In this paper, a multiheterodyne architecture for molecular dispersion spectroscopy based on a coherent dual-comb source generated using a single continuous wave laser and electro-optic modulators is presented and validated. The phase-sensitive scheme greatly simplifies previous dual-comb implementations by the use of an electro-optic dual comb and by phase-locking all the signal generators of the setup eliminating, in this way, the necessity of any reference optical path currently mandatory in absorption-based instruments. The architecture is immune to the classical baseline and normalization problems of absorption-based analyzers and provides an output linearly dependent on the gas concentration. In addition, the simultaneous parallel multi-wavelength measurement approach has the ability to deliver an improved output bandwidth (measurement speed) over gas analyzers based on tunable lasers.
© 2015 Optical Society of America
Molecular dispersion spectroscopic methods are based on detecting the variations in the index of refraction of a gas sample that occur in the vicinity of molecular transitions. Therefore, only the phase shift introduced in an optical signal by the spectral feature is analyzed (unlike most techniques that use a measurement of absorption). Dispersion spectroscopy is a well-established approach and different methods have been demonstrated, from the Roschdestwensky hook method  and its variants [2–6], to Dispersive Fourier Transform Spectrometry [7–9] and Frequency Modulation Spectroscopy [10–12]. More recently, Chirped Laser Dispersion Spectroscopy (CLaDS) [13,14] and Heterodyne Phase-Sensitive Dispersion Spectroscopy (HPSDS)  have also been demonstrated for the measurement of dispersive features. These two later techniques present distinctive characteristics that make them very well suited to be used in gas analyzers. The main benefit of these approaches is the inherent immunity to baseline and normalization problems that results in robustness to optical power fluctuations. Therefore, these sensors are insensitive to fast power fluctuations caused by particles in suspension partially blocking the optical path of the sensor and to atmospheric turbulences or pointing instabilities (on the contrary, the normalization problem is a highly limiting factor of absorption-based methods). Besides this, the dependency between gas concentration and the change in the index of refraction is linear (as opposed to the exponential dependency between concentration and optical absorption), enabling dispersion based methods to have a better dynamic range in comparison with absorption techniques.
Both CLaDS and HPSDS are based on monochromatic tunable laser sources that are swept over the spectral line of interest. The phase shift induced in the optical wave by the change in the index of refraction associated to the molecular transition is then detected, following different procedures, to estimate the dispersion profile and the concentration of the gas. Therefore, the dispersed optical spectrum can be characterized continuously throughout the tuning range of the laser source. Nonetheless, the sweep time of the laser and the corresponding integration times in detection imply a limit in the speed of operation of the gas analyzers based on these techniques. Such limitations might be overcome by employing a multi-tone Optical Frequency Comb (OFC) source. Even though OFCs can only perform measurement at discrete wavelengths, these points can be continuously monitored achieving in this way higher speeds of operation.
OFC sources provide an optical spectrum which consists of evenly spaced narrow linewidth modes. Passively mode-locked lasers can generate OFCs with tens of thousands of individual frequency components  that are spread over a spectral range of more than an octave. Furthermore, the frequency of each of the teeth of an actively stabilized or monitored comb can be referenced to a frequency standard being possible to achieve frequency accuracies far beyond the reach of any other optical spectroscopic method . This combination of large bandwidth and high spectral accuracy and resolution has revolutionized the field of high-precision optical metrology . Although different detection schemes for OFCs have been proposed, dual-comb detection [19–23] allows one-to-one mapping each mode of the measurement OFC into the radio-frequency (RF) domain by heterodyning with a second (reference) local oscillator (LO) comb. The resulting RF comb can therefore be electronically acquired and processed to obtain the amplitude and the (optical) phase of each tooth of the original comb.
Even tough, wideband OFCs based on Ti:sapphire  or Er-doped fiber  lasers have shown unequal potential and extraordinary capabilities, the performance, complexity and cost of these setups usually exceed the requirements of most practical applications. On the contrary, the narrow bandwidth of simple OFCs generated by electro-optic modulation of a continuous wave laser  is more appropriate for gas analysis and monitoring. Dual comb systems based on electro-optic OFCs present several advantages over conventional schemes, like removing the need of comb synchronization and the self-compensation of amplitude and phase fluctuations of the laser. Single laser electro-optic dual combs spectrometers have already been demonstrated [27,28] for trace gas sensing.
In this paper, a new multiheterodyne architecture based on a coherent dual-comb source generated by electro-optic modulation of a single continuous wave laser source for molecular dispersion spectroscopy is presented. This phase-sensitive scheme takes advantage of the high coherence between the repetition rates of the two OFCs and the clock used for the acquisition hardware (through phase-locking all the RF oscillators involved in the scheme) to eliminate the necessity of the reference optical path currently present in all architectures based on electro-optic dual-comb sources and thus greatly simplifying previous setups [27,28]. On top of that, and as it was previously said, since comb sources allow the parallel characterization of multiple spectral points simultaneously, the operation speed achievable by a multiheterodyne analyzer could improve by several orders of magnitude the output data rate of current tunable laser based gas detectors.
2. Molecular dispersion spectroscopy with a dual comb source using multiheterodyne detection
The basic phase-sensitive architecture of the setup for dispersion based gas analysis is shown in Fig. 1. It is a simplified version of a basic dual comb spectroscopic setup in which the reference optical path has been removed. Instead, a reference phase measurement is obtained through a calibration process that takes advantage of the high coherence between the repetition frequencies of the RF oscillators needed to fix the repetition frequency of the combs and the sampling frequency of the acquisition hardware, as all the RF oscillators involved in the set-up are phase-locked (see below).
2.1 Principles of operation
As it was previously stated, the sensor architecture has been developed for molecular dispersion spectroscopy and, consequently, only the measurement of optical dispersion (and not absorption) is used to estimate the concentration of the target gas. In fact, the detection scheme proposed in this paper has been designed to isolate the phase of each teeth of the comb independently of its amplitude. The main advantages of this approach, as presented in the introduction, are the inherent solution to the baseline and normalization problems and the extended dynamic range.
The profile of the index of refraction in the vicinity of a molecular transition of center fc (it is worthwhile to note that the peak to peak difference of the refractive index is directly proportional to the concentration of gas) has the shape shown in Fig. 2(a). Therefore, the speed at which a monochromatic light propagates through the gas is a function of its wavelength. Thus, after propagation over a certain distance, the phase shift induced in the optical wave by the molecular sample will be given by:
The first phase modulator of Fig. 1 (upper branch) generates an ideal OFC in which the modes are described by:Fig. 2(b), travels through a gas sample, the changes in the index of refraction induce an optical phase shift in the modes of the comb that is a function of their frequency and have the spectral profile shown in Fig. 2(c). Therefore, a phase term must be added to the previous expression:Fig. 1) can be described as:27]. For illustration, the spectra of the measurement and LO combs are shown in Fig. 3.
When the measurement comb is heterodyned with the LO on a square law detector, the phase shifts will be unequivocally mapped into the RF domain:Eq. (6)). This RF comb can be acquired and processed to extract the value of phase at each frequency recovering from them the dispersion profile of the sample. A multi-channel lock-in parallel scheme has been proposed for the detection of the phase of the different teeth of the RF comb [29,30]. Apart from its improved isolation to noise and interference in comparison with other detection methods, the parallel multiple channel lock-in arrangement can operate at high speed generating fast output data rates. As it was previously said, the proposed detection setup is immune to optical intensity variations and therefore the effects of the different amplitudes of the teeth and absorption can be neglected.
2.2 Extracting Optical Phase Information: Requirements for phase coherence signal generators
From Eq. (6), the frequency of each one of the teeth of the RF comb generated by the dual comb setup is given by:
The proposed architecture is designed to obtain the optical phase shifts induced in the optical modes to infer the amount of a certain analyte. To achieve this objective, the electronic phases associated to the different teeth of the RF comb of Eq. (6) must replicate the optical phase of the different optical modes, and what it is most important, must be phase-coherent with the sampling frequency and the reference frequencies used in detection. These requirements are achieved in the proposed architecture by locking in phase all the oscillators involved in the set-up. A similar approach has been used for example for phase recovery in two-color heterodyne interferometry .
2.3 High speed spectroscopic measurements: Comb configuration and integration times in detection
Previous electro-optic dual OFCs implementations have been demonstrated for semi-static measurements in which the integration times were in the order of tens of seconds . In front of this, the architecture here proposed is devised to provide fast operation, but before that several considerations must be taken into account in terms of dual OFCs configuration (repetition frequencies) and integration times adjustments.
The minimum integration time for a digital lock-in amplifier used for the phase recovery of the different signals described in Eq. (6) is equal to the repetition period of the RF comb. In fact, phase acquisition and detection is greatly simplified if the integration time is adjusted to a value equal to a multiple of the repetition period of the mentioned RF comb:
The integration time given by Eq. (8) is inversely proportional to the difference between the repetition frequencies of the optical combs (that are equal to the frequencies of the signals driving the modulators and ). Therefore, if high speed operation is required, the separation between the repetition frequencies of the optical combs must be increased. The upper limit for this separation is, nevertheless, related to the number of optical modes of the comb () and the modulation frequency of the AOM :
In sum, if high output data rates are targeted, the separation between the teeth of the RF comb has to be adjusted to a point close to its maximum. In this way, the pulse repetition period and hence the required integration time is minimized.
2.4 Phase calibration procedure
The multiheterodyne dual-comb architecture of Fig. 1 is a dispersion-based characterization system that, as a difference with previous schemes, does not need a reference optical path (a second interferometer) to obtain a reference measurement for the normalization of the spectrum . For this purpose, there are two key aspects that are crucial in the setup: the use of phase-locked signal generators for the generation of the combs and signal digitization (sampling clock), and that only the phase (and not the amplitude) of the teeth of the comb is measured. The first point ensures that the phase coherence between the optical teeth and the acquisition system is maintained during the operation of the spectrometer. Therefore, even though the amplitude of the modes of the comb can be affected by many factors, the phases of the optical teeth are constant with time. Only variations in the index of refraction of the medium will induce phase shifts that, in what it is the second consideration, can be measured by the detection system to recover the changing dispersion profile of the sample.
As proven by Eq. (6) the phases of the teeth of the RF comb are independent of the wavelength of emission of the laser. Therefore, and having into account the previous points, a laser wavelength step can be introduced to obtain a reference phase measurement for normalization. In this way, the reference phases can be measured in a spectral region far from any absorption feature (constant value of the refractive index) before retuning the laser again into the vicinity of the molecular transition of interest for monitoring the concentration of gas.
2. 5 Multiheterodyne electro-optic dual comb System architecture
A detailed scheme of the dual-comb architecture for molecular dispersion spectroscopy presented in this paper is shown in Fig. 4. The light of a continuous wave laser source is divided in two fibers that are connected to the two modulators that generate the measurement and LO combs. As a point of reference, a regular spectrum of an OFC generated by the setup is shown at the bottom left part of Fig. 4. The measurement comb is collimated into a gas cell and launched again into fiber for the combination with the LO comb. An AOM is positioned in the LO branch to shift the optical frequency of the LO comb ensuring, as it was previously said, the unambiguous one to one mapping of the measurement comb from the optical to the RF domain. An added advantage of the use of the AOM is that the resultant RF comb is centered at the modulation frequency of the AOM reducing the influence of Flicker noise and therefore improving the SNR of the sensor. After polarization matching, the two combs are combined on a single fiber and detected on a photodiode. As previously justified, to ensure phase coherence between the teeth of the combs all the signal generators must be phase-locked to a common reference oscillator. When the wavelength of the laser is tuned to the vicinity of an absorption line the modes of the measurement OFC are dispersed by variations in the index of refraction of the molecular sample and, thus, when the comb is heterodyned with the LO on the photodetector, the induced phase shifts in each optical tooth are mapped into RF comb. Also a typical RF comb has been included for illustration in the bottom right corner of Fig. 4. The RF comb is band-pass filtered to remove lower and higher harmonics and synchronously sampled. Finally, a multi-channel phase-sensitive lock-in detection scheme measures the phase of each of the teeth of the comb.
The spectra of the optical and RF combs that are included in Fig. 4 show that the amplitudes of the teeth of the combs (unlike the phase) are not constant. Moreover, these amplitudes and the overall distribution of optical intensity are highly influenced by many factors like the power with which the modulators are driven or the temperature of the modulators. Therefore, absorption based setups include a reference optical path to compensate from these changes. The dispersion-based spectrometer here presented takes advantage of the phase coherence between optical modes to remove this reference path simplifying the optical design of the setup and increasing its robustness.
3. Experimental validation
The dispersion dual OFC based gas analyzer has been experimentally validated by measuring the ro-vibrational transition of HCN at 1544.51 nm. A HCN gas cell (HCN-13-H(5.5)-100-FCAPC, Wavelength References Inc., Oregon, USA) with a path length of 55 mm and a pressure of 100 Torr was used in the tests. The architecture was implemented using Discrete Mode laser (EP 1550-DM-HAA, Eblana Photonics Ltd., Dublin, Ireland) and two Lithium Niobate electro-optical phase modulators (PM-5S4-10-PFA-PFA-UV, EOSPACE Inc., Washington, USA) for the generation of the two OFCs. The operation range of these modulators goes from DC to 10 GHz. The measurement OFC is then collimated into the HCN cell and propagates through the gas for 55 mm before being again launched into a fiber. On the other hand, the LO comb is shifted in frequency by the AOM (T-M040-0.5C8J-3-F2S, Gooch and Housego PLC, Ilminster, United Kingdom) and polarization matched (FPC030, Thorlabs Inc., New Jersey, USA) before the combination with the measurement comb. The optical combined signal is detected by an amplified InGaAs photodetector (PDA10CF, Thorlabs Inc., New Jersey, USA) and the resulting RF comb band pass filtered (SIF-40 + , Mini-Circuits Inc., New York, USA) and digitized by a 14-bit acquisition board (PDA14, Signatec Inc., California, USA). A Holzworth HS9004A (Holzworth Instrumentation Inc., Colorado, USA) 4 channel phase coherent synthesizer was used for the generation of the modulation signals of the acousto-optic and phase modulators and the acquisition clock. The phase of each of the teeth of the comb is measured, after acquisition, by a digital 99 channel parallel lock-in amplifier implemented in Matlab (MathWorks Inc, Massachusetts, USA) with fully configurable reference frequencies, integration times and data output rates. More details of this parallel phase-sensitive detection scheme have been given elsewhere .
In this experimental validation, the output power of the laser was adjusted to approximately 2 mW acting over its temperature to get the emission wavelength roughly in the center of the absorption feature. The modulation frequencies of the PMs were 500 MHz and 500.1 MHz resulting in a RF repetition frequency of 100 kHz. The modulators were driven with the amplified modulation signals (with a power of around 30 dBm) to generate combs with a spectral coverage of 25 GHz (200 pm). The setup takes advantage of the distortion introduced by the power amplifiers (at power levels that are close to the maximum power output) in the signals driving the phase modulators to produce extra harmonics that allow the obtaining of a flatter comb spectrum when compared to pure sinusoidal signal excitation of the modulators. The 40 MHz signal that drives the AOM was amplified to a level of 20 dBm generating a RF comb centered at 40 MHz and with over 50 spectral components separated 100 kHz. After band pass filtering the output of the photodetector, the RF signal is synchronously subsampled at 36 MS/s generating a frequency-shifted comb centered at 4 MHz while maintaining the repetition frequency. The phases extracted by the digital multi-channel lock-in amplifier are box-smoothed to filter out multiplicative phase noise .
The results of one of spectral measurements are shown in Fig. 5 for an integration time of 10 ms together with the fit of the data. The available data output rate of this demonstration is therefore 100 measurements per second, however, this figure could be greatly improved by the use of sliding window integrating algorithms. The average SNR of the dispersion-based gas analyzer is 35 dB*Hz-1/2 calculated as the ratio of the peak to peak phase and the average standard deviation in phase of the teeth of the comb. For this SNR an estimated detection limit of 17.5 ppm*m/Hz1/2 is obtained for HCN and the extrapolation of the results to the stronger absorption features of methane in the 1650 nm region will result in a resolution of approximately 1 ppm*m/Hz1/2. This value is slightly better than the resolutions obtained by classical and optical heterodyne CLaDS sensors (2.7 ppm*m/Hz1/2  and 6.43 ppm*m/Hz1/2  respectively) and also improves the resolution in the detection of methane of the first HPSDS demonstration (11.7 ppm*m/Hz1/2 ).
In this paper a multiheterodyne architecture based on a coherent dual-comb source for molecular dispersion spectroscopy has been presented and experimentally validated. The analyzer is capable of high speed operation and uses the measurement of optical dispersion to estimate the concentration of gas. Therefore, it is immune to the classical baseline and normalization problems of absorption-based analyzers and provides a linear relationship between gas concentration and the output signal. Since the multiheterodyne approach allows the simultaneous characterization of multiple spectral points, the operation speed achievable by the presented analyzer could improve by several orders of magnitude the output data rate of current tunable laser based gas detectors.
The dual-comb source is generated by the electro-optic modulation of a single continuous wave laser. Even though the spectral coverage of these combs is smaller than the coverage of comb generated by passively mode-lock lasers, these synthesizers offer numerous advantages. The main point in favour is that the complexity in the implementation of the dual OFC system is translated from the optical to the electrical domain, where there is a great number of tools and techniques available. This results in a huge reduction of the complexity and cost of the setups and ease of configuration and operation. The power of the spectral components is also higher resulting in increased sensitivities. On top of that, the phase-sensitive scheme takes advantage of the phase coherence between the repetition rates of the two combs and the acquisition hardware to eliminate any reference optical path used by current electro-optic dual-comb architectures.
The performance of the dispersion analyzer has been experimentally validated using the spectral line of HCN at approximately 1544.51 nm. With a setup configured for providing a good spectral resolution in the measurement of the narrow spectral feature, the analyzer was able to obtain a high SNR for integration times of 10 ms. The estimated detection limit in the analysis of HCN of this first demonstration is 17.5 ppm*m/Hz-1/2. Finally, it is important to note that this scheme can also be used for the spectral characterization of optical components and fiber sensors interrogation.
References and links
1. D. Roschdestwensky, “Anomale dispersion im natriumdampf,” Ann. Phys. 344(12), 307–345 (1912). [CrossRef]
3. E. Kindel, M. Kettlitz, C. Schimke, and H. Schöpp, “Application of the hook method and emission spectroscopy for the determination of radial density and temperature profiles in high-pressure mercury discharges,” J. Phys. D Appl. Phys. 31(11), 1352–1361 (1998). [CrossRef]
4. R. Gross, R. Chodzko, E. Turner, and J. Coffer, “Measurements of the anomalous dispersion of HF in absorption,” IEEE J. Quantum Electron. 16(7), 795–798 (1980). [CrossRef]
5. A. B. Duval and A. I. McIntosh, “Measurement of oscillator strength by tunable laser interferometry,” J. Phys. D Appl. Phys. 13(9), 1617–1624 (1980). [CrossRef]
6. S. Marchetti and R. Simili, “Measurement of the refractive index dispersion around an absorbing line,” Opt. Commun. 249(1–3), 37–41 (2005). [CrossRef]
7. A. J. Kemp, J. R. Birch, and M. N. Afsar, “The refractive index of water vapour: a comparison of measurement and theory,” Infrared Phys. 18(5–6), 827–833 (1978). [CrossRef]
8. J. R. Birch and M. N. Afsar, “The rotation spectrum of methyl alcohol vapour between 8 and 50 cm−1,” Spectrochim. Acta, Part A 35(6), 669–672 (1979).
9. J. R. Birch, “Recent progress in dispersive fourier transform spectrometry,” Proc. SPIE 0289, 362–384 (1981). [CrossRef]
12. M. Gehrtz, G. C. Bjorklund, and E. A. Whittaker, “Quantum-limited laser frequency-modulation spectroscopy,” J. Opt. Soc. Am. B 2(9), 1510–1526 (1985). [CrossRef]
16. E. Baumann, F. R. Giorgetta, W. C. Swann, A. M. Zolot, I. Coddington, and N. R. Newbury, “Spectroscopy of the methane ν3 band with an accurate midinfrared coherent dual-comb spectrometer,” Phys. Rev. A 84(6), 062513 (2011). [CrossRef]
17. T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place,” Science 319(5871), 1808–1812 (2008). [CrossRef] [PubMed]
18. M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hansch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, “Measurement of the hydrogen 1S- 2S transition frequency by phase coherent comparison with a microwave cesium fountain clock,” Phys. Rev. Lett. 84(24), 5496–5499 (2000). [CrossRef] [PubMed]
21. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent dual-comb spectroscopy at high signal-to-noise ratio,” Phys. Rev. A 82(4), 043817 (2010). [CrossRef]
22. M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311(5767), 1595–1599 (2006). [CrossRef] [PubMed]
23. B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010). [CrossRef]
26. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Widely wavelength-tunable ultra-flat frequency comb generation using conventional dual-drive Mach-Zehnder modulator,” Electron. Lett. 43(19), 1039 (2007). [CrossRef]
27. D. A. Long, A. J. Fleisher, K. O. Douglass, S. E. Maxwell, K. Bielska, J. T. Hodges, and D. F. Plusquellic, “Multiheterodyne spectroscopy with optical frequency combs generated from a continuous-wave laser,” Opt. Lett. 39(9), 2688–2690 (2014). [CrossRef] [PubMed]
28. P. Martin-Mateos, M. Ruiz-Llata, J. Posada-Roman, and P. Acedo, “Dual comb architecture for fast spectroscopic measurements and spectral characterization,” IEEE Photonics Technol. Lett. 27(12), 1309–1312 (2015). [CrossRef]
29. D. P. Blair and P. H. Sydenham, “Phase sensitive detection as a means to recover signals buried in noise,” J. Phys. Educ. 8(8), 621–627 (1975).
30. P. Martín-Mateos, S. Crespo-Garcia, M. Ruiz-Llata, J. R. Lopez-Fernandez, J. L. Jorcano, M. Del Rio, F. Larcher, and P. Acedo, “Remote diffuse reflectance spectroscopy sensor for tissue engineering monitoring based on blind signal separation,” Biomed. Opt. Express 5(9), 3231–3237 (2014). [CrossRef] [PubMed]
31. J. Irby, R. Murray, P. Acedo, and H. Lamela, “A two-color interferometer using a frequency doubled diode pumped laser for electron density measurements,” Rev. Sci. Instrum. 70(1), 699–702 (1999). [CrossRef]
33. G. Plant, M. Nikodem, D. M. Sonnenfroh, and G. Wysocki, “Chirped laser dispersion spectroscopy for remote sensing of methane at 1.65µm - analysis of system performance,” in CLEO:2013 OSA Technical Digest Series (Optical Society of America, 2013), paper JW2A.79.
34. P. Martín-Mateos, B. Jerez, and P. Acedo, “Heterodyne architecture for tunable laser chirped dispersion spectroscopy using optical processing,” Opt. Lett. 39(9), 2611–2613 (2014). [CrossRef] [PubMed]