Open Access
Add to BibSonomy
Abstract
A single-frequency distributed Bragg Reflector (DBR) fiber laser operating at 1091 nm was demonstrated by using a Yb:YAG crystal-derived silica fiber (YDSF). The YDSF was prepared via the molten core (MC) method, with a Yb2O3 doping concentration of 5.60 wt.% in the core, resulting in a gain coefficient of 1.45 dB/cm at 1091 nm. Employing 0.8 cm of the YDSF, we attained a single-frequency laser with a maximum output power of 145 mW and a slope efficiency of 31.8%. The laser exhibited an optical signal-to-noise ratio (OSNR) exceeding 71 dB, a linewidth of ∼34 kHz, and a stabilized relative intensity noise (RIN) at -132 dB/Hz for frequencies over 4.5 MHz. The fiber laser could serve as an outstanding seed source for high-power, narrow-linewidth fiber amplifiers operating at 1091 nm.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The ∼1.0 µm-band single-frequency fiber lasers (SFFLs) have been widely used in the fields of in coherent beam combining, high-resolution spectroscopy, gravitational wave detection, and laser LIDAR for their outstanding performance in terms of narrow linewidth, low noise, and long coherence length [1–4]. Currently, Yb3+-doped fibers are the most commonly used laser gain medium for SFFLs in the band. Although Yb3+ can provide a wide emission spectral range of 970-1200 nm [5], the reported high-efficiency SFFLs usually operate in the range of 976-1185 nm [6–9]. In contrast, achieving efficient SFFLs at wavelengths beyond 1085 nm is significantly more challenging, which is due to the small emission cross-section above 1085 nm, resulting in severe competition between the signal wavelength and the amplified spontaneous emission (ASE) parasitic laser [10]. However, the SFFLs above 1085 nm are urgently desired. For example, SFFLs operating at 1091 nm can be used in areas such as astronomy, the semiconductor industry and the biomedical field [10–15]. In particular, the 545.5 nm laser produced by direct frequency doubling can be used to excite a continuous-wave Lyman-α source based on four-wave sum-frequency mixing in mercury vapor [16] for future laser cooling of trapped antihydrogen [17] and Rydberg excitation of trapped Ca+ ions [18]. Moreover, the 363.8 nm laser generated after triple frequency doubling can be utilized to detect defects in semiconductor wafers and to excite Raman spectroscopy [13,14].
To date, the implementations of SFFLs are mainly categorized into ring-cavity [19], distributed feedback (DFB) [20], and distributed Bragg reflection (DBR) configurations [8]. The ring-cavity belongs to the structure of travelling-wave cavity, which can effectively eliminate the space burning effect, together with a narrow-band filter to achieve a single longitudinal mode (SLM) operation. In 2011, Xu et al. achieved an SFFL at 1091 nm at 22.5 mW with a slope efficiency of 5.26% using a ring-cavity [21]. Unfortunately, the mode-hopping will unavoidably occur in ring-cavity fiber lasers due to the small longitudinal mode spacing resulting from the longer laser cavity length, coupled with the high sensitivity of the narrow-band filter to environmental variations. Compared with the ring-cavity, the DFB and DBR cavities are easier to achieve stable SFFL because of their short cavity structure resulting in a large laser longitudinal mode spacing [22,23]. However, the short cavity structure severely limits the length of the gain fiber. Especially for the DBR structure, combined with the bandwidth of commercial gratings, the gain fiber length is only a few centimeters to achieve a stable SFFL in the 1 µm band. Therefore, gain fibers with high doping concentration are required to provide sufficient gain. For traditional silica fiber, the low level of rare earth doping makes it difficult to achieve high-efficient SFFL above 1085 nm. As for Yb3+-doped phosphate optical fiber, although it is capable of high rare earth ion doping, the thermal and mechanical properties are relatively poor, and the introduction of P elements will lead to a sharp decrease in the intensity of the radiation spectrum in the long-wave band. [24,25].
Recently, a newly developed Re:YAG crystal-derived silica fiber using MC method has been widely used in SFFLs [9,26–31] due to its high rare-earth doping level [32], high threshold of stimulated Brillouin scattering (SBS) [33], low photo-darkening effect [34], and good fusion splice compatibility with traditional silica fibers [35]. So far, among them, SFFLs based on Yb:YAG crystal-derived silica fiber (YDSF) have been most widely studied due to the advantages of Yb3+ such as simple energy level structure, high quantum efficiency, and no excited state absorption [9,26–28]. The first single-frequency DBR YDSF laser was demonstrated with a laser wavelength of 1064 nm and a slope efficiency of 3.8% in 2018 [26]. In 2019, our group realized the first hundred milliwatt single-frequency DBR YDSF fiber laser at 1064 nm with a slope efficiency of 18.5% [27]. In 2021, Wan et al. reported a 258 mW DBR-structured SFFL at 1030 nm based on YDSF with a slope efficiency of 28.5% [28]. After that, they achieved line-polarized single-frequency lasing at 1030 nm in a DBR cavity using YDSF with a slope efficiency of 44.4% [9]. However, the reported DBR-structured SFFLs utilizing YDSF as the gain medium all operate at conventional wavelengths (1030 nm and 1064 nm), no SFFLs operating above 1064 nm have been reported so far.
In this paper, a YDSF was prepared by the MC method with a Yb2O3 doping concentration of 5.60 wt.%. The gain factor and transmission loss of the YDSF were measured to be 1.45 dB/cm and 0.6 dB/m, respectively. Utilizing a 0.8 cm length of the YDSF, a stable single-frequency DBR laser at 1091 nm was achieved. The SFFL has a maximum output power of 145 mW with a slope efficiency of 31.8%. The OSNR was larger than 71 dB and the laser linewidth was ∼34 kHz, while the measured RIN stabilized at -132 dB/Hz at frequencies over 4.5 MHz. To the best of our knowledge, this is the first reported use of YDSF for generating SFFLs with a DBR structure in wavelengths above 1064 nm.
2. Preparation and characterization of YDSF
The preparation of YDSF using the MC method is shown in Fig. 1(a). First, a 10 at.% Yb:YAG crystal rod with a diameter of 1.6 mm and a length of 20 mm was put into a high-purity quartz tube to form a fiber preform. A section of the quartz tube was sealed with an inner diameter of 2.8 mm and an outer diameter of 10 mm. The temperature of the graphite furnace was raised to about 2050°C to match the melting point temperature of the YAG crystals. During the drawing process, the fiber core was transformed into yttrium-aluminum-silicate (YAS) glass due to the mutual diffusion of the quartz tube and the melted Yb:YAG crystal at high temperature, as shown in Fig. 1(b). By controlling the temperature, feeding speed and pulling speed, we successfully fabricated a YDSF with a cladding diameter of 125 µm. Figure 1(c) shows the external morphology of the YDSF, while Fig. 1(d) displays the microscopic image of the YDSF cross-section. The YDSF had a core diameter of approximately 20 µm and a cladding diameter of 125 µm. The distinct boundary between the core and cladding affirms a good waveguide structure of the YDSF.
Fig. 1. (a) Schematic diagram of the MC method. (b) Schematic of the interdiffusion of Yb:YAG and quartz cladding. (c) External morphology of the YDSF. (d) Microscopic image of the YDSF end face.
Fig. 2. (a) One-dimensional element distribution of the fiber cross-section. (b) Two-dimensional element distribution of fiber cross-section. (c) Refractive index (RI) difference profiles of the fiber cross-section.
The elemental distributions and the refractive index (RI) difference of the YDSF cross-section were measured using an energy dispersive analyzer (EDS, Thermo Scientific UltraDry) and a refractive index profiler, respectively. Figure 2(a) displays the elemental composition of YDSF. In the core, the mass percentages of SiO2, Y2O3, Al2O3, and Yb2O3 are 52.94%, 21.32%, 20.14%, and 5.60%, respectively. Obviously, interdiffusion occurred between the Yb:YAG crystal and the quartz cladding. The two-dimensional distribution of the elements is shown in Fig. 2(b). The elements Yb, Y, and Al were uniformly distributed in the core, while the Si and O element were distributed both in the core and the cladding. Figure 2(c) shows the RI distribution of the YDSF. The trend of the RI distribution is essentially the same as that of the elements, showing a gradual distribution at the edges due to interdiffusion. The RI difference (Δn) between the core and cladding is 0.092, corresponding to a numerical aperture (NA) of 0.516.
The absorption spectra of the YDSF was measured using a broadband light source (HLS-1, Kewlab) and an optical spectrum analyzer (AQ6370D, Yokogawa). As shown in Fig. 3(a), the YDSF has obvious characteristic absorption peaks near 915 nm and 976 nm. The absorption coefficients at 915 nm and 976 nm are 9.2 dB/cm and 33.5 dB/cm, respectively. These high absorption coefficients result from the high concentration of Yb3+ ion doping. Consequently, this implies a high core absorption efficiency, allowing for efficient absorption of strong pumping with a short gain fiber. The fiber transmission loss was measured by the cut-back method. A 1550 nm laser was chosen as the test light source in the experiment. As shown in the inset of Fig. 3(a), the transmission loss of the prepared YDSF at 1550 nm is 0.6 dB/m. Figure 3(b) shows the normalized fluorescence spectra of the fiber sample in the range of 925 nm-1250 nm under 915 nm laser pumping. The YDSF has strong emission peaks at 976 nm and 1022 nm, which correspond to the 5F5/2 to 5F7/2 energy levels of Yb3+ ions. The inset of Fig. 3(b) shows the emission spectra of the fiber in the range of 1050 nm-1100 nm. It can be seen that the fluorescence intensity of the fiber at 1091 nm is about 1/9 of that at 1022 nm.
Fig. 3. (a) Absorption spectrum of YDSF. Inset: the transmission loss of the YDSF at 1550 nm. (b) Emission spectrum of YDSF in the wavelength range of 925-1250 nm. Inset: Emission spectrum of YDSF fiber in the wavelength range of 1050-1110 nm.
The small-signal gain coefficient of the YDSF at 1091 nm was measured through a fiber amplification system. The experimental setup is shown in Fig. 4(a). A 1091 nm seed laser and 976 nm pump light were simultaneously injected into a 2 cm long YDSF fiber through a filter wavelength division multiplexer (FWDM). Another FWDM was employed to separate the amplified signal light from the remaining pump light. Figure 4(b) shows the gain coefficients versus pump power with different signal power. At a signal power of -5 dBm and a pump power of 315 mW, the fiber’s gain coefficient at 1091 nm reached 1.45 dB/cm. The spectrum of the output signal is shown in Fig. 4(c), and the laser OSNR is ∼ 38.3 dB.
Fig. 4. (a) Schematic diagram of the small signal amplifier. (b) Fiber gain coefficients at different pump powers. (c) Signal output spectrum at a pump power of 315 mW.
To demonstrate the superior performance of the YDSF in emitting light at 1091 nm, we compared the gain characteristics and fluorescence properties of YDSF at 1091 nm to those of three types of commercially Yb3+-doped silica fibers. The gain characteristics of several fiber samples at 1091 nm were measured using the small-signal amplifier setup illustrated in Fig. 4(a). The injected signal powers were set at -5 dBm and the measurements were presented in Fig. 5(a), where the gain coefficients of the YDSF, Yb406, Yb1200-4/125, and SM-YSF-HI-HP fibers at 1091 nm wavelength were about 1.45 dB/cm, 0.92 dB/cm, 0.38 dB/cm, and 0.12 dB/cm, respectively. At pump powers less than 58 mW, the gain achieved with the YDSF is lower than that obtained with Yb406 fiber, primarily due to the self-absorption resulting from the higher Yb3+ concentration. In Fig. 5(b), the normalized fluorescence spectra of the four fibers under 980 nm laser excitation are presented. The power of 980 nm laser was set at 150 mW, and all the tested fiber samples were 1 cm in length. The fluorescence intensity of YDSF is significantly higher than that of the other three silica fibers. Figure 5(b) inset displays the fluorescence spectra of these samples in the 1078-1132 nm range. The fluorescence intensity at 1091 nm for Yb406, Yb1200-4/125, and SM-YSF-HI-HP fibers is ∼56.25%, ∼21.88%, and ∼7.30% of that for YDSF, respectively. These experimental results are consistent with the measured laser gain.
Fig. 5. (a) Gain coefficient versus pump power for four fiber samples. (b) Normalized fluorescence spectra of four fiber samples within the 1000-1200 nm wavelength range under 980 nm laser excitation. Inset: The emission spectra of four fiber samples within the 1078-1132 nm wavelength range under 980 nm laser excitation.
Furthermore, we investigated the output characteristics of DBR-structured fiber laser at 1091 nm employing YDSF and Yb406, respectively. The experimental setup is shown in Fig. 6(a). The YDSF and Yb406, each with a length of 0.8 cm, were fused separately with a pair of wavelength-matched 1091 nm fiber Bragg gratings (FBGs) sets to form a resonant cavity. The FBGs consist of a low reflectance FBG (LR-FBG) with a peak reflectance of approximately 80% at 1091 nm and a 3-dB bandwidth of 0.05 nm, as well as a high reflectance FBG (HR-FBG) with a peak reflectance of ≥ 99.5% at 1091 nm and a 3-dB bandwidth of 0.35 nm. The LR-FBG and HR-FBG were written on a polarization-maintained (PM) passive fiber (Nufern, PM980) and a passive fiber (Nufern, 1060-XP), respectively. The 976 nm pump light was injected backward into the laser cavity via a 976/1091nm PM wavelength division multiplexer (PM-WDM). The signal side of the PM-WDM was connected to a 1091 nm PM isolator (PM-ISO) to prevent backscattered light. As shown in Fig. 6(b), when the pump power was 471 mW, the obtained maximum output power for the YDSF and Yb406 were 151.2 mW and 54.2 mW, respectively. The corresponding slope efficiencies were 33.68% and 11.90%, respectively. The slope efficiency of fiber laser using YDSF is ∼2.83 times higher than that of the one using Yb406, indicating that YDSF is more suitable for generating 1091 nm single-frequency laser.
Fig. 6. (a) The schematic diagram of the fiber laser at 1091 nm. (b) Output powers with different pump powers employing YDSF and Yb406, respectively.
3. Single-frequency YDSF laser at 1091 nm
A 1091 nm ultrashort-cavity DBR single-frequency fiber laser was realized based on the YDSF fiber, as shown in Fig. 7. A 0.8 cm long YDSF fiber was directly fused to the grid portion of the HR-FBG and LR-FBG mentioned in Fig. 6(a). Due to the birefringence effect of the PM980 fiber, only the reflected wavelength in the direction of the slow axis of the LR-FBG matches that of the HR-FBG, so the output laser is in a single-polarization state. The 976 nm pump laser was injected into the cavity via a PM-WDM. The entire cavity was encapsulated in an aluminum heat sink block with a temperature control accuracy of 0.01°C. Meanwhile, to prevent the backward scattered light from affecting the cavity stability, a PM-ISO was fused at the output of the PM-WDM. The theoretically calculated effective cavity length of the laser cavity is ∼1.406 cm, resulting in a longitudinal mode spacing of ∼7.11 GHz [36]. Combined with the LR-FBG bandwidth limitations (12.60 GHz), the cavity supports only a single longitudinal mode operation.
The output power of the fiber laser versus the pump power is shown in Fig. 8(a). The threshold of the fiber laser is 12 mW and the output power increases linearly with the pump power. A maximum laser output power of 145 mW was obtained at pump power of 471 mW, corresponding to a slope efficiency of 31.8%. To the best of our knowledge, this is the highest output power and highest slope efficiency achieved by a single-frequency laser utilizing Yb3+-doped fiber in the wavelength range above 1064 nm. No output power saturation was observed during the experiment. The laser output power at 128 mW was continuously monitored over a 4-hour period, as indicated in the inset of Fig. 8. The power stability of the fiber laser was found to be ∼0.35% (RMS). The output spectral characteristics of the fiber laser was measured using a spectrum analyzer (AQ6370D, Yokogawa). As shown in Fig. 8(b), the center wavelength of the laser is 1091.2 nm. The inset of Fig. 8(b) displays the laser spectrum measured within the 970-1200 nm range. There is no significant shortwave ASE, and the laser OSNR exceeds 71 dB. In addition, the polarization state of the SFFL at 1091 nm was measured using a half-wave plate and a polarizing beam splitter cube. The polarization-extinction ratio (PER) was calculated to be 24.5 dB.
Fig. 8. (a) The output power of the 1091 nm SFFL with respect to the input pump power. Inset: The laser stability recorded within 4 hours at 128 mW. (b) Output spectrum of 1091 nm SFFL in the wavelength range of 1089.5-1093.5 nm. Insert: Output spectrum of the fiber laser in the wavelength range of 970-1200 nm.
The longitudinal mode characteristics of the 1091 nm single-frequency YDSF laser were monitored by a scanning Fabry-Perot (F-P) interferometer with a free spectral range (FSR) of 1.5 GHz and a fineness of 30. As shown in Fig. 9(a), the DBR fiber laser consistently operated in single longitudinal mode at its highest output power, and it was monitored for 1 hour without any mode hopping. The laser linewidth was measured using the delayed self-external difference method. The measurement system uses a 48 km single-mode fiber (28-e) as a fiber delay line, offering a linewidth measurement resolution of 4.2 kHz [37]. As shown in Fig. 9(b), the laser linewidth increases from 11 kHz to 34 kHz when the output power increased from 33 mW to 145 mW. The inset of Fig. 9(a) shows a typical outlier signal with a Lorentzian function at maximum output power. The 20-dB linewidth of the outlier signal is ∼0.68 MHz, indicating a laser linewidth of ∼34 kHz. This broadening of the laser linewidth may be attributed to the growing ASE resulting from heat accumulation in the cavity as the laser power increased [38].
Fig. 9. (a) Longitudinal modeling of the 1091 nm single-frequency YDSF laser. (b) Linewidth versus pump power for a single-frequency fiber laser. Inset: The laser linewidth at maximum output power.
The relative intensity noise (RIN) of the single-frequency DBR fiber laser was measured using a spectrum analyzer (Keysight N9020B) with a resolution bandwidth of 5 kHz. Figure 10 shows the RIN spectrum of the single-frequency DBR fiber laser in the frequency range 0-10 MHz at a maximum laser power of 145 mW. The RIN peak is -112 dB/Hz at a frequency of 2.1 MHz, after which it rapidly decreases with increasing frequency. The RIN stabilizes at - 132 dB/Hz at frequencies above 4.5 MHz.
4. Conclusion
In summary, we have demonstrated a high-efficiency stable single-frequency DBR fiber laser at 1091 nm based on a YDSF fiber. The YDSF core, containing 5.60 wt.% Yb2O3 doping, exhibits a high gain coefficient of 1.45 dB/cm at 1091 nm. Utilizing a 0.8 cm YDSF, a maximum output power of 145 mW single-frequency laser was obtained, corresponding to a slope efficiency of 31.8%. To the best of our knowledge, this is the highest output power and highest slope efficiency achieved in SFFLs based on Yb3+-doped fiber in the wavelength band above 1064 nm. At maximum output power, the OSNR exceeded 71 dB, and the laser linewidth was ∼34 kHz. In addition, the measured RIN stabilized at -132 dB/Hz for frequencies over 4.5 MHz. The experimental results show that YDSF holds significant promise for single-frequency lasers above the 1064 nm wavelength band.
Funding
National Natural Science Foundation of China (62075117, 62075116); Taishan Scholar Foundation of Shandong Province (tsqn202103004); Key research program of Shandong Province (2020JMRH0302); Natural Science Foundation of Shandong Province (ZR2020MF114); Qilu Young Scholars program of Shandong University.
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. Y. X. Ma, X. L. Wang, J. Y. Leng, et al., “Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique,” Opt. Lett. 36(6), 951–953 (2011). [CrossRef]
2. T. Chen, W. Kong, H. Liu, et al., “Frequency-stepped pulse train generation in an amplified frequency-shifted loop for oxygen A-band spectroscopy,” Opt. Express 26(26), 34753–34762 (2018). [CrossRef]
3. F. Wellmann, M. Steinke, F. Meylahn, et al., “High power, single-frequency, monolithic fiber amplifier for the next generation of gravitational wave detectors,” Opt. Express 27(20), 28523–28533 (2019). [CrossRef]
4. C. F. Abari, A. T. Pedersen, and J. Mann, “An all-fiber image-reject homodyne coherent Doppler wind lidar,” Opt. Express 22(21), 25880–25894 (2014). [CrossRef]
5. H. W. Zhang, H. Xiao, P. Zhou, et al., “322 W single-mode Yb-doped all-fiber laser operated at 1120 nm,” Appl. Phys. Express 7(5), 052701 (2014). [CrossRef]
6. K. AlYahyaei, X. S. Zhu, L. Z. Li, et al., “Ultralow-quantum-defect single-frequency fiber laser,” Opt. Lett. 48(14), 3817–3820 (2023). [CrossRef]
7. S. H. Xu, Z. M. Yang, W. N. Zhang, et al., “400 mW ultrashort cavity low-noise single-frequency Yb3+-doped phosphate fiber laser,” Opt. Lett. 36(18), 3708–3710 (2011). [CrossRef]
8. S. J. Fu, X. S. Zhu, J. Zong, et al., “Diode-pumped 1.15 W linearly polarized single-frequency Yb3+-doped phosphate fiber laser,” Opt. Express 29(19), 30637–30643 (2021). [CrossRef]
9. Y. Wan, J. X. Jiang, C. Jiang, et al., “Over 60% Optical-to-Optical Conversion Efficiency Linearly Polarized Single-Frequency Fiber Laser Based on Yb: YAG Crystal-Derived Silica Fiber,” J. Lightwave Technol. 41(16), 5452–5459 (2023). [CrossRef]
10. M. Stappel, R. Steinborn, D. Kolbe, et al., “A high power, continuous-wave, single-frequency fiber amplifier at 1091 nm and frequency doubling to 545.5 nm,” Laser Phys. 23(7), 075103 (2013). [CrossRef]
11. M. Stappel, D. Kolbe, and J. Walz, “Continuous-wave, double-pass second-harmonic generation with 60% efficiency in a single MgO:PPSLT crystal,” Opt. Lett. 39(10), 2951–2954 (2014). [CrossRef]
12. F. Markert, M. Scheid, D. Kolbe, et al., “4W continuous-wave narrow-linewidth tunable solid-state laser source at 546nm by externally frequency doubling a ytterbium-doped single-mode fiber laser system,” Opt. Express 15(22), 14476–14481 (2007). [CrossRef]
13. M. Yashima, M. Kakihana, R. Shimidzu, et al., “Ultraviolet 363.8-nm Raman Spectroscopic System for in Situ Measurements at High Temperatures,” Appl. Spectrosc. 51(8), 1224–1228 (1997). [CrossRef]
14. V. Poborchii, T. Tada, T. Kanayama, et al., “Optimization of tip material and shape for near-UV TERS in Si structures,” J. Raman Spectrosc. 40(10), 1377–1385 (2009). [CrossRef]
15. M. Rajalakshmi, A. K. Arora, B. S. Bendre, et al., “Optical phonon confinement in zinc oxide nanoparticles,” J. Appl. Phys. 87(5), 2445–2448 (2000). [CrossRef]
16. M. Scheid, D. Kolbe, F. Markert, et al., “Continuous-wave Lyman-α generation with solid-state lasers,” Opt. Express 17(14), 11274–11280 (2009). [CrossRef]
17. G. Gabrielse, R. Kalra, W. S. Kolthammer, et al., “Trapped Antihydrogen in Its Ground State,” Phys. Rev. Lett. 108(11), 113002 (2012). [CrossRef]
18. D. Kolbe, M. Scheid, and J. Walz, “Triple resonant four-wave mixing boosts the yield of continuous coherent vacuum ultraviolet generation,” Phys. Rev. Lett. 109(6), 063901 (2012). [CrossRef]
19. X. B. Gao, Z. H. Cong, Z. G. Zhao, et al., “Single-Frequency kHz-Linewidth 1070 nm Laser Based on Yb:YAG Derived Silica Fiber,” IEEE Photonics Technol. Lett. 32(14), 895–898 (2020). [CrossRef]
20. Y. Tao, M. Jiang, C. Li, et al., “Low-threshold 1150 nm single-polarization single-frequency Yb-doped DFB fiber laser,” Opt. Lett. 46(15), 3705–3708 (2021). [CrossRef]
21. J. Xu, X. Dong, J. Leng, et al., “Efficient, 62.5 watts all-fiber single-mode 1091 nm MOPA laser,” Front. Optoelectron. China 4(4), 426–429 (2011). [CrossRef]
22. Q. Fang, Y. Xu, S. J. Fu, et al., “Single-frequency distributed Bragg reflector Nd doped silica fiber laser at 930 nm,” Opt. Lett. 41(8), 1829–1832 (2016). [CrossRef]
23. Y. Tao, S. Zhang, M. Jiang, et al., “High power and high efficiency single-frequency 1030 nm DFB fiber laser,” Opt. Laser Technol. 145, 107519 (2022). [CrossRef]
24. A. S. Kurkov, “Oscillation spectral range of Yb-doped fiber lasers,” Laser Phys. Lett. 4(2), 93–102 (2007). [CrossRef]
25. M. A. MelKumov, I. A. Bufetov, K. S. Kravtsov, et al., “Lasing parameters of ytterbium-doped fibers doped with P2O5 and Al2O3,” Quantum Electron. 34(9), 843–848 (2004). [CrossRef]
26. Y. M. Zhang, W. W. Wang, J. Li, et al., “Multi-component yttrium aluminosilicate (YAS) fiber prepared by melt-in-tube method for stable single-frequency laser,” J. Am. Ceram. Soc. 102(5), 2551–2557 (2019). [CrossRef]
27. Z. J. Liu, Y. Y. Xie, Z. H. Cong, et al., “110 mW single-frequency Yb: YAG crystal-derived silica fiber laser at 1064 nm,” Opt. Lett. 44(17), 4307–4310 (2019). [CrossRef]
28. Y. Wan, J. X. Wen, C. Jiang, et al., “Over 255 mW single-frequency fiber laser with high slope efficiency and power stability based on an ultrashort Yb-doped crystal-derived silica fiber,” Photonics Res. 9(5), 649–656 (2021). [CrossRef]
29. Y. Y. Xie, Z. H. Cong, Z. G. Zhao, et al., “Preparation of Er:YAG crystal-derived all-glass silica fibers for a 1550-nm single-frequency laser,” J. Lightwave Technol. 39(14), 4769–4775 (2021). [CrossRef]
30. G. Q. Qian, M. B. Wu, G. W. Tang, et al., “Single-frequency distributed Bragg reflector Tm: YAG ceramic derived all-glass fiber laser at 1.95 µm,” Chinese Phys. B 31(12), 124205 (2022). [CrossRef]
31. Z. S. Wei, J. Z. Luan, L. Huang, et al., “Single-frequency fiber laser of 315 mW at 1940 nm based on a Tm:YAG/Ho:YAG-co-derived silica fiber,” Opt. Lett. 48(19), 5109–5112 (2023). [CrossRef]
32. P. D. Dragic, J. Ballato, T. Hawkins, et al., “Feasibility study of Yb:YAG-derived silicate fibers with large Yb content as gain media,” Opt. Mater. (Amsterdam, Neth.) 34(8), 1294–1298 (2012). [CrossRef]
33. P. Dragic, P.-C. Law, J. Ballato, et al., “Brillouin spectroscopy of YAG-derived optical fibers,” Opt. Express 18(10), 10055–10067 (2010). [CrossRef]
34. C. Z. Li, Z. X. Jia, Z. H. Cong, et al., “Gain characteristics of ytterbium-doped SiO2–Al2O3–Y2O3 fibers,” Laser Phys. 29(5), 055804 (2019). [CrossRef]
35. S. P. Zheng, J. Li, C. L. Yu, et al., “Preparation and characterizations of Nd:YAG ceramic derived silica fibers drawn by post-feeding molten core approach,” Opt. Express 24(21), 24248–24254 (2016). [CrossRef]
36. Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, et al., “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006). [CrossRef]
37. P. Horak and W. H. Loh, “On the delayed self-heterodyne interferometric technique for determining the linewidth of fiber lasers,” Opt. Express 14(9), 3923–3928 (2006). [CrossRef]
38. G. Agrawal, “Line narrowing in a single-mode injection laser due to external optical feedback,” IEEE J. Quantum Electron. 20(5), 468–471 (1984). [CrossRef]
