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Abstract
A narrow-linewidth and low relative intensity noise (RIN) Tm/Ho co-doped fiber laser based on a saturable absorber and self-injection locking was demonstrated for the first time. Utilizing self-injection locking technology, the frequency noise power spectral density is remarkably reduced by more than 17.1 dB from 1.21 × 106 Hz2/Hz to 7.30 × 103 Hz2/Hz when the frequency is approximately 1 kHz. Furthermore, a laser with a linewidth compressed to a quarter of the original linewidth from 44.386 kHz to 2.850 kHz, a RIN of less than -127.74 dB/Hz, and an optical signal-to-noise ratio of more than 71.6 dB can be obtained. Using a delay fiber, the relaxation oscillation peak frequencies move to lower frequencies, from 27.9 kHz to 15.8 kHz. The proposed laser is highly competitive in advanced coherent light detection fields, including coherent Doppler wind lidar, high-speed coherent optical communication, and precise absolute distance coherent measurement.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single-longitudinal-mode (SLM) narrow-linewidth fiber laser has attracted increasing interest due to its promising performances of compact all-fiber configuration, low noise, and kHz-level linewidth, making it versatile in the field of coherent communication, coherent beam combination, high-resolution laser spectroscopy, optical atomic clocks, and gravitational wave detection [1–5]. The 2 µm band laser exhibits unique advantages in transmission performance and absorption characteristics, and this region contains many absorption lines of important atmospheric gases, such as CO2 [6]. Eye-safe fiber lasers operating near 2 µm presenting strong absorption in animal/human tissues and minimal damage to the retina are extensively used in medical fields [7,8]. Therefore, a stable SLM narrow-linewidth fiber laser covering the operation spectral range of 1940nm to 2050nm has broad application potential and significant research value.
Over the past decades, several schemes have been employed to realize SLM operation in fiber lasers, such as short linear cavity fiber lasers with distributed feedback (DFB) and a distributed Bragg grating reflector (DBR) structure. However, the output power of these lasers is usually too low due to the limitation of cavity length and gain fiber length [9]. An alternative to this is ring cavity fiber lasers. This scheme allows for optimizing the active fiber length to improve the pump absorption and laser gain for high output power [10]. By further incorporating a rare-earth-doped fiber-based saturable absorber (SA) and a high reflectivity mirror or fiber Bragg grating (FBG), a narrow bandwidth dynamic Bragg grating could be established inside the SA based on the standing-wave interference effect, forcing the intracavity laser to operate in a SLM state. In addition, the saturable absorption process in the SA would introduce frequency-dependent loss. The weak longitudinal modes, which deviate from the center frequency, would undergo a larger absorption loss and can be effectively suppressed due to mode competition [11]. A highly absorbent fiber SA would enhance the strength of the dynamic Bragg grating and the absorption loss, resulting in strong mode selection capability [12]. However, the bandwidth of the induced dynamic Bragg grating gradually becomes wider as the doping concentration of the saturated absorber fiber increases, leading to severe mode-hopping [13]. Therefore, by using a low/moderate dopant fiber, the doped rare-earth ions, which have a large absorption cross section at the signal wavelength, would induce a strong dynamic Bragg grating with a narrower bandwidth, allowing it to be more beneficial for powerful single-frequency operation that also presents stability.
Numerous efforts have been devoted to suppressing the linewidth of SLM fiber lasers, such as optical injection locking feedback, the optical fiber scattering effect, and dynamic narrow-band filters consisting of subring cavities [14–17]. Among them, injection locking is a well-developed linewidth reduction technique that leads to lower intracavity losses. Intracavity optical devices, including wave plates and filters, are needed to achieve linewidth suppression and thereby exhibit high intracavity loss. Noteworthy research has been conducted on the theoretical study of the self-injection locking of semiconductor lasers [18,19]. The Langevin approach, which is a means of evaluating the optical feedback effect, can be used to obtain an analytical expression for the linewidth of a self-injection locked laser. Current research on self-injection locking primarily focuses on erbium-doped fiber lasers, with limited attention devoted to thulium-doped fiber lasers and no reported instances of thulium-holmium co-doped fiber lasers. This paper investigates the Tm/Ho co-doped fiber laser (THDFL) based on self-injection locking for the first time.
A narrow-linewidth and low relative intensity noise (RIN) THDFL based on self-injection locking is proposed in the present paper. In the presented scheme, a FBG is embedded in the laser cavity to enable wavelength selection, while a SA composed of Tm/Ho co-doped fiber (THDF) is used to realize the SLM operation. Additionally, an analytical model based on the semi-phenomenological approach was adopted to analyze the linewidth narrowing effect in a self-injection locked fiber laser. The obtained expression predicts the linewidth narrowing with additional external cavity photon lifetime. Ultimately, a SLM THDFL with the linewidth reduced from 44.386 kHz to 12.056 kHz is achieved by self-injection locking with a 50 m delay fiber. After applying injection locking in the laser cavity, the relaxation oscillation frequency (ROF) is shifted to the left by tens of kilohertz.
2. Experimental setup and principle
The experimental setup of the self-injection locking scheme of narrow-linewidth and low-RIN THDFL based on self-injection locking is displayed in Fig. 1(a). A commercial 1570 nm laser diode (LD, RZPL-1570-5-D-SM-1-1-FA, Rayzer) with a maximum output power of 5 W is used as the optical pump. The pump signal is transmitted to a 3 m THDF (CorActive, TH512, with an absorption coefficient of 15.4 dB/m near 1550 nm, a core diameter of 8.4 µm, a cladding diameter of 124.7 ± 0.8 µm, and a numerical aperture of 0.16) by a 1570/2000nm wavelength division multiplexer (WDM1). The residual pump light is transmitted clockwise out of the laser cavity through one of the ports of the WDM2. A circulator (CIR) is used to determine the unidirectional working state of the laser and to prevent the spatial hole-burning effect in the SLM main cavity, which may affect the stable operation of the laser. A section of the THDF with a length of 1.42 m is connected to Port 2 of the CIR as a SA, which can act as a dynamic narrow-band filter. A FBG fused to the right port of the SA serves as the wavelength-selection element. An optical coupler (OC, 60:40) is connected to Port 3 of the CIR, leading to the laser output. Moreover, the cavity length of the main laser is approximately ∼14.9 m, and the corresponding free spectral range (FSR) is about ∼13.8 MHz. An optical spectrum analyzer (OSA, AQ6375E, YOKOGAWA) was used to measure the output spectra of the OC. The noise characteristics of the proposed fiber laser are measured using a signal analyzer with an InGaAs photodetector (PD). The laser transmitted from the FBG is first launched into the delay fiber and a variable optical attenuator (VOA) and then reinjected into the ring laser cavity through one of the left ports of the OC to achieve self-injection locking.
Fig. 1. (a) Schematic diagram of the experimental setup of the proposed narrow-linewidth all-fiber ring laser. LD: laser diode; WDM: wavelength division multiplexer; THDF: Tm/Ho co-doped fiber; OC: optical coupler; VOA: variable optical attenuator; FBG: fiber Bragg grating; CIR: circulator. (b) Transmission and reflection spectra of FBG. (c) Full-width at half-maximum (FWHM) of the dynamic narrow-band filter as a function of length.
The transmission and reflection spectra of the FBG detected by the OSA are presented in Fig. 1(b). The 3 dB bandwidth of the measured FBG was 0.18 nm (14.3 GHz). The FWHM $\Delta {f}$ of the SA-based dynamic narrow-band filter in the 1.42 m unpumped THDF at a lasing wavelength of 1941.18 nm can be calculated as follows [20]:
In addition, the laser linewidth decreases with increasing photon lifetime in the cavity based on the theoretical analysis of Schawlow-Townes [21]. In SLM lasers, the ROF and the photon lifetime τ are related as follows [21–23]:
3. Experimental results and discussion
When pump power was set to 822 mW, the amplified spontaneous emission (ASE) of the 3 m gain THDF was measured with the OSA from Point A and Point B (Fig. 1), as shown in Fig. 2(a) and Fig. 2(b), respectively. The optical gain of 1940nm at Point A was lower than at Point B. Therefore, the backward pumping method is chosen. With self-injection locking (Points C and D are connected), the output spectrum was measured over approximately 60 min to investigate the lasing stability of the SLM fiber laser by repeatedly scanning the OSA, as shown in Fig. 3(a). The center wavelength was 1941.18 nm, and the optical signal-to-noise ratio (OSNR) was higher than 71.6 dB with the pump power of 536 mW. The SLM operation at the wavelength of 1941.18 nm was investigated using a 12.5 GHz InGaAs PD (EOT-5000F) and signal analyzer (Keysight, N9020A). The radio frequency (RF) beating spectra were set to 0–100 MHz with a resolution bandwidth (RBW) of 100 kHz, as shown in Fig. 3(b). In addition, the RF spectrum of the output laser was examined for 1 h, with data recorded at 5 min intervals, as shown in the inset. There was no beat frequency signal with a non-zero frequency, which reflects the stable SLM operation of the THDFL. The output power of SLM THDFL is determined by pump power. Figure 3(c) shows the output power of the fiber laser measured by an optical power meter (LaserPoint). The circular and square curves represent the output power with and without self-injection locking, respectively. It can be seen that the two curves are very similar. By increasing the pump power from 0.5 W to 2.0 W, the output power of THDFL increases linearly, and the output power increases more quickly with self-injection locking than the output power without self-injection locking. However, the slope efficiency decreases with the 100 m delay fiber due to the optical loss of single-mode fiber (SMF) at 2 µm.
Fig. 2. ASE of THDF measured from (a) Point A and (b) Point B with 822 mW pump power. ASE: amplified spontaneous emission; THDF: Tm/Ho co-doped fiber.
Fig. 3. (a) Optical spectrum of the single-wavelength at 1941.18 nm. The inset is the optical spectra of scans repeated 13 times at 5 min intervals. (b) Longitudinal-mode characteristics lasing at 1941.18 nm measured by InGaAs PD and signal analyzer. The inset is the RF spectra scans repeated 13 times at 5 min intervals. (c) Output power of the laser with and without self-injection locking under different pump powers. PD: photodetector; RF: radio frequency.
The linewidth measurement of the laser was achieved by using an imbalanced Michelson interference (MI) system, which was composed of a 3 × 3 OC, 50 m SMF, and two Faraday rotating mirrors (FRMs), as shown in Fig. 4(a). The measured laser was transmitted from Port 1 through the 3 × 3 OC to Ports 4, 5, and 6. A 50 m SMF and FRM1 was connected to Port 4, and FRM2 was connected to Port 5. The light reflected from the two FRMs passed through the 3 × 3 OC and generated an interference signal received by PD1 and PD2, which then transmitted to the data acquisition board. The received interference fringes contained information on different phase fluctuations accumulated in the delay time of the imbalanced MI. Furthermore, the power spectral density (PSD) of the laser’s instantaneous phase fluctuation S$\varphi $ (f) and frequency fluctuation Sv(f) can be calculated. Considering the relationship between the measured laser linewidth and frequency, the linewidth value was calculated using the β-separation line method proposed by Domenico [24]. With the separation line of $\beta = {Sv}({f}) = 8\ln (2){f}/{\pi ^2}$, the frequency noise spectrum can be divided into two sections. The first section is the region of ${Sv}({f}) > 8\ln (2){f}/{\pi ^2}$, which contains Gaussian noise and determines the center part of the laser spectral line shape and the laser linewidth. The second section is part of ${Sv}({f}) < 8\ln (2){f}/{\pi ^2}$. This part of the noise is categorized as Lorentzian noise, which determines the side part of the laser spectral line shape and has no effect on the linewidth of the laser, which can be ignored. Since the noise level in the first part is high relative to the other Fourier frequencies, a slow-frequency modulation with a high modulation index was formed. The noise component of this part produces a Gaussian autocorrelation function that is multiplied and then Fourier transformed to obtain the laser spectral line shape. The laser linewidth, i.e., the half-height full width of the spectrum, can be approximated as $\Delta \textrm{v} = \sqrt {8\ln (2)\textrm{A}}$.
Fig. 4. (a) Configuration of the linewidth measurement system. FRM: Faraday rotation mirror; PD: photodetector; SMF: single-mode fiber; (b) Frequency noise PSD of the constructed SLM THDFL with and without self-injection locking and β-separation line. PSD: power spectral density; SLM: single longitudinal mode; THDFL: Tm/Ho co-doped fiber. (c) Laser linewidth evolution with and without self-injection locking vs. the pump power. (d) Stability performances of the output power with and without self-injection locking over 60 min.
Adjust pump power to 521 mW, the comparison results of frequency noise PSD with and without self-injection locking are shown in Fig. 4(b). The green solid line is the frequency noise PSD without self-injection locking. The blue solid line and the orange solid line are in the case where the delay fiber is 50 m and 100 m at self-injection locking, respectively. The red solid line is the β-separation line. In general, lasers are affected by flicker noise caused by the random fluctuations of electrons and thermodynamic noise caused by temperature fluctuations and vibrations in low-frequency regions. The resonant optical feedback from the cavity shows significant noise suppression with a measurement frequency of 100 Hz to 10 kHz. At low Fourier frequencies, the frequency noise of the lasers is mainly 1/f noise, which was reduced substantially with resonant optical feedback [25]. At high Fourier frequencies, the frequency noise of the laser is primarily white noise, and it is effectively suppressed using optical feedback from a 50 m long external ring cavity [26,27]. The frequency noise in the low-frequency region was suppressed by ∼17.1 dB from 1.21 × 106 Hz2/Hz to 7.09 × 104 Hz2/Hz when the frequency was approximately 1 kHz. With increasing delay fiber increasing to 100 m the frequency noise decreases to 7.30 × 103 Hz2/Hz. The higher noise peaks around 10 kHz originated from the external environment, denoting that this effect may be avoided by properly shielding the laser system. In addition, the integrated linewidths, including low-frequency noise with or without self-injection locking calculated by the β-separation line, are 12.056 kHz and 44.386 kHz at integration times of 0.001 s, respectively. The linewidth is reduced to 2.850 kHz when using a 100 m delay fiber. It can be seen that the proposed self-injection locking also suppresses the frequency noise in the low-frequency region of the laser.
Figure 4(c) shows the variation of the laser linewidth against the pump power with and without self-injection locking, where the delay fiber used for injection locking are 50 m and 100 m, respectively. Due to the significant influence of temperature fluctuations and vibration noise in the fiber optic loop, the intrinsic linewidth distribution in the unlocked fiber laser is between 44 kHz and 47 kHz. Moreover, the intrinsic linewidth distribution in the self-injection locked fiber laser is between 11 kHz and 13 kHz, which is narrowed by three times compared to the unlocked linewidth. To further investigate the effect of delay fiber on the output laser linewidth, the delay fiber is extended from 50 m to 100 m, and the laser linewidth is between 2 kHz and 3 kHz. This is a distinctive indication that narrow linewidth performance is maintained when the output power of the pump LD is changed. The above results support that the varying pump power will not change the laser’s SLM characteristics or hamper the narrow linewidth output. Moreover, the evolution of the output power is further monitored to fully illustrate the long-term stability of the proposed tunable fiber laser system based on self-injection locking. Figure 4(d) provides a comparison of the output power of THDFL with and without self-injection locking over 60 min, where the red dots represent the output power without self-injection locking the unlocked power, the blue diamond dots represent the output power of the 50 m delay fiber, the green square dot represents the output power of 100 m delay fiber. The stability of the output power fluctuations without self-injection locking and with 50 m delay fiber were less than 0.055 mW and 0.018 mW, respectively. In addition, the output power decreases with 100 m delay fiber and power fluctuation is 0.020 mW.
The jitter of the laser power was characterized by RIN, an important index to evaluate laser output power stability. The extension of the photon lifetime would be verified by the low-frequency shift ROF and the suppression of the RIN. Figure 5(a) depicts the RIN of the initial free-running laser and the self-injection locked laser with the pump power of 521 mW, where the lengths of the fibers with self-injection delay fiber are 50 m and 100 m, respectively. It can be revealed that the ROF shifts to a lower frequency using the delay fiber. The frequencies corresponding to the first, second and third peaks are 15.8 kHz, 21.2 kHz and 29.9 kHz, respectively. As indicated in Fig. 5(a), when the self-injection locking using 50 m delay fiber is further incorporated into the laser system, the oscillation peaks in the noise spectrum are all effectively suppressed. A maximum noise suppression of more than 3 dB of the intensity noise peak around the ROF is achieved from -84.7 dB/Hz to -88 dB/Hz. As the delay fiber in the self- injection locking increases to 100 m, the ROF decreases to -92.4 kHz. It can be concluded that the external photon lifetime, which is the time needed for the light field to travel back and forth to the external cavity, is extended with the addition of the delay line. The above results show that the proposed self-injection locked mechanism exhibits a suppressive effect of laser intensity noise. Moreover, the laser power injected into the main cavity was regulated by a VOA with an injected SMF delay fiber length of 50 m. The peak value of the ROF of the output laser was higher without injection locking and decreased with the presence of injection locking, as presented in Fig. 5(b).
Fig. 5. (a) The RIN spectrum of the laser with and without self-injection locking; (b) The RIN spectrum of the self-injection locked fiber laser with different injection powers. (c) RIN spectra of the self-injection locking fiber laser with varying pump powers. RIN: relative intensity noise.
The resultant RINs in different frequency ranges with self-injection locking are shown in Fig. 5(c). The laser power was attenuated to 1 mW to ensure consistency before being launched into an InGaAs PD. Fixing the cavity length and adjusting the pump power changes the optical power in the cavity, which, in turn, affects the position of the relaxation oscillation peak. As depicted by the red, blue, and green curved lines, the RIN floor is -127.74 dB/Hz for frequencies beyond 0.5 MHz. Moreover, the inset in Fig. 5(c) shows the RIN spectrum of the laser in the low-frequency region from 0–200 kHz. Herein, the ROF are 28.6 kHz, 49.2 kHz, and 61.6 kHz for the pump powers of 524.08 mW, 583.71 mW, and 643.34 mW, respectively. As indicated in Fig. 5(c), when the pump power is further increased in the laser system, the oscillation peak in the noise spectrum gradually shifts to the right, which is consistent with Eq. (2).
4. Conclusion
In this paper, a SLM narrow-linewidth THDFL was developed and comprehensively tested based on SA and self-injection locking. Combining the wavelength-selective and filter-reflective properties of fiber gratings and the selection of THDFs as narrowband filters, a stable laser output at 1941.18 nm was obtained. A comparison of the laser output characteristics with and without injection locking reveals that injection locking using 50 m delay fiber increases the slope efficiency of the output lasing from 3.47% to 3.85%. The laser linewidth is 2.850 kHz at integration times of 0.001 s, and the RIN is -127.74 dB/Hz with self-injection locking. The output power fluctuation is reduced from 0.055 mW to 0.020 mW, and the ROF shifts left from 27.9 kHz to 15.8 kHz after the injection locking mechanism is employed. The theoretical and experimental findings suggest that laser linewidth compression can be accomplished by prolonging the external cavity photon lifetime. This provides a novel perspective for achieving a more comprehensive understanding of the linewidth reduction mechanism in self-injection locked SLM THDFLs.
Funding
Fundamental Research Funds for the Central Universities (2023YJS123); National Key Research and Development Program of China (2021YFB2800900); National Natural Science Foundation of China (61827818); Natural Science Foundation of Hebei Province for Distinguished Young Scholars (F2023201024).
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. Omiya, K. Toyoda, M. Yoshida, et al., “400 Gbit/s 256 QAM-OFDM transmission over 720 km with a 14bit/s/Hz spectral efficiency by using high-resolution FDE,” Opt. Express 21(3), 2632–2641 (2013). [CrossRef]
2. R. Su, P. Zhou, X. Wang, et al., “Active coherent beam combining of a five-element, 800 W nanosecond fiber amplifier array,” Opt. Lett. 37(19), 3978–3980 (2012). [CrossRef]
3. T. Wu, X. Peng, W. Gong, et al., “Observation and optimization of 4He atomicpolarization spectroscopy,” Opt. Lett. 38(6), 986–988 (2013). [CrossRef]
4. C. W. Chou, D. B. Hume, T. Rosenband, et al., “Optical clocks and relativity,” Science 329(5999), 1630–1633 (2010). [CrossRef]
5. Q. Zhang, Y. Hou, X. Wang, et al., “5 W ultra-low-noise 2 microm single-frequency fiber laser for next-generation gravitational wave detectors,” Opt. Lett. 45(17), 4911–4914 (2020). [CrossRef]
6. T. M. Taczak and D. K. Killinger, “Development of a tunable, narrow-linewidth, cw 2.066-µm Ho: YLF laser for remote sensing of atmospheric CO2 and H2O,” Appl. Opt. 37(36), 8460–8476 (1998). [CrossRef]
7. J. H. Geng, Q. Wang, Y. W. Lee, et al., “Development of eye-safe fiber lasers near 2 µm,” IEEE J. Sel. Top. Quantum Electron 20(5), 150–160 (2014). [CrossRef]
8. M. Tendean, T. D. B. Mambu, F. Tjandra, et al., “The use of Thulium-Doped Fiber Laser (TDFL) 1940nm as an energy device in liver parenchyma resection, a-pilot-study in Indonesia,” Ann. Med. 60, 491–497 (2020). [CrossRef]
9. W. Walasik, D. Traore, A. Amavigan, et al., “2-µm Narrow Linewidth All-Fiber DFB Fiber Bragg Grating Lasers for Ho- and Tm-Doped Fiber-Amplifier Applications,” J. Lightwave Technol. 39(15), 5096–5102 (2021). [CrossRef]
10. L. Zhang, J. X. Zhang, Q. Sheng, et al., “Watt-level 1.7-um single-frequency thulium-doped fiber oscillator,” Opt. Express 29(17), 27048–27056 (2021). [CrossRef]
11. L. Zhang, Q. Sheng, L. Chen, et al., “Single-frequency Tm-doped fiber laser with 215 mW at 2.05 µm based on a Tm/Ho-codoped fiber saturable absorber,” Opt. Lett. 47(15), 3964–3967 (2022). [CrossRef]
12. S. Stepanov, “Dynamic population gratings in rare-earth-doped optical fibres,” J. Phys. D: Appl. Phys. 41(22), 224002 (2008). [CrossRef]
13. R. Poozesh, K. Madanipour, and P. Parvin, “High SNR Watt-Level Single Frequency Yb-Doped Fiber Laser Based on a Saturable Absorber Filter in a Cladding-Pumped Ring Cavity,” J. Lightwave Technol. 36(20), 4880–4886 (2018). [CrossRef]
14. T. Zhu, F. Chen, S. Huang, et al., “An ultra-narrow linewidth fiber laser based on Rayleigh backscattering in a tapered optical fiber,” Laser Phys. Lett. 10(5), 055110 (2013). [CrossRef]
15. H. Ahmad, N. Razak, M. Zulkifli, et al., “Ultra-narrow linewidth single longitudinal mode Brillouin fiber ringlaser using highly nonlinear fiber,” Laser Phys. Lett. 10(10), 105105 (2013). [CrossRef]
16. X. Huang, Q. Zhao, W. Lin, et al., “Linewidth suppression mechanism of self-injection locked single-frequency fiber laser,” Opt. Express 24(17), 18907–18916 (2016). [CrossRef]
17. D. D. Yang, F. P. Yan, T. Feng, et al., “Stable narrow-linewidth single-longitudinal-mode thulium-doped fiber laser by exploiting double-coupler-based double-ring filter,” Infrared Phys. Technol. 129, 104568 (2013). [CrossRef]
18. G. P. Agrawal, “Line Narrowing in a Single-Mode Injection Laser Due to External Optical Feedback,” IEEE J. Quantum Electron 20(5), 468–471 (1984). [CrossRef]
19. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron 16(3), 347–355 (1980). [CrossRef]
20. L. H. Huang, C. S. Yang, T. Y. Tan, et al., “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]
21. A. L. Schawlow and C. H. Townes, “Infrared and Optical Masers,” Phys. Rev. 112(6), 1940–1949 (1958). [CrossRef]
22. Y. Shevy, D. Shevy, R. Lee, et al., “Slow light laser oscillator,” Optical Fiber Communication Conference. Optical Society of America, OThQ6 (2010).
23. Z. Q. Pan, Q. Ye, H. W. Cai, et al., “Fiber Ring With Long Delay Used as a Cavity Mirror for Narrowing Fiber Laser,” IEEE Photonics Technol. Lett. 26(16), 1621–1624 (2014). [CrossRef]
24. G. D. Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49(25), 4801–4807 (2010). [CrossRef]
25. H. Li and N. B. Abraham, “Analysis of the noise spectra of a laser diode with optical feedback from a highfinesse resonator,” IEEE J. Quantum Electron. 25(8), 1782–1793 (1989). [CrossRef]
26. Q. Lin, M. A. Van Camp, H. Zhang, et al., “Long-external-cavity distributed Bragg reflector laser with subkilohertz intrinsic linewidth,” Opt. Lett. 37(11), 1989–1991 (2012). [CrossRef]
27. P. Samutpraphoot, S. Weber, Q. Lin, et al., “Passive intrinsic-linewidth narrowing of ultraviolet extended-cavity diode laser by weak optical feedback,” Opt. Express 22(10), 11592–11599 (2014). [CrossRef]
