1. Introduction

Optical frequency combs (OFCs) [1,2] which output a broad spectrum of evenly spaced coherent spectral lines with very well-known absolute frequency positions have been an enabling tool for high precision spectroscopic applications. In particular, a dual-comb setup which allows rapid acquisition of molecular spectra with high spectral resolution has drawn extensive attention in recent years [3–7]. Dual-comb spectroscopy (DCS) is based on a pair of OFCs with slight repetition rate offset. As the local comb naturally walks through the signal comb, the time delay is scanned at a high speed without the need of a mechanical delay line which is commonly used in the conventional Michelson-based Fourier-transform infrared (FTIR) spectrometers [8]. In the frequency domain, multi-heterodyne between the signal comb after molecular absorption and the local comb effectively converts the OFC to the radio frequency (RF) region, enabling molecular absorption spectroscopy with a single photo-diode.

The first proof-of-principle DCS experiments were demonstrated with two free-running OFCs [4,7], while the spectral resolution was not comparable to that of the conventional FTIR technique due to the large relative comb line frequency noise. I. Coddington, et al. [9] solved this problem by tightly phase locking the two combs to common cavity-stabilized continuous wave lasers. Come-line resolved molecular gas spectra with absolute frequency accuracy and high signal-to-noise ratio (SNR) was obtained. Despite of the superior performance, the real-world applications are hindered by the sophisticated and bulky phase-locking sub-systems that establish the mutual coherence between the two combs. Much attention has been drawn to simplify the DCS setup afterwards. The need for optical cavity reference is removed by using two self-referenced OFCs phase locked to a common, free-running, commercial external cavity diode laser, allowing fieldable DCS applications [10]. A number of post-data processing [11,12] and adaptive sampling methods [13] has also been proposed. They only require two free running mode-locked lasers and the relative instability can be corrected by electronic signal processing. Recently, there is a new trend to produce a pair of OFCs with an offset repetition rate from a single laser cavity via bidirectional lasing [14,15], polarization multiplexing [16] as well as dual-wavelengths lasing [17]. Alternatively, a pair of mode-locked waveguide lasers integrated on a single glass-chip platform have also been used for DCS experiment [18,19]. To this end, the common-mode environmental noise can be significantly rejected, enabling intrinsically mutual coherence without any active phase lock [20]. Picometer resolution DCS has been demonstrated in a single dual-wavelength mode-locked Er-fiber laser [17].

The capability of dual-comb spectroscopy to identify various molecular species relies on broadband spectral coverage of the OFCs. Until recently, DCS has been widely validated from the THz to the UV spectral region [13, 14, 21–26]. Tm-doped fiber lasers have been proved as high average power and highly efficient light sources with wide gain spectrum spanning from 1.8 to 2.1 µm, where a number of important molecular absorptive lines locates. As a result, Tm-doped fiber OFCs [27, 28] are promising for a number of attractive molecular spectroscopic applications, particularly for Light Detection and Ranging (LIDAR) [29] and remote gas sensing [7] by taking advantage of the high brightness and broad gain bandwidth. H. Yang, et al. [26] has demonstrated DCS based on a pair of self-referenced Tm-doped fiber lasers phase-locked to a common narrow linewidth continuous wave (CW) optical reference. A. E. Akosman and M. Y. Sander [30] have demonstrated dual-comb generation from a single semiconductor saturable Bragg reflector mode-locked Tm/Ho co-doped, while the DCS experiment is still absent. In this paper, we demonstrate, for the first time to the best of our knowledge, a DCS experiment based on a single Tm-doped mode-locked laser in the vicinity of 2 µm. In a proof-of principle experiment, a single free-running nonlinear amplifying loop mirror (NALM) mode-locked Tm-fiber laser permits the characterization of spectral absorption lines caused by OH⁻¹ in fiber. The obtained down-converted radio frequency spectrum exhibits a comb-line resolved absorptive pattern which is attributed to the passive stability of the dual-wavelength dual-comb Tm-doped fiber laser.

2. Mode-locked Laser design and dual-comb operation characteristics

The setup of the dual-wavelength dual-comb mode-locked Tm-fiber laser is shown in Fig. 1. The main cavity is composed of a NALM and a half-transmissive fiber mirror serving as the output coupler, connected by a 2×1 broadband fused fiber coupler with a splitting ratio of 50/50. The NALM includes a 1550/2000 nm wavelength division multiplexer (WDM), a piece of 0.16 m long Tm-doped fiber (Nufern, SM-TSF-5/125), a piece of 1.3 m long dispersion compensation fiber (DCF, Nufern, UHNA4) and a free space segment. The other fiber segments used in the cavity are Corning SMF28-e. The net cavity dispersion is estimated to be 0.02 ps² at 1950 nm, working in stretched-pulse regime, enabling broad bandwidth laser spectrum to take advantage of the large gain bandwidth of Tm-doped fiber. The counter-propagating laser fields in the NALM interfere with each other after combination at the 50/50 fiber coupler. This results in an intensity dependent transmission, enabling additive pulse mode-locking (APM). The free space segment consisting of two quarter-wave plates (QWPs) with a free space Faraday rotator (FR) in between provides an additional phase bias which is beneficial for the self-starting of the mode-locking [31, 32]. The laser is pumped by a home-made 1564 nm continuous-wave (CW) fiber laser. Self-starting mode-locking is obtained at a pump power of 700 mW by proper selection of the orientation of the two QWPs. The fundamental repetition rate is around 71.88 MHz.

 

Fig. 1 Schematic of the dual-comb spectroscopy (DCS) with a single mode-locked Tm-doped fiber laser. Two combs with offset repetition rate Δf_r are directly generated by the nonlinear amplifying loop mirror mode-locked Tm-doped fiber laser. A grating-based filter separates the two combs into two arms. After power scaling and nonlinear spectral-broadening, the overlapped spectra are combined and filtered for DCS. FR: Faraday rotator; λ/4: quarter-wave plate; WDM: wavelength division multiplexer; DCF: dispersion compensation fiber; TDF: Tm-doped Fiber; C: collimator; BPF: band-pass filter; PD: photo-diode; LPF: low-pass filter. Inset: The direct output spectrum from the laser oscillator (black) and the separated spectra after the grating-based filter (red, blue).

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Dual-wavelength oscillation is enabled by the NALM filter effect, which stems from the non-symmetrical phase shift accumulated between the counter-propagating laser pulses in the fiber loop mirror [33–35]. The dual-wavelength dual-comb operation can be routinely obtained as follows. By adjusting the orientation of the two QWPs, the additional phase bias can vary in a large range, enabling transition in several mode-locking states with different central wavelengths. Only two of them hold the potential to further evolve into a dual wavelength operation. Figure 2(a) shows their optical spectra. Each mode-locking spectrum is accompanied by a broadband ASE clearly visible in the optical spectral analyzer. When the laser is mode-locked at 1920 nm, a strong ASE component will be observed at 1980 nm, and vice versa. This indicates that the two emitting wavelengths overlap with two neighboring transmissive windows of the artificial filter caused by the NALM [35]. Either ASE band will first emit CW and then achieve mode-locking by increasing the pump power, thus resulting in the dual-wavelength dual-comb operation. The optical spectra are shown in Fig. 2(b), both using linear and logarithmic scales. The typical spectral bandwidth at full-width-half-maximum (FWHM) is 35 nm at 1917 nm and 20 nm at 1981 nm, respectively, corresponding to pulses with transform limit durations of 270 fs and 250 fs. The total average power of the output is about 6 mW. The energy ratio of those two bands may vary according to the mode-locking state and can be balanced by adjusting the pump power or the orientation of the QWPs. Figure 2(c) shows the directly photo-detected pulse train observed in an oscilloscope. The beat note signal with an interval τ = 0.31 ms corresponds to an offset repetition rate 3.2 kHz, resulting from the differential round-trip group delay of the two wavelengths which experience different refractive indexes. The offset repetition rate can be tuned in a small range from 2.8 to 3.3 kHz by slight adjustments of the QWPs orientation, as the offset repetition rate is proportional to the cavity dispersion parameter and the wavelength interval [35]. The radio frequency spectra of the dual-comb pulse trains measured at the fundamental repetition rate clearly resolve the two repetition rates with a 3.27 kHz offset, as shown in Fig. 2(d).

 

Fig. 2 The output characteristics of the dual-comb fiber laser: (a) the spectra of the single-comb states (blue and orange) which hold the potential to evolve into the dual-comb operation; (b) the output dual-wavelength spectrum in linear (blue) and logarithmic (orange) scale; (c) the direct output pulse trains that characterizes a beat-note with an interval τ = 0.31 ms; (d) the radio frequency spectrum of the repetition rates measured with 100 Hz resolution bandwidth.

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We characterize the offset frequency stability which is essential for high precision dual-comb spectroscopic applications. The offset repetition rate component is filtered from the photo-detected pulse train and the frequency is measured with a frequency counter (Agilent 53220A). Figure 3(a) shows a 10 s measurement updated every 1.5 ms. The frequency counter gate time is set as 0.3 ms. The standard deviation of Δf_r fluctuation is 225 mHz. Figure 3(b) shows the measurement of both offset repetition rate frequency (blue) and one of the repetition rate frequencies (orange) at a longer time scale. Frequency data of 10 minutes is collected with a gate time of 0.1 s. The standard deviation of Δf_r fluctuation is scaled down to 116 mHz, while the standard deviation of f_rep is larger than 30 Hz. Figure 3(c) plots the modified Allan deviation of the offset repetition rate calculated with the data from Figs. 3(a) and 3(b). According to the characteristic slopes of the σ–τ plot, the typical noise processes affecting the stability of Δf_r can be derived. On the short time scale (<0.1 s), Δf_r is mostly affected by white frequency noise. The frequency stability is better than 3.7 × 10⁻⁵. On the longer time scale >0.1 s, Δf_r fluctuations characterize a frequency flicker. The repetition rate is heavily affected by frequency drift while the disturbance is well suppressed in the offset repetition rate by the shared laser cavity. Long term averaging for high sensitivity dual-comb spectroscopy is allowed since the offset repetition rate stability does not degrade over time.

 

Fig. 3 Frequency stability of the offset repetition rate from the dual-comb laser: (a) offset repetition rate acquired during 10 s every 1.5 ms with a gate time duration of 0.3 ms; (b) offset repetition rate frequency (blue) and one of the repetition rate frequencies (orange) acquired during 10 min with a gate time of 0.1 s; (c) modified Allan deviation of the offset repetition rate frequency measurement above. FM: frequency modulation.

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3. Dual-comb spectroscopy experiments

The configuration of the DCS based on the single mode-locked Tm-fiber laser is illustrated in Fig. 1. The dual-wavelength pulse trains emitted by the laser oscillator are separated by a grating-based bandpass filter. The transmissive windows of the filters are shown as the inset of Fig. 1. The selected optical spectra corresponding to two different repetition rate pulse trains are directed into separate Tm-doped fiber amplifiers (TDFA) for power amplification. A segment of DCF following the TDFA in each arm is used for self phase modulation (SPM) based spectral broadening. The two spectra are combined again in a 3 dB fiber coupler and a bandpass filter centered at 1940 nm is used to select the optical spectra at their spectral overlap. A 3 nm width bandpass filter is selected so as to avoid the frequency aliasing in the down converted electrical spectrum. An interferogram is generated by directing the combined laser beams to a single photo-diode (EOT-5000F, >12 GHz bandwidth). After passing through a low pass filter that cuts off at 32 MHz, the photo-received interferogram is digitized by a 100 MS/s, 14 bit digitizer (National Instrument, PXIe-5122) and is post-processed on the computer to derive the optical spectral information. Note that we do not use an additional gas cell for the spectroscopy. As a proof-of-principle experiment, we only detect the absorption dips caused by OH⁻¹ in the optical path by taking advantage of the existing water absorption peaks around 1940 nm.

DCS experiment is conducted at an offset repetition rate of about 3.2 kHz. An interferogram frame is acquired in 0.3 ms, as shown in the blue curve of Fig. 4. The signal is presented with two abscissas, namely the experimental time base and the effective time base. The experimental time is the time taken to construct an interferogram and is characterized by a sampling interval equaling to the comb repetition period 1/f_r. The span of the experimental time equals the period of the repetitive beat note signals, i.e. the inverse of Δf_r in the millisecond timescale. The effective time corresponds to the timescale of a single reconstructed optical pulse and is characterized by a much smaller sampling interval being equal to $\mathrm{\Delta }T=\Delta f_{\mathrm{r}}/f_{\mathrm{r}}^2$. The span of effective time is in the timescale of several nanoseconds. The two axes are bridged with a time magnification factor M = f_r/Δf_r. The interferogram shown in Fig. 4 is typically characterized by double peaks, the spurious signal shaded in gray and the interferogram in the center. The spurious signal is observed after the separation of the two arms. Although it’s really weak at the beginning, it gets amplified through the amplifier and stands out here. This spurious signal may result from the energy fluctuation in each comb originated from the nonlinear coupling between the two branches of pulse trains when they collide inside the dual-wavelength laser cavity [36]. The intensity of the spurious signal is higher than the interferogram because the spurious signal is amplified by the Tm-doped fiber amplifier while the interferogram is generated following the nonlinear spectral broadening stage well after the fiber amplifier. Spectroscopic information carried by the spurious signal may overlap with the desired interferogram. To minimize this effect, one can change the delay in one arm of the interferometer such as to place the spurious midway between two maxima of the desired signal. Even with this configuration, one must make sure that measured spectra do not contain too narrow spectral content such that free induction tails are well separated, thus making sure that the desired interferogram can be retrieved via multiplying by zero the interferogram points where the spurious is non-negligible.

 

Fig. 4 Time domain data traces illustrating the co-existing of a spurious signal and an interferogram. As the offset repetition rate is 3.2 kHz, a frame of sampled signal (blue trace) is acquired in an experimental time of 0.3 ms. The spurious signal is shaded in gray. The black trace shows the signal averaged over 3000 times with spurious signal removed. Inset: the interferogram with abscissa expanded 200 times.

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About 3000 frames of interferograms are collected within 1 s and are used for averaging direct in time domain. By using the first frame of interferogram as reference, all the other frames are aligned by the reference based on cross-correlation analysis. Alignment is accomplished when the cross correlation coefficient reaches maximum. The time-averaged result is shown as the black line in Fig. 4. The inset shows the interferogram signal after expanding the abscissa by 200 times. The effectiveness of background noise suppression by time-domain averaging is validated via expanding the y-axis by 10 times, as shown in Fig. 5(a). Following the definition in [5], the temporal SNR is measured as the ratio of the peak of the interferogram to the standard deviation of the noise. The corresponding temporal SNR improves with the increased number of frames and reaches 10400 after time-domain averaging over 1 s. The interferogram has a central burst followed by a low intensity tail which is above the noise level after time-domain averaging and shown in the black curve in Fig. 5(a). The central burst corresponds to the overlap of the two combs. We are more interested in the tailing signal which represents the effect of molecular absorption that generates a free-induction decay (FID) signal extending to longer delays. The availability of direct time-domain averaging for significant SNR improvement of interferogram and temporal identification of molecular FID also reflects the intrinsically stability of the relative carrier-envelope phase (CEP) between the two combs.

 

Fig. 5 (a) The same single (blue) and averaged (black) interferogram after expanding the y-axis in Fig. 4 by 10 times; (b) the optical spectra retrieved by Fourier transform of the interferogram. Blue: single trace; Black: 3000 averages using time-domain averaging method. Inset: the calculated absorbance according to the time-domain averaged spectrum compared with the HITRAN database.

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Figure 5(b) shows the retrieved optical spectra after the Fourier transform of the interferograms. A Gaussian-shaped optical spectrum that reflects the transfer function of the 3 nm bandpass filter is barely visible on the Fourier transform of the single-shot interferogram, as shown in the blue curve. The molecular absorptive features are not visible due to poor SNR. The black curve shows optical spectrum after Fourier transform of the time-domain averaged interferograms within 4 s. The significantly improved SNR makes a few absorptive dips distinguishable in the optical spectrum.

In order to retrieve the magnitude of molecular absorption, a reference laser spectrum should be obtained. This is commonly acquired by an independent molecular absorption free measurement without the gas cell under test. Note that we are measuring the water absorption inside the spectrometer, not from an external gas cell, an independent reference is not directly accessible. To solve this problem, a pseudo-reference is extracted by fitting the measured spectrum with asymmetric Gaussian function. Because the fit inevitably distorts the real absorption-free reference, the absolute absorption amplitude and the width of the spectral dips are not retrieved faithfully. The resulted absorbance according to the time-domain averaged spectrum is shown in the inset of Fig. 5(b). The absorptive spectrum according to HITRAN database [37] is shown in the same figure in red. It’s calculated under unit atmospheric pressure, assuming 20% relative humidity and 1 m propagating length at room temperature [38]. The absolute optical frequency of the spectrum is calibrated by cross-correlation analysis. To this end, the standard HITRAN absorption data across 1930–1950 nm is cross-correlated with the measured absorptive spectrum at various frequency delays. The frequency axis of the measured spectrum can thus be calibrated by subtracting a frequency delay when the highest cross-correlation coefficient occurs. Several picometer residual frequency error is visible after calibration since the precision of the cross correlation approach is sensitive to the noise in the absorptive peaks.

We further conduct an electrical comb-line resolved experiment by taking advantage of the intrinsic mutual coherence between the two optical frequency combs. Data acquired in a 4 s duration is directly Fourier transformed to obtain a spectrum with an expected resolution of 0.25 Hz, shown in Figure 6(a). For comparison, the standard HITRAN absorption lines caused by the OH⁻¹ are plotted in the same figure. To validate the comb-line resolving capability, the radio frequency spectrum is further examined after frequency-axis expansion, as shown in Figs. 6(b) and 6(c). Figure 6(b) shows the spectrum after the frequency-axis is expanded by 50 times. The blue curve corresponds to the experimental result, while the orange dotted line shows the data from HITRAN database. The absorption dips resolved by DCS match well with the HITRAN database. The absorption line shown here exhibits a FWHM width of 43.4 pm. Figure 6(c) shows the spectrum around one electrical comb mode when the frequency axis is expanded by 50 000 times. The fine structure of a single comb line is clearly observed. The measured linewidth is 0.25 Hz, indicating that the linewidth of a single comb-line is still only limited by the 4 s temporal sampling duration and even finer comb structure could be expected with a longer acquisition time.

 

Fig. 6 (a) The comb-resolved spectrum (blue line) and the absorption data from HITRAN (orange); (b) part of the spectrum after expanding the x-axis in (a) for 50 times; (c) part of the spectrum after expanding the x-axis in (a) for 50 000 times.

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4. Conclusion

To conclude, we demonstrate dual-comb spectroscopy in the 2 µm spectral region based on a single dual-wavelength dual-comb Tm-doped fiber laser oscillator. The absorption characteristics caused by the water in the optical path that composes the dual-comb spectrometer are measured. A direct time-domain averaging approach is used to significantly increase the measurement sensitivity, reflecting a stable relative carrier-envelope phase due to common-mode noise suppression in the shared laser cavity. Besides, a comb-line resolved radio frequency spectrum is demonstrated, which further verifies the intrinsic mutual coherence between the two combs. In either case, the retrieved spectral positions of water absorption dips match well with the HITRAN database. The DCS principle determines a narrow optical spectral band of ~1 THz in this measurement given the ∼3 kHz offset repetition rate. Note that over 100 nm optical spectral bandwidth which covers a variety of water and carbon dioxide absorptions is routinely available after nonlinear spectral broadening. In order to extend the optical spectral coverage, the offset repetition rate should be tuned to several Hz, which is not allowed by our dual-wavelength mode-locking mechanism. Nevertheless, multiple measurements by using a tunable bandpass filter can be stacked to reach the broadband spectral measurement in the future. In combination of the average power scalability of Tm-doped fiber technology, this setup further holds the potential for applications in remote gas sensing as well as combustion diagnostics [39].