were signal mixed that to generatecould be retrieved the 100 kHz using external the lock reference-in amplifier. for the To lock-in improve amplifier. the measurement precision, the outputs of the two RF generators were mixed to generate the 100 kHz external reference for the lock-in amplifier. 4. Results and Discussion 4. Results and Discussion Gas mixtures of N2O/N2 at different concentrations were prepared using a commercial gas dilution systemGas (Jinwei mixtures Inc., of Wuhan, N2O/N China).2 at different Figure3 concentrations presents the representative were prepared spectra using of N a 2 commercialO measured gas by thedilution HPSDS system sensor (Jinwei at 200 TorrInc., forWu fourhan, di Chinafferent). concentrations. Figure 3 presents The the slight representative asymmetry of spectra the measured of N2O measured by the HPSDS sensor at 200 Torr for four different concentrations. The slight asymmetry of the measured spectra was mainly due to the asymmetry of the sidebands generated by IM and FM of the QCL. The calculated HPSDS spectra based on the analytical model for the corresponding N2O concentrations are also plotted in Figure 3 for comparison. The spectral calculations were in good agreement with the measurements with a standard deviation <3%. Considering the standard

Sensors 2020, 20, 6176 6 of 9 spectra was mainly due to the asymmetry of the sidebands generated by IM and FM of the QCL. Sensors 2020, 20, 6176 6 of 9 The calculated HPSDS spectra based on the analytical model for the corresponding N2O concentrations are also plotted in Figure3 for comparison. The spectral calculations were in good agreement with the deviation of the detection noise (1σ) of ~0.37°, we obtained a signal-to-noise ratio (SNR) of 12 for the measurements with a standard deviation <3%. Considering the standard deviation of the detection N2O concentration of 189 ppm, corresponding to a minimum detectable N2O of 16 ppm using the noise (1σ) of ~0.37 , we obtained a signal-to-noise ratio (SNR) of 12 for the N O concentration of current HPSDS sensor.◦ 2 189 ppm, corresponding to a minimum detectable N2O of 16 ppm using the current HPSDS sensor.

Figure 3. Representative HPSDS phase signals measured at 200 Torr for different N2O concentrations Figure(symbol, 3. experiment;Representative line, HPSDS simulation): phase signals (a) 189 ppm,measured (b) 394 at 200 ppm, Torr (c) for 600 different ppm, and N (2Od) concentrations 805 ppm. (symbol, experiment; line, simulation): (a) 189 ppm, (b) 394 ppm, (c) 600 ppm, and (d) 805 ppm. It should be noted that all the simulations were conducted using the characterized QCL parameters It should be noted that all the simulations were conducted using the characterized QCL (β, m, and θ) and the known spectroscopic parameters of the R(18) line of N2O (line-strength and parametersline broadening (β, m, coe andffi cients).θ) and the The known intrinsic spectroscopic QCL parameters parametersβ, m ,of and theθ R(18)can beline experimentally of N2O (line- strengthdetermined and using line direct broadening measurement coefficients). [18] or by The fitting intrinsic a HPSDS QCL spectrum paramet ofers known β, m gas, and concentration θ can be experimentallywith the analytical determined model. using These direct parameters measurement are found [18] or onlyby fitting associated a HPSDS with spectrum the bias of current,known gasmodulation concentration frequency, with andthe modulationanalytical model. depth These of the parameters QCL. are found only associated with the bias current,The peak-to-peak modulation values frequency, of the and measured modulation dispersion depth of spectra the QCL. were compared with the model The peak-to-peak values of the measured dispersion spectra were compared with the model simulations to infer N2O concentrations. Figure4 compares the HPSDS-determined N 2O concentrations simulationswith the nominal to inferconcentrations N2O concentrations. determined by Figurethe gas dilution 4 compares system. the The HPSDS horizontal-determined error bars show N2O concentrationsthe uncertainty with of concentration the nominal values concentrations for dilutions determin by takinged into by account the gas the dilution uncertainty system. of flow The horizontalmeters. The error uncertainties bars show in line-strength the uncertainty and of the concentration detection noise values of the for sensor dilutions led to aby measurement taking into account the uncertainty of flow meters. The uncertainties in line-strength and the detection noise of error bar (2σ) of 32 ppm in the N2O concentration. A linear relation (y = x) was obtained with an theR-square sensor value led to of a 0.999,measurement demonstrating error bar the (2σ) precision of 32 ppm of the in calibration-free the N2O concentration. HPSDS method. A linear relation (y = x)As was discussed obtained previously, with an R compared-square value with of absorption 0.999, demonstrating spectroscopy, the dispersionprecision of spectroscopy the calibration has- freethe advantageHPSDS method. of intrinsic immunity to laser power fluctuations [2]. We thus investigated the HPSDS sensor performance by adjusting the laser power using an iris with all the other parameters unchanged. Figure5 depicts the measured HPSDS phase signals for the same N 2O mixture (496 ppm) at three different optical powers (3 mW, 6 mW, and 9 mW). These spectra show the negligible difference (<2.7%) of the peak-to-peak amplitude. In addition, we observed a slightly improved detection SNR at the lower laser power under the current experimental conditions.

Figure 4. Comparison of the measured N2O concentration using HPSDS with the nominal concentration determined by the gas dilution system.

Sensors 2020, 20, 6176 6 of 9 deviation of the detection noise (1σ) of ~0.37°, we obtained a signal-to-noise ratio (SNR) of 12 for the N2O concentration of 189 ppm, corresponding to a minimum detectable N2O of 16 ppm using the current HPSDS sensor.

Figure 3. Representative HPSDS phase signals measured at 200 Torr for different N2O concentrations (symbol, experiment; line, simulation): (a) 189 ppm, (b) 394 ppm, (c) 600 ppm, and (d) 805 ppm.

It should be noted that all the simulations were conducted using the characterized QCL parameters (β, m, and θ) and the known spectroscopic parameters of the R(18) line of N2O (line- strength and line broadening coefficients). The intrinsic QCL parameters β, m, and θ can be experimentally determined using direct measurement [18] or by fitting a HPSDS spectrum of known gas concentration with the analytical model. These parameters are found only associated with the bias current, modulation frequency, and modulation depth of the QCL. The peak-to-peak values of the measured dispersion spectra were compared with the model simulations to infer N2O concentrations. Figure 4 compares the HPSDS-determined N2O concentrations with the nominal concentrations determined by the gas dilution system. The horizontal error bars show the uncertainty of concentration values for dilutions by taking into account the uncertainty of flow meters. The uncertainties in line-strength and the detection noise of the sensor led to a measurement error bar (2σ) of 32 ppm in the N2O concentration. A linear relation (y = x) was obtained with an R-square value of 0.999, demonstrating the precision of the calibration- freeSensors HPSDS2020, 20 method., 6176 7 of 9

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As discussed previously, compared with absorption spectroscopy, dispersion spectroscopy has the advantage of intrinsic immunity to laser power fluctuations [2]. We thus investigated the HPSDS sensor performance by adjusting the laser power using an iris with all the other parameters unchanged. Figure 5 depicts the measured HPSDS phase signals for the same N2O mixture (496 ppm) at three different optical powers (3 mW, 6 mW, and 9 mW). These spectra show the negligible Figure 4. Comparison of the measured N2O concentration using HPSDS with the nominal concentration differenceFigure (<2.7%) 4. Comparison of the peak of the-to - measuredpeak amplitude. N2O concentration In addition, u sing we observed HPSDS with a slightly the nominal improved determined by the gas dilution system. detectionconcentration SNR at thedetermined lower laser by the power gas dilution under system. the current experimental conditions.

Figure 5. Measured HPSDS phase signals at different optical power levels for the same N2O Figure 5. Measured HPSDS phase signals at different optical power levels for the same N2O concentration (496 ppm). The three signals are shifted vertically for viewing purposes. concentration (496 ppm). The three signals are shifted vertically for viewing purposes. Finally, based on the theoretical model in Equation (9), we performed detailed simulations to examineFinally, the influencebased on of the di fftheoreticalerent laser parametersmodel in Equation on HPSDS (9), phase we performed signals. In particular,detailed simulations we compared to examinethe three thetypical influence cases with of different different laserβ/m ratios parameters and θ values on HPSDS (case 1: phaseβ = 0.004, signals.m = In0.002, particular,θ = 0.71 weπ; comparedcase 2: β = the0.001, threem =typical0.002, casesθ = 0; with case different 3: β = 0.0025, β/m ratiosm = 0.002,and θ θvalues= 0.31 (caseπ). Note 1: β = that 0.004, the m ratio = 0.002, of β/ mθ =a ff0.71π;ects the case output 2: β = phase 0.001, more m = significantly0.002, θ = 0; thancase the3: β individual= 0.0025, m parameter = 0.002, θβ =or 0.31π).m. Figure Note6 illustratesthat the ratio the of β/m affects the output phase more significantly than the individual parameter β or m. Figure 6 simulation results of the HPSDS spectra for the four N2O concentrations (100 ppm, 500 ppm, 900 ppm, illustrates the simulation results of the HPSDS spectra for the four N2O concentrations (100 ppm, 500 and 2000 ppm). The corresponding absorbance normalized by N2O concentration is plotted at the ppm,bottom 900 panel ppm, of and Figure 20006. Forppm). each The concentration, corresponding the threeabsorbance HPSDS normalized signals with by di Nff2erentO concentration combinations is plottedof β, m, at and theθ bottomintersect panel at the of sameFigure point, 6. For corresponding each concentration, to the the line-center three HPSDS of the signals absorption with profile.different combinationsIt should of be β noted, m, and that θ weintersect could at not the experimentally same point, corresponding verify Equation to (11) the usingline-center the current of the absorptionsetup mainly profile. due to the lack of appropriate locking techniques for the QCL to the molecular transition.It should Although be noted the that third-harmonic we could not locking experimentally technique verify is commonly Equation used (11) in wavelengthusing the current modulation setup mainlyspectroscopy due to [ 24the], itlack modulates of appropriate the laser locking frequency techniques periodically for the at QCL a low to frequency the molecular that introducestransition. Althoughunwanted phasethe third fluctuations-harmonic to locking the beat technique note signal. is We commonly believe that used the in high-frequency wavelength modulation spectroscopylike the Pound–Drever–Hall [24], it modulates technique the laser is a possiblefrequency solution, periodically as it may at a stabilize low frequency the carrier that by introduces narrowing unwantedthe linewidth phase of QCL. fluctuations However, to the it is beat out ofnote the signal. technical We scope believe of thethat current the high study-frequency and will mo bedulation further likepursed the in Pound the future.–Drever–Hall technique is a possible solution, as it may stabilize the carrier by narrowing the linewidth of QCL. However, it is out of the technical scope of the current study and will be further pursed in the future.

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Figure 6.6. CalculatedCalculatedHPSDS HPSDS spectra spectra of of N 2NO2O at at (a )( 100a) 100 ppm, ppm, (b) 500(b) 500 ppm, ppm, (c) 900 (c) ppm, 900 ppm,and ( dand) 2000 (d) ppm,2000 forppm, three for dithreeﬀerent different combinations combinations of laser of parameters laser parametersβ, m, and β, θm., Caseand θ 1:. Caseβ = 0.004, 1: β =m 0.004,= 0.002, m = θ0.002,= 0.71 θπ =; case0.71π; 2: caseβ = 0.001,2: β = 0.001,m = 0.002, m = 0.002,θ = 0; θ and = 0; case and 3:caseβ = 3:0.0025, β = 0.0025,m = 0.002, m = 0.002,θ = 0.31 θ = π0.31π..

5. Conclusions In conclusion,conclusion, we we performed performed the the theoretical theoretical and and experimental experimental study study of mid-infrared of mid-infrared HPSDS HPSDS using ausing directly a directly current current modulated modulated QCL. To QCL. accurately To accurately simulate simulate the detected the detected HPSDS spectra,HPSDS spectra, the IM and the FMIM ofand QCL, FM the of physicalQCL, the processes physical of processes absorption of and absorption dispersion, and and dispersion, the phase and sensitive the phase detection sensitive are considereddetection are in considered the analytical in the model. analytical A final model. analytical A final model analytical for the model phase offor the the beat phase note of signalthe beat in HPSDS is derived. We experimentally validated the theoretical model by detecting N2O at 200 Torr in note signal in HPSDS is derived. We experimentally validated the theoretical model by detecting N2O µ aat 10 200 cm Torr long in gas a cell10 cm using long a 4.5gas mcell DFB-QCL. using a 4.5 The μm model DFB simulations-QCL. The model show goodsimulations agreement show with good the experimentalagreement with data. the Although experimental the laser data. characterization Although the laser process characterization is required for process the current is required HPSDS model,for the wecurrent theoretically HPSDS model, proved we that theoretically a complete calibration-freeproved that a complete measurement calibration may be-free achieved measurement by performing may be dispersionachieved by detection performing at the dispersion line-center detection of the molecular at the line transition.-center of Mid-infrared the molecular HPSDS transition. provides Mid an- alternativeinfrared HPSDS gas sensing provides method an alternative with unique gas sensing advantages method compared with unique with absorption advantages spectroscopy. compared with Authorabsorption Contributions: spectroscopy.Conceptualization, Z.W.; methodology, Z.W. and K.-P.C.; software, K.-P.C. and M.L.; validation, Z.W.; formal analysis, Z.W. and W.R.; investigation, Z.W.; resources, Z.W.; data curation, Z.W.; writing—originalAuthor Contributions: draft preparation,Conceptualization, Z.W.; writing—reviewZ.W.; methodology, and Z.W. editing, and Z.W.,K.-P.C.; Q.W., software, and W.R.; K.-P visualization,.C. and M.L.; Z.W.validation, and K.-P.C.; Z.W.; supervision, formal analysis, Q.W. Z.W. and W.R.; and W.R.; project investigation, administration, Z.W.; Q.W. resources, and W.R.; Z.W.; funding data acquisition, curation, Z.W.; W.R. Allwriting authors—original have read draft and prepar agreedation, to theZ.W.; published writing version—review of and the manuscript.editing, Z.W., Q.W., and W.R.; visualization, Funding:Z.W. and KGeneral.-P.C.; supervision, Research Fund Q.W. from and the W University.R.; project Grants administration, Committee Q. ofW. the and Hong W.R.; Kong funding SAR, Chinaacquisition, (14206317), W.R. SeedAll authors Project have from read the and Innovation agreed to andthe published Technology version Commission of the manuscript. of Hong Kong SAR, China (ITS/242/19), Natural Science Foundation of Guangdong Province, China (2019A1515011372), and Open Research Fund ofFunding: State Key General Laboratory Research of Applied Fund Optics from the (SKLAO-201901). University Grants Committee of the Hong Kong SAR, China Conflicts(14206317), of Interest: Seed ProjectThe authors from the declare Innovation no conflict and of Technology interest. Commission of Hong Kong SAR, China (ITS/242/19), Natural Science Foundation of Guangdong Province, China (2019A1515011372), and Open Research Fund of State Key Laboratory of Applied Optics (SKLAO-201901). References Conflicts of Interest: The authors declare no conflict of interest. 1. Wysocki, G.; Weidmann, D. Molecular dispersion spectroscopy for chemical sensing using chirped mid-infrared quantum cascade laser. Opt. Express 2010, 18, 26123–26140. [CrossRef] References 2. Martín-Mateos, P.; Acedo, P. Heterodyne phase-sensitive detection for calibration-free molecular dispersion 1. spectroscopy.Wysocki, G.; Weidmann,Opt. Express D.2014 Molecular, 22, 15143–15153. dispersion [CrossRef spectroscopy] for chemical sensing using chirped mid- 3. Martinfraredín-Mateos, quantum P.; cascade Paul, S.; laser. Heermeier, Opt. Express N.; Küppers, 2010, 18 F.;, 26123 Acedo,–26140 P. Multispecies. heterodyne phase sensitive 2. dispersionMartín-Mateos, spectroscopy P.; Acedo, over 80P. nm Heterodyne using a MEMS-VCSEL. phase-sensitiveACS detection Photonics 2017 for , calibration4, 2664–2668.-free molecular 4. Ye,dispersion J.; Ma, L.; spectroscopy. Hall, J.L. Ultrasensitive Opt. Express detections 2014, 22, in 15143 atomic–15153. and molecular physics: Demonstration in molecular 3. overtoneMartín-Mateos, spectroscopy. P.; Paul,J. S.; Opt. Heermeier, Soc. Am. N.; B 1998 Küppers,, 15, 6–15. F.; Acedo, [CrossRef P. Multispecies] heterodyne phase sensitive dispersion spectroscopy over 80 nm using a MEMS-VCSEL. ACS Photonics 2017, 4, 2664–2668.

Sensors 2020, 20, 6176 9 of 9

5. Ding, W.; Sun, L.; Yi, L.; Ming, X. Dual-sideband heterodyne of dispersion spectroscopy based on phase-sensitive detection. Appl. Opt. 2016, 55, 8698–8704. [CrossRef] 6. Nikodem, M.; Wysocki, G. Chirped laser dispersion spectroscopy for remote open-path trace-gas sensing. Sensors 2012, 12, 16466–16481. [CrossRef] 7. Plant, G.; Nikodem, M.; Mulhall, P.; Varner, R.K.; Sonnenfroh, D.; Wysocki, G. Field test of a remote multi-path CLaDS methane sensor. Sensors 2015, 15, 21315–21326. [CrossRef][PubMed] 8. Nikodem, M.; Plant, G.; Sonnenfroh, D.; Wysocki, G. Open-path sensor for atmospheric methane based on chirped laser dispersion spectroscopy. Appl. Phys. B 2015, 119, 3–9. [CrossRef] 9. Nikodem, M.; Wysocki, G. Diﬀerential optical dispersion spectroscopy. IEEE J. Sel. Top. Quant. 2016, 23, 464–468. [CrossRef]

10. Ma, L.; Wang, Z.; Cheong, K.-P.; Ning, H.; Ren, W. Temperature and H2O sensing in laminar premixed flames using mid-infrared heterodyne phase-sensitive dispersion spectroscopy. Appl. Phys. B 2018, 124, 117. [CrossRef] 11. Ma, L.; Wang, Z.; Cheong, K.-P.; Ning, H.; Ren, W. Mid-infrared heterodyne phase-sensitive dispersion spectroscopy in flame measurements. Proc. Combust. Inst. 2019, 37, 1329–1336. [CrossRef] 12. Martín-Mateos, P.; Jerez, B.; Acedo, P. Dual electro-optic optical frequency combs for multiheterodyne molecular dispersion spectroscopy. Opt. Express 2015, 23, 21149–21158. [CrossRef][PubMed] 13. Sterczewski, L.A.; Westberg, J.; Wysocki, G. Molecular dispersion spectroscopy based on Fabry-Perot quantum cascade lasers. Opt. Lett. 2017, 42, 243–246. [CrossRef] 14. Martín-Mateos, P.; Jerez, B.; Dios, C.D.; Acedo, P. Mid-infrared heterodyne phase-sensitive dispersion spectroscopy using difference frequency generation. Appl. Phys. B 2018, 124, 66. [CrossRef] 15. Martín-Mateos, P.; Hayden, J.; Acedo, P.; Lendl, B. Heterodyne phase-sensitive dispersion spectroscopy in the mid-infrared with a quantum cascade laser. Anal. Chem. 2017, 89, 5916–5922. [CrossRef] 16. Hinkov, B.; Hugi, A.; Beck, M.; Faist, J. Rf-modulation of mid-infrared distributed feedback quantum cascade lasers. Opt. Express 2016, 24, 3294–3312. [CrossRef] 17. Gellie, P.; Barbieri, S.; Lampin, J.F.; Filloux, P.; Manquest, C.; Sirtori, C.; Sagnes, I.; Khanna, S.; Linfield, E.; Davies, A.; et al. Injection-locking of terahertz quantum cascade lasers up to 35 GHz using RF amplitude modulation. Opt. Express 2010, 18, 20799–20816. [CrossRef] 18. Hangauer, A.; Spinner, G.; Nikodem, M.; Wysocki, G. High frequency modulation capabilities and quasi single-sideband emission from a quantum cascade laser. Opt. Express 2014, 22, 23439–23455. [CrossRef] 19. Hangauer, A.; Spinner, G.; Nikodem, M.; Wysocki, G. Chirped laser dispersion spectroscopy using a directly modulated quantum cascade laser. Appl. Phys. Lett. 2013, 103, 191107. [CrossRef] 20. HITRANonline. Available online: http://hitran.org/ (accessed on 7 October 2020). 21. Teich, M.C.; Saleh, B. Fundamentals of Photonics; Wiley Interscience: Hoboken, NJ, USA, 1991. 22. Whiting, E.E. An empirical approximation to the Voigt profile. J. Quant. Spectrosc. Radiat. Transf. 1968, 8, 1379–1384. [CrossRef] 23. Hanson, R.K.; Spearrin, R.M.; Goldenstein, C.S. Spectroscopy and Optical Diagnostics for Gases; Springer: New York, NY, USA, 2016.

24. Ma, Y.; Lewicki, R.; Razeghi, M.; Tittel, F.K. QEPAS based ppb-level detection of CO and N2O using a high power CW DFB-QCL. Opt. Express 2013, 21, 1008–1019. [CrossRef]

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