Open Access
Add to BibSonomy
Abstract
An all-fiber-based mode-filtering technique is developed for generating a gigahertz-repetition-rate fiber-based frequency comb with a multiplication factor of 21. A high side-mode suppression ratio of approximately 65 dB is achieved by introducing a thermally diffused expanded core fiber between the dispersion compensating fiber and single-mode fiber to reduce splice loss. The fiber cavity length is also stabilized such that the resonance frequency is locked to the comb mode by applying the Pound–Drever–Hall stabilization technique. The proposed stabilized all-fiber-based mode-filtering technique is expected to be an attractive choice for a variety of applications that require a high-repetition-rate frequency comb.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical frequency combs have emerged as versatile tools for frequency metrology and other applications [1,2]. An optical frequency comb with a high repetition rate (frep) of greater than gigahertz possesses higher available power per mode than a frequency comb with a low frep, and each comb mode can be resolved using a wavemeter or spectrometer. Therefore, high-frep combs are used in several applications such as direct-frequency comb spectroscopy [3,4], high-bit-rate optical communication [5], astronomical spectrograph calibration [6], low-noise microwave generation [7], and absolute distance measurement [8]. Many of these applications require the detection and stabilization of frep and the carrier-envelope offset frequency (fceo). A 15-GHz mode-spacing optical frequency comb has been generated using a Kerr-lens mode-locked Yb:Y2O3 ceramic laser [9], and the direct generation of a frequency comb with frep = 23.8 GHz has been reported [10]. However, the self-referencing technique is difficult to realize because of the low pulse energy for mode spacing above a few gigahertz. A microresonator [11] and an electro-optic modulator [12] can generate a gigahertz frequency comb; however, a self-referencing scheme requires the use of complicated systems [13,14]. In contrast, fiber-based frequency combs [15,16] have been widely used as standard systems since they were first reported in the early 2000s [17,18]. However, a typical value of frep for such combs is approximately 100 MHz, and it is difficult to shorten the length of the fiber laser cavity because of physical limitations to keep enough gain and contain necessary components. Moreover, a shortening of the cavity length will reduce the peak power, which should be above a certain threshold to maintain the nonlinearity required for a stable mode-locking operation. The development of an Yb:fiber laser that gives an frep value close to 1 GHz and the direct detection of fceo using a self-referencing technique have been reported [19,20]. However, to achieve a higher fundamental frep, the laser cavity length needs to be shortened, which is difficult to realize owing to physical limitations, as mentioned before.
To overcome these limitations, a mode-filtering technique has been developed for low-frep frequency combs using Fabry–Perot cavities [7,21], in which both frep and fceo of the fundamental frequency comb are phase stabilized. However, the system consists of two mirrors and free space; hence, it suffers from environmental fluctuations. On the other hand, fiber-based ring cavities consisting of a single fiber coupler and a delay line have recently gained attention as a simple and robust system for mode filtering [22]. However, the cavities have been able to achieve only a low multiplication factor (M) of 2 because the physical limitations that inhibit the shortening of the fiber cavity length finally matter. In addition, the finesse of the fiber cavity has been very low (∼6) because of the large coupling loss (∼74%) of the free-space optical delay line inside the cavity and the large splice loss between the dispersion compensating fiber (DCF) and single-mode fiber (SMF). Recently, an all-fiber-based harmonic injection locking technique has been demonstrated for realizing highly tunable frep multiplication [23]. However, the system requires two mode-locked fiber lasers and the output spectrum exhibits fringe-like patterns owing to the two free-running lasers. On the other hand, we have proposed an all-fiber-based mode-filtering technique that incorporates a long fiber-based ring cavity whose length is greater than that of the laser cavity (i.e., the pulse separation) [24]. Because the physical limitations on the cavity length is considerably mitigated, this technique is able to substantially multiply frep, and an M of 11 is achieved. That is, an frep value of 48.7 MHz is multiplied to 536.0 MHz with a side-mode suppression ratio (SMSR) of 25 dB. However, the cavity length has not been stabilized, which requires for long-term stable operation.
In this study, we stabilized the fiber cavity length such that the resonance frequency was locked to the comb mode by applying the Pound–Drever–Hall (PDH) stabilization technique [25] that used an auxiliary continuous wave (CW) laser. We also achieved a substantial improvement in the SMSR of the fiber cavity by introducing a thermally diffused expanded core (TEC) fiber [26] between the DCF and SMF to reduce the splice loss. Further, owing to the TEC fiber and all-fiber-based double-pass configuration, we were able to generate a 1-GHz-frep mode-filtered frequency comb with a high M of 21 and a high SMSR of 65 dB based on a low-frep fiber-based frequency comb with a 48.7-MHz repetition rate.
2. Experimental setup
Figure 1 shows the experimental setup for the frep-multiplying all-fiber-based mode-filtering system with cavity length stabilization. An Er-fiber-based frequency comb is used as the seed source, and a fiber delay line is used in the laser cavity to make frep tunable from 48.55 to 48.95 MHz. The output is passed into the fiber ring cavity via a circulator (CIR), an Er-doped fiber amplifier (EDFA1), a polarization controller (PC1), and a fiber coupler (FC1). The fiber cavity consists of an SMF, a DCF, and two fiber couplers (FC2 and FC3) with a 99:01 split ratio. The input and output of the fiber cavity are connected to 1% of the ports of the couplers, and the interior of the cavity is connected to the remaining 99% of the ports. When the light is coupled into the fiber cavity through the 1% port on the left side of the FC2, there is no reflected output of the cavity. Instead, the output from the 1% port on the right side of the FC2 corresponds to the reflected output in the case of the conventional Fabry–Perot cavity. A piezoelectric actuator (PZT) is installed in the cavity for length stabilization. The DCF is included inside the cavity to compensate for the zero-net dispersion in the cavity around the wavelength of 1560 nm. Owing to the large difference between the mode field diameters (MFDs) of the SMF (SMF28e+, Corning, MFD = 10.4 µm at 1.55 µm) and DCF (DCF38, Thorlabs, MFD = 6.0 µm at 1.55 µm), the splice loss is large (our best achieved value: 0.8 dB). Previously, to reduce the loss, an intermediate fiber with MFD = 6.8 µm was introduced between the SMF and DCF [24], which achieved the splice loss of approximately 0.3 dB. In this work, by introducing a TEC fiber [26] between the SMF and DCF, the splice loss is substantially reduced and approximately 0.01 dB is achieved. The cavity finesse is approximately 70; therefore, the resonant width of the cavity is 1.3 MHz with the free spectral range (FSR) of 92.9 MHz. The output of the cavity is sent to the fiber loop mirror via PC4, a polarizer (P2), EDFA2, and FC4 with a 70:30 split ratio to obtain a single-pass cavity output. In the output of FC3, i.e., the fiber cavity output, the frequency comb component is isolated from the CW laser component by adjusting PC4 and P2. Then, the output is made to reflect from the fiber loop mirror and sent into the same cavity via the same fiber pass. At the 1% port on the right side of FC3, the comb light is not reflected, thus there is no reflected output of the cavity. After passing through the cavity again, the double-pass cavity output is obtained from the CIR. From this output, the all-fiber-based double-pass configuration is realized. In this experimental setup, the fiber cavity is installed in an enclosure with a simple housing made of styrene foam to suppress the environmental polarization change, and the temperature is also controlled.
Fig. 1. Experimental setup. CW: Continuous wave; EOM: Electro-optic phase modulator; CIR: Circulator; EDFA: Er-doped fiber amplifier; PC: Polarization controller; FC: Fiber coupler; TEC: Thermally diffused expanded core; DCF: Dispersion compensating fiber; PZT: Piezoelectric actuator; FG: Function generator; P: Polarizer; BPF: Bandpass filter; PD: Photodetector.
To perform cavity length stabilization, the PDH technique that uses an auxiliary single-frequency CW laser is employed. The CW laser output is divided into two paths (not shown in Fig. 1). In one of the paths, a fiber-coupled acousto-optic modulator (AOM, Fibre-Q, Gooch & Housego) is used as a frequency shifter with a drive frequency (fAOM) of 80 MHz. The beat note between the AOM-shifted CW laser and comb mode is detected and is phase locked to fAOM – frep via the drive current of the CW laser. Therefore, in the other path, the CW laser is phase locked to the comb mode without the offset frequency. With this offset-free CW laser, a simple phase-locking technique [27] can be applied as follows. As shown in Fig. 1, the offset-free CW laser output is modulated using an electro-optic phase modulator (EOM, LN53S-FC, Thorlabs), and it is combined with the fiber comb output via FC1. The polarization of the CW laser and frequency comb are optimized for the fiber cavity using PC1 and PC2, i.e., both polarizations are the same. Then, both the CW laser and frequency comb are introduced into the mode-filtering fiber cavity via a 2 × 2 coupler (FC2). The output from the 1% port of the FC2 corresponds to the reflection components at the resonance frequencies. Although both the CW laser and frequency comb are coupled out from the same port of the FC2, only the CW laser component is detected by the photodetector (PD) used for cavity length stabilization by adjusting PC3, P1, and an optical bandpass filter (BPF, TFF, Alnair Labs, bandwidth: 1 nm) in the transmission port of FC2. For PDH error signal detection, the P1 is not sufficient to fully separate the CW laser from the comb light, therefore, the BPF is also used. As shown in Fig. 2(a), (a) sharp PDH error signal (black curve) is obtained at cavity resonance (red curve) and is fed back to the intracavity PZT. In this manner, the fiber cavity length is successfully stabilized, as shown in Fig. 2(b). The slope of the PDH error signal and the stability of the transmission are estimated to 1.1 MHz/V and 0.008 MHz, respectively. Therefore, the relative stability of the cavity lock is 0.006 for the fiber cavity with the resonant width of 1.3 MHz.
Fig. 2. PDH error and transmission signals in (a) free-running and (b) locked cases. At t = -0.14 s, the cavity length is stabilized. Red and black curves are resonant transmittance curve and corresponding PDH error signal of the fiber cavity.
The optical length of the fiber ring cavity nL (n: refractive index of fiber, L: cavity length) is preset to (M + m)/M times the pulse separation c/frep, where c is the speed of light in vacuum and m is an integer, i.e., M × frep = (M + m) ×FSR of the fiber cavity. The fiber cavity length is not a multiple of the laser cavity length. In this experiment, mode filtering with M = 21 is demonstrated; hence, the optical length of the cavity is set to 3.2 m with m = –10 (nL = (M – 10)/M × c/frep) for frep = 48.7 MHz. Therefore, the FSR of the fiber cavity is 92.9 MHz. Thus, the relationship (21–10) × FSR = 21 × frep = 1.02 GHz is obtained. As shown in Fig. 3, the frequencies of two comb modes with a separation of 21 × frep match the transmission peaks of the fiber cavity with a separation of 11 × FSR in this case, thus, filtered comb with 1.02 GHz separation should be obtained. The physical lengths of the SMF and DCF are 1.5 and 0.7 m, respectively. For the adjustment of the transmission peaks and comb modes, frep of the fiber-based frequency comb is changed using a fiber delay line in the laser cavity.
Fig. 3. Mode-filtering effect with long-fiber-based ring cavity. Here, multiplication factor M = 21 and integer m = –10, i.e., 21 × frep = 11 × FSR.
3. Experimental results
3.1 Optical and RF spectra of single- and double-pass cavity outputs
Figure 4 shows the optical and RF spectra of the input [Figs. 4(a)–4(c)], single-pass cavity output [Figs. 4(d)–4(f)], and double-pass cavity output [Figs. 4(g)–4(i)]. As shown in Figs. 4(d) and 4(g), the full width at half maximum of the optical spectra of the single- and double-pass cavity outputs is approximately 6 nm. Compared to the input spectrum shown in Fig. 4(a), the spectral bandwidth becomes narrower owing to the difference between the high-order dispersions of the SMF and DCF. The RF spectra shown in Figs. 4(b), 4(e), and 4(h) are measured using a fast photodiode (F7096FC, Hamamatsu) along with a bias tee (Picosecond Pulse Labs), an RF amplifier (ALS04-0153, ALC Microwave Inc.), and an RF spectrum analyzer (FSV13, Rohde & Schwarz). The incident powers are ∼0.4 mW in all the cases. As shown in Figs. 4(e) and 4(h), a strong peak at 1.02 GHz and some harmonics are observed. Figures 4(f) and 4(i) show the magnified beat notes at around 1.02 GHz. The single-pass cavity suppresses the fundamental and secondary off-resonant modes by 28 and 14 dB, respectively. Unlike the results in ref.25, the secondary off-resonant mode is more significant than the fundamental one. The formation of this characteristic structure in the RF spectra can be attributed to the selection of the cavity parameter of M and integer m, as shown in Fig. 3. In contrast, in Fig. 4(i), the suppression ratio of the fundamental and secondary off-resonant modes is improved to 65 and 34 dB, respectively, owing to the double-pass cavity output. Comparing to the results in Ref. [24], owing to TEC fiber, the finesse of the cavity is improved from 19 to 70, therefore, the suppression ratio of the fundamental off-resonant mode is improved from 25 dB to 65 dB. The suppression ratio of 65 dB is already sufficient for various applications in the frequency domain, e.g., sensitivity improvement in dual-comb spectroscopy [28] and precision length measurement [8].
Fig. 4. Optical and RF spectra of (a)–(c) input, (d)–(f) single-pass cavity output, and (g)–(i) double-pass cavity output. (c), (f), and (i) show magnified RF beat notes at around 1.02 GHz.
3.2 Evaluation in time domain
Next, the time domain characteristics are evaluated. The output of the cavity is detected using a fast photodiode and displayed on a fast oscilloscope (DSOX6004A, Keysight). Figure 5 shows the time domain signals of the input [Fig. 5(a)], single-pass cavity output [Fig. 5(b)], and double-pass cavity output [Fig. 5(c)]. As shown in Figs. 5(b) and 5(c), the single-pass cavity output shows more than 45% amplitude modulation at two time constants of 10.8 and 9.8 ns. In the fiber cavity, the original pulse period T ( = 1/frep) is modulated at the period of (M + m)/M × T ( = 1/FSR = nL/c). In this experiment, T = 20.6 ns ( = 1/48.7 MHz) and the modulation period = 20.6 ns × 0.52 (= (21–10)/21) = 10.8 ns, thus the residual time constant is observed at the period = 20.6 ns – 10.8 ns = 9.8 ns. Except these modulations, the generated pulse trains in Figs. 5(b) and 5(c) clearly show the period of 1.0 ns which matches to T/M ( = 20.6 ns/21 = 1.0 ns), confirming the successful mode filtering. The double-pass cavity output shows less than 6% amplitude modulation. These results imply that the all-fiber-based mode-filtering technique is a powerful tool for generating a high-repetition-rate frequency comb in the time domain.
Fig. 5. Time domain signals of (a) input, (b) single-pass cavity output, and (c) double-pass cavity output.
3.3 Evaluation in optical frequency domain
In addition to the RF domain evaluation of the self-beat notes, the heterodyne beat signal between the filtered comb mode and another single-frequency CW laser (DL pro, Toptica) is measured at a wavelength of 1556 nm. The CW laser is free running. As shown in Fig. 6(a), the single-pass cavity suppresses the fundamental and secondary off-resonant modes by ∼35 and ∼20 dB. The double-pass cavity output provides a fundamental off-resonant mode suppression of more than 50 dB, which is limited by the measurement noise floor, and a secondary off-resonant mode suppression of ∼38 dB. Comparing to the results in Ref. 24, owing to TEC fiber, the finesse of the cavity is improved from 19 to 70, therefore, the suppression ratio of the fundamental off-resonant mode is improved from 25 dB to more than 50 dB. From these results, the generation of mode-filtered comb and an improvement in off-resonant mode suppression in the optical frequency domain are confirmed. To the best of our knowledge, this is the highest multiplication factor ever achieved (M = 21) with high off-resonant mode suppression and frep using a fiber-based ring cavity.
Fig. 6. Heterodyne beat signal between mode-filtered comb mode and CW laser for (a) single-pass cavity output and (c) double-pass cavity output. Solid circles: beat notes of fbeat; dotted circles: beat notes of frep – fbeat; solid cubes: harmonics of 48.7-MHz repetition rate.
3.4 Generation of 10.2-GHz microwave signal using all-fiber-based mode-filtering technique
Here, in order to demonstrate the effectiveness of the developed technique, the achievable RF power in the 10.2-GHz harmonic component is evaluated for an all-fiber-based mode-filtering cavity. The RF spectrum of the double-pass mode-filtered frequency comb is recorded by changing the average optical powers. The results are summarized in Fig. 7, where the RF power in the 10.2-GHz harmonic is plotted as a function of the input average optical power to the photodiode; the figure also presents the results for the unfiltered 48.7-MHz frequency comb. In the linear regime, the 10-GHz power is proportional to the input optical power. The linear response is observed in all the cases for an average optical power of less than 60 µW. However, in the case of the 48.7-MHz pulse train, the 10.2-GHz harmonic saturates above 70 µW. For the mode-filtered frequency comb, the linear regime for the 10.2-GHz generation extends further from the average optical power of 70 µW to a higher value of 2 mW. The highest 10.2-GHz power achieved is –22 dBm, as measured by the RF spectrum analyzer. These results clearly demonstrate the effectiveness of the developed mode-filtering technique in the suppression of the photodetector saturation, which is essential to generate high power microwave signal.
Fig. 7. RF power in 10.2-GHz microwave harmonic as function of input average optical power to the photodiode for with and without 1-GHz mode-filtering. (Inset) RF spectrum around 10.2 GHz with incident power of 600 µW on the photodiode.
4. Conclusions
In this study, we developed a phase-stabilized all-fiber-based mode-filtering technique for generating a gigahertz frequency comb based on a low-frep fiber-based frequency comb. We achieved a substantial improvement in the SMSR by introducing a TEC fiber between the DCF and SMF to reduce the splice loss to 0.01 dB. In addition, we used the all-fiber-based double-pass cavity configuration to generate a 1-GHz-frep mode-filtered frequency comb with a high multiplication factor of 21 and a high SMSR of 65 dB based on a 48.7-MHz fiber-based frequency comb. The suppression ratio of 65 dB is sufficient for various applications in the RF frequency domain, e.g., sensitivity improvement in dual-comb spectroscopy and precision length measurement. The effectiveness of the developed technique was demonstrated by the power enhancement in generation of 10.2-GHz microwave signal by suppression of the detector saturation. In future, with the already demonstrated multiplication factor of 21, we can generate mode-filtered comb modes with a frequency of 5.25 GHz ( = 21 × 250 MHz) using our technique based on a commercially available fiber-based frequency comb with an frep value of 250 MHz. The proposed stabilized all-fiber-based mode-filtering technique is expected to be an attractive choice for a variety of applications that require a high-repetition-rate frequency comb.
Funding
Exploratory Research for Advanced Technology (JPMJER1304); Japan Society for the Promotion of Science (JP15H05894, JP17K14122).
Disclosures
The authors declare no conflicts of interest.
References
1. R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000). [CrossRef]
2. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef]
3. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445(7128), 627–630 (2007). [CrossRef]
4. M. C. Stowe, M. J. Thorpe, A. Pe’er, J. Ye, J. E. Stalnaker, V. Gerginov, and S. A. Diddams, “Direct frequency comb spectroscopy,” Adv. At., Mol., Opt. Phys. 55, 1–60 (2008). [CrossRef]
5. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011). [CrossRef]
6. T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. G. Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012). [CrossRef]
7. S. A. Diddams, M. Kirchner, T. Fortier, D. Braje, A. M. Weiner, and L. Hollberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17(5), 3331–3340 (2009). [CrossRef]
8. K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000). [CrossRef]
9. M. Endo, I. Ito, and Y. Kobayashi, “Direct 15-GHz mode-spacing optical frequency comb with a Kerr-lens mode-locked Yb:Y2O3 ceramic laser,” Opt. Express 23(2), 1276–1282 (2015). [CrossRef]
10. S. Kimura, S. Tani, and Y. Kobayashi, “Kerr-lens mode locking above a 20 GHz repetition rate,” Optica 6(5), 532–533 (2019). [CrossRef]
11. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). [CrossRef]
12. A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, A. Takada, T. Sogawa, and M. Koga, “Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser,” Opt. Express 21(24), 29186–29194 (2013). [CrossRef]
13. K. Beha, D. C. Cole, P. Del’Haye, A. Coillet, S. A. Diddams, and S. B. Papp, “Electro synthesis of light,” Optica 4(4), 406–411 (2017). [CrossRef]
14. J. D. Jost, T. Herr, C. Lecaplain, V. Brasch, M. H. P. Pfeiffer, and T. J. Kippenberg, “Counting the cycle of light using a self-referenced optical microresonator,” Optica 2(8), 706–711 (2015). [CrossRef]
15. H. Inaba, Y. Daimon, F.-L. Hong, A. Onae, K. Minoshima, T. R. Schibli, H. Matsumoto, M. Hirano, T. Okuno, M. Onishi, and M. Nakazawa, “Long-term measurement of optical frequencies using a simple, robust and low-noise fiber based frequency comb,” Opt. Express 14(12), 5223–5231 (2006). [CrossRef]
16. Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F.-L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010). [CrossRef]
17. T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, A. Onae, H. Matsumoto, I. Hartl, and M. E. Fermann, “Frequency metrology with a turnkey all-fiber system,” Opt. Lett. 29(21), 2467–2469 (2004). [CrossRef]
18. B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, M. F. Yan, and C. G. Jørgensen, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett. 29(3), 250–252 (2004). [CrossRef]
19. C. Li, Y. Ma, Z. Gao, F. Niu, T. Jiang, A. Wang, and Z. Zhang, “1 GHz repetition rate femtosecond Yb:fiber laser for direct generation of carrier-envelope offset frequency,” Appl. Opt. 54(28), 8350–8353 (2015). [CrossRef]
20. Y. Ma, B. Xu, H. Ishii, F. Meng, Y. Nakajima, I. Matsushima, T. R. Schibli, Z. Zhang, and K. Minoshima, “Low-noise 750 MHz spaced ytterbium fiber frequency combs,” Opt. Lett. 43(17), 4136–4139 (2018). [CrossRef]
21. J. Chen, J. W. Sickler, P. Fendel, E. P. Ippen, F. X. Kärtner, T. Wilken, R. Holzwarth, and T. W. Hänsch, “Generation of low-timing-jitter femtosecond pulse trains with 2 GHz repetition rate via external repetition rate multiplication,” Opt. Lett. 33(9), 959–961 (2008). [CrossRef]
22. J. Lee, S.-W. Kim, and Y.-J. Kim, “Repetition rate multiplication of femtosecond light pulses using a phase-locked all-pass fiber resonator,” Opt. Express 23(8), 10117–10125 (2015). [CrossRef]
23. C.-G. Jeon, S. Zhang, J. Shin, and J. Kim, “Highly tunable repetition-rate multiplication of mode-locked lasers using all-fibre harmonic injection locking,” Sci. Rep. 8(1), 13875 (2018). [CrossRef]
24. Y. Nakajima, A. Nishiyama, and K. Minoshima, “Mode-filtering technique based on all-fiber-based external cavity for fiber-based optical frequency comb,” Opt. Express 26(4), 4656–4664 (2018). [CrossRef]
25. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983). [CrossRef]
26. Deltafiber homepage, http://www.deltafiber.jp/english/index.html.
27. S. Okubo, A. Onae, K. Nakamura, T. Udem, and H. Inaba, “Offset-free optical frequency comb self-referencing with an f-2f interferometer,” Optica 5(2), 188–192 (2018). [CrossRef]
28. A. Nishiyama, S. Yoshida, T. Hariki, Y. Nakajima, and K. Minoshima, “Sensitivity improvement of dual-comb spectroscopy using mode-filtering technique,” Opt. Express 25(25), 31730–31738 (2017). [CrossRef]
