Optical frequency combs are indispensable tools in various scientific and technical fields, such as metrology, high-resolution spectroscopy, high-speed optical communication, astronomical spectrography, and absolute distance measurement [1,2]. Among these, dual-comb spectroscopy has garnered significant attention owing to its advantages over other spectroscopic techniques in terms of data acquisition time, sensitivity, and resolution [3–5]. Owing to its excellent capabilities, dual-comb spectroscopy has been applied in several applications [6–10]. It is a type of mechanically scan-less Fourier transform spectroscopy [11], wherein multi-heterodyne detection is performed using two optical frequency combs with slightly different repetition frequencies ($\Delta {f_{\rm{rep}}}$). For high-resolution, broadband, and high-sensitivity spectroscopy, the two frequency combs are required to have high mutual coherence and relative stability.

In the conventional dual-comb spectroscopy setup, two independent mode-locked lasers are used to generate two optical frequency combs with a small $\Delta {f_{\rm{rep}}}$. Owing to independent fluctuations in the free-running laser operation, the relative stability between the two frequency combs is poor. Accordingly, the mutual coherence degrades. Therefore, the interferogram is destructive. To overcome this problem, tight phase locking [5–7,12–15] or high-speed signal processing [16] is typically used to achieve a high mutual coherence between the two frequency combs. Despite the broad application capabilities of dual-comb spectroscopy, this technique is mainly restricted to researchers with expertise because of its complex phase-locking system. Therefore, a simple, robust, and compact dual-comb laser source could offer an alternative solution to a wide range of users, including non-experts.

Recently, a dual-comb laser that can generate two optical frequency combs with a slight ${f_{\rm{rep}}}$ difference from a single-laser cavity has attracted attention because of its high relative stability and mutual coherence through passive common-mode noise suppression without complex tight phase locking [17–26]. Moreover, various dual-comb fiber lasers have been developed based on dual-wavelength [17], polarization-multiplexed [18,19], and bidirectional [20–22] mode-locked Er-fiber lasers.

Fiber-based frequency combs offer an inexpensive, compact, and robust setup owing to their all-fiber-based configuration [12,27]. In particular, an all-polarization-maintaining (PM) mode-locked fiber laser is robust under all practical environmental conditions [28]. In this fiber laser, a semiconductor saturable absorber mirror (SESAM) is often used as the mode-locking mechanism. However, owing to the slow relaxation time of the SESAM, the phase noise of fiber-based frequency combs with only the SESAM mode-locking mechanism is worse than that of the combs with a nonlinear polarization rotation mode-locking mechanism. In contrast, an all-PM mode-locked fiber laser with a nonlinear amplifying loop mirror (NALM) mode-locking mechanism is an attractive option because of its low phase noise capability for frequency comb generation [29,30]. Recently, all-PM dual-comb fiber lasers with an NALM were reported for dual-wavelength [31] and polarization-multiplexed schemes [19]. However, these all-PM dual-comb fiber lasers have a complex laser cavity configuration for dual-comb generation with a small $\Delta {f_{\rm{rep}}}$. Moreover, a previous study [23] reported undesired nonlinear interactions between the two frequency combs, which restricts the usable range of the interferogram.

To overcome these difficulties, in this study we developed an all-PM dual-comb fiber laser based on two independent all-PM fiber lasers that share the laser cavities mechanically. The two frequency combs, which are generated from independent cavities, have a high relative stability and mutual coherence due to technical common-mode noise suppression with a mechanical sharing laser cavity. As a proof-of-principle demonstration, we performed dual-comb spectroscopy with a free-running dual-comb fiber laser. This simple, flexible, and robust laser configuration is expected to be highly effective for practical environmental instabilities.

 

Fig. 1. Schematic of an all-PM dual-comb fiber laser with mechanical sharing cavity and an NALM. EDF, Er-doped fiber; LD, laser diode; PBC, polarization beam combiner; HWP and QWP, half- and quarter-wave plate, respectively; FR, Faraday rotator; PBS, polarization beam splitter.

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Figure 1 illustrates a schematic of the all-PM dual-comb fiber laser, comprising two all-PM mode-locked fiber lasers with an NALM mode-locking mechanism. The laser comprises a linear arm based on free space and an NALM part based on the fiber. The NALM part comprises a polarization beam combiner (PBC), a non-doped PM fiber (PMF), and an Er-doped PMF (EDF, Liekki, Er80-4/125/HD-PMF), which is pumped by a 976 nm laser diode (LD). At both sides of the PBC, the slow axis of the PMF is connected. Therefore, the pulse transmitted at the entrance of the NALM is reflected at the exit. As shown in Fig. 1, all fiber components in the two-laser cavity are placed at the same position. Therefore, the NALM parts share the technical noise mechanically, i.e., the parts are mechanically shared. Moreover, to improve common-mode noise suppression, the EDFs in the two laser cavities are pumped by the same LD via a 50/50 optical coupler at 980 nm. The free space comprises a half-wave plate (HWP1), a 45° Faraday rotator (FR), a quarter-wave plate (QWP), a polarization beam splitter (PBS), a HWP2, and a mirror. All components are enclosed in a simple housing made of an acrylic box for better environmental isolation. Moreover, the NALM mode-locking mechanism can generate a low-phase-noise frequency comb. The HWP1 is used to finely tune the intracavity loss, and it contributes to the easiness in mode-locking. The FR and the QWP between the PBC and the PBS function as a nonreciprocal phase shifter and assist the self-starting mode-locking operation. The pulse with a linear polarization at ${{\pm}}{{45}}^\circ$ returns to itself when passing through the NALM using the FR. The phase shift, $\Delta \varphi$, of the QWP leads to a nonreciprocal phase shift of $\Delta {\varphi _0} = {{2}}\Delta \varphi$ per round trip. The splitting ratio of the PBS is tuned by changing the angular orientation of the HWP2. All free-space components are placed near each other to share mechanical vibrations. Additionally, both laser outputs (comb1 and comb2) are coupled to a PMF with a collimator (not shown in Fig. 1) and measured using an optical spectrum analyzer (Yokogawa, AQ6370D) and radio-frequency (RF) spectrum analyzer (RIGOL, DSA815) via a fast photodetector (Newfocus, 1611). In both laser cavities, the length of the EDF and the non-doped PMF is 0.6 and 2.3 m, respectively. The net dispersion of the laser cavity was estimated to be ${-}{0.05}\;{\rm{p}}{{\rm{s}}^2}$ at 1550 nm. In this study, all experiments were conducted in a free-running operation, as described in the following section.

When the pump power is increased, the mode-locking operation is self-initiated owing to the presence of the NALM with a nonreciprocal phase shifter. As the pump power is decreased, a single-pulse mode-locking operation is realized. Figure 2(a) shows the optical spectra of the two mode-locked fiber laser outputs [comb1 (red) and comb2 (blue)]. In the comb1 output, the center wavelength, full-width at half-maximum (FWHM) bandwidth ($\Delta \lambda$) of the spectrum, and output power are 1567.9 nm, 8.7 nm, and ${\sim}{{1}}\;{\rm{mW}}$, respectively. In the comb2 output, the center wavelength, $\Delta \lambda$, and output power are 1570.8 nm, 10.0 nm, and ${\sim}{{1}}\;{\rm{mW}}$, respectively. The slight difference in the optical spectra between the two outputs is due to the individual differences in the optical components of the two laser cavities, which can be further improved by ensuring that the cavities are better aligned. Figure 2(b) shows the RF spectra of combs1 and 2 at a resolution bandwidth (RBW) of 300 kHz. The repetition rate (${f_{\rm{rep}}}$) for the two frequency combs was found to be 51.601 MHz, and $\Delta {f_{\rm{rep}}}$ was found to be 26.8 Hz. Owing to the configuration of the mechanical sharing cavity instead of the sharing optical cavity, ${f_{\rm{rep}}}$ values can be tuned independently by adjusting the position of each mirror in the free-space section. Additionally, $\Delta {f_{\rm{rep}}}$ can be varied without any undesirable nonlinear interaction in the gain fiber or saturable absorber [23,32].

 

Fig. 2. (a) Optical spectra and (b) RF spectra of two laser outputs. (c) Temporal variation in the repetition rates of the two frequency combs and the difference in the repetition rate ($\Delta {f_{\rm{rep}}}$). (d) Allan deviation of $\Delta {f_{\rm{rep}}}$ with (red) and without (black) mechanical sharing.

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To evaluate the relative stability in the RF domain, we measured ${f_{\rm{rep}}}$ for the two frequency combs simultaneously using two frequency counters (Tektronix, FCA3100) with reference to an Rb frequency standard (SRS, FS725). Figure 2(c) shows the temporal variation in ${f_{\rm{rep}}}$ for the two frequency combs (upper) and $\Delta {f_{\rm{rep}}}$ (lower) in the free-running operation. A change of ${\sim}{{20}}\;{\rm{Hz}}$ was observed in ${f_{\rm{rep}}}$ due to environmental perturbation, and a high relative stability was obtained for $\Delta {f_{\rm{rep}}}$ with a standard deviation of 0.3 Hz (Allan deviation of 0.01 Hz for an averaging time of 1 s) at $\Delta {f_{\rm{rep}}}$ of 26.8 Hz without servo control, i.e., owing to the mechanical sharing laser cavity and passive common-mode noise cancellation. Figure 2(d) shows the Allan deviation of $\Delta {f_{\rm{rep}}}$ with (red) and without (black) mechanical sharing (red). It was measured using a dead-time free frequency counter implemented on a field-programmable gate array (FPGA) [33]. The figure shows a drastic improvement in relative stability owing to the mechanical sharing cavity configuration. This is a significant advantage for dual-comb spectroscopy, where $\Delta {f_{\rm{rep}}}$ should be kept constant during the measurement of the interferograms. The mode-locking operation can be maintained without realignment or maintenance. Moreover, owing to the all-PM configuration, the mode-locking operation can be maintained even if perturbations are caused by touching the fibers or vibration. $\Delta {f_{\rm{rep}}}$ can be further stabilized using micro-optic packaging in the free-space setup.

 

Fig. 3. (a) RF spectrum and (b) spectral density (upper) and integrated (lower) phase noise of the relative beat note between a pair of comb teeth from dual-frequency combs at 1565 nm. The beat note has a linewidth of  ${\sim}{{50}}\;{\rm{Hz}}$ for a measurement duration of 38 ms. (c) Multi-heterodyne beat notes between the two frequency combs with $\Delta {f_{\rm{rep}}}$ of 150 Hz. (d) Magnified and normalized multi-heterodyne beat notes of red square bracket in (c).

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To evaluate the relative coherence between the two frequency combs of the two lasers in the optical frequency domain, we detected the relative beat note between each frequency comb and a narrow-linewidth single-frequency laser (Toptica, DL-pro) at 1565 nm, which was used as an intermediate laser. We obtained two beat notes with a high signal-to-noise ratio of ${\sim}{{30}}\;{\rm{dB}}$ at an RBW of 100 kHz. The two beat notes for the two frequency combs were extracted using a low-pass filter and amplified using a low-noise RF amplifier. Subsequently, the two beat notes were mixed using a double-balanced mixer, and only the difference between the two beat notes were extracted by filtering. As shown in Fig. 3(a), the difference beat note has a linewidth of ${\sim}{{50}}\;{\rm{Hz}}$ for a measurement time of 38 ms with an RBW of 50 Hz in the free-running operation. The measured linewidth was limited by the measurement resolution because long-time averaging could not be applied without phase locking between the intermediate laser and comb teeth. To investigate the difference beat note on a short-term time scale, we also measured the phase noise using a digital phase meter implemented on an FPGA [33]. Figure 3(b) shows the phase noise of the relative beat note. Here, to investigate the effect of sharing a pump LD between the two lasers, we compared the phase noise in the case when the pump LD was not shared. The measured integrated phase noise under pump LD sharing (red curve) and non-sharing (black curve) were 420 and 1280 rad, respectively, which were estimated by integrating the spectral density of the phase noise from 10 Hz to 1 kHz. These results indicate that pump LD sharing is effective for improving the mutual coherence between the two lasers.

In addition, we directly detected the multi-heterodyne beat notes between the two frequency combs with $\Delta {f_{\rm{rep}}}$ of 150 Hz in the free-running operation. The two frequency combs were combined using a 50/50 coupler and launched into a fast photodetector (Newfocus, 1811) via an optical band-pass filter with a bandwidth of ${\sim } {\rm nm}$ at 1565 nm (Alnair Labs, TFF-1550). Figure 3(c) shows the RF spectra of the detected multi-heterodyne beat notes between the two combs. We confirmed that they are not the mixing products in the RF domain because when we manually changed the center wavelength of the band-pass filter, the center frequency of the beat note varied [red dotted square in Fig. 3(c)]. As shown in Fig. 3(d), we obtained mode-resolved multi-heterodyne beat notes using an RF spectrum analyzer (Rohde & Schwartz, FSV-13). These results suggest that the two frequency combs from the two free-running lasers exhibit high mutual coherence. A comparison between Figs. 3(c) and 3(d) showed that the amplitude of the beat signal varies slightly depending on the measurement resolution, i.e., the measurement time. This can be attributed to the residual non-common-mode noise in the mechanical sharing cavity. By employing a compact system, such as micro-optic packaging for free space, the multi-heterodyne beat note can be further passively stabilized. Nevertheless, we obtained mode-resolved beat notes with $\Delta {f_{\rm{rep}}}$ of 150 Hz with an RBW of 30 Hz. The FWHM of each beat note was ${\sim}{{30}}\;{\rm{Hz}}$, and it was limited by an RBW of 30 Hz. Thus, the relative linewidth between the two frequency combs could be 30 Hz or less. This result implies that the developed dual-comb fiber laser with the mechanical sharing laser cavity can maintain coherence for 0.03 s without servo control.

 

Fig. 4. Dual-comb spectroscopy of an HCN cell with a mechanical sharing dual-comb fiber laser ($\Delta {f_{\rm{rep}}} = {{150}}\;{\rm{Hz}}$). (a) Temporal interferogram, (b) magnified signal of (a), and (c) dual-comb spectra obtained by implementing Fourier transform on the interferogram (a) with an acquisition duration of $20\,\,\unicode{x00B5}{\rm s}$ around the burst point. (d) Transmitted spectrum of the same cell obtained by using an optical spectrum analyzer.

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Finally, we performed dual-comb spectroscopy using the developed mechanical sharing dual-comb fiber laser. Figure 4(a) shows the dual-comb interferogram acquired by detecting two spatially overlapped frequency combs with $\Delta {f_{\rm{rep}}}$ of 150 Hz. The two frequency combs were launched into a fast photodetector (Newfocus, 1811) via an HCN cell (Wavelength References, HCN-13-H(5.5)-25-FCAPC) and an optical band-pass filter with a bandwidth of ${\sim}{{1}}\;{\rm{nm}}$ at 1558 nm (Alnair Labs, TFF-1550). The temporal interferogram was observed using a digital oscilloscope (Keysight, DSOX6004). Figure 4(b) shows a magnified interferogram of the one shown in Fig. 4(a) with ${\sim}{{10}}\;\unicode{x00B5} {\rm{s}}$ around the burst point. We then performed dual-comb absorption spectroscopy on the HCN cell with a spectral resolution of 1.7 GHz (14 pm) and an acquisition duration of ${\sim}{{200}}\;\unicode{x00B5} {\rm{s}}$ centered at 1558 nm. As shown in Fig. 4(c), the dual-comb spectrum demonstrated the absorption line of the HCN. The spectrum is in good agreement with the spectrum of the same HCN cell obtained by an optical spectrum analyzer (Yokogawa, AQ6370D). Note that a significantly long sweep time of ${\sim}{{5}}\;{\rm{s}}$ was required to realize a spectral resolution of 6.2 GHz (50 pm) with an optical spectrum analyzer. The fast data acquisition duration of dual-comb spectroscopy with a high resolution (in GHz) is superior to that of the optical spectrum analyzer.

In conclusion, we developed a mechanical sharing dual-comb fiber laser based on an all-PM configuration for a robust and simple dual-comb source. An NALM was used as the saturable absorber for passive and low-phase noise mode-locking operations. Owing to common-mode noise cancellation originating from the mechanical sharing laser cavity, the mutual coherence between the two frequency combs was passively high without active stabilization, i.e., a relative beat note linewidth of ${\sim}{{50}}\;{\rm{Hz}}$. In the mechanical sharing configuration, unnecessary nonlinear interactions can be prevented between the two frequency combs, and $\Delta {f_{\rm{rep}}}$ can be tuned freely. In addition, dual-frequency combs with $\Delta {f_{\rm{rep}}}$ were generated at the same center wavelength without extra-cavity nonlinear spectral broadening. Therefore, we demonstrated the direct detection of mode-resolved multi-heterodyne beat notes. Here, we realized a proof-of-principle demonstration of dual-comb spectroscopy using a dual-comb laser. Furthermore, the all-PM-based configuration was found to be robust against practical environmental perturbations. Therefore, all free-space setups can be integrated to further improve the stability and reduce the size using micro-optic packaging. In this laser, piezo actuators can be installed on free-space mirrors to further stabilize $f_{\rm{rep}}$. Additionally, the long-term relative stability can be improved even without complicated tight phase locking. A practical dual-comb spectroscopy system based on a mechanical sharing all-PM dual-comb laser can be used beyond special laboratories and without expertise for laser stabilization. Furthermore, the flexible mechanical sharing laser configuration can be applied to a broad range of platforms beyond dual-comb spectroscopy, such as for synchronization or asynchronization between ultrashort pulse trains with different colors for various nonlinear optical measurements and integrated fiber sensing systems with optical sources and sensing parts.