1. Introduction

Optical pulses emitted from a mode-locked laser possess a spectral feature of a comb, which describes discrete, equally-spaced lines, each representing a longitudinal mode of the laser cavity [1]. Because the interval of the lines is precisely the repetition frequency ($f_{\rm {rep}}$), the feature has sublimated into the optical frequency comb used as a precise ruler in frequency metrology and high-precision spectroscopy [1]. The comb stands when all the phases of the cavity modes are locked. When the comb line, or comb tooth, is broad, the modes can easily go out of phase, and the comb is lost. Therefore, narrowing the linewidth of the cavity modes becomes essential for stabilizing the comb [2].

Mode-locked fiber lasers have met numerous applications in metrology and precision spectroscopy due to their excellent stability in the optical frequency. Table 1 summarizes the longitudinal-mode linewidth of various solid-state and fiber mode-locked lasers measured through the heterodyne beating of one comb tooth against a continuous-wave (CW) laser [3–12]. The narrowest is 10 kHz obtained for some fiber lasers [3,8,9]. We noticed, however, that systematic comparison among the literature values is not straightforward due to the following reasons. (1) While the amplified spontaneous emission ultimately limits the comb linewidth, it is mainly dominated by temperature and pump intensity fluctuations [2], which have no reason to be the same among the studies. (2) The linewidth of the reference CW laser varies among the studies, leading to variations in the resolution. (3) The resolution bandwidth (RBW), or inverse acquisition time by the spectrum analyzer, also affects the linewidth of the beat note in a free run, as we shall elaborate on later. Thus, it is not clear which type of cavity configuration is suited to realize a sharp comb and whether there is a guideline if at all, to have a cavity mode less prone to environmental fluctuations. It is also unclear whether the comb tooth in a free run can go beyond the record linewidth of 10 kHz [3,8,9].

Table 1. Longitudinal-mode linewidths of various mode-locked lasers in a free run.

View Table

In this work, we surveyed the longitudinal-mode linewidth of five homemade ytterbium-doped fiber (Yb:fiber) lasers: Three were mode-locked with the nonlinear polarization rotation (NPR) scheme [13] and $f_{\rm {rep}}$’s were 244, 90, and 10 MHz; the remaining two cavities consisted of all-normal dispersion (ANDi) elements [14] and $f_{\rm {rep}}$’s were 30 and 1 MHz. Special care was taken for the environmental fluctuations: We enclosed each cavity in a sound-proof box fixed on an optical table and kept the temperature fluctuation below $0.1^\circ$C. Besides, we employed a high-finesse cavity to stabilize the wavelength of the CW laser [15] and ensured that the reference source did not limit the beat-note resolution; the CW bandwidth was narrower than 1 Hz [15]. By systematically varying the RBW when recording the heterodyne beat note, the linewidth became as sharp as 200 Hz for the 1-MHz ANDi laser, which surpassed the records in the literature by 50 times. Based on the survey, we provide our point of view to achieve low noise in mode-lock lasers in a free run.

2. Experimental setup

The optical frequencies of mode-locked lasers are far too high to be detected directly by any electronics. Thus, the longitudinal-mode linewidth has been routinely measured by taking the beat note between one comb tooth and CW laser, which falls into the radiofrequency (RF) range [3–12]. Figure 1(a) shows the setup for recording the beat note spectrum. We mixed the output of the mode-locked and CW lasers with a fiber coupler, cut a spectral portion of the mixed beam by using a set of grating and iris, and introduced the portion into a fast avalanche photodiode (APD). Because the APD signal includes both the beat note frequency $f_{\rm {beat}}$ and $f_{\rm {rep}}$, we diminished the $f_{\rm {rep}}$ component by inserting a low pass filter and then electronically amplified the filtrated signal. Finally, we obtained the power spectrum of the amplified signal with a spectrum analyzer (Rohde & Schwarz, FSV-30).

 

Fig. 1. Experimental setup. (a) The detection scheme of the longitudinal-mode linewidth. (b) Estimation of the CW laser linewidth after passing through a 50-meter-long polarization-maintaining fiber. (c-g) The five mode-locked fiber lasers, each contained in a sound-proof box: NPR1 (c), NPR2 (d), NPR3 (e), ANDi1 (f), and ANDi2 (e). The bottom row displays the mode-locked laser spectra. (h) Typical record of the temperature around the lasers.

Download Full Size | PDF

Having a narrow linewidth CW laser is a key to increase the resolution of the beat note spectrum. In the present study, we adopted a homemade CW laser that had attained the sub-1 Hz linewidth [15]; it was obtained by actively stabilizing the wavelength of an external cavity diode laser (ECDL) by using a high-finesse Fabray-Perrot cavity [15]. Because ECDL was located in another laboratory space, we transferred the EDCL output to the heterodyne setup by using a 50-meter-long polarization maintaining fiber (PMF). The linewidth broadens after passing through the long PMF owing to the environmental noise around the PMF [16]. In order to estimate the broadening, we measured the beat note between the output just after the ECDL and the CW line that passed twice the 50-meter PMF. As shown in Fig. 1(b), the full width at half the maximum (FWHM) of the beat note was 20 Hz when we set the RBW of the spectrum analyzer to 10 Hz. That is to say, the CW reference limited the resolution to 20 Hz at most.

Figures 1(c-g) shows the five homemade mode-locked Yb:fiber lasers that we surveyed. NPR1-NPR3 had been used in the previous studies [17–19], and their $f_{\rm {rep}}$’s were 244 [17], 90 [18] and 10 MHz [19], respectively. We had set the cavity dispersions of NPR1-NPR3 in one round trip to near-zero by adjusting the distance of the grating pair inside the cavity [13] and mode-locked them through the NPR scheme. ANDi1 and ANDi2 consisted of fibers and optical devices with normal dispersion for 1 $\mu$m wavelength and a bandpass filter that clips temporal wings of the up-chirped pulse. ANDi2 had been used in Ref. [20], and $f_{\rm {rep}}$ was 1 MHz. ANDi1 was prepared for this study according to the cavity configuration described in Ref. [14], in which we used a 1064 nm bandpass filter of 8 nm bandwidth, and $f_{\rm {rep}}$ was 30 MHz. Each of the five cavities was enclosed in an aluminum sound-proof box fixed on an optical table. The characteristics of the lasers, such as the spectrum, center wavelength, bandwidth, and the wall thickness of the sound-proof box, are described in Figs. 1(c-g).

To reduce the temperature fluctuation, we installed a high-precision air conditioning system in our laboratory, in which we located the five lasers. The temperature fluctuation around the lasers was below $0.1^\circ$C during the measurements; see Fig. 1(h) for the typical record of the temperature for two days.

3. Results

In the ideal case when the optical frequency comb stands still in the frequency domain, the beat note between the comb tooth and reference CW laser line keeps the same tone; that is to say, the beat-note frequency ($f_{\rm {beat}}$) does not move. In such a case, we can take the acquisition time of the beat note as long as the memory depth of the spectrum analyzer allows and increase the resolution of the beat-note power spectrum, which corresponds to setting the RBW of the spectrum analyzer to the narrowest value. However, in the present case, $f_{\rm {beat}}$ drifts because the comb is freely running in the frequency domain. Because we cannot have an infinitely-short acquisition time of the beat-note power for extracting its frequency components, there will be an optimal acquisition time, or optimal RBW, by which the $f_{\rm {beat}}$ peak in the power spectrum appears the narrowest.

We searched for the optimal RBW to obtain the sharpest $f_{\rm {beat}}$ peak by varying the RBW value ($\varGamma$) stepwise from 30 kHz to 30 Hz. Figure 2 shows the typical $f_{\rm {beat}}$ peak observed in the power spectra. In all cases, one can immediately see the tendency that the peak sharpens when $\varGamma$ decreases from 30 kHz. For NPR2 and NPR3, one can also see that the peak no more sharpens up when $\varGamma$ is below $\sim$1 kHz, indicating that the optimal RBW is around 1 kHz for those cases.

 

Fig. 2. The power spectra of the beat note. (a) NPR1. (b) NPR2. (c) NPR3. (d) ANDi1. (f) ANDi2. The upper panels show the spectra recorded with the resolution bandwidth (RBW) values $\varGamma$ varied from 30 to 0.03 kHz, and the lower panels show the expanded views for the spectra recorded with $\varGamma \le 1$ kHz.

Download Full Size | PDF

To quantify the peak width of the beat note, we recorded the $f_{\rm {beat}}$ peak five times at each RBW value $\varGamma$ and obtained the average and standard deviation of the FWHM of the peak. Figure 3 shows the FWHMs for the five mode-locked Yb:fiber lasers plotted as functions of $\varGamma$. When $\varGamma$ decreases from 30 kHz, FWHM initially follows the trade-off line, indicating that the RBW of the spectrum analyzer is limiting the peak width. Subsequently, FWHM levels off and then shows an upturn. The upturn indicates that the amount of the $f_{\rm {beat}}$ drift during the acquisition time surpassed the peak width; that is to say, the drift of the beat note is limiting the peak width. We found the optimal RBW around $\varGamma$ = 5, 1, 1, 0.1 and 0.1 kHz for NPR1, NPR2, NPR3, ANDi1 and ANDi2, respectively, and the FWHM values at those $\varGamma$’s were 15.4 $\pm$ 6.4, 5.0 $\pm$ 1.4, 3.1 $\pm$ 1.4, 0.24 $\pm$ 0.11 and 0.21 $\pm$ 0.04 kHz, respectively. All the FWHM values were more than one order of magnitude larger than the 20 Hz FWHM of the beat-note peak for the CW laser [Fig. 1(b)], indicating that the broadening due to the CW laser linewidth was negligible.

 

Fig. 3. The peak width of the beat note for the five free-running mode-locked Yb:fiber lasers, NPR1-NPR3, ANDi1 and ANDi2. We also plotted the longitudinal-mode linewidth of the free-running mode-locked lasers reported in Refs. [3,5–8,10].

Download Full Size | PDF

The minimum FWHM of $f_{\rm {beat}}$ met around the crossover from the RBW-limiting region to the drift-limiting region is the measure of the longitudinal-mode linewidth referred to in the heterodyne beat-note experiment. The longitudinal-mode linewidths of 0.24 $\pm$ 0.11 and 0.21 $\pm$ 0.04 kHz obtained for the two ANDi lasers were the narrowest among the five mode-locked lasers (Fig. 3). We also observe that the longitudinal-mode linewidth tends to narrow as the $f_{\rm {rep}}$ decreases, particularly in the three NPR-mode-locked lasers. Finally, we note that the $f_{\rm {beat}}$ linewidths of ANDi1 and NPR2 broadened by a factor of 4 when we opened the aluminum box, which indicated the importance of soundproofing with the cavity fully enclosed with the box.

To facilitate the comparison to the literature values, we also plotted in Fig. 3 the longitudinal-mode linewidths reported in Refs. [3,5–8,10], in which the RBW values (or the acquisition times) and linewidths of the CW lasers during the heterodyne beat-note measurements were indicated.

4. Discussion

First of all, the longitudinal-mode linewidths of 0.21 $\pm$ 0.04 and 0.24 $\pm$ 0.11 kHz obtained for 1-MHz ANDi2 and 30-MHz ANDi1 lasers, respectively, are not only narrower than those of NPR1-NPR3 but surpassed all the reported values plotted in Fig. 3 and listed in Table 1. To our best knowledge, the 200 Hz linewidth is the narrowest among the values found for solid-state and fiber mode-locked lasers in the free run. The longitudinal-mode linewidths of NPR2 and NPR3, respectively being 5.0 $\pm$ 1.4 and 3.1 $\pm$ 1.4 kHz at the optimal RBW setting of $\varGamma =1$ kHz, were also narrower than the previous results obtained at the $\varGamma =1$ kHz settings [3,6,7,10].

The narrowing of the longitudinal-mode linewidth seen in the series from NPR1 of $f_{\rm {rep}}=244$ MHz to NPR3 of $f_{\rm {rep}}=10$ MHz (Fig. 3) suggests that lowering $f_{\rm {rep}}$, or elongating the cavity, is a viable approach for narrowing the linewidth. When the cavity is long, the pulse can be less susceptible to the pump-power fluctuation because the pulse less frequently passes through the gain medium, which is the section in the cavity where the pump fluctuation is transferred to the pulse. Alternatively, because $0<f_{\rm {beat}}<f_{\rm {rep}}$, reducing the comb spacing $f_{\rm {rep}}$ can also restrict the upper limit of the linewidth that cannot exceed $f_{\rm {rep}}$. Although the thought experiments are challenging to verify, the observation that the linewidth did not broaden while reducing $f_{\rm {rep}}$ indicates that we have sufficiently suppressed the linewidth broadening through the change in the cavity length; long cavities would have suffered more from the cavity-length fluctuations, which is another leading source of noise that broadens the comb linewidth [7]. The strategy of lowering $f_{\rm {rep}}$ will eventually be limited by the difficulty to mode-lock the long cavity.

The longitudinal-mode linewidths for the two ANDi oscillators were consistently narrower than those of the three NPR lasers (Fig. 3), suggesting that the ANDi scheme is favorable for narrowing the linewidth. One possible reason could be that the mode-locking through NPR has a looser intensity tolerance (or window) than that for the giantly-chirped pulse circulating in the ANDi cavity; the NPR scheme can therefore accept more intensity fluctuation and, hence, the broader longitudinal-mode linewidth. Another possible reason is that the ANDi cavity is simpler than the NPR laser cavity since it does not need an intra-cavity grating-pair compressor. Whatever the reason, our results show that the cavity configuration, besides its length, strongly affects the linewidth.

For narrowing the longitudinal-mode linewidth, we conclusively allege that the following two techniques were vital: (1) Using a sound-proof box with the wall thicker than 5 mm; 15-mm thick wall ensured the 200-Hz bandwidth. (2) Keeping the lasers in a stable temperature environment; in our case, we attained the $\pm 0.1^{\circ }$C stability of the laboratory temperature by installing the precision air cooling system. A temperature drift of $0.1^{\circ }$C in 1000 seconds causes the beat note to broaden by 200 Hz in 10 ms, which sets the measurement limit. Finally, for detecting the narrow linewidth through the heterodyne beat note, using the narrow-linewidth CW laser for the reference is a prerequisite; then, the narrowest linewidth can be searched through systematically sweeping the RBW value of the spectrum analyzer.

5. Conclusion

We surveyed the longitudinal-mode linewidth of five homemade mode-locked Yb:fiber lasers by taking the beat note with a sub-1-Hz CW laser and found that the linewidth can be as narrow as 200 Hz, which surpassed the records for free-running mode-locked lasers in the literature, to our best knowledge. The demonstration of the 200-Hz linewidth expands the possibility of mode-locked fiber lasers and helps realize a robust optical frequency comb with a simple feedback system, which would widen the optical frequency comb application. Based on the survey, we proposed that making the cavity long and simple can be a good working hypothesis for narrowing the linewidth and provided practical techniques to reduce the environmental fluctuations in temperature and vibrations.