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Abstract
Optical enhancement cavities enabling laser pulses to be coherently stacked in free space are used in several applications to enhance accessible optical power. In this study, we develop an optical cavity that accumulates harmonically mode-locked laser pulses with a self-resonating mechanism for X-ray sources based on laser-Compton scattering. In particular, a Fabry-Perot cavity composed of 99% reflectance mirrors maintained the optical resonance in a feedback-free fashion for more than half an hour and automatically resumed the accumulation even if the laser oscillation was suspended. In contrast to conventional optical enhancement cavity systems with a dedicated feedback controller, this characteristic is highly beneficial in practical applications, such as for laser-Compton scattering X-ray sources. Lastly, upscaling and adoption of the proposed system might improve the operability and equipment use of laser Compton-scattering X-ray sources.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical cavities have played a crucial role in various scientific research fields. The narrow linewidth and effective elongation of the optical path length have been applied to frequency stabilization [1,2], gravitational wave detection [3], and spectroscopy [4]. Another essential feature of the cavity is that a high peak power with high-repetition frequency laser pulses can be obtained without using a laser amplifier by coherently stacking laser pulses inside the cavity. This feature is beneficial for applications such as the generation of high-energy photon beams via laser-Compton scattering (LCS) [5], high-harmonic generation [6], and phase manipulation in transmission electron microscopes [7].
In the LCS, laser photons are scattered by relativistic electron beams and become high-energy photons in the X- to gamma-ray region, depending on the energy of the electron beams. An essential advantage of the LCS is that the required electron energy is lower than that of the synchrotron radiation, which is suitable for constructing a compact photon source. In addition to compactness, its features, such as energy-tunability, quasi-monochromaticity, and polarization controllability, are attractive for scientific studies and industrial applications [8]. However, a limitation of the LCS system is providing intense laser pulses to generate sufficient photon flux for particular applications. Stacking laser pulses in an optical cavity is an idea for realizing high peak power and repetition rate without a large-scale laser system, which is advantageous, if achievable, for compact X-ray sources. The authors have been conducting optical cavity R&Ds for LCS X-/gamma-ray sources at various accelerator complexes, such as the compact normal conducting linac [9], compact superconducting linac [10], energy recovery linac [5], and accelerator test facility [11] in the High Energy Accelerator Research Organization (KEK) in Japan.
To accumulate the laser light in the cavity, the cavity length must satisfy the following resonance condition:
where $L_{\mathrm {cav}}$, $\lambda$, and $n$ are the lengths of the cavity, wavelength, and integer, respectively. The precision required for Eq. (1) is the wavelength divided by the finesse and reaches $O$(10 pm) for an enhancement factor of $10^4$ assuming a 1 µm wavelength. This requirement can be satisfied by developing sophisticated feedback systems, as described in [5,9–11]. In particular, the precision of the achieved cavity length has been shown to be $14$ pm, as reported in [11]. Note that the precision has currently reached $O$(10 pm). Moreover, in general, the system can be installed in an accelerator complex, where the system faces various types of external disturbances, such as high-power electric noise or environmental vibration. Thus, the feedback technique could be a significant bottleneck for developing LCS X-/gamma-ray sources with optical cavities.To circumvent the feedback problem, we have proposed a new scheme called the "self-resonating mechanism." This principle was initially introduced in [12]. In this scheme, the optical cavity automatically selects a wave satisfying the conditions in Eq. (1). Therefore, in principle, the laser oscillation continues by itself, with wavelengths chosen by $L_{\mathrm {cav}}$, using Eq. (1) without external feedback system. Details of the self-resonating mechanism and operation in the CW regime were reported in [13], where 2.52 kW storage with 1.8% stability was achieved with a finesse of 394,000. This approach can be applied to LCS-based X-ray sources; however, mode-locked pulsed oscillation is required to obtain high peak power and repetition laser pulses. We have demonstrated a mode-locked pulsed operation with self-resonating cavities [14]. Although it successfully showed mode-locked oscillation with self-resonant scheme, the system was developed for demonstration purposes with a low (41.4 MHz) repetition rate, and the mode-locked oscillation lasted only several seconds.
This article reports the results of an improved system that achieves continuous operation for more than an hour. In addition, the repetition rate of the system is 357 MHz, which matches the electron beam repetition of an existing accelerator at KEK [15].
2. Methods
Maintaining the resonant condition in Eq. (1) is typically performed with a feedback control based on the error signal generated from the reflected light and a stable reference signal. For example, the Pound-Drever-Hall technique [16] is frequently used for feedback. The enhancement factor can be limited by the accuracy or speed of feedback response. A previous demonstration of a self-resonating optical cavity in a single longitudinal mode operation showed that the thermal drift in a cavity spacer halted laser oscillation [17], that is, laser accumulation. However, the system was automatically rebuilt repeatedly during a large thermal drift, representing a significant advantage of this scheme.
To mode-lock a self-resonating optical cavity, the following condition must be satisfied:
where $n$ is an integer, $f_\mathrm {cav}$ is the free spectral range (FSR) of an optical cavity used in the laser accumulation, and $f_\mathrm {loop}$ is the fundamental repetition frequency of the entire loop of a ring laser oscillator constituting the self-resonating system. This condition is required for the timing of the incoming pulses to the cavity and the circulating pulse inside the cavity (Fig. 1). Furthermore, the system operated as a harmonically mode-locked ring laser when $n>1$[18]. Moreover, $n$ pulses circulate in the oscillator loop, whereas only one pulse exists in the cavity.
Fig. 1. Schematic concept of a self-resonating optical enhancement cavity. Multiple pulses circulate in the oscillator loop. The number of pulses depends on the optical path length of the oscillator. The red triangles represent the optical pulses.
2.1 Experimental setup
A schematic of the experimental setup is presented in Fig. 2. In the fiber space (solid orbital lines in Fig. 2), a 20-cm-long ytterbium-doped fiber (YDF, Coractive Yb406, GVD: 32.58 ps$^2$/km at 1030 nm) is core-pumped by a 976 nm stabilized laser diode (LD). The pump light was guided through a pump protector (PP) and a wavelength division multiplexing (WDM) coupler. Considering the insertion loss of PP and WDM, the maximum measured optical pump power was 660 mW. The undoped fibers were single-mode fibers (SMF, Corning HI1060, GVD:23 ps$^2$/km at 1030 nm). The fiber part was 45 cm in total, with the group delay dispersion (GDD) of approximately +0.1053 ps$^2$. The transmissive diffraction grating pair (GP: LSFSG-1000-3225-94, LightSmyth, 1000 lines/mm) had a separation of 23 mm to compensate for the normal dispersion of the optical fibers. The total net GDD of the ring-fiber laser was estimated as -0.0367 ps$^2$. Note that the optical fiber and GP were the dominant components in the setup. The output from the polarizing beam splitter (PBS) was used for the analyses: the waveform and pulse width. The spectrum was taken after the cavity output. A photodiode with a bandwidth of 2 GHz (PD0) and an oscilloscope (MSO44, Tektronix, bandwidth:1 GHz) were used to monitor the laser pulse shape.
Fig. 2. Schematic of the experimental setup. Solid orbital lines are fiber-space, and dashed lines are free-space. The cross mark implies a fusion splice. Abbreviations: LD, laser diode; PP, pump protector; WDM, wavelength division multiplexing; FC, fiber collimator/coupler; HWP, half-waveplate; QWP, quarter-waveplate; PBS, polarizing beam splitter; ISO, isolator; BS, beam sampler; PZT, piezoelectric transducer; GP, grating pair; DL, delay line; PD, photodiode; OSA, optical spectrum analyzer; AC, autocorrelator.
An optical enhancement cavity is placed between two free-space Faraday isolators (ISO) to prevent parasitic oscillation and ensure that only the transmitted light contributes to lasing. Lens pairs were used for spatial mode matching from/to a fiber collimator/coupler (FCs). Moreover, beam samplers (BS) and photodiodes (PD1, PD2, and PD3) were placed to measure the incident, reflected, and transmitted power to the cavity. Half- and quarter-wave plates (HWPs and QWPs) were used to orient the polarization of light in a direction aligned with the ISOs and to produce fast saturable absorption action relying on nonlinear polarization rotation [19]. A mirror placed after the GP was set on a linear stage and functions as a delay line (DL). The free-space optical path length could be controlled using a stage micrometer with a resolution of $20\pm 2$ µm. The minimum reading of the micrometer was 10 µm, and the uncertainty was assumed to be 1 µm.
2.2 Optical enhancement cavity
A photograph of the cavity is shown in Fig. 3, which is a Fabry-Perot type cavity comprising two concave mirrors with a high-reflection dielectric coating. The cavity length was $\sim 420$ mm, corresponding to an FSR of $\sim 357$ MHz. In contrast, the curvature of the mirrors was 250 mm. The cavity spacer and mirror mounts are made of SUS304 stainless steel. One mirror mount was equipped with a piezoelectric transducer (PZT) to scan the cavity length.
Fig. 3. Photograph of the optical cavity. 420 mm cavity length corresponds to 357 MHz repetition rate, equivalent to the electron beam repetition rate.
First, the FSR and finesse of the cavity were measured using a narrow-linewidth laser source with a wavelength of 1064 nm (Mephisto Innolight). The output was fiber-coupled, and subsequently, a nearly fundamental Gaussian beam from a single-mode fiber was coupled to the cavity. The input laser was phase-modulated using an electro-optic modulator to generate the sideband frequencies. In contrast, the cavity length was scanned using PZT. Moreover, the FSR and linewidth of the Airy-distributed resonance signal can be measured accurately using the sideband signals as frequency reference markers [20]. The obtained FSR and full width at half maximum (FWHM) of the linewidth were $358.880\pm 0.006$ MHz and $1.168\pm {0.029}$ MHz, respectively. Hence, the finesse at a wavelength of 1064 nm was $\mathscr {F} = \mathrm {FSR}/\nu _\mathrm {FWHM} = 307.2\pm 7.6$, which corresponded to an average reflectance of $98.98\pm 0.03\%$ for the two cavity mirrors. These results are in good agreement with the specification value of 99% reflectance.
2.3 Harmonic mode-locking
Subsequently, we tested the mode-locking without an optical cavity. The two cavity mirrors were removed from the mirror mounts. Moreover, the mode-locked oscillation was self-initiated by rotating the waveplates and increasing the pump power. An RF spectrum analyzer was used to measure the fundamental repetition frequency of the output laser pulses to confirm that the frequency was controllable from 32.58 to 32.68 MHz using the DL. Here, one-eleventh of the FSR of the cavity was $\sim 32.63$ MHz.
In particular, the ramping-up of the pump power and harmonic mode-locking were observed, as shown in Fig. 4. Note that the number of generated pulses $n$ is discontinuously proportional to the pump power, which is consistent with the results reported in [18]. The overlapping of the plot lines indicates that the two harmonic mode-locking states can be selected by adjusting the waveplates. Moreover, the lasing mode changed to another mode requires a few seconds to settle into the clean mode-locked oscillation. Note that seven stages in the build-up process are present. In addition, the optoacoustic effect finally stabilizes the pulse-to-pulse spacing [21].
Fig. 4. Harmonics number with respect to the pump power. At overlapping regions, the number of harmonics depends on the orientation of the waveplates.
3. Results of mode-locking with an optical cavity
We reattached the cavity mirrors to the mirror mounts and aligned the cavity again using a 1064 nm laser source. Because the cavity mirror had a thickness of 6 mm, the DL amount was slightly detuned from the optimum value obtained in the preliminary experiment. In particular, we succeeded in harmonic mode-locking with the cavity by slightly scanning the DL and rotating the waveplates. The waveform obtained using PD0 is shown in Fig. 5. A clean laser oscillation with no Q-switch instability was confirmed, as shown in Fig. 5(b). The RF spectrum obtained by a 500 MHz oscilloscope is shown in Fig. 6, showing 70 dB supermode suppression. The repetition frequency was 358.88 MHz, which is equivalent to the FSR and 11th harmonic mode-locking.
Fig. 5. Waveform of the self-resonating mode-locked pulses obtained by a 2 GHz photodiode (PD0) and a 1 GHz oscilloscope. (a) Nanosecond scale and (b) microsecond scale.
Fig. 6. RF spectrum of the self-resonating mode-locked pulses, obtained by a 500 MHz oscilloscope. The second harmonic peak shows lower intensity due to the limited bandwidth.
Let us refer to the amount of the DL as the “length of a delay optical path (LDOP)”. We swept the LDOP with 20 µm steps and measured the spectrum and autocorrelation trace (ACT). The changes in the spectrum are shown in Fig. 7. The ACT and corresponding pulse widths as functions of the LDOP are shown in Fig. 8. Here, the pulse width is derived by assuming a sech$^2$ pulse shape. The observed spectral widths ranged from 3.2 nm to 6.2 nm (FWHM), and the shapes were stable and substantially different from the widely varying spectral shape with a width of 1.1 nm in the non-mode-locked state, as shown in Fig. 9. The central wavelength was monotonically shifted proportionally to the LDOP; however, it jumped at approximately LDOP = 0 µm. When the LDOP was 0 µm, the center wavelength and the widest width were 1031.1 nm and 6.2 nm, respectively, while the mode-locking was unstable. The same phenomenon was reported in the scheme of coupled-cavity resonant passive mode-locking [22]. The scheme is unstable when the repetition frequencies of the two cavities are exactly harmonic [23]. However, it becomes stable when the harmonic relationship is detuned. Owing to the widest spectral width, the shortest pulse width of 329 fs was observed when LDOP = 0 µm. Moreover, the Fourier-transform-limited pulse width was calculated as 179 fs, indicating that the generated pulses were chirped solitons.
Fig. 7. (a) Spectra for different LDOP values. (b) Center wavelength (circle plot) and spectral width (square plot) for different LDOP values.
Fig. 8. (a) Autocorrelation trace for different LDOP values. (b) Pulse width for different LDOP values. Sech$^2$ pulse shape was assumed.
4. Characteristics of the laser accumulation
We set the pump power and LDOP to 660 mW and -60 µm, respectively, and achieved continuous harmonic mode-locked laser oscillation over a long time. The incident, reflected, and transmitted optical power to/from the cavity were measured using the PD1-3 and the BSs. Note that the splitting ratios were confirmed in advance. In particular, the splitting ratios of the incident, reflected, and transmitted lights were 3.45%, 3.31%, and 3.59%, respectively. Figure 10(a) shows the observed optical power acquired after one hour. The stability of the mode-locking was significantly improved compared to a previous study [14], which adopted the all-normal dispersion (ANDi) configuration. Although both the anomalous dispersion and ANDi regimes can work with harmonic mode-locking [24,25], soliton pulses generally tolerate lower energy per pulse, benefiting high-order harmonic mode-locking with limited pump power. Another reason for obtaining a long-term operation might be the difference in the optical cavities. In a previous experiment, the cavity was constructed with commercial mirror mounts and post rods, with robustness limitations.
Fig. 10. (a) Power and (b) temperature measurement after one hour. Self-initiation was confirmed immediately after mode hopping at 2348 s. The data representing the transmitted power are less noisy than others due to the use of a photodiode detector with a built-in amplifier (PD3), unlike other detectors.
Note that lasing was suspended at 2348 s, which was not due to mechanical shock but to temperature changes in the optical system. The thermal drift of the ambient air and cavity spacer were measured during the operation, as shown in Fig. 10(b). The gradients of thermal drift were 0.102 and 0.050 °C/hour, respectively. As shown in the previous section, the light propagation path in an optical fiber has a large degree of freedom, which can buffer changes in the optical path length in the fiber and free space. However, no such degree of freedom exists in the resonator space defining $f_\mathrm {cav}$. Therefore, the thermal stabilization of the cavity might be the dominant factor in achieving stable mode-locked oscillations.
Figure 11 shows the optical spectra obtained at the beginning and end of the operation. The mode-locked state had hopped to another mode-locked state at 2348 s. No change in the shape and spectral width of the light centered at 1035 nm was observed, indicating that the system was in a harmonically mode-locked state after restarting.
Fig. 11. Spectra of the beginning (dashed line) and the end (solid line) in the one hour power measurement. After the suspension at 2348 s in Fig. 10(a), it hopped to a different mode-locking state.
As with any enhancement cavity system, the coupling efficiency optimization of the light entering the cavity is vital to obtain the best performance. In particular, in our system, the coupling efficiency also affects the loss in the ring-fiber laser oscillator. The results of the power measurements obtained after meticulous cavity alignment are shown in Fig. 12. The average stored power inside the cavity can be calculated from the transmittance of the cavity mirror, 1.24% at 1030 nm, and the transmitted power. Thus, the average stored power reached $9.04\pm 0.22$ W with root-mean-square stability of 2.4%. The coupling efficiency was improved by optimizing the alignment, reaching $\sim 60$%.
Fig. 12. Power measurement of the incident, reflected, and transmitted light for 100 s. The average power inside the cavity was $9.04\pm 0.22$ W.
5. Discussions
Because one-hour operation has been demonstrated in this study, the self-resonating laser system will be applied to an LCS photon source. Furthermore, stable mode-locked oscillations can be established by developing an improved temperature environment. Thus, we plan to prepare an air conditioner with a larger cooling capacity and surround the optical table with vacuum insulation panels.
A higher circulating power is required, in the order of 100 kW for the LCS. In this regard, two possible approaches can be applied to scaling up our achievements. One is to replace the single-mode fibers with rod-type photonic crystal fibers [26]. For instance, ten W-class average-power oscillators with near-diffraction-limit beam quality have been reported [27,28]. This promising technology can readily scale our results by two orders of magnitude. The second approach is to increase cavity finesse. Thus, the following step is to conduct experiments with 99.9% reflectance mirrors and verify their performance. If the self-resonating mechanism can be well demonstrated with 99.99% reflectance mirrors, the enhancement factor would be two orders of magnitude higher, comparable to state-of-the-art optical enhancement cavities for femtosecond laser pulses [29]. However, the dispersion of the cavity mirrors, which was ignored in this study, was considered significant. The deterioration of the coupling efficiency or elongation of the pulse width may occur. In this regard, achieving a finesse of up to 10,000 is feasible using low-dispersion, high-reflectance mirrors, or compensating with negative-dispersion mirrors [30]. The scaling of both seeding power and enhancement factor would lead to a 100 kW-class average power in the optical cavity, which is similar to that of state-of-the-art LCS X-ray sources [31].
Regarding pulse width, we achieved the accumulation of femtosecond pulses. A shorter pulse contributes to a higher LCS X-ray flux owing to its higher photon density. This pulse width might be an advantage because the optical enhancement cavities currently used in LCS light sources operate in a few tens of picoseconds [31].
6. Conclusions
We successfully demonstrated harmonic mode locking with a self-resonating optical cavity. The oscillation was observed over a broad range of optical path-length detuning of $\pm 60$ µm. The accumulation of laser pulses in an optical cavity for 39 minutes was achieved without any external feedback circuits, and automatically resumed the accumulation even if the laser oscillation was suspended, an improvement from several seconds with respect to a previous study [14]. The results indicated that changes in ambient temperature surrounding the system must be controlled to less than $\pm 0.05$ °C/h for stable operation. In contrast to conventional optical enhancement cavity systems with a dedicated feedback controller, the self-resonating system showed that the mode-locked oscillation, namely, the ultrashort laser pulse accumulation, automatically resumed even after the thermal drift frustrated the continuous lasing. This characteristic is highly beneficial in practical applications, such as LCS X-ray sources.
The average power in the optical cavity reached a maximum of $9.04\pm 0.22$ W in this experiment. By scaling the handling power of the gain fiber and the finesse of the optical cavity, a 100-kW-class circulating laser power can be expected. It will be practical if such a laser system could be realized in a feedback-free manner because the frequent re-lock of the system is not required. This can contribute to better operability and equipment utilization.
Funding
Japan Society for the Promotion of Science (19H00691).
Acknowledgments
We would like to thank Editage for English language editing.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. T. Hansch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity,” Opt. Commun. 35(3), 441–444 (1980). [CrossRef]
2. R. Drever, J. L. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31(2), 97–105 (1983). [CrossRef]
3. B. P. Abbott, R. Abbott, T. D. Abbott, et al., “Gw150914: The advanced ligo detectors in the era of first discoveries,” Phys. Rev. Lett. 116(13), 131103 (2016). [CrossRef]
4. G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19(4), 565–607 (2000). [CrossRef]
5. T. Akagi, A. Kosuge, S. Araki, R. Hajima, Y. Honda, T. Miyajima, M. Mori, R. Nagai, N. Nakamura, M. Shimada, T. Shizuma, N. Terunuma, and J. Urakawa, “Narrow-band photon beam via laser Compton scattering in an energy recovery linac,” Phys. Rev. Accel. Beams 19(11), 114701 (2016). [CrossRef]
6. I. Pupeza, S. Holzberger, T. Eidam, H. Carstens, D. Esser, J. Weitenberg, P. Rußbüldt, J. Rauschenberger, J. Limpert, T. Udem, A. Tünnermann, T. W. Hänsch, A. Apolonski, F. Krausz, and E. Fill, “Compact high-repetition-rate source of coherent 100 eV radiation,” Nat. Photonics 7(8), 608–612 (2013). [CrossRef]
7. O. Schwartz, J. J. Axelrod, S. L. Campbell, C. Turnbaugh, R. M. Glaeser, and H. Müller, “Laser phase plate for transmission electron microscopy,” Nat. Methods 16(10), 1016–1020 (2019). [CrossRef]
8. R. Hajima, T. Hayakawa, T. Shizuma, C. Angell, R. Nagai, N. Nishimori, M. Sawamura, S. Matsuba, A. Kosuge, M. Mori, and M. Seya, “Application of Laser Compton Scattered gamma-ray beams to nondestructive detection and assay of nuclear material,” Eur. Phys. J. Spec. Top. 223(6), 1229–1236 (2014). [CrossRef]
9. M. Fukuda, S. Araki, Y. Honda, Y. Sumitomo, N. Terunuma, J. Urakawa, K. Sakaue, and M. Washio, “Improvement of X-ray generation by using Laser Compton scattering in Laser Undulator Compact X-ray Source (LUCX),” in North American Particle Accelerator Conf. (NAPAC’16) (JACOW, 2017), pp. 1207–1209.
10. H. Shimizu, M. Akemoto, Y. Arai, et al., “X-ray generation by inverse Compton scattering at the superconducting RF test facility,” Nucl. Instrum. Methods Phys. Res., Sect. A 772, 26–33 (2015). [CrossRef]
11. T. Akagi, S. Araki, Y. Funahashi, Y. Honda, S. Miyoshi, T. Okugi, T. Omori, H. Shimizu, K. Sakaue, T. Takahashi, R. Tanaka, N. Terunuma, Y. Uesugi, J. Urakawa, M. Washio, and H. Yoshitama, “Demonstration of the stabilization technique for nonplanar optical resonant cavities utilizing polarization,” Rev. Sci. Instrum. 86(4), 043303 (2015). [CrossRef]
12. Y. Honda, H. Shimizu, T. Akagi, J. Urakawa, and T. Omori, “Development of self-start optical build-up cavity,” in Proceedings of the 7th Annual Meeting of Particle Accelerator Society of Japan (2010), pp. 1102–1103.
13. Y. Uesugi, Y. Hosaka, Y. Honda, A. Kosuge, K. Sakaue, T. Omori, T. Takahashi, J. Urakawa, and M. Washio, “Feedback-free optical cavity with self-resonating mechanism,” APL Photonics 1(2), 026103 (2016). [CrossRef]
14. Y. Hosaka, Y. Honda, T. Omori, J. Urakawa, A. Kosuge, K. Sakaue, T. Takahashi, Y. Uesugi, and M. Washio, “Mode-locked pulse oscillation of a self-resonating enhancement optical cavity,” in Journal of Physics: Conference Series, vol. 1350 (IOP Publishing, 2019), p. 012028.
15. A. Aryshev, A. Potylitsyn, G. Naumenko, M. Shevelev, K. Lekomtsev, L. Sukhikh, P. Karataev, Y. Honda, N. Terunuma, and J. Urakawa, “Monochromaticity of coherent Smith-Purcell radiation from finite size grating,” Phys. Rev. Accel. Beams 20(2), 024701 (2017). [CrossRef]
16. E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69(1), 79–87 (2001). [CrossRef]
17. Y. Uesugi, A. S. Aryshev, M. Fukuda, T. Omori, N. Terunuma, J. Urakawa, T. Takahashi, Y. Koshiba, S. Otsuka, M. Washio, Y. Hosaka, and S. Sato, “Development of self-resonating enhancement cavity operating in single-longitudinal-mode,” in CLEO: QELS_Fundamental Science, (Optical Society of America, 2020), paper JW2B.10.
18. Y. Deng and W. H. Knox, “Self-starting passive harmonic mode-locked femtosecond Yb 3+-doped fiber laser at 1030 nm,” Opt. Lett. 29(18), 2121–2123 (2004). [CrossRef]
19. T. Kurita, H. Yoshida, H. Furuse, T. Kawashima, and N. Miyanaga, “Dispersion compensation in an Yb-doped fiber oscillator for generating transform-limited, wing-free pulses,” Opt. Express 19(25), 25199–25205 (2011). [CrossRef]
20. N. Uehara and K. Ueda, “Accurate measurement of ultralow loss in a high-finesse Fabry-Perot interferometer using the frequency response functions,” Appl. Phys. B 61(1), 9–15 (1995). [CrossRef]
21. X. Liu and M. Pang, “Revealing the buildup dynamics of harmonic mode-locking states in ultrafast lasers,” Laser Photonics Rev. 13(9), 1800333 (2019). [CrossRef]
22. U. Keller, W. H. Knox, and H. Roskos, “Coupled-cavity resonant passive mode-locked Ti: sapphire laser,” Opt. Lett. 15(23), 1377–1379 (1990). [CrossRef]
23. H. A. Haus, U. Keller, and W. H. Knox, “Theory of coupled-cavity mode locking with a resonant nonlinearity,” J. Opt. Soc. Am. B 8(6), 1252–1258 (1991). [CrossRef]
24. J.-H. Lin, H.-Y. Lee, and W.-F. Hsieh, “Multiple pulses and harmonic mode locking from passive mode-locked Ytterbium doped fiber in anomalous dispersion region,” Proc. SPIE 9513, 951314 (2015). [CrossRef]
25. J. Wang, X. Bu, R. Wang, L. Zhang, J. Zhu, H. Teng, H. Han, and Z. Wei, “All-normal-dispersion passive harmonic mode-locking 220 fs ytterbium fiber laser,” Appl. Opt. 53(23), 5088–5091 (2014). [CrossRef]
26. J. Limpert, N. Deguil-Robin, I. Manek-Hönninger, F. Salin, F. Röser, A. Liem, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “High-power rod-type photonic crystal fiber laser,” Opt. Express 13(4), 1055–1058 (2005). [CrossRef]
27. B. Ortaç, M. Baumgartl, J. Limpert, and A. Tünnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34(10), 1585–1587 (2009). [CrossRef]
28. M. Baumgartl, C. Lecaplain, A. Hideur, J. Limpert, and A. Tünnermann, “66 W average power from a microjoule-class sub-100 fs fiber oscillator,” Opt. Lett. 37(10), 1640–1642 (2012). [CrossRef]
29. H. Carstens, N. Lilienfein, S. Holzberger, C. Jocher, T. Eidam, J. Limpert, A. Tünnermann, J. Weitenberg, D. C. Yost, A. Alghamdi, Z. Alahmed, A. Azzeer, A. Apolonski, E. Fill, F. Krausz, and I. Pupeza, “Megawatt-scale average-power ultrashort pulses in an enhancement cavity,” Opt. Lett. 39(9), 2595–2598 (2014). [CrossRef]
30. I. Pupeza, T. Eidam, B. Bernhardt, A. Ozawa, J. Rauschenberger, E. Fill, A. Apolonski, T. Udem, J. Limpert, Z. A. Alahmed, A. M. Azzeer, T. W. Hänsch, A. Tünnermann, and F. Krausz, “Power scaling of a high-repetition-rate enhancement cavity,” Opt. Lett. 35(12), 2052–2054 (2010). [CrossRef]
31. B. Günther, R. Gradl, C. Jud, E. Eggl, J. Huang, S. Kulpe, K. Achterhold, B. Gleich, M. Dierolf, and F. Pfeiffer, “The versatile X-ray beamline of the Munich Compact Light Source: design, instrumentation and applications,” J. Synchrotron Radiat. 27(5), 1395–1414 (2020). [CrossRef]
