Open Access
Add to BibSonomy
Abstract
Throughout the development of single frequency fiber lasers (SFFLs), gain fiber is one of the most important components, which can greatly affect the quality of SFFLs. Here, we fabricated an Er: YAG crystal-derived silica fiber (EYDSF) using a CO2 laser-heating drawing technique, with a high gain coefficient of 1.74 dB/cm. Employing the EYDSF of only 10 cm as a gain medium, we constructed a continuous-wave ring-cavity SFFL with an all-fiber system. An ultra-narrow linewidth <660 Hz was achieved harnessing a homemade low-concentration Er-doped silica fiber as a saturable absorber. Importantly, the SFFL output power was up to 32.7 mW at 1560 nm. What’s more, no multi longitudinal mode or mode hopping were found in 2 hours, and the fluctuation of power was <0.63% in 8 hours. Furthermore, the relative intensity noise was lower to -145 dB/Hz at frequencies over 1 MHz. The results indicate that the ring-cavity SFFL has desirable performance in output power, linewidth, stability and noise, which serves a prospective candidate applied to coherent optical communications, high-precision sensors, laser radars and other advanced fields.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Er-doped single-frequency fiber lasers (SFFL) have been put into various applications such as gravitational wave detection [1], coherent optical communication [2], biomedical detection [3] and high-precision sensing [4]. In order to meet the increasing demands for potential usage, the performance of SFFLs, including output power, slope efficiency, linewidth and noise, has become a research focus [5–8], which has strong correlation with the feasibility, stability, and accuracy of SFFL-based systems. Three kinds of cavity schemes are commonly applied to SFFLs: distributed feedback (DFB) [9], distributed Bragg reflector (DBR) [10], and traveling-wave ring cavity [11]. DFB and DBR configurations have the advantages of high slope efficiency and output power. However, a sharp increase in linewidth and relative intensity noise (RIN) may occur due to heat accumulation in the ultra-short gain fiber, which is detrimental to narrow-linewidth and low-noise lasing output. In comparison, a ring-cavity structure is an effective method to solve these problems. However, since the length of the ring cavity itself is relatively long, the phenomenon of multi-longitudinal mode (MLM) may occur. Accordingly, several ultra-narrow bandwidth filters were proposed to get single-longitudinal mode (SLM) operation, including Fabry-Perot filters [12], multi-ring filters [13] and induced gratings using unpumped gain fibers as saturable absorbers (SAs) [14]. Among these methods, the solution with SA is characterized with all-fiber structure and wavelength tunability. Furthermore, the bandwidth and insertion loss of the induced grating can be purposely engineered through the design of SA fiber, such as doping concentration, refractive index, and length, which provide tremendous flexibility for the ring cavity to get a SLM laser output.
However, further optimization in parameters of ring-cavity SFFLs such as output power and stability is limited by the typical silica Er-doped fibers (EDF) with relatively low gain coefficient. Although the longer cavity length induced by silica EDFs is beneficial to obtain a narrow-linewidth laser, the output power and stability are restricted mainly due to the caused higher cavity loss and vulnerability to ambient environment, respectively. The application of high-gain active fiber thus can be the key to solve this problem. As for the selection of gain fibers, new-type YAG crystal-derived silica fibers (YDSFs), fabricated with yttrium aluminosilicate glass cores, could be a good candidate, which have been widely proposed and developed in recent years [15–17]. Compared with other multi-component glass core fibers such as phosphate fiber [18] and bismuth fiber [19], YDSFs are dominant in stable physical and chemical properties, and strong adaptability to commercial silica fibers, which are significant highlights for the long-term reliability of SFFLs. In 2021, Xie et al. fabricated an Er: YAG crystal-derived silica fiber (EYDSF), and thus realized a 1.55-µm pulsed DBR SFFL with a high output power of 24.2 mW and slope efficiency of 15.1%, which is the first to get an EYDSF-based SFFL operating at ∼1.55 µm [20]. However, because of the severe self Q-switching effect [21], almost no continuous-wave (CW) SFFLs based on EYDSFs have been reported, to the best of our knowledge.
In this work, we fabricated an EYDSF with high gain coefficient based on a CO2 laser-heating drawing technique, and then using the EYDSF as a gain medium, we explored an all-fiber CW working ring-cavity SFFL in which a homemade low-concentration EDF was exploited as a SA. The characteristics of the SFFL have been systematically demonstrated, including output power, linewidth, stability, and noise.
2. Characterization of Er-doped fiber and ring-cavity structure
2.1 Er: YAG crystal-derived silica fiber
The process of fiber fabrication is schematically shown in Fig. 1. The preform of EYDSFs was made of 6.5 at. % Er: YAG crystal rod (Lanjing Optoelectronic Technology, China) and a high-purity silica tube. The Er: YAG rod was 1.8 mm in diameter, while the outer diameter of the silica tube was 20 mm. EYDSFs were fabricated using the molten-core method [22] at ∼2100 °C on a CO2 laser-heating drawing tower. Compared with conventional graphite heating, CO2 laser-heating drawing takes more advantages in parameter control and reduction in cladding diffusion due to faster heating speed and smaller high temperature zone [23]. The preform feeding speed in drawing process was 0.04 mm/min, while the fiber drawing speed was 1 m/min. By simultaneously balancing the fiber feeding and drawing speed, uniform EYDSFs were obtained. No obvious scattering point was found as the transmission of red light through the obtained fiber, indicating a complete bubble-free waveguide structure.
Fig. 1. Schematic diagram of (a) preform preparation and (b) fiber drawing in the EYDSF fabrication process
The core element distributions were measured with an electron probe micro-analyzer (EPMA-1720, SHIMADZU, Japan) along the diameter of the EYDSF. As presented in Fig. 2(a), a tremendous mutation of element distribution is demonstrated at the boundary of core and cladding. The existence of element Si in the fiber core suggests the diffusion from the fiber cladding to core. The concentrations of SiO2, Y2O3, Al2O3, and Er2O3 are 53.94, 29.13, 13.44, and 3.49 wt.%, respectively. The element of Er is uniformly distributed in the fiber core.
Fig. 2. (a) Element distribution curve along the diameter of EYDSF core. (b) The refractive index distribution of EYDSF (The inset is the profile of the EYDSF observed under a microscope).
The refractive index distribution of the EYDSF, as shown in Fig. 2(b), is measured and analyzed by a fiber refractive index analyzer (S14, Photon Kinetics Inc., U.S.). The profile of the fabricated EYDSF sample can be seen in the inset, which demonstrates a clear boundary of the fiber cladding and core. The EYDSF has a uniform core and cladding measured as 12.5 µm and 126.4 µm, respectively. The calculated relative refractive index contrast and numerical aperture was up to 3.2% and 0.38 at 633 nm. The core refractive index is relatively high, mainly due to the high-concentration doping materials in the fiber core.
The absorption characteristic of the fabricated EYDSF, as shown in the Fig. 3(a), was tested using an optical spectrum analyzer (OSA, AQ6315, YOKOGAWA, Japan) with the cut-back method. The absorption peaks of the EYDSF are located at 652.4 nm, 798 nm, 978.7 nm, and 1532.2 nm, intensities of which are respectively 6.35 dB/cm, 1.35 dB/cm, 2.13 dB/cm, and 6.15 dB/cm. The jagged peaks from 1200 nm to 1400 nm suggests the existence of interference at the fusion point because of mode-field mismatch. The background loss was measured to be 0.31 dB/cm at 900 nm, which can be further optimized by purification of the precursor materials and development in fabrication process.
Fig. 3. (a) Absorption spectrum of EYDSF from 600 nm to 1600 nm. (b) The excitation and emission spectrum of EYDSF at 980 nm (black) and 1532 nm (red). (c) The fluorescence decay curve of the Er: YAG crystal and EYDSF excited at 980 nm. (d) The net gain coefficient as a function of pump powers with different signal powers.
The excitation and emission spectrum, as well as fluorescence decay curves of the EYDSF were measured using a fluorescence spectrophotometer (Edinburgh FLS-980, England). Seen from Fig. 3(b), the optimal excitation and emission peaks of the EYDSF are located at 980 nm and 1532 nm, respectively. Excited at 980 nm, the EYDSF has a fluorescence decay time measured as ∼6.5 ms, which is much shorter than that of the Er: YAG crystal (∼11.49 ms), as shown in Fig. 3(c). The main reason for it is the existence of concentration quenching effect due to the solubility difference of Er3+ between YAG crystal and EYDSF core [24].
In order to evaluate the potential of laser performance, amplification characteristics were investigated based on forward pump scheme using signal light at 1560 nm and pump light at 980 nm. A 2 cm EYDSF was employed as the gain medium, and three signal light powers, -20, -10 and 3 dBm, were selected. The gain coefficient of the obtained EYDSF is shown in Fig. 3(d) as the function of pump power. At a low pump power of <50 mW, a negative gain coefficient was observed mainly due to the absorption of EYDSF. As the rise of pump power, the gain coefficient increased gradually and finally saturated. The gain coefficient reached 1.74 dB/cm, 1.69 dB/cm, and 1.61 dB/cm with the signal of -20, -10 and 3 dBm, respectively. Moreover, the properties of EYDSF have been compared with those of different multi-component EDFs listed in Table 1. Consequently, although the gain coefficient of obtained EYDSF is inferior to that of phosphate fiber due to relatively higher Er3+ solubility in phosphate glass, the homemade EYDSF with gain coefficient of 1.74 dB/cm has clearly demonstrated advantages compared with other silica or bismuth-based EDFs.
Table 1. Basic parameters of different Er3+-doped multi-component glass fibers
2.2 Ring cavity setup and saturable absorber mechanism
The experimental setup of the single-frequency ring-cavity fiber laser is shown in Fig. 4. A 10-cm EYDSF was spliced into the cavity as a gain medium. As seen in Fig. 4(a), the fusion splicing between EYDSF and SMF is smooth and uniform. A single-mode wavelength division multiplexer (WDM) was applied to input the 980 nm pump as well as output the amplified spontaneous emission (ASE). An optical circulator (CIR) ensures the unidirectional transmission of light. Propagating through the SA fiber, the ASE light is reflected by a fiber Bragg grating (FBG), forming a complete ring-cavity structure. The total length of the ring cavity was 6.5 m. The FBG has a reflectivity of 74.1% and a 3 dB bandwidth of 0.08 nm, serving not only as a wavelength selector but also as a laser output port. A polarization controller (PC) was equipped in the cavity to control the polarization in advantage of stable SLM operation. A 1.6 m homemade low-concentration EDF was inserted into the cavity as a SA, which can provide ultra-narrow induced grating in advantage of SLM [27]. In addition, since the self-pulsing threshold increases with the cavity loss [28], the additional loss induced by the SA can suppress the self Q-switching effect of the EYDSF.
Fig. 4. Experimental setup of ring-cavity SFFL based on EYDSF and SA. (a) Photograph of the fusion point between EYDSF and SMF. (b) The absorption spectrum and (c) refractive index distribution of the SA fiber (inset shows the profile of the SA fiber).
The schematic diagram of transient-induced grating generated in a SA fiber compared with typical single mode fiber (SMF) is demonstrated in the first-row figures of Fig. 5(a) and (b). As the bidirectional propagating ASE light Ai and Bi encounters in the SA fiber, a standing wave occurs due to the light interference. Because of the millisecond-order relaxation of EDF, the interference creates spatial burning holes inside the fiber core, leading to periodic change of absorption coefficient, which doesn’t exist in typical SMFs. According to the Kramer-Kronig relation [29], the refractive index is approximately proportional to the absorption coefficient of fiber, and thus an induced grating is formed in the SA fiber along the periodical standing wave [30]. Therefore, the absorption of the SA fiber is significant for the stable formation of induced gratings. The absorption spectrum of the selected SA fiber is shown in Fig. 4(b), indicating a low absorption of 4.8 dB/m at 1560 nm. In addition, the refractive index difference between the fiber core and cladding of the SA fiber was approximately 0.007, and the refractive index of the fiber core is 1.463, shown in Fig. 4(c).
Fig. 5. Schematic diagram and simulated spectra of the narrow-band gratings (a) without SA and (b) with SA.
In order to assess the performance of narrowband grating induced by the homemade low-concentration EDF, a simulation of the reflection spectrum was conducted. The relationship between the bidirectional light input (Ai, Bi) and output (Ao, Bo) of the grating can be given by Eq. (1) according to Transfer Matrix Theory [31], where F is the transfer matrix:
The equivalent bandwidth ($\Delta f$) of the grating can be further estimated based on Coupled-Mode Theory by the Eq. (2), where c is the speed of light, and $\varepsilon $ is the dimension compensation parameter of mode coupling, estimated as 1 m:
According to Eq. (1), the simulated reflection spectra of the induced grating and commercial FBG are demonstrated in the second-row figures of Fig. 5(a) and (b). The commercial FBG with 0.08 nm bandwidth definitely cannot meet the demand of a stable SLM operation in the ring-cavity configuration. However, as for our 1.6 m homemade SA fiber, an ultra-narrow induced grating is produced. In addition, the equivalent bandwidth is less than 11.5 MHz according to Eq. (2), which preliminarily indicates the potential of the SA fiber as a longitudinal mode filter.
Furthermore, for a ring-cavity configuration, the longitudinal mode spacing ($\Delta v$) follows the Eq. (3):
where n is the refractive index of fiber core and l is the length of the ring cavity.In order to get a SLM operation, the relationship between $\Delta v$ and $\Delta f$ should be satisfied with the expression (4):
Therefore, the calculated longitudinal mode spacing was 31.8 MHz. As shown in the third-row figure of Fig. 5(b), the bandwidth of induced grating is much smaller than twice of the longitudinal mode spacing, which completely meets the condition of SLM in the expression (4). Consequently, by using a 1.6 m homemade low-concentration EDF as SA, it is theoretically feasible for the manufacture of the ring-cavity system to operate in the SLM.
3. Performance of the single-frequency ring-cavity laser
The longitudinal-mode characteristics of the ring cavity was evaluated based on Mach-Zehnder interference. An 80 MHz acoustic optical modulator (AOM) was used to generate a frequency shift. Figure 6(a) shows the radio frequency (RF) beating intensity of the output fiber laser at different pump powers, measured by an electrical spectrum analyzer (ESA, R&S, Germany). The frequency detection span was set from 30 MHz to 300 MHz, covering the range of 270 MHz, and the resolution bandwidth was 100 kHz. Only one prominent beating peak at 80 MHz was found and no other peaks existed as pump power rising, indicating that a SLM operation has been obtained in the demonstrated ring-cavity system.
Fig. 6. Radio frequency beating intensity of the SFFL (a) at different pump powers and (b) pumped at 950 mW in 120 mins.
To ensure the long-term stability of the longitudinal mode, beating spectrum was continuously monitored for every 5 seconds in 120 mins. As seen in Fig. 6(b), no other longitudinal mode was found except for a steady beating peak at 80 MHz. Consequently, due to the ultra-narrow grating induced by the 1.6 m homemade SA, a long-term stable SLM operation without any mode hopping is promised.
The output power performance of the SFFL with regard to pump power is shown in Fig. 7(a), measured by a power meter (PM100D, Thorlabs, U.S.). A high maximum single-frequency output power of 32.7 mW was observed when the SFFL was pumped at 950 mW. The slope efficiency and threshold power of the SFFL was 5.3% and 382 mW, respectively. The output power was continuously monitored for every 5 seconds in 8 hours. As shown in Fig. 7(b), the fluctuation of output power (FOP) was less than 0.63% of the average power, and in the range from 3 to 5 hours, the variation of the power was even smaller than 0.13 mW as seen in the inset. The majority of the weak power fluctuation may mainly result from pump-induced thermal effects [33], while the fluctuation of pump power and ambient temperature may also cause a minor instability. The power stability of the ring-cavity SFFL is promised in the laboratory environment without any temperature control.
Fig. 7. (a) Output power of the SFFL laser as a function of pump power. (b) Power fluctuation recorded in 8 hours at the maximum output of the SFFL (The inset demonstrates the minimum power variation in 2 hours).
As shown in Fig. 8(a), the output spectrum of the SFFL ranging from 900 nm to 1650 nm at the maximum output power is demonstrated using an OSA (AQ6370D, YOKOGAWA, Japan) with the resolution of 0.02 nm. Almost no residual pump was observed in the spectrum. The enlarged region from 1559.0 nm to 1560.5 nm (inset in Fig. 8(a)) manifests a lasing peak located at 1559.8 nm, the optical signal-to-noise ratio (OSNR) of which was measured to be 68.1 dB. The linewidth of the SFFL was evaluated using delayed self-heterodyne method, which shared the same system with longitudinal-mode characteristics testing. A 50 km delayed SMF was employed, providing a delay of 2.42 ms and measurement resolution bandwidth of ∼3.8 kHz. Presented in Fig. 8 (b), a typical Lorentzian-like signal was observed using an ESA, the resolution bandwidth of which was set as 100 Hz. The red-lined Lorentzian fitting curve reviews a 20 dB linewidth of 13.2 kHz, while the corresponding 3 dB linewidth of the SFFL is estimated to be ∼660 Hz, indicating that a linewidth compression has been realized by SA. Since this value is smaller than the linewidth resolution of measurement, the laser linewidth should be less than 660 Hz.
Fig. 8. (a) The SFFL spectrum ranging from 900 nm to 1650 nm at maximum output (inset shows the enlarged laser peak). (b) The heterodyne signal of the SFFL
Figure 9 demonstrates the RIN of the SFFL at the maximum output power measured with an InGaAs photodetector (PD, PDA05CF2, Thorlabs, U.S.) and ESA. Within the frequency range from 10 Hz to 10 MHz, a sharp peak was found at the relaxation oscillation frequency of 156 kHz. The RIN finally stabilized at -145 dB/Hz at the frequency greater than 1 MHz, and no other large noise peaks were found. The inset shows the direct-current signal measured by the PD and oscilloscope, indicating that CW working operation of the SFFL.
Fig. 9. The relative intensity noise of the SFFL pumped at 950 mW (inset demonstrates the laser output power dependences on time measured by a PD and oscilloscope).
Table 2 shows the comparison of ring-cavity SFFLs based on different EDFs. Almost all reported SFFLs obtained a sub-kHz linewidth [6,34–38]. Some of them were even as narrow as ∼200 Hz [34,35], while their output powers are <1 mW; Wei et al. reported a tunable ring-cavity SFFL with extremely low RIN of -154 dB/Hz. However, the laser power fluctuates within <15% [36]. Wang et al. obtained a SFFL with extraordinarily high OSNR >80 dB, low power fluctuation <0.23% and relatively high power of 23.6 mW in an all-polarization-maintaining (PM) system [6]. While, the RIN is not recorded and, generally, all-PM systems expect for higher requirements than non-PM systems in gain fiber and components. Here, compared with other all-fiber ring cavity SFFLs, a higher output power, up to >32 mW, is obtained with only 10 cm length EYDSF. What’s more, no multi longitudinal mode or mode hopping exists in 2 hours, and the fluctuation of power is <0.63% in 8 hours. In addition, the relative intensity noise was lower to -145 dB/Hz, and the sub-kHz linewidth, specifically <660 Hz, is also notable. It is the high gain of EYDSF, low insertion loss of SA and system simplicity that ensure the high output power and stability of the obtained ring-cavity SFFL. In general, the ring-cavity SFFL based on homemade EYDSF has shown promising performance in output power, RIN, stability, and linewidth.
Table 2. Parameters of ring-cavity SFFLs based on different active fibers
4. Conclusion
In summary, an EYDSF was fabricated by a CO2 laser-heating drawing technique. The Er2O3 doping concentration and gain coefficient of the EYDSF were up to 3.49 wt.% and 1.74 dB/cm, respectively. In addition, a CW working ring-cavity SFFL was established using only 10-cm-long EYDSF as gain medium and 1.6 m homemade low-concentration EDF as SA, which induced a narrow-bandwidth grating of 11.5 MHz. A stable SLM operation has been obtained in the SFFL. In particular, the maximum lasing output power was up to 32.7 mW at 1560 nm. the SFFL had a high OSNR of 68.1 dB and ultra-narrow linewidth of ∼660 Hz. A long-term stability has also been demonstrated in the constructed SFFL, which guarantees a mode-hopping-free SLM operation in 2 hours and slight FOP of <0.63% in 8 hours. Moreover, the RIN stabilized at -145 dB/Hz at frequencies over 1.0 MHz, and no other large noise peak was found except for the relaxation oscillation peak at 156 kHz. To the best of knowledge, it is the first time that all-fiber CW working ring-cavity SFFL based on an EYDSF with such a high performance of output power, linewidth, stability, and noise. The achieved performance demonstrates great potential of EYDSF as gain fiber and further applications of obtained SFFL in coherent optical communications, high-precision sensors, laser radars and other fields.
Funding
National Natural Science Foundation of China (61935002, 61975113, 62275148); 111 Project (D20031); Shanghai Professional Technical Public Service Platform of Advanced Optical Waveguide Intelligent Manufacturing and Testing (19DZ2294000); Jiangsu Province's Industry Outlook and Key Core Technologies - Key Projects (BE2022055-4).
Acknowledgments
We are grateful to Prof. Liang Zhang at the Shanghai University for invaluable analyses and discussions on the linewidth characteristics of the fiber laser.
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. O. De Varona, W. Fittkau, P. Booker, T. Theeg, M. Steinke, D. Kracht, J. Neumann, and P. Wessels, “Single-frequency fiber amplifier at 1.5 µm with 100 W in the linearly-polarized TEM00 mode for next-generation gravitational wave detectors,” Opt. Express 25(21), 24880–24892 (2017). [CrossRef]
2. D. Pan, C. J. Ke, S. N. Fu, Y. P. Liu, D. M. Liu, and A. E. Willner, “All-optical spectral linewidth reduction of lasers for coherent optical communication,” Opt. Lett. 38(24), 5220–5223 (2013). [CrossRef]
3. Z. Qiao, X. R. Gong, P. Guan, Z. Y. Yuan, S. L. Feng, Y. Y. Zhang, M. Kim, G. E. Chang, and Y. C. Chen, “Lasing action in microdroplets modulated by interfacial molecular forces,” Adv. Photon. 3(01), 016003 (2021). [CrossRef]
4. C. Li, T. G. Ning, J. Li, C. Zhang, C. B. Zhang, H. Lin, and L. Pei, “Fiber-optic laser sensor based on all-fiber multipath Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 28(18), 1908–1911 (2016). [CrossRef]
5. K. Ying, H. Liang, D. J. Chen, Y.G. Sun, H. Y. Pi, F. Wei, F. Yang, and H. W. Cai, “Ultra low noise DFB fiber laser with self-feedback mechanics utilizing the inherent photothermal effect,” Opt. Express 28(16), 23717–23727 (2020). [CrossRef]
6. Z. K. Wang, J. M. Shang, S. Q. Li, K. L. Mu, Y. J. Qiao, and S. Yu, “All-polarization maintaining single-longitudinal-mode fiber laser with ultra-high OSNR, sub-kHz linewidth and extremely high stability,” Opt. Laser Technol. 141, 107135 (2021). [CrossRef]
7. Q. L. Zhao, Z. T. Zhang, B. Wu, T. Y. Tan, C. S. Yang, J. L. Gan, H. H. Chen, Z. M. Feng, M. Y. Peng, Z. M Yang, and S. H. Xu, “Noise-sidebands-free and ultra-low-RIN 1.5 µm single-frequency fiber laser towards coherent optical detection,” Photon. Res. 6(4), 326–331 (2018). [CrossRef]
8. J. T. Lin, S. Farajollahi, Z. W. Fang, N. Yao, R. Gao, J. L. Guan, L. Deng, T. Liu, M. Wang, H. S. Zhang, W. Fang, L. L. Qiao, and Y. Cheng, “Electro-optic tuning of a single-frequency ultranarrow linewidth microdisk laser,” Adv. Photon. 4(03), 036001 (2022). [CrossRef]
9. K. Ying, D. J. Chen, H. Y. Pi, Z. Y. Wang, X. Li, Y. G. Sun, F. Wei, F. Yang, N. Cheng, Q. Ye, and H. W. Cai, “Ultra-stable fiber laser based on intracavity dual mode self-reference mechanism,” J. Lightwave Technol. 40(13), 4379–4384 (2022). [CrossRef]
10. Y. Wan, J. X. Wen, Y. H. Dong, C. Jiang, M. Jia, F. Z. Tang, N. Chen, Z. W. Zhao, S. J. Huang, F. F. Pang, and T. Y. Wang, “Exceeding 50% slope efficiency DBR fiber laser based on a Yb-doped crystal-derived silica fiber with high gain per unit length,” Opt. Express 28(16), 23771–23783 (2020). [CrossRef]
11. C. H. Yeh, B. Y. Wang, W. H. Hsu, W. Y. You, J. R. Chen, C. W. Chow, and J. H. Chen, “Stable and selectable erbium multiple-ring laser with self-injection loop,” Opt. Laser Technol. 141, 107106 (2021). [CrossRef]
12. H. Wei and S. Krishnaswamy, “Adaptive fiber-ring lasers based on an optical fiber Fabry-Perot cavity for high-frequency dynamic strain sensing,” Appl. Optics 59(2), 530–535 (2020). [CrossRef]
13. D. Cheng, F. P. Yan, T. Feng, W. G. Han, L. N. Zhang, Q. Qin, T. Li, Z. Y. Bai, D. D. Yang, Y. Guo, and W. Wang, “Five-Wavelength-Switchable Single-Longitudinal-Mode Thulium-Doped Fiber Laser Based on a Passive Cascaded Triple-Ring Cavity Filter,” IEEE Photonics J. 14(1), 1–8 (2022). [CrossRef]
14. N. R. Poddubrovskii, I. A. Lobach, and S. I. Kablukov, “Regular mode-hopping dynamics in Erbium-doped ring fiber laser with saturable absorber,” Opt. Laser Technol. 156, 108568 (2022). [CrossRef]
15. S. P. Zheng, J. Li, C. L. Yu, Q. L. Zhou, and D. P. Chen, “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]
16. G. W. Tang, G. Q. Qian, W. Lin, W. L. Wang, Z. G. Shi, Y. Yang, N. L. Dai, Q. Qian, and Z. M. Yang, “Broadband 2 µm amplified spontaneous emission of Ho/Cr/Tm: YAG crystal derived all-glass fibers for mode-locked fiber laser applications,” Opt. Lett. 44(13), 3290–3293 (2019). [CrossRef]
17. Y. Wan, J. X. Wen, C. Jiang, F. Tang, J. Wen, S. J. Huang, F. F. Pang, and T. Y. Wang, “Over 255 mW single-frequency fiber laser with high slope efficiency and power stability based on an ultrashort Yb-doped crystal-derived silica fiber,” Photon. Res. 9(5), 649–656 (2021). [CrossRef]
18. C. S. Yang, S. H. Xu, C. Li, S. P. Mo, Z. M. Feng, Z. M. Yang, and Z. H. Jiang, “Ultra-compact kilohertz-linewidth high-power single-frequency laser based on Er3+/Yb3+-codoped phosphate fiber amplifier,” Appl. Phys. Express 6(2), 022703 (2013). [CrossRef]
19. M. R. A. Moghaddam, S. W. Harun, S. Shahi, and H. Ahmad, “Broadband amplifier and high performance tunable laser with an extinction ratio of higher than 60 dB using bismuth oxide-based erbium-doped fiber,” J. Mod. Opt. 59(12), 1106–1112 (2012). [CrossRef]
20. Y. Y. Xie, Z. H. Cong, Z. G. Zhao, X. Y. Zhang, X. Zhao, W. Zhao, X. B. Shao, and Z. J. Liu, “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]
21. S. Colin, E. Contesse, P. Le Boudec, G. Stephan, and F. Sanchez, “Evidence of a saturable-absorption effect in heavily erbium-doped fibers,” Opt. Lett. 21(24), 1987–1989 (1996). [CrossRef]
22. J. Ballato and A. C. Peacock, “Perspective: Molten core optical fiber fabrication—A route to new materials and applications,” APL Photonics 3(12), 120903 (2018). [CrossRef]
23. X. Y. Ji, S. M. Lei, S. Y. Yu, H. Y. Cheng, W. J. Liu, N. Poilvert, Y. H. Xiong, I. Dabo, S. E. Mohney, J. V. Badding, and V. Gopalan, “Single-crystal silicon optical fiber by direct laser crystallization,” ACS Photonics 4(1), 85–92 (2017). [CrossRef]
24. A. Vonderhaar, M. P. Stone, J. Campbell, T. W. Hawkins, J. Ballato, and P. D. Dragic, “Concentration quenching and clustering effects in Er: YAG-derived all-glass optical fiber,” Opt. Mater. Express 11(10), 3587–3599 (2021). [CrossRef]
25. S. H. Xu, Z. M. Yang, T. Liu, W. N. Zhang, Z. M. Feng, Q. Y. Zhang, and Z. H. Jiang, “An efficient compact 300 mW narrow-linewidth single frequency fiber laser at 1.5 µm,” Opt. Express 18(2), 1249–1254 (2010). [CrossRef]
26. A. A. Rybaltovsky, S. E. Sverchkov, V. V. Vel’miskin, D. V. Przhiialkovskii, A. P. Bazakutsa, B. I. Galagan, B. I. Denker, and O. V. Butov, “Single-frequency continuous-wave laser based on the novel Er/Yb-doped composite phosphosilicate fiber,” Opt. Laser Technol. 151, 108049 (2022). [CrossRef]
27. Y. Wan, J. X. Wen, C. Jiang, F. Z. Tang, T. Yusufu, F. F. Pang, A. Sidike, and T. Y. Wang, “Broadband high-gain Yb: YAG crystal-derived silica fiber for low noise tunable single-frequency fiber laser,” Opt. Express 30(11), 18692–18702 (2022). [CrossRef]
28. F. Sanchez, P. Le Boudec, P. L. François, and G. Stephan, “Effects of ion pairs on the dynamics of erbium-doped fiber lasers,” Phys. Rev. A 48(3), 2220–2229 (1993). [CrossRef]
29. V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, “Kramers-Kronig relations in optical materials research” Springer:New York, NY, USA, 2005, vol. 110.
30. X. W. Shu and S. Jung, “Fiber grating Sagnac loop and its multiwavelength-laser application,” IEEE Photon. Technol. Lett. 12(8), 980–982 (2000). [CrossRef]
31. M. Yamada and K. Sakuda, “Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach,” Appl. Opt. 26(16), 3474–3478 (1987). [CrossRef]
32. D. R. Chen, C. Shu, and S. L. He, “Multiple fiber Bragg grating interrogation based on a spectrum-limited Fourier domain mode-locking fiber laser,” Opt. Lett. 33(13), 1395–1397 (2008). [CrossRef]
33. Y. Z. Xu, H. Y. Tam, S. Y. Liu, and M. S. Demokan, “Pump-induced thermal effects in Er-Yb fiber grating DBR lasers,” IEEE Photon. Technol. Lett. 10(9), 1253–1255 (1998). [CrossRef]
34. L. H. Huang, C. S. Yang, T. Y. Tan, W. Lin, Z. T. Zhang, K. J. Zhou, Q. L. Zhao, X. D. Teng, S. H. Xu, and Z. M. Tang, “Sub-kHz-linewidth wavelength-tunable single-frequency ring-cavity fiber laser for C- and L-band operation,” J. Lightwave Technol. 39(14), 4794–4799 (2021). [CrossRef]
35. Y. J. Li, L. Huang, L. Gao, T. Y. Lan, Y. L. Cao, I. P. Ikechukwu, L. L. Shi, Y. F. Liu, F. H. Li, and T. Zhu, “Optically controlled tunable ultra-narrow linewidth fiber laser with Rayleigh backscattering and saturable absorption ring,” Opt. Express 26(21), 26896–26906 (2018). [CrossRef]
36. D. Wei, T. Feng, W. W. Sun, F. P. Yan, and X. S. Yao, “Widely Wavelength-Swept Single-Longitudinal-Mode Fiber Laser with Ultra-Narrow Linewidth in C + L-Band,” IEEE Photonics J. 14(4), 1–10 (2022). [CrossRef]
37. L. Li, M. J. Zhang, Y. Liu, Y. T. Li, and Y. C. Wang, “Stable single-longitudinal-mode erbium-doped fiber laser with narrow linewidth utilizing parallel fiber ring resonator incorporating saturable absorber and fiber Bragg grating,” Appl. Opt. 54(13), 4001–4005 (2015). [CrossRef]
38. J. M. Shang, Z. K. Wang, S. Q. Li, E. Zhu, S. Yu, and Y. J. Qiao, “Tunable narrow linewidth linear cavity fiber laser based on a one-way round-trip structure,” Opt. Fiber Technol. 68, 102780 (2022). [CrossRef]
