1. Introduction

Optical frequency combs (OFC) have found a countless number of applications [1,2] in fields that include astronomy [3,4] optical ranging [5–7], frequency synthesis [8,9] and atmospheric analysis [10]. Indeed, the performance provided by OFC-based systems has set the new standards of optical accuracy and resolution, leading to a completely new generation of high-performance instruments that can operate at virtually all frequency ranges [11–16]. In the progress of these systems, especially noteworthy is the quest for single tooth resolved spectra, which in this past decade drove the development of dual-comb (DC) spectroscopy [17–19]. This method, based on the use of two OFCs (sample and local oscillator combs) with slightly different repetition rates, has demonstrated an unparalleled combination of sensitivity, frequency accuracy, and optical resolution. Besides this, DC systems have no moving parts, resulting in tools that are exceptionally interesting for fast and time-resolved measurements. In terms of optical span, DC spectrometers based on mode-locked lasers (MLL) cover ranges of hundreds of nanometers [20–22], largely meeting the requirements of many important applications. Nonetheless, and in order to guarantee the interferometric coherence between combs that ensures an adequate mapping of the teeth of the sample OFC into the RF domain, both OFCs have to be actively locked [23,24]. The equipment required to force mutual coherence is however complicated, and this leads to bulky and expensive systems. To circumvent this problem, two different approaches have been validated, the first uses digital interferogram corrections and the second is based on adaptive interferogram digitization. The first concept was introduced by Deschênes et al. [25] with a system based on the simultaneous acquisition of the interferometric signal and the fluctuations of two loosely stabilized combs. Long averaging periods in real-time were possible through the calculation of correction factors that restore mutual OFC coherence [26]. Burghoff et al. [27] re-engineered this approach for their work on THz QCLs and proved that all the parameters that are required for rebuilding phase coherence can be extracted computationally from the interferogram. Likewise, Sterczewski et al. [28] further simplified the high computational demands of Burghoff’s method demonstrating multiheterodyne spectroscopy using interband cascade lasers. On the other side, the adaptive interferogram acquisition method was presented by Ideguchi et al. [29,30] enabling high-performance DC spectroscopy in real-time with free-running MLLs. In this method, various beat frequencies, produced by heterodyning a pair of lasers with the two OFCs, are processed to generate two adaptive clock signals that compensate timing jitter and the fluctuations of the relative carrier-envelope phase respectively. The adaptive approach has also been demonstrated on THz DCs with noteworthy results [31].

The advantages of employing DC systems based on electro-optic (EO) comb generators as an alternative to traditional MLLs-based DCs, have been only recently exploited for spectroscopy [32–38]. Arguably the most important feature of narrowband EO DCs is that, as the two OFCs are generated from the same laser, a reasonably high level of coherence between them is inherently inherited [19], directly overcoming the need for forcing or reconstructing mutual coherence of MLLs-based DC systems. EO combs are generated from a continuous-wave (CW) laser by a strongly driven EO modulator; hence the teeth spacing, or repetition frequency f_r, is controlled by the frequency of the signal that drives the modulator. Nevertheless, and mainly because of the limitations in the half-wave voltage of EO devices, regular EO OFCs have a modest number of lines in comparison to that of MLLs (although far wider optical coverages, which can exceed an octave using supercontinuum generation, can be achieved by different methods [35,37,39–41]). Besides allowing for large teeth brightness, the moderate spans of EO DCs can be rapidly tuned and optimized for different measurements and applications with unprecedented flexibility. The absolute control over the repetition rates of the combs also enables virtually unrestricted spectral compression factors (down-conversion bandwidths) that simplify interferogram digitization. In terms of frequency uncertainty, EO DCs implemented using a free-running CW laser are unable to perform absolute spectroscopy and frequency wanders obscure their high-resolution capabilities. It is possible however to create an EO DC from a laser whose wavelength has been fixed by conventional optical frequency stabilization [37,39–43]. In this way, as the repetition rate of the combs can be referenced to a frequency standard, the frequency accuracy of the DC system will be dominantly determined by the performance of the stabilization method. With regard to the signal-to-noise ratio (SNR), the teeth of narrowband EO-generated combs exhibit a close mutual coherence that is nonetheless degraded by, low-frequency, interferometric phase noise (due to drifts in path lengths and refractive indexes in the interferometer). Therefore, whereas fast measurements providing moderate SNRs are straightforwardly taken without the need for any extra hardware, a phase stabilization mechanism is required for long averaging times [37].

In this manuscript, we present a simple, robust, and cost-efficient absolute real-time EO DC instrument that employs a molecular-line-locked CW laser providing a frequency accuracy of 0.2 ppm, as demonstrated by experimental calibration against acetylene molecular transitions. In addition, we demonstrate a novel real-time all-RF adaptive interferogram acquisition approach for EO DCs that, operating with complete independence from the DC system, reconstructs phase coherence between combs allowing for SNRs in excess of 10000 in an integration time of only 30 seconds.

2. Frequency accurate adaptive electro-optic dual-comb spectroscopy

2.1 Absolute electro-optic dual-comb spectroscopy

Many are the factors that have raised the interest in OFCs and contributed to its development and widespread use. We could argue, nevertheless, that the single most important feature that these optical sources provide is frequency accuracy. The progress of methods for comb self-referencing led to DC spectrometers in which the frequency of every single mode of the comb can be referenced to a frequency standard, enabling highly accurate absolute optical spectroscopy. The main requirement for self-referencing is an octave-spanning spectral span, that even though is very common on MLL combs, is rarely observed on their EO counterparts [39–41], particularly on those used for spectroscopy. It should be clearly noted that a self-referenced EO comb was already demonstrated in 2015 achieving a fractional accuracy and stability 10⁻¹⁴ [41]. Nonetheless, for a less expensive, robust, field-deployable instrument, a much simpler frequency stabilization system is required. In this manuscript, we propose the use of a conventional stabilization method to frequency-lock the CW laser (center frequency of the DC) to a molecular transition.

The architecture of the system proposed for absolute EO DC spectroscopy is presented in Fig. 1. Before the generation of the combs, the wavelength of the master CW laser is locked to a spectral line using the architecture that is highlighted by the dashed line. Accordingly, a fraction of the optical intensity emitted by the continuous wave laser (EP 1550-DM-HAA, Eblana Photonics Ltd., Ireland) is branched off by way of a beam splitter and taken to the input of the line-locking system. Firstly, a phase modulator (LN65S-FC, Thorlabs Inc., USA) modulates the laser beam that is next sent through a gas reference cell. Between the different options available, a NIST-traceable H¹³C¹⁴N gas cell at (HCN-13-H(5.5)-100-FCAPC, Wavelength References Inc., USA) a pressure of 100 Torr (SRM 2519 [44]) was chosen for wavelength referencing, targeting the R8 line at 1536.703427 nm (considering the pressure shift of the transition) [45]. The optical signals are detected by a high-speed photodiode (R402, Discovery Semiconductors Inc., USA) and the generated RF beat note is compared (on a phase detector) to the modulation signal. This comparison gives rise to an error signal (the waveform of this signal, which has a zero-crossing exactly at the central frequency of the absorption line, is shown in the inset of Fig. 1) that is fed to the servo controller that, with 3 kHz of bandwidth, stabilizes the laser frequency via laser current feedback. From this frequency-stable optical seed, the dual-comb can be obtained following an architecture based on two EO modulators (EOSPACE Inc., USA) for the generation of combs with marginally different repetition frequencies f_r1 and f_r2, being f_r2 = f_r1 - Δf_r. An acousto-optic modulator (AOM) (T-M080-0.5C8J-3-F2S, Gooch and Housego PLC, United Kingdom) is used to adjust the frequency offset (f_off) between combs to 80 MHz. After propagating the two combs through the sample cell, the optical signals are heterodyned on an amplified 150 MHz InGaAs photodetector (PDA10CF, Thorlabs Inc., USA) generating an RF comb centered at f_off with a spacing between teeth equal to Δf_r.

 

Fig. 1 Block diagram of the dual-comb and the line-locking mechanism. Yellow lines represent optical fiber and black lines represent RF cables. The dashed line highlights the frequency stabilization system allowing for absolute frequency DC spectroscopy. As shown in the inset, the error signal has a zero-crossing at the center of the spectral feature.

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2.2 Adaptive interferogram acquisition

High-performance optical spectroscopy requires not only frequency accuracy but also high SNRs. As presented in the introduction, because of the particular characteristics of EO DCs, where both, sample and local oscillator, combs are generated from the same CW laser, the resulting OFCs feature a close mutual coherence. Nevertheless, these two optical sources are not as phase-locked as could be expected: interferometric phase noise widens the linewidths of the multiheterodyne beat notes strongly restricting the coherence time of the system and, subsequently, the SNR. DC architectures are therefore highly sensitive to surrounding changes in temperature, mechanical vibrations and fiber movements. This obstacle was addressed in the past by Fleisher et al. [37] with an RF phase-locked loop that, acting over the frequency of the signal that drives the acousto-optic modulator, stabilized the EO DC enabling coherent interferogram integration for more than two hours. In this manuscript, we analyze in depth the problem and propose a novel method for removing interferometric phase drifts in EO DC systems. The technique is based on a simple, all-electronic, adaptive interferogram acquisition scheme that promptly reconstructs in real-time an exquisite mutual coherence between the two EO combs (without including any of the components of the DC system within the feedback loop and with complete independence from the optical path).

Adaptive dual-comb acquisition [30] was proposed as a tool for compensating the instabilities between two free-running combs. Hence, instead of forcing a tight active lock between the OFCs, the method forces mutual coherence by compensating the frequency/phase fluctuations in the interferograms. The requirements for an adaptive acquisition approach for EO DCs are however less severe than those that are necessary for free-running MLLs. As in the general case, phase coherence between combs is only ensured by properly stabilizing both timing jitter and carrier-envelope offset frequency. Nevertheless, the intrinsic timing jitter of narrowband EO combs is similar to that of actively stabilized MLLs and, hence, the variations between repetition frequencies can be neglected (due to the small bandwidth of the combs). In practice, the phase noise from the EO DC interferometer causes a (non-linear for wide optical spans) mode-to-mode phase shift proportional to both the difference in length between the two interferometric branches and the total amount of change of the refractive index and/or the length of the optical paths (Fig. 1). However, and unless the interferometer is strongly imbalanced by design (or ultra-wideband EO combs [39–41] are used); with the actual magnitude of the changes (temperature, vibrations, …) that an interferometer might suffer out of a laboratory, a steady timing jitter can be assumed even for reasonably long integration times. This point is further discussed in the next section. With regard to the carrier-envelope offset phase, since in EO DCs the two combs are generated symmetrically from the same optical signal, an offset frequency f_off has to be introduced by frequency shifting one of the combs with an AOM to avoid the interference between lower and upper sidebands. Nevertheless, as each EO comb is generated on a different optical branch of the interferometer, interferometric phase noise is directly coupled into f_off. Therefore, in an EO DC the fluctuations of the relative carrier-envelope phase correspond directly to the interferometric phase noise of the system limiting the coherence time of the spectrometer. We can hence conclude that an adaptive interferogram digitization system designed for EO DCs only requires the compensation of relatively slow fluctuations of the general phase of the interferogram and can, therefore, be straightforwardly implemented without the need of special, high-performance components.

Figure 2 provides an illustration of the fundamentals of the proposed adaptive interferogram digitization scheme in a comparison with a traditional acquisition approach. In the traditional method, interferograms are digitized using a steady clock, which derives on digitized interferograms that suffer from phase fluctuations. The adaptive acquisition scheme proposed in this manuscript performs by adjusting the frequency/phase of the acquisition clock in order to remove interferometric phase noise (relative carrier-envelope phase fluctuations). The result is a remarkably coherent, drift-free train of digitized interferograms.

 

Fig. 2 Comparison of traditional and adaptive EO DC acquisition schemes. φ_ROCP, phase of the relative offset frequency; φ_CLK, phase of the acquisition clock; φ_DIG, phase of the digitized interferograms.

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The block diagram of the proposed adaptive interferogram digitization scheme for EO DCs is shown in Fig. 3. A perfectly constant general phase on the digitized signal is ensured by directly comparing the phase of one of the teeth of the RF comb to an RF reference on a phase detector. Any deviation is directly compensated by a servo controller that adjusts the voltage controlled oscillator (VCO) providing the acquisition clock for the digitization hardware. In order to close the feedback loop, the VCO signal is in parallel mixed with the RF comb before phase detection is performed. As an example of operation, our AOM is driven at 80 MHz, hence the frequency offset of the RF comb will be equal to this frequency and lower and upper optical teeth will be mapped to RF frequencies around this central value with a spacing equal to Δf_r. If the multiheterodyne signal is to be acquired at a sampling rate of 1000 MS/s, the VCO has to operate at this frequency. Therefore, in parallel with the digitization of the train of interferograms, the RF comb is upshifted to 1080 MHz after the first mixer. Fluctuations of the relative phase will be maintained on the upshifted frequencies and, thus, by comparing on a mixer the phase of any of the teeth to that of an RF reference (1080 MHz on the example), a direct measurement of the relative carrier-envelope phase wander is obtained. By inputting this signal to the servo controller (after low-pass filtering at a cutoff frequency that is below Δf_r), carrier envelope phase fluctuations are eliminated from the digitized interferogram restoring a precise coherence between combs.

 

Fig. 3 Adaptive interferogram acquisition scheme. Black lines represent RF connections. An example of comb spectra and operation frequencies is shown in clear blue.

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The high frequency sampling rate from the previous example considerably complicates real-time data processing. Therefore, we have opted for an interferogram subsampling approach that has already demonstrated noteworthy performances in the past [33,34,37]. This method takes advantage of the absolute flexibility that EO DCs provide over the control of the compression factor m = f_r /Δf_r to generate an RF comb that is well-gathered around the offset frequency f_off). As our signal bandwidth is roughly 12 MHz, we employ a 72 MHz acquisition clock with a reference frequency of 8 MHz or 152 MHz with similar results. It should be noted that any line of the RF comb can be employed for phase detection without a noticeable change in the performance of the system. The main benefit of the low sampling frequency is a low computation cost that enables straightforward real-time operation but still providing fast measurement rates.

For RF signal processing, an FPGA-based (DK-DSP-2S60N, Altera Corp., USA) multi-channel lock-in amplifier capable of real-time operation with configurable integration times and data rates has been developed. In this way, a simple digitization and processing platform for real-time EO DC detection is made accessible. This equipment, together with a 14-bit acquisition board (PDA14, Signatec, Inc.), is employed in the various demonstrations presented in this manuscript. Single-tone measurements for system tuning and optimization were carried out with a high-frequency HF2LI lock-in amplifier (Zurich Instruments Ltd., Switzerland).

3. Characterization of performance

The capabilities of the proposed frequency accurate adaptive electro-optic dual-comb instrument have been assessed through several tests for determining both wavelength stability and the performance of the adaptive interferogram digitization scheme. For this characterization, the DC was configured with repetition frequencies of 100 MHz and 99.9 MHz and an offset frequency of 80 MHz. The resulting RF comb is displayed in Fig. 4, showing that over 100 individual lines are generated. The overall optical power is 300 µW.

 

Fig. 4 Illustration of an RF comb measured on a signal analyzer (resolution bandwidth 1 kHz).

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3.1 Frequency stability and reproducibility

As previously presented, an H¹³C¹⁴N gas cell at a pressure of 100 Torr (SRM 2519 [44]) was chosen for frequency referencing; specifically, the CW laser was locked (using the architecture presented in Fig. 1) to the R8 ro-vibrational line of HCN at 1536.703427 nm [45]. It is likely that virtually any other molecular transition can be employed for referencing. As discussed before, in EO DCs, frequency-locking the CW laser source results in the frequency-stabilization of the whole dual-comb; therefore, and in order to evaluate the performance of the proposed approach, the emission wavelength of the CW laser was monitored with a wavemeter (OSA207, Thorlabs Inc., USA). The obtained results, which are depicted in Fig. 5, clearly demonstrate that the system for frequency-locking provides high wavelength reproducibility and stability. Hence, no measurable drifts affect the comb when the line-locking system is engaged; providing, at the same time, a repeatability that is better than the resolution of the wavemeter. On the contrary, when deactivating the wavelength stabilization mechanism, a strong frequency wander is clearly visible on a consistent basis, mainly due to thermal drifts of the laser and the laser current source.

 

Fig. 5 Measurement of wavelength provided by the wavemeter. The operation is illustrated under wavelength-locked and unlocked conditions.

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It should be noted at this point that the proposed stabilization method provides a performance that is superior to the specifications of the wavemeter used in the tests ( ± 1 ppm of wavelength accuracy and 0.2 ppm of precision). Therefore, any numeric results that could be extracted from Fig. 5 are hindered by this limitation. It is then obvious that the figures obtained: wavelength accuracy of 0.52 ppm and a precision of 0.22 ppm are strongly dominated by the performance of the wavemeter. The actual specifications of the DC system are expected to be well below these values. In any case, the simple line-locking arrangement from Fig. 1 has demonstrated sub-ppm frequency stability and a precision and reproducibility that are better than those of the wavemeter employed.

3.2 SNR enhancement through adaptive acquisition

A representative view of the problem that the adaptive interferogram acquisition scheme from Fig. 3 is designed to address is provided in Fig. 6(a). The graph shows the general offset phase drift as a function of time, measured on the central tone of the RF comb. Even though on a far lower scale in comparison to MLL-based DCs, these phase fluctuations, that can reach slopes of several hundreds of degrees per second, strongly limit the coherence time of the spectrometer.

 

Fig. 6 (a) Relative carrier offset phase of an EO DC with respect to time. (b) Evolution of the phases of the teeth at 80.1 MHz, 80.2 MHz, 80.3 MHz, 80.4 MHz, 80.5 MHz and 80.6 MHz (from dark to light, or top to bottom, blue colors) with respect to the phase of the mode at 80 MHz (black line).

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With regard to the timing jitter, Fig. 6(b) shows a measurement of the tooth-to-tooth phase difference between the central mode of the RF comb and the first, second, third, fourth, fifth and sixth tones to the right (corresponding to RF frequencies of 80 MHz, 80.1 MHz, 80.2 MHz, 80.3 MHz, 80.4 MHz, 80.5 MHz and 80.6 MHz). In this figure, a clear relative phase shift between teeth proportional to the difference in frequency to the central (reference) mode is clearly seen. Nonetheless, quantitatively, Δf_r is affected by variations of only a few thousandth of a degree per second, which does not impose an actual limit on the achievable averaging times for most practical narrow bandwidth applications. Hence, as an outline and confirming the discussion presented in the previous section of the paper, whereas phase variations of the offset frequency f_off have a profound impact on the SNR of the instrument, the effect of the timing jitter can be overlooked in experimental scenarios in which narrowband EO comb are employed. It has to be noted nonetheless that the timing jitter will ultimately limit the phase stability of very high-order comb teeth [39–41].

As introduced in the previous Section, the proposed adaptive interferogram digitization system (Fig. 3) is designed for adjusting the phase of the acquisition clock for closely compensating drifts of the relative carrier-envelope phase, immunizing in this way the digitized multiheterodyne signal against interferometric phase noise and reconstructing the high levels of coherence that are required for long integration times. An example of the performance of the system is presented in Fig. 7, in which the phase and the amplitude of an individual line of the EO DC are shown when the adaptive digitization system is activated and then deactivated (integration time 164 ms). Under operation conditions, the standard deviation of the phase is consistently in the proximity of 90 × 10⁻³ degrees, what is in clear contrast to the very strong fluctuations that appear when the proposed acquisition system is disabled. The impact of the adaptive acquisition is also evident in the amplitude of the tooth, with an SNR that improves from 80 to roughly 1500 when the set-up is activated. This improvement is a direct consequence of the steady phase coherence that the proposed acquisition scheme actively guarantees during the whole integration time period.

 

Fig. 7 Phase and amplitude of a line of the EO DC when the adaptive interferogram acquisition system is activated and deactivated.

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To provide a clearer picture of the capabilities of the adaptive acquisition mechanism, the Allan variance of a digitized frequency of the teeth of the DC (the central tone in this example) is plotted in Fig. 8. This graph demonstrates that mutual coherence can be reconstructed for a period greater than 1000 s, corresponding to a phase noise lower than 1 × 10⁻³ degrees and an equivalent RF linewidth of roughly 700 µHz. Intensity fluctuations due to polarization drifts ultimately limit the coherence time attainable by the system. In the same way, polarization wanders also restrict the maximum integration time in which the SNR (intensity fluctuations) scales with the square root of the integration time. This is emphasized in Fig. 9, where the average SNR of the measurement of optical intensity (defined as the ratio, in average, of the mean intensity of a tooth to its standard deviation) with respect to the integration time is shown. We can see how the maximum integration time that provides noticeable improvements in the SNR is limited to a few tens of seconds. It should be remarked nonetheless that the adaptive acquisition scheme enables the SNR to exceed 10000 in approximately 30 seconds, providing high sensitivity at a noteworthy operation speed. Hence, the presented adaptive EO DC digitization system has demonstrated an outstanding ability to improve the performance of a DC spectrometer allowing for long coherence times and SNRs that are, in this case, only limited by polarization drifts.

 

Fig. 8 Overlapped Allan deviation of the digital frequency of an individual line of the digitized RF comb (8 MHz) with adaptive acquisition.

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Fig. 9 Signal-to-noise ratio versus integration time.

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4. Impact on spectroscopic applications

After the characterization of the performance of the presented frequency accurate adaptive EO DC scheme, the system is tested for various applications. We carried out measurements of molecular samples for gas detection and analysis and also demonstrate that this low-cost EO DC spectrometer can be a valuable tool for the rapid determination of the emission wavelength of a laser.

4.1 Applications for gas spectroscopy

A frequency accurate and stable instrument is of prime importance for the study of the sharp spectral features that are characteristic of low-pressure molecular samples. We tested these features of our EO DC spectrometer by measuring a 5.5 cm long, 50 Torr acetylene gas sample with typical linewidths that are below 1 GHz. An optical switch is employed to bypass the cell in order to perform the normalization measurement, and the transmittance of the sample is then determined as the ratio between the actual measurement of the gas cell and the normalization intensities. As before, the repetition frequencies employed were 100 MHz and 99.9 MHz and the offset frequency was 80 MHz. This multiheterodyne signal is subsampled using the adaptive acquisition scheme at a rate of 72 MS/s. The interferogram period is equal to 10 µs and 250 interferograms were averaged for the characterization of the sample. The results obtained are shown in Fig. 10 together with the spectrum calculated using the HITRAN database. The Voigt profile fit of the measurements yields a central frequency that is consistently shifted by less than 40 MHz. This calibration sets the wavelength accuracy, limited by DC drifts within the feedback loop, in 2 × 10⁻⁷. It should be noted that this value is undoubtedly more reliable than the one obtained using the wavemeter from the previous Section and this clearly emphasizes the adequate functioning of the frequency stabilization mechanism.

 

Fig. 10 Experimental measurements (squares) of a C2H2 absorption line and the simulated spectrum from HITRAN data (blue line).

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From the measurement shown in Fig. 10, the spectroscopic SNR of the system was calculated as the line absorption divided by the average standard deviations of the intensities of the teeth of the comb. Thus, a SNR of 180 is obtained for an integration time of 2.5 ms, which results in an equivalent 1σ limit of detection of 1 ppmv⋅m⋅Hz^-1/2.

4.2. Rapid determination of the absolute frequency of a laser

From their very earliest stages of development, OFCs have been described as frequency rulers. In this section, we adopt this definition and demonstrate how the EO DC source here presented can be also employed to accurately and univocally determine the emission wavelength of a laser. We should first note that the basics of the measurement of the frequency of monochromatic signals using dual-OFCs have been thoroughly reviewed in [46,47] and only essential details are to be provided in this manuscript. For this test, the configuration of the DC system is completely different from that used for high-resolution gas spectroscopy. The repetition frequencies of the two combs are now adjusted to 1000 MHz and 1024 MHz and the offset frequency is kept at 80 MHz. The two EO combs are directly combined with the monochromatic laser (the frequency of which is to be determined) and heterodyned on a fast photodiode. Under this configuration, the RF bandwidth of interest extends from DC to 1000 MHz, as the beat notes of the laser with the two closest teeth from each comb will fall within this frequency range. RF spectral analysis is performed with a general purpose signal analyzer (N9010A, Agilent Technologies Inc., USA) configured with a resolution bandwidth of 8 MHz and a video bandwidth of 1 kHz for a total sweep time of 97.5 ms.

In Fig. 11, as an example, actual measurements of two slightly detuned lasers are represented. For the measurement shown in Fig. 11(a), and through the procedure described in [44], we can determine that the laser is beating against the third and fourth upper comb teeth and that the distance from the central frequency of the DC is 3.696 GHz. Then, as the previously calibrated accuracy of the system is 0.2 ppm, the absolute wavelength of the laser can be provided as 1536.7346 nm ± 0.0003 nm. In the second example, shown in Fig. 11(b), the beat notes correspond to the first and second lower comb lines, being the absolute wavelength equal to 1536.6909 nm ± 0.0003 nm. The accuracy of both measurements was confirmed by a wavemeter.

 

Fig. 11 RF spectra of lasers at different frequencies.

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5. Conclusion

EO DCs were conceived as a straightforward, inexpensive alternative to MLLs-based DC systems. As the two EO OFCs are generated from the same CW monochromatic laser, EO DCs inherently overcome the highly demanding requirements for active stabilization and/or signal processing and acquisition systems that characterize traditional DC spectrometers. In this way, and in clear contrast to fieldable MLLs-based DC spectrometers [48,49], uncomplicated fieldable DC solutions based on EO-generated OFCs (that have already been demonstrated [50]) finally hold the potential for standardizing the use of DC technology beyond optics and metrology laboratories.

EO DC systems still have, nonetheless, some limitations that must be addressed, and frequency accuracy is one of them. In the past, EO DC sources were self-referenced (providing an accuracy of 10⁻¹⁴ [41]) or locked to an actively-stabilized optical cavity (yielding frequency uncertainties of 10⁻¹⁰ [37]). However, in a field deployable instrument, a much simpler, more convenient frequency stabilization method is required. In this manuscript, we demonstrate an absolute EO DC that takes advantage of a molecular wavelength calibrator for providing a frequency accuracy of 0.2 ppm and a precision and reproducibility that are well below the specifications of the wavemeter used in the tests. This level of performance is far in excess of the requirements needed for regular applications in, for example, high-precision analytical chemistry, optical communications, telemetry or biomedical optics. On the other side, in traditional EO DCs the SNR is limited by global phase drifts due to interferometric phase noise. In this paper, we have also addressed this problem and proposed a new coherence-enforcing architecture based on an adaptive digitization method that rebuilds in real-time any loss of mutual coherence between combs. This permits RF linewidths to reach 700 µHz and SNRs (intensity noise) above 10000 for integration times of 30 seconds, both limited by polarization drifts. The simple adaptive digitization scheme, which is implemented using basic RF components, is designed to operate without including any of the building blocks of the DC system or the optical path of the signal within the feedback loop. Therefore, this enables a complete independence between the acquisition subsystem and the optical set-up that ensures an exquisite robustness to changing operation conditions. The performance and flexibility of the system were finally put to test by characterizing the transmittance of a gas sample and measuring the absolute emission frequency of a laser. With the features previously demonstrated, simple and reliable, real-time absolute EO DC instruments have a huge potential of becoming standard commercially available off-the-shelf equipment in the years to come.