Coherent sources with a narrow linewidth have been required for precision spectroscopy and frequency metrology. Ultra-high resolution spectroscopy was demonstrated by Hall and his co-workers in the early days of laser spectroscopy using accidental frequency coincidence between a 3.39 μm He–Ne laser and the P(7) $F_2^{(2)}$ transition of the ${\nu }_3$ band of methane [1]. The observed Lamb dips were only 1.3 kHz wide, and the recoil splitting was resolved. Their Letter profoundly benefited from gas lasers that inherently have narrow linewidths, whereas the tuning range is quite narrow.

Widely tunable sources with a narrow spectral linewidth were developed rather slowly in the mid-infrared region compared with the visible and near-infrared regions. Technical progress in the last decade has finally provided widely tunable 3 μm coherent sources such as continuous-wave optical parametric oscillators and difference frequency generation (DFG) sources. They were employed for sub-Doppler resolution atomic and molecular vibrational spectroscopy of ${\mathrm{CH}}_4$ [2,3], Xe [4], ${\mathrm{CH}}_3\mathrm{I}$ [5], ${\mathrm{H}}_3^{+}$ [6–9], ${\mathrm{HCO}}^{+}$ [9], and ${\mathrm{CH}}_5^{+}$ [9]. The observed Lamb dips were as broad as 0.5–110 MHz partly because the linewidth of the sources was considerably larger than that of gas lasers (e.g., He–Ne laser).

We developed a DFG spectrometer across 86.7 and 93.1 THz (3.22 and 3.46 μm). The source contains a ridge waveguide periodically poled-lithium-niobate (PPLN) crystal [10], a 1.064 μm Nd:YAG laser as a pump source, and a 1.55 μm external-cavity laser diode (ECLD) as a widely tunable signal source. The pump and signal frequencies are controlled, referenced to an optical frequency comb (OFC) based on an erbium-doped fiber laser linked to international atomic time (TAI) through an Rb atomic clock. This comb-referenced DFG spectrometer was applied to sub-Doppler resolution spectroscopy [11–13], in which the DFG source was about 20 kHz wide or broader, and the recorded Lamb dips were 230–300 kHz wide. Recently, the carrier envelope offset (CEO) frequency of the OFC was controlled, and the OFC modes were thereby steadily maintained at 20 kHz wide. Accordingly, the DFG source, which had a linewidth similar to that of the OFC modes, was employed to observe the 80 kHz-wide Lamb dips of ${\mathrm{CH}}_3\mathrm{D}$ [14].

In this Letter, we have further reduced the linewidth of the DFG source by narrowing the signal source using laser linewidth transfer [15]. The 1.064 μm Nd:YAG laser with a nominal linewidth of a few kilohertz is used as a frequency reference to control the repetition rate of the OFC. When the CEO frequency of the OFC is controlled at the same time, all the OFC modes become spectrally narrow. The linewidth of the 1.57 μm ECLD is then reduced, referenced to the nearest one of the narrowed OFC modes. The pump wave from the Nd:YAG laser and the signal wave from the ECLD spectrally narrowed by laser linewidth transfer provide a 3.5 kHz wide idler wave, which is used to observe the Lamb dip of methane with a 21 kHz resolution. To the best of our knowledge, it is the first application of laser linewidth transfer to sub-Doppler resolution spectroscopy in the 3 μm region. The OFC was first applied to molecular spectroscopy in the 3 μm region as a frequency ruler [7,9] and, subsequently, employed for frequency control of the sources [5,8,11–14]. In this Letter, it has been used for linewidth transfer as well as the frequency control.

Figure 1 depicts a schematic diagram of the DFG source. Pump and signal sources are a 1.06 μm Nd:YAG laser and a widely tunable 1.5 μm ECLD. The pump and signal waves are combined using a wavelength division multiple coupler and launched to a ridge waveguide PPLN module [10] in which the idler wave is generated. An OFC based on an erbium-doped fiber laser has an electro-optic modulator (EOM) in the laser cavity for fast control of the effective cavity length [16]. A broad servo bandwidth is required to narrow the OFC mode and eventually enables us to apply laser linewidth transfer [15]. The repetition rate of the OFC is approximately 97 MHz. The output of the OFC is divided into three outputs. The first output is used to control the CEO frequency and reduce the linewidth of the OFC mode. The second is delivered to control the repetition rate, and the third is delivered to control the ECLD frequency.

 

Fig. 1. Linewidth narrowing and frequency control scheme of the DFG source. RF REF, radio frequency reference; Mix., mixer; HNLF, highly nonlinear fiber; PPLN, periodically poled lithium niobate crystal; SHG, second-harmonic generation; BPF, optical band-pass filter; Det., detector; EOM, electro-optic modulator; DFG, difference frequency generation; ECLD, external-cavity laser diode.

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To determine the CEO frequency using the self-reference technique [17], the first output of the OFC passes through a highly nonlinear fiber, a PPLN for second-harmonic generation, and an optical band-pass filter and is detected with an InGaAs detector. The CEO frequency is phase-sensitively compared with an rf signal (RF REF 1), and the obtained error signal is fed back to the injection current of a laser diode pumping the OFC. Radio frequency references, designated as RF REFs in Fig. 1, are based on an Rb atomic clock linked with TAI through the global positioning system. The OFC beam reflected at the band-pass filter overlaps with part of the pump wave from the Nd:YAG laser for observing the beat note between them. The beat frequency is phase-sensitively compared with another rf signal (RF REF 2), and the obtained error signal is fed back to the EOM, a PZT, and a temperature controller in the OFC, which control the effective cavity length with different response times and dynamic ranges.

Figures 2(a) and 2(b) depict rf spectra of the in-loop CEO signal and the in-loop beat signal between the Nd:YAG laser and the nearest OFC mode. The servo bandwidth of the CEO signal is estimated to be 400 kHz, and that of the beat note is estimated to be 1 MHz from the position of the servo bumps. Those at $\pm 400\mathrm{kHz}$ in Fig. 2(b) are attributed to those of the CEO signal. The wide servo bandwidth in the repetition rate control is due to introducing the EOM to the OFC. The coherent delta-function peaks are estimated to have a signal-to-noise ratio of approximately 75 dB/Hz from that of 30 dB at a 30 kHz resolution bandwidth in Fig. 2.

 

Fig. 2. Observed rf spectra of (a) the in-loop controlled CEO beat note and (b) the in-loop controlled beat note between the Nd:YAG laser and the nearest comb mode. The resolution bandwidth and video bandwidth are 30 kHz.

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When the CEO frequency and the beat frequency between the Nd:YAG laser and the nearest OFC mode are controlled, the repetition rate is determined by the Nd:YAG laser frequency. Accordingly, frequency drift of the Nd:YAG laser induces drift in the repetition rate. To eliminate frequency drift, we servo-control the Nd:YAG laser frequency. The second output of the OFC in Fig. 1 is used to detect the repetition rate. The detected signal is then phase-sensitively compared with another rf signal (RF REF 3), and the obtained error signal is fed back to the injection current of the Nd:YAG laser. The servo bandwidth is confined to less than 10 Hz because the Nd:YAG laser inherently has low frequency noise at high Fourier frequencies. The linewidths of the OFC modes thus follow that of the Nd:YAG laser, whereas the averaged frequencies of the OFC modes are determined, referenced to TAI.

The third output of the OFC is combined with the signal wave from the ECLD, and the beat note between them is phase-locked to another rf signal (RF REF 4). The error signal is fed back to the injection current and the PZT of the ECLD with an entire servo bandwidth of 250 kHz. Thus, the linewidth of the Nd:YAG laser is transferred to that of the ECLD. Eventually, the DFG source becomes as narrow as the Nd:YAG laser.

To evaluate the linewidth of the DFG source, we observe the beat note with a free-running 3.39 μm He–Ne laser using a liquid-nitrogen-cooled InSb detector with a response bandwidth of 30 MHz. Figure 3 depicts an rf spectrum of the beat note, which was acquired when the frequency drift of the He–Ne laser was rather small. The spectral line is fitted to a Lorentzian profile, and the half-width at half-maximum (HWHM) is determined to be 3.5(2) kHz, which is one-sixth, compared with the recent work [14]. Here, the number in parentheses is the uncertainty in the last digit. The frequency drift of the He–Ne laser limits this value, and the DFG source is 3.5 kHz wide at most.

 

Fig. 3. Observed rf spectrum of the beat note between the He–Ne laser and the DFG source. The resolution bandwidth and video bandwidth are 3 kHz.

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To demonstrate improvements in a spectral resolution of the spectrometer, the narrowed DFG source is applied to saturated absorption spectroscopy of the ${\nu }_3$ band of methane. Figure 4 illustrates the experiment setup of the saturated absorption spectroscopy. The DFG wave is generated in the ridge waveguide PPLN module with a conversion efficiency of 46%/W, and the output power level is reduced to narrow the power broadening of the Lamb dip. The output beam is expanded to a beam radius of 8.1 mm and collimated by two ${\mathrm{CaF}}_2$ convex lenses. The central part of the beam passes through an iris of 3 mm radius, and the 72% power level of the DFG wave is incident onto an absorption cell of a glass tube fitted with a fused silica window. A corner cube at the bottom of the cell redirects the incident beam upward. It is then reflected in the opposite direction by a mirror outside the cell for performing saturated absorption spectroscopy with the total absorption length of 120 cm. Three quarters of the absorption length is cooled with liquid nitrogen to reduce thermal velocity of molecules and, accordingly, pressure and transit-time broadenings. The DFG frequency is swept in a step of 1 kHz every 10 ms by changing the offset frequency between the ECLD and the nearest OFC mode.

 

Fig. 4. Experimental setup of sub-Doppler resolution spectroscopy of methane.

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Figure 5 depicts the observed Lamb dip of the ${\nu }_3$ band R(2) $E$ transition of ${{}^{12}\mathrm{CH}}_4$ with a sample pressure of 0.1 Pa. The spectrum is averaged over 50 measurements for 5 min without any appreciable frequency drift. The spectral line absorbs 60% of the incident power at the top of the Doppler-broadened profile. The absorbance is larger than that at room temperature because the lower level with a low angular momentum quantum number of 2 is more abundantly populated. The poor signal-to-noise ratio is caused by the vibration of the absorption cell induced by seething liquid nitrogen and the power reduction for decreasing power broadening. The spectral line is fitted to a Lorentz profile with adjustable parameters of center frequency, linewidth, amplitude, and background level. The linewidth is determined to be 21(2) kHz (HWHM), which reflects the resolution of the DFG spectrometer because the $E$ tetrahedral component has a single magnetic hyperfine subcomponent (total nuclear spin angular momentum quantum number $I=0$). The $A$ and $F$ tetrahedral components contain five ($I=2$) and three ($I=1$) intense subcomponents, respectively, separated by about 10 kHz [1]. The attained linewidth of 21 kHz is appreciably narrower than 80 kHz in the recent work [14], but not narrow enough to resolve the magnetic hyperfine structure of the $A$ and $F$ tetrahedral components.

 

Fig. 5. Recorded Lamb dip of the ${\nu }_3$ band R(2) $E$ transition of methane. A solid curve is the fitting result.

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The linewidth of the Lamb dip is determined by natural linewidth, pressure broadening, transit-time broadening, and power broadening beside source linewidth. The natural linewidth ranges from 10 to 100 Hz for mid-infrared vibrational transitions. Transit-time broadening is estimated to be 12.5 kHz for the 3 mm beam radius and the liquid-nitrogen temperature [18]. Pressure broadening is estimated to be 3 kHz for 0.1 Pa [1,19]. Therefore, we attribute the remaining 5 kHz to the DFG source linewidth and the power broadening. When the power broadening dominates the source linewidth, the relative contrast of the Lamb dip to the Doppler-broadened linear absorption line is 0.05, and the DFG power level incident to the absorption cell is estimated 5 μW. The spectral resolution of the Lamb dip is currently limited by transit-time broadening. This limit can be lowered by laser cooling and buffer–gas cooling as well as the 11 cm beam radius [1].

The center frequency of the Lamb dip is determined to be 91 381 810 597.3 (31) kHz. Uncertainty comes from the fitting uncertainty of 1.6 kHz and the uncertainty of the reference Rb atomic clock of 2.7 kHz. The determined center frequency agrees with 91 381 810 593.2 (27) kHz within the uncertainties, which was obtained using a 0.7 mm wide DFG beam at room temperature and an optical frequency comb for frequency determination [12]. Even though the present resolution is considerably better than that of the previous work [12], the uncertainty is larger because of the poor signal-to-noise ratio.

In conclusion, we have reduced the linewidth of a 3.3 μm DFG source to 3.5 kHz using laser linewidth transfer via an optical frequency comb with a wide servo bandwidth. This source enables us to record the sub-Doppler resolution spectrum of the ${\nu }_3$ band R(2) $E$ transition of methane with a spectral linewidth of 21 kHz. The master Nd:YAG laser for the laser linewidth transfer is nominally a few kilohertz wide. Further narrowing of the DFG source is realized by stabilizing the master laser to a high-finesse cavity [15,20]. Quite recently, a 10 μm quantum cascade laser was spectrally narrowed to the sub-hertz level using an ultra-stable 1.54 μm reference laser and an OFC and applied to record saturated absorption spectrum of ${\mathrm{OsO}}_4$ with the corresponding Lorentz linewidth of 38 kHz [21].