1. INTRODUCTION

Mid-infrared (mid-IR) is known as one of the most useful wavelength regions for spectroscopy due to the presence of fundamental vibrational transitions in molecules [1]. Moreover, it has medical potential as human breath contains numerous volatile chemical compounds (VOC), many of which can be associated with diseases [2]. Presently, mid-IR spectroscopy is primarily based on Fourier transform infrared (FTIR) spectrometers [3] that are bulky and have limited resolution and acquisition time. Over the past decade, dual-comb spectroscopy (DCS) has emerged as an approach that can alleviate some of these shortcomings [4,5]. This approach that emerged with the invention of optical frequency combs [6–8] enables fast detection, scanning without moving parts, high resolution spectra, and has no limitation on size, as the device length is independent on resolution, contrary to the FTIR. It is also well known for accessing a broad spectral range yet maintaining a high sensitivity comparable with traditional spectroscopic approaches such as wavelength or frequency modulation spectroscopy [9,10]. DCS has today seen significant advances [11] and has also been successfully applied to an increasing portion of the mid-IR spectrum using a number of mid-IR comb sources [12], including quantum cascade lasers (QCLs) [13], microresonator Kerr frequency combs [14], difference frequency generation (DFG) [15–18], cascaded quadratic nonlinear process [19–23], and optical parametric oscillators (OPO) [24–27]. Yet to date, generating phase locked mid-IR frequency combs that exhibit high brightness, broad bandwidth, and fine resolution remains challenging. The most advanced approaches have used DFG that typically requires the synchronization of two laser beams (even one powerful laser source can be used, it is separated to be one pumping beam and one supercontinuum beam as the probe) and features limited instantaneous spectral bandwidth. To reach a larger spectral coverage, either mechanically tuning the phase matching of the nonlinear crystal or implementing a custom-designed chirped quasi-phase-matching (QPM) is required [17]. OPO-based mid-IR frequency combs have attained some of the broadest spectra to date, allowing for massive parallel sensing of trace molecules [27]. Although capable of a miniature size, this approach is mostly based on solid-state laser cavities that contain discrete bulk optics and components.

Here, we demonstrate a new approach to mid-IR DCS that offers unprecedented simplicity, based on supercontinuum generation in “coupled” nanophotonic integrated silicon nitride (${{\rm Si}_{3}}{{\rm N}_{4}}$) waveguides, and is driven by conventional low-noise fiber-laser-based optical frequency combs in the well developed telecommunication (telecom) band, as shown schematically in Fig. 1. In particular, we propose a coupled waveguide structure that represents an advanced approach to dispersion engineering in the mid-IR, under which the supercontinuum process, seeded in the telecom-band ($1550\;{\rm nm} $), is along with the mode coupling in the waveguide [Fig. 1(b)] and is tailored to have a large spectral bandwidth and high flatness accessing the mid-IR typically beyond $2500\;{\rm nm} $ [Fig. 1(c)]. The dual-comb spectrometer we presented offers state-of-the-art signal to noise and large instantaneous spectral bandwidth in the mid-IR (over $800\;{{\rm cm}^{- {1}}}$). It combines both low-noise fiber lasers and photonic integrated waveguides. Each in itself is a well developed technology, is commercially available, and therefore can contribute to high-performance mid-IR DCS.

 

Fig. 1. Nanophotonic supercontinuum-based mid-IR dual-comb spectroscoppy. (a) Schematic setup for mid-IR dual-comb gas-phase spectroscopy, in which two mid-IR frequency combs are generated via coherent supercontinuum process in nanophotonic chip-based ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguides, seeded by a mutually locked dual-frequency-comb source at the telecom-band (i.e., ${\sim}1550\;{\rm nm} $). HWP, half-wave plate; PD, (mid-IR) photodetector. A schematic of the dual-core ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguide, with temporal evolution of the supercontinuum generation, is presented. (b) Microscopic pictures of a photonic integrated chip with coupled ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguides, corresponding to both the input section, where the beginning of the waveguide contains an inverse taper structure, and the output section showing dual-core waveguide structures. The false-colored scanning electron microscopic (SEM) picture of the waveguide cross section is also presented. (c) Principle of enhanced mid-IR continuum generation serving as the frequency comb, which corresponds to a dispersion landscape that is engineered and flattened in the mid-IR, particularly by the anomalous GVD produced in the coupled waveguide. Dispersion landscape is defined as relative phase constant compared with the pump pulse, i.e., $\beta (\omega) - {\beta _{\rm s}}(\omega)$. In addition, a visible dispersive wave is also supported in this type of waveguide due to the phase matching.

Download Full Size | PDF

2. NANOPHOTONIC SUPERCONTINUUM GENERATION WITH SUPERMODE DISPERSION ENGINEERING

Supercontinuum generation is one of the most dramatic nonlinear optical processes [28] and has been essential for enabling femtosecond lasers to be self-referenced, making fully stabilized optical frequency combs [29]. Fundamentally, it constitutes a way to access ultra-broadband and coherent comb sources and is the key component in DFG for mid-IR frequency comb generation as well as the mid-IR DCS [15,16,30,31]. Recent advances have been on nanophotonic integrated waveguides, where lithographically tailorable supercontinuum generation is enabled at low pulse energies [32–39], in association with diverse photonic regimes such as QPM [40] and mode perturbation [41,42], and have been applied for laser self-referencing [43,44] and offset frequency detection [37,45] for DFG [46], as well as for spectroscopy [41,47]. In particular, ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguides [48], combining a wide transparency with nanophotonic dispersion engineering, have been demonstrated to support mid-IR frequency comb generation based on dispersive wave generation from a femtosecond erbium fiber laser via supercontinuum generation [36,49]. In this way, they provide access to the high-demand mid-IR range by bridging a coherent link with well developed fiber laser technology in the near-infrared (near-IR), amiable for DCS.

The spectral extent and efficiency of supercontinuum generation in nanophotonic waveguides critically depends on the dispersion properties. While the geometry (width and height) of the waveguide can be controlled to achieve dispersion engineering, leading to mid-IR dispersive waves upon the near-IR pump [36], this control poses limitations on achieving a high conversion efficiency and ultra-broadband mid-IR continuum.

Here, we employ coupled structures consisting of multiple ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguide cores, typically dual-core waveguides [cf. Fig. 1(b)]. When two waveguide cores are in close proximity, the optical mode propagating in one core is coupled to the other core, which effectively changes its phase, i.e., the propagation constant of the mode ($\beta (\omega)$, where $\omega$ is the angular frequency of the light). In this way, the group velocity dispersion (GVD) is also changed as it corresponds to the frequency-dependent phase change induced by the mode coupling (${\rm GVD} = {\partial ^2}\beta /\partial {\omega ^2}$). Physically, mode coupling leads to the hybridization of mode-field distributions, resulting in a pair of supermodes, namely the symmetric and anti-symmetric superpositions of the original uncoupled waveguide modes [50,51]. The coupling induced dispersion (also known as supermode dispersion [52,53]) is then reflected by the phase profile of these supermodes, which is curved to bridge that of the uncoupled modes, and feature an avoided crossing between each other [cf. Fig. 2(a)]. Deterministically, anomalous GVD is always produced by the anti-symmetric mode, while normal GVD is produced by the symmetric mode. In principle, such mode coupling (formally termed “mode hybridization”) can be engineered at arbitrary wavelength regions, particularly in the mid-IR, where anomalous GVD is essentially required for dispersion compensation [54] and for tailoring a flattened dispersion profile (with values close to zero over a large bandwidth), but is hardly accessible in conventional single-core waveguides. In detail, the dispersion profile is defined as the relative propagation constant compared with the pump pulse (assumed as temporal soliton):

 

Fig. 2. Design and mid-IR supercontinuum generation in coupled ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguides. (a) Calculated effective refractive indices of symmetric (purple curve) and anti-symmetric (orange curve) modes in a dual-core ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguide, compared with initial uncoupled modes separated in each core. The geometry of the waveguide is ${w_1} = 1.3\,\,\unicode{x00B5}{\rm m}$, ${w_2} = 3.4\,\,\unicode{x00B5}{\rm m}$, $h = 0.85\,\,\unicode{x00B5}{\rm m}$, and $g = 0.8\,\,\unicode{x00B5}{\rm m}$. The mode coupling is between the fundamental ${{\rm TE}_{{00}}}$ mode [marked as ${n_1}(\lambda)$] in the narrow core (blue curve) and the ${{\rm TE}_{{10}}}$ mode in the wide core (green curve). Insets are the electric-field distribution of the supermodes at different wavelengths. (b) Calculated dispersion (orange curves) of the anti-symmetric mode (corresponding to three gap distances $g = 0.6, 0.7, 0.8\,\,\unicode{x00B5}{\rm m}$), which produces additional anomalous GVD in the mid-IR compared with the uncoupled mode (blue curve). (c) Calculated dispersion profile of the anti-symmetric mode (with $g = 0.8\,\,\unicode{x00B5}{\rm m}$) compared with that of a selected single-core waveguide ($w = 1.8\,\,\unicode{x00B5}{\rm m}$, $h = 0.85\,\,\unicode{x00B5}{\rm m}$). Both show a similar phase matching wavelength in the mid-IR (ca. $3500\;{\rm nm} $). (d) Experimentally observed supercontinuum generation in a dual-core ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguide, with measured geometry ${w_1} = 1.3\,\,\unicode{x00B5}{\rm m}$, ${w_2} = 3.5\,\,\unicode{x00B5}{\rm m}$, $h = 0.90\,\,\unicode{x00B5}{\rm m}$, and $g = 0.65\,\,\unicode{x00B5}{\rm m}$. OSA, optical spectral analyzers; FTIR, Fourier-transform infrared spectrometer. (e) Simulation of the supercontinuum generation in the dual-core waveguide (cf. Supplement 1 for simulation details). (f) Spectral overlapped two mid-IR supercontinua from two ${{\rm Si}_{3}}{{\rm N}_{4}}$ chip samples.

Download Full Size | PDF

Figure 2 illustrates the design of the ${{\rm Si}_{3}}{{\rm N}_{4}}$ dual-core waveguide. The cross section of the two ${{\rm Si}_{3}}{{\rm N}_{4}}$ cores are separately selected, in which two modes (one from each core) can feature the hybridization in the mid-IR region, by matching their propagation constants (or equivalently by matching the effective refractive index (${n_{{\rm eff}}}$), since $\beta = {n_{{\rm eff}}}\omega /c$, where $c$ indicates the speed of light in vacuum). For a choice of ${{\rm Si}_{3}}{{\rm N}_{4}}$ core widths of ${w_1} = 1.3\,\,\unicode{x00B5}{\rm m}$ and ${w_2} = 3.4\,\,\unicode{x00B5}{\rm m}$, respectively, and for an identical core height of $h = 0.85\,\,\unicode{x00B5}{\rm m}$, two modes, i.e., the fundamental ${{\rm TE}_{{00}}}$ mode in the narrow core and the ${{\rm TE}_{{10}}}$ mode in the wide core, would have the same ${n_{{\rm eff}}}$ at the wavelength of $3200\;{\rm nm} $ [Fig. 2(a)]. Then, for the dual-core waveguide with a coupling gap distance of $g = 0.8\,\,\unicode{x00B5}{\rm m}$, the propagation constants as well as the mode-field distributions of supermodes are re-calculated. It can be observed that, in the mid-IR where mode hybridization occurs, the propagation constants of supermodes are strongly curved, while in the near-IR away from the hybridization region, they are degenerate to uncoupled modes corresponding to the narrow and wide cores. Therefore, strong and dominant anomalous GVD is induced in the mid-IR from the anti-symmetric modes [at ${\sim}3200\;{\rm nm} $, cf. Fig. 2(b)], which is evolved from the narrow core mode in the near-IR. Counterintuitively, the larger change in the supermode dispersion is not achieved by a closer proximity of the two waveguides, as this causes the mode hybridization to occur over a larger spectral range such that the frequency dependency of mode’s phase constant is reduced.

A designed dispersion profile of the dual-core waveguide is then shown in Fig. 2(c), which is largely tailored and flattened when compared with that of a conventional single-core waveguide [note that the width of the single-core waveguide is selected such that both waveguides have a similar phase matching ($\Delta \beta (\omega) = 0$) wavelength in the mid-IR for the dispersive wave generation [36,55]].

Significantly, to exploit anomalous GVD in the mid-IR for engineering the supercontinuum, it is imperative to selectively excite the anti-symmetric mode only. This is accomplished by designing the waveguide input section to be the narrow core alone (with an inverse taper in the beginning [56], which efficiently excites the ${{\rm TE}_{{00}}}$ mode), followed by the dual-core section [cf. Fig. 1(b)]. The length of the input section is chosen such that the pulse propagation enters into the dual-core section before significant spectral broadening occurs. Physically, supercontinuum generation is a process that is self-confined in one mode type, where the efficiency of the self-phase modulation (SPM) is maximized. Therefore, being launched into the mode of the narrow core, the near-IR pumping wave upon the supercontinuum process will be self-confined into the anti-symmetric mode and features induced anomalous GVD, when its spectral broadening reaches the hybridization region in the mid-IR.

We next carried out experiments to investigate the supercontinuum generation in the designed ${{\rm Si}_{3}}{{\rm N}_{4}}$ dual-core waveguides. The waveguides are fabricated using the photonic Damascene process [57], in which thermal annealing steps are critical for reducing the hydrogen content and the related absorption losses [58]. The waveguide length is $5\;{\rm mm} $, including the inverse taper section at the beginning. In waveguides similar to the design, supercontinuum generation was observed [Fig. 2(d)], which is seeded by the amplified femtosecond fiber laser in the telecom-band (pulse duration ${\lt}70\;{\rm fs} $, maximum averaged power ${\gt}350\;{\rm mW} $, pulse energy ${\gt}1\;{\rm nJ} $, repetition rate ${\sim}250\;{\rm MHz} $). Significantly, with respect to the pumped wavelength (i.e., $1550\;{\rm nm} $), the supercontinuum is mostly extended to the long wavelength side, leading to an ultra-broadband mid-IR continuum ranging from $2000$–$3700\;{\rm nm} $, while at the short wavelength side, it features a sharp edge (stopping at $1000\;{\rm nm} $) followed by a dispersive wave in the visible range (at $600\;{\rm nm} $). The spectral envelope exactly reflects the designed dispersion landscape, i.e., the optical power spectrum is inversely proportional to the square of the relative phase constant. Filtering out the mid-IR continuum by an edge-filter (cut-on at $2500\;{\rm nm} $), we measured the net power in the mid-IR to be $1$–$3\;{\rm mW} $, depending on the intensity of the pump wave. Note that such a power level already comprises the insertion loss of the waveguide and the loss in the light collecting component (including a mid-IR collecting lens that has a transparency of ${\sim}70\%$), thereby producing sufficient power to implement DCS. The conversion efficiency from the pump wave to the mid-IR frequency comb is estimated to be $1$–$5\%$.

In addition, apart from the generation of a flat mid-IR supercontinuum, we also observed a vertically polarized wavelet, i.e., orthogonal to the pump wave that is horizontally polarized, which is narrow-band and comparatively strong in the intensity. This wave is the result of mode coupling between the anti-symmetric mode (TE mode) and a high-order hybrid mode (TM mode) in the dual-core waveguide.

We performed numerical simulations on the supercontinuum process in the dual-core waveguide, see Fig. 2(e), based on two coupled nonlinear Schrödinger equations (cf. Supplement 1 for simulation details), corresponding to the anti-symmetric mode and the high-order mode in the dual-core waveguide. Simulation result shows a high level of agreement with the experiment, in terms of both the supercontinuum envelope and the vertically polarized wavelet in the high-order mode, which confirms that the dual-core waveguide does support a flat mid-IR supercontinuum.

Moreover, we can duplicate the flat mid-IR supercontinuum among separate ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguide chips. With a high level of spectral overlap, a broadband mid-IR dual-comb spectrometer is constructed, see Fig. 2(f).

 

Fig. 3. Parallel gas-phase spectroscopy by mid-IR broadband dual-comb spectrometer. (a) Retrieved mid-IR spectrum from the detected and coherent averaged interferogram trace, after the averaging of $52 {\rm s}$ (net data acquisition time, cf. Supplement 1 for details on the coherent averaging process), which covers a large span from $2800$–$3600\;{{\rm cm}^{- {1}}}$. The gas species in the gas cell, i.e., ${\rm CH}_4$ and ${\rm C}_2{\rm H}_2$,g as well as water vapor in the circumstance, are featured as sharp absorbance in the spectrum. Insets show the temporal interferogram trace recorded by the photodetector. The blue shading area marks the mode coupling between the anti-symmetric mode and a higher-order hybrid mode, which exhibits a deep and narrow-band absorption in the spectrum. (b) In this panel, the measured gas absorbance (blue curves), ${\rm CH}_4$ (left) and ${\rm C}_2{\rm H}_2$ (right), are fitted and compared with the HITRAN database (red curves, inverted for clarity) within a large span in the spectrum. The gas cell has the total pressure of $1 {\rm atm}$, the fitted concentration is ${\rm CH}_4$ at $136.4\;{\rm ppm} $ and ${\rm C}_2{\rm H}_2$ at $406.5\;{\rm ppm} $, with nitrogen as the buffer gas. (c) In this panel, detailed gas absorbance, including both the intensity and the phase information, are compared with the HITRAN database. The residual signal from the fitting is also presented, with an offset value (0.15 for ${{\rm CH}_{4}}$ data and 0.5 for ${{\rm C}_{2}}{{\rm H}_{2}}$) artificially imposed merely for plotting purpose.

Download Full Size | PDF

3. NANOPHOTONIC SUPERCONTINUUM-BASED MID-IR DUAL-COMB SPECTROMETER

The schematic setup of the nanophotonic supercontinuum-based mid-IR dual-comb spectrometer is shown in Fig. 1(a). The pump source consists of two ultra-low noise femtosecond fiber lasers with sub-millihertz (mHz) individual linewidth (FC-1500-ULN from Menlo Systems, wavelength ${\sim}1550\;{\rm nm} $, repetition rate ${f_{{\rm rep}}} \sim 250\;{\rm MHz} $). Both lasers have the carrier-offset frequency locked via self-referencing [7,29], and one comb mode is optically locked to a shared reference laser [at ${\sim}1542\;{\rm nm} $, the laser is free-running with a frequency drift of ${\cal O}(100 \;{\rm MHz})$ over 24 h]. The locked mode index is different by one, which leads to a small difference in the repetition rate, i.e., $\Delta {f_{{\rm rep}}} \approx 320\;{\rm Hz} $, and, in principle, allows the dual-comb spectrometer to cover a large span in the optical window, i.e., ${\sim}100\;{\rm THz} $ (cf. Supplement 1 for detailed analysis on the spectral coverage). In principle, the mid-IR frequency comb from the supercontinuum process is viewed as the spectral extension of the frequency comb structure of the original pump source, therefore it inherits the full properties of the source comb. Based on such a configuration, a phase-resolved mid-IR dual-comb spectrometer was built up, with one mid-IR comb passing through a gas cell for gas-phase detection and the other comb serving as the local reference. After detection, the two combs are interfered on a mid-IR photodetector [VIGO PV-4TE, mercury cadmium telluride (${\rm HgCdTe}$) detector]. In the presence of a difference in the repetition rate, they generate a radio frequency (RF) comb composed of distinguishable heterodyne beats between pairs of optical comb teeth. In the time domain, it corresponds to a periodic interferogram pattern that can be directly recorded by the detector. The data acquisition was implemented by a field programmable gate array (FPGA). The dynamical range is ${\gt}40\;{\rm dB} $ supported by sufficient power (${\gt}1\;{\rm mW} $) in the mid-IR, and by a 16 bit analog-to-digital (ADC) converter embedded in the FPGA. The real-time coherent averaging process [59] is also enabled with a computer for multiple sets of signals (cf. Supplement 1 for details on the coherent averaging process). The normalized signal-to-noise ratio of our spectrometer has a peak value of $25/\sqrt {\rm s}$ at the region of $3400\;{{\rm cm}^{- {1}}}$ (where the spectral intensity is strongest). The typical bandwidth in the mid-IR is $2800 - 3600\;{{\rm cm}^{- {1}}}$ (${\sim}25\;{\rm THz} $), consisting of more than $100,000$ comb elements. The averaged signal-to-noise ratio across this bandwidth is $10/\sqrt {\rm s}$. Therefore, we can conclude a figure of merit of $1.0 \times {10^6}/\sqrt {\rm s}$ for our ultra-broadband mid-IR dual-comb spectrometer, which is mostly limited by the relative intensity noise (RIN) on the mid-IR frequency combs (cf. Supplement 1 for RIN information). Although this figure of merit does not reach the shot-noise limit, it is comparable to reported results in other works, which for most DFG-based dual-comb spectrometers is from $1 - 6 \times {10^6}/\sqrt {\rm s}$.

 

Fig. 4. ${\rm CH}_4$ isotopologues resolved by mid-IR dual-comb spectrometer. Measured absorbance of ${\rm CH}_4$ (blue curve, averaging time 3.9 s) is compared with the HITRAN database (red curve, inverted for clarity) in the case of high concentration, i.e. ${\sim}12.5 \%$. The total pressure of the gas cell is ${\sim}0.1 {\rm atm}$. Insets show the absorbance of $^{{12}}{{\rm CH}_{4}}$, $^{{13}}{{\rm CH}_{4}}$, and $^{{12}}{{\rm CH}_{3}}{\rm D}$ at selected regions. Note: for isotopologues such as $^{{12}}{{\rm CH}_{3}}{\rm D}$, the noise floor becomes significant, since the absorption signal is very weak. The detection sensitivity remains unchanged.

Download Full Size | PDF

4. MID-IR GAS-PHASE SPECTROSCOPIC RESULTS

We next applied the dual-comb spectrometer for mid-IR gas-phase spectroscopy. A gas cell (length $104\;{\rm cm} $) was constructed with wedged sapphire windows to avoid etalon effects and filled with a low concentration of methane (${{\rm CH}_{4}}$) and acetylene (${{\rm C}_{2}}{{\rm H}_{2}}$) as targeted gas samples and nitrogen as the buffer gas. The overall pressure in the cell is $1 {\rm atm}$. Figure 3 shows a result of parallel gas detection for both samples. The spectrum [cf. Fig. 3(a)] is retrieved from a coherent averaged temporal interferogram pattern. The averaging time is 52 s. To extract the absorption spectrum, we measure first the spectrum through the gas cell with samples $T$, then purge the cell, fill it back to the original pressure with pure nitrogen, and measure the reference spectrum ${T_0}$. The spectral absorbance is then calculated as ${-}{\rm ln}(T/{T_0})$. Due to a limited accuracy in the control of gas pressure as well as the concentration, we made the nonlinear least-square fitting of our measured data with the HITRAN database and left the gas pressure and concentration as floating parameters. These parameters will determine the line intensity and the pressure related collisonal broadening induced linewidth of the absorption spectrum and, by means of the Kramers–Kronig transformation, contribute to reveal the phase spectrum. As a result, the fitted gas pressure and the concentration [cf. Figs. 3(b) and 3(c)] are in good agreement with the measured values, with a relative difference of a few percent that is within the uncertainty level of our gas control instruments. Nevertheless, we noticed that there is a shift on the line center frequency between our measurement and the database, on the order of $100\;{\rm MHz} $, which is understood as the underlying frequency instability in the spectrometer (i.e., due to the frequency drift of the reference laser). In addition to gas samples, the concentration of water vapor in the circumstance was also detected as ${\sim}1.8 \%$. The normalized and noise limited gas detection sensitivity was estimated to be ${\cal O}(10 \; {\rm ppm} \cdot {\rm m/}\sqrt {{\rm Hz}})$ (cf. Supplement 1 for detailed analysis on the performance), which is mainly limited by the optical comb power in the mid-IR.

Moreover, the performance of our supercontinuum-based mid-IR DCS was also benchmarked by successful detection of natural isotopologues of ${\rm CH}_4$ (Fig. 4), i.e., $^{{12}}{{\rm CH}_{4}}$, $^{{13}}{{\rm CH}_{4}}$, and $^{{12}}{{\rm CH}_{3}}{\rm D}$. For such a measurement, the gas cell is operated at low pressure such that the collisional broadening of spectral lines is reduced, and those corresponding to isotopologues (i.e., $^{{13}}{{\rm CH}_{4}}$, natural abundance $1.11\%$; $^{{12}}{{\rm CH}_{3}}{\rm D}$, $0.06\%$) can be resolved as separated modes from traditional elements ($^{{12}}{{\rm CH}_{4}}$). In experiments, we set the pressure of the gas cell to be ${\sim}0.1 {\rm atm}$ and the ${\rm CH}_4$ concentration to ${\sim}12.5\%$. At this pressure, the full width at half-maximum spectral linewidth of ${\rm CH}_4$ is reduced to ${\sim}480\;{\rm MHz} $, which is both sufficient for distinguishing isotopologues and resolvable by our sub-Doppler resolution (i.e., 250 MHz, determined by the mode spacing) of the mid-IR frequency comb. The capability of identifying a natural abundance of isotopologues is of high importance, as it provides signatures in earth science as well as in cosmology.

5. DISCUSSION

We have demonstrated a high-performance mid-IR dual-comb spectrometer based on the supercontinuum process in nanophotonic integrated nonlinear ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguides. The proposed coupled waveguide structure has revealed unprecedented ways of performing dispersion engineering, which can lead to flat-envelope, ultra-broadband mid-IR frequency combs. Such a supercontinuum-based dual-comb spectrometer has not only detected traditional chemical species, but can also trace their isotopologues. Our approach combines fiber laser combs technology with nanophotonic integrated devices, each in itself a well established technology, yet it exhibits a performance competitive to DFG-based dual-comb spectrometers, which is amiable for applications outside the protected laboratory environment. In addition, this approach can benefit from superior laser stabilization methods, e.g., adaptive laser stabilization [60], frequency alignment [61], or feed forward locking [18,62]. At the moment, the long wavelength edge of our spectrometer is limited to $4000\;{\rm nm} $ ($2500\;{{\rm cm}^{- {1}}}$), which is mostly as a result of the ${{\rm SiO}_{2}}$ cladding of our ${{\rm Si}_{3}}{{\rm N}_{4}}$ waveguides. Although ${{\rm Si}_{3}}{{\rm N}_{4}}$ shows a much larger transparency window reaching the beginning of the backbone region (${\lt}2500\;{{\rm cm}^{- {1}}}$), mode coupling will expose the propagating light mostly to the cladding and therefore feature strong loss in ${{\rm SiO}_{2}}$. Such a problem can be solved with air-cladding waveguides or substrates that are mid-IR transparent (e.g., sapphire).