Open Access
Add to BibSonomyAbstract
The frequency and intensity noise of an Yb3+-doped single-frequency distributed Bragg reflector (DBR) fiber laser are effectively reduced by a simple, passive optical-feedback loop (POFL), which consists of only two optical couplers. The feedback loop, which has resonance with the high reflective grating of the DBR laser and relative long optical path compared to the DBR cavity, results in narrower linewidth and lower relative intensity noise (RIN) in the feedback signal. The RIN of relaxation oscillation is reduced by 20dB from −99.9dB/Hz @ 993 kHz to −119.4dB/Hz @ 192 kHz, and the frequency noise was suppressed at frequencies higher than 1 kHz, with a maximum reduction of about 30 dB from 10 kHz to 100 kHz, which results in a spectral linewidth compression from 3.96 kHz to 540 Hz. Even after one fiber amplification stage, the noise did not increase significantly, and a spectral linewidth well below 1 kHz were also achieved at output power of 10W.
© 2016 Optical Society of America
1. Introduction
High power single-frequency lasers with narrow linewidth and low noise have attracted considerable attentions, because of their potential applications [1–8], such as laser cooling [6], gravitational wave detection [7] and space high-precision interference measurement [8]. For example, laser cooling [6], which needs low noise and high power single frequency laser as the laser source for manipulating and probing atoms. The sources of this type will allow for higher flux and collection efficiency in magneto-optical traps, as well as further improvements in lattice-based cooling techniques.
Up to now, some works have been done to reduce the linewidth and noise of single frequency laser for these cutting-edge applications. The most common methods for linewidth compression and noise reduction are electronic feedback and optical feedback. For instance, G. A. Cranch realized the frequency noise suppression in erbium-doped fiber distributed-feedback lasers by electronic feedback, and the frequency noise spectral density of the laser is reduced by as much as 20 dB over the frequency range 1 Hz–10 kHz [9]. However, the electronic feedback scheme is inevitably limited by response bandwidth and speed of the electronic system. Moreover, additional electronic noise will also be introduced in the feedback loop further compromising their performance [9, 10].
Recently, optical feedback technology [11–13], which suppress linewidth broadening and noise has attracted extensive attentions. J. Chang et al. reported a simple self-injection locking (SIL) configuration of erbium-doped distributed feedback fiber lasers (DFB-FL) [13], the RIN of the DFB-FL is suppressed about 16 dB around the relaxation oscillation frequency. But, generally, in this configuration also has the residual pump power circulates in the self-injection loop, which deteriorates the laser performance. So the noise suppression and linewidth compression isn’t significant.
Another optical feedback configuration used a DBR fiber laser that was injected by a fiber feedback ring which mainly includes a semiconductor optical amplifier (SOA) and a fiber Bragg grating (FBG). Taking advantage of this configuration, Z Yang et al. demonstrated that the frequency noise has been reduced by about 25 dB and the relative intensity noise (RIN) is within 5 dB of the shot noise limit at frequencies from 1.5 to 3MHz [14]. However, the active element, SOA, introduces extra noise and the FBG is very sensitive to external perturbation limiting the performance of this scheme.
In this paper, we propose a simple, effective, passive optical-feedback loop (POFL) which fulfills the demands of a low noise, ultra-narrow linewidth single frequency laser. Our POFL is based on only two optical couplers, a simple and passive element which does not introduce extra noise and is insensitive to external perturbation. The feedback loop and the DBR laser constitute a complex cavity, then the DBR structure can ensure the single-frequency laser output, and the long cavity which forms by the high reflectivity grating in the DBR structure and the feedback loop has narrower linewidth and lower RIN [15, 16]. By the resonance of the long cavity, the linewidth and noise of the laser are remarkably reduced, and the effect is better than the above. The linewidth is compressed from 3.96 kHz to 540 Hz. The RIN of relaxation oscillation shifts from 993 kHz down to 192 kHz, and the intensity is reduced by 20dB from −99.9dB/Hz to −119.4dB/Hz. The frequency noise was suppressed at frequencies higher than 1 kHz compared to the DBR laser, with a maximum reduction of about 30 dB from 10 kHz to 100 kHz. The optical signal-to-noise ratio (OSNR) is improved from 60dB to 70dB. Even after amplification to an output power of 10W, the linewidth well below 1 kHz and the OSNR still 65dB are achieved.
2. Experimental setup
The experimental setup of the laser is shown in Fig. 1. The laser system consists of two parts, a DBR-POFL laser (a) and a subsequent fiber amplifier (b). The DBR-POFL laser consists of a Distributed Bragg reflector (DBR) fiber laser and a passive optical-feedback loop (POFL) with two 50/50 couplers.
Fig. 1 Schematic diagram of the narrow-linewidth single-frequency fiber laser. It includes a DBR-POFL laser (a) and a subsequent fiber amplifier (b). The DBR fiber laser is a homemade single-frequency fiber laser which is pumped by a 974nm LD. WDM is wavelength division multiplexing. The first optical coupler (coupler-1) directs half of the light into a fiber loop mirror based on a second coupler (coupler-2) to supply optical feedback for the DBR laser. The amplification stage consists of a 25W LD, a combiner and a section of active fiber (the length is 5.7m and the cladding absorption is 3.90 dB/m @975nm). By the 99/1 coupler, the backward power can be monitored. The pump stripper is a section of 30cm length 10/125 single cladding fiber which is coated by high refractive index UV adhesive.
The DBR fiber laser was a homemade single-frequency fiber laser. The laser cavity was constructed by fusion splicing a narrow-band fiber Bragg grating (FBG) and a broad-band FBG on either end faces of a 1-cm-long highly Yb3+-doped silicon fiber. The active fiber is a commercial fiber (Coractive, DCF-YB-7/128-FA) with a core absorption of about 1800dB/m at 975nm, and the 1-cm-long active fiber could offer sufficient gain. The couplers constitute an optical feedback loop for the DBR fiber laser. The first optical coupler (coupler-1) directs half of the light into a fiber loop mirror based on the second coupler (coupler-2) to supply optical feedback for the DBR laser.
The fiber amplifier (Fig. 1(b)) consists of a 25W laser diode (LD) for optical pumping, a combiner and a section of active fiber (nufern, LMA-YDF-10/130-VIII). The length of the active fiber is 5.7m and the cladding absorption is 3.90 dB/m @975nm. A pump stripper eliminates most of the residual pump light. The whole amplifier is mounted on a water-cooled base plate. To determine the generation of stimulated Brillouin scattering (SBS), the backward power is monitored by the 1% port of the 99/1 coupler.
3. Result and discussion
3.1 Frequency- and intensity-noise suppression
The DBR laser is pumped by a 974nm LD. The DBR laser output power was 41.23mW, and the DBR-POFL laser output power was 21.78mW at a pump power of 140.6mW. All of the measurements were performed at 140.6mW pump power.
We measured the output spectrum of the DBR laser and the DBR-POFL laser using an Optical Spectrum Analyzer (AQ6373, Yokogawa), respectively. With this simple POFL setup, the OSNR was improved by 10dB to 70dB (Fig. 2(a), OSA resolution 0.02nm, span 5nm).
Fig. 2 (a) Spectra of DBR-POFL laser and DBR laser at the same pump power. By the POFL effect, the OSNR was improved by 10dB from 60dB to 70dB. (b) Measured RINs of the laser, also shown is the calculated shot noise limit (green). The peak of relaxation oscillation shifts from 993 kHz of the DBR laser to 192 kHz for the DBR-POFL laser and the peak value reduces by 20dB. The DBR-POFL laser’s noise floor is within 10dB of the shot noise limit.
By using an InGaAs photo detector (PD, Thorlabs, DET01CFC) and a spectrum analyzer (Agilent N9030A PXA), the relative intensity noise (RIN) was measured. Figure 2(b) shows the RIN spectrum of the DBR (black) and the DBR-POFL laser before (red), respectively. The spectra were measured from 0 Hz to 3 MHz. For comparison, the calculated shot noise limit (green) is also shown. The pronounced peak in Fig. 2(b) comes from relaxation oscillations. The relaxation oscillations frequency (ROF) is inversely proportional to the length or the photon lifetime of the cavity [17]. The feedback loop will increase the length and the photon lifetime of the cavity, the ROF will shift to the lower frequency. The peak of relaxation oscillation shifts from 993 kHz of the DBR laser to 192 kHz for the DBR-POFL laser. The peak value is reduced by 20dB from −99.9dB/Hz to −119.4dB/Hz. At frequencies beyond 1MHz, the DBR-POFL laser’s RIN is approaching the noise floor and is within 10dB of the shot noise limit. The maximum noise reduction of about 40 dB occurs at around 1MHz.
The linewidth is measured via the delayed self-homodyne technique [18], with a delay-line of 100 km. The average time and the resolution are 1.8 s and 1 Hz, respectively. The heterodyne signals of the DBR-POFL laser is shown in Fig. 3(a), and the 20 dB linewidths of the DBR-POFL laser are estimated to be 10.8 kHz, indicating the laser linewidth is about 540 Hz. Figure 3(a) shows that the POFL approximately narrows the linewidth of the laser from 3.96 kHz to 540 Hz.
Fig. 3 (a) Spectrum of the self-heterodyne linewidth measurements of DBR laser (black) and DBR-POFL laser (red). The green line is the average of all points in the spectrum, we select the points in the green line to calculate the linewidth. The inset shows the enlarged linewidth of the DBR-POFL laser. The DBR-POFL laser narrows the linewidth of the DBR laser (3.96 kHz) to 540Hz. (b) Measured frequency noise spectra of the fiber laser.
Figure 3(b) shows the frequency noise spectrum, which is measured by 1 km delay-line. The delay line corresponding the frequency upper limit is about 200 kHz, so the cut-off frequency of the frequency noise spectrum is 200 kHz. The frequency noise of the DBR-POFL laser was reduced at frequencies higher than 1 kHz compared to the DBR laser, with a maximum reduction of about 30 dB from 10 kHz to 100 kHz.
Frequency noise is related to laser linewidth. Lower frequency noise means narrower linewidth. Various noise sources such as acoustical noise, thermal noise and 1/f frequency noise, introduce frequency noise in the laser and broaden its linewidth [19–21]. Spontaneous emission is considered as the source of the 1/f frequency noise [21]. The DBR-POFL laser effectively suppressed the 1/f frequency noise relative to the DBR laser at the frequency range from 1 kHz to 200 kHz (Fig. 3(b)). The noise at low frequencies arises from acoustical noise and thermal noise. This part of the noise influences the whole setup, i.e. DBR fiber laser, POFL setup, and amplifier and therefore cannot be effectively suppressed. Therefore, the linewidth reduction mainly is due to the effective suppression of the 1/f frequency noise.
3.2 Principle of passive optical-feedback loop
As results above, the linewidth and noise of the DBR laser are effectively reduced by the POFL. The reason is that the feedback loop and the DBR laser constitute a complex cavity, then the DBR structure can ensure the single-frequency laser output, and the long cavity which forms by the high reflectivity grating in the DBR structure and the feedback loop has narrower linewidth and lower RIN [15, 16]. The resonance condition of the complex cavity is that the free spectrum range (FSR) of the DBR laser is integer multiple of the long cavity’s. Under the condition, the single longitude mode can resonate in the complex cavity. By the resonance of the long cavity, the linewidth and noise of the laser are remarkably reduced. As shown in Fig. 4, we measure the linewidth of different cavity length. The black line is the DBR-POFL laser’s (CavityI, cavity length is about 6m), and the red line is the longer cavity’s (CavityII, cavity length adds 8.5m). The linewidth of the two cavities are 10.8 kHz and 5.5 kHz with −20 dB from the peak, which indicates that laser linewidth are less than 600 Hz and 300 Hz respectively. The linewidth narrows about a factor of 2. The longer cavity is sensitive to the environment and the stability is reduced. So the length of cavity should not be too long.
Fig. 4 The linewidth of different cavity length. The black line is the DBR-POFL laser’s (Cavity I, cavity length is about 6m), and the linewidth is about 540Hz. The red line is the longer cavity’s (Cavity II, cavity length adds 8.5m), and the linewidth is about 275Hz.
The beam split ratio of coupler-1 also influences the intracavity photonics lifetime as the same with the feedback setup length. The beam split ratio was confirmed by taking into consideration various factors, such as the output power, the stability and the effect of noise suppression. If the ratio of coupler is larger, the feedback power is increased and the influence of long cavity is enhanced, the stability of laser is reduced for the long cavity is unstable. Conversely, if the ratio of coupler is smaller, the feedback power is decreased and the effect of noise suppression is reduced. Therefore, we chose a beam split ratio of 50/50.
3.3 Power scaling
With one fiber amplification stage, the frequency- and intensity- noise is not obvious increase, and the spectral linewidth is still less than 1 kHz. The amplified power and backward power as a function of the pump power are displayed in Fig. 5(a). The maximum output power is 10.86 W, the slope efficiency of the fitting line is 64%. The saturation phenomenon doesn’t occur in the amplifier by observing the curve, and the power could be increase more. By the amplifier, the amplification ratio is near 30dB from 20mW to 10W, so we don’t use more pump power. Via monitoring the backward power, the ratio of backward power to output signal μ is less than 0.01. According to the SBS threshold condition μ = 0.01, the amplifier did not occur SBS phenomenon.
Fig. 5 (a) Output power and backward power as the function of the launched pump power. The maximum output power is 10.86W, and the slope efficiency of fitting line is 64%. Ratio of backward power to output signal μ is less than 0.01, and below the SBS threshold condition; (b) Power stability measurement of the DBR-POFL laser over 120 min. The fluctuation is less than 2% over two hours.
The power stability of the laser was measured at an output power of 10W and a wavelength of 1063 nm over two hours Fig. 5(b). The variation of the output power is less than 1% within the first hour as well as within the second hour. The overall variation is less than 2%. A possible reason for the observed variation is that the DBR laser is not temperature controlled. During long time operation, the DBR laser power might drift because of the impact of the heat of pump. The long-term stability could be further improved by temperature controlling the DBR fiber laser.
After amplification to 10 W the OSNR of DBR-POFL laser is still more than 65dB (Fig. 6(a), OSA resolution 0.02nm, span 100nm). Spectral content of amplifier indicating ASE suppression >65 dB during 100nm range.
Fig. 6 (a) Spectrum of the amplifier at 10W output power. Spectral content of amplifier indicating ASE suppression >65 dB during 100nm range. (b) Measured RINs of the amplifier (blue). The RIN spectrum after amplification is similar to the spectrum of the DBR-POFL laser with a relaxation oscillation peak of −109.1dB/Hz at 237 kHz.
Figure 6(b) shows the RIN spectrum after amplification is similar to the DBR-POFL laser spectrum, with a peak value of −109.1dB/Hz at 237 kHz, and approaching the noise floor is within 10dB of the shot noise limit beyond 1.5 MHz. These findings indicate that the amplifier does not introduce extra intensity noise. Furthermore, the peak noise levels of DBR-POFL laser and after amplification are below the DBR laser, showing that the intensity stability was improved.
As Fig. 7(a) shows, after amplification the linewidth slightly increased, the corresponding values were 718Hz (1W)、700Hz (3.2W)、773Hz (5.5W)、764Hz (7W)、746Hz (10W). The linewidth fluctuations arise from our measurement system which is highly sensitive to environmental perturbations. After amplification the linewidth is still well below 1 kHz.
Fig. 7 (a) Spectrum of the self-heterodyne linewidth measurements of amplifier. Subsequent amplification increases the linewidth, but it is still below 1 kHz for an output power of 10 W. (b) Measured frequency noise spectra of the amplifier. After amplification to 10W the noise spectrum is still below the DBR laser from 5 kHz to 200 kHz.
Figure 7(b) shows that the frequency noise after amplification is not obviously increased, but it is still below the DBR laser’s in a frequency range from 5 kHz to 200 kHz.
4. Conclusion
We have proposed a low frequency- and intensity- noise, ultra-narrow linewidth Yb3+-doped single-frequency fiber laser by a simple POFL setup constituted by passive elements, two optical couplers. The POFL setup effectively suppressed both the intensity noise and the frequency noise. Even after the amplifier, the noise did not increase significantly. This way we could achieve a linewidth well below 1 kHz after amplification to 10W output power. The simple scheme has high adaptability and stability. It can be used for many applications that require narrow linewidth and low noise, for example coherent communication, quantum optics, coherent detection and LIDAR.
Acknowledgments
The authors acknowledge the financial support from the National Natural Science Foundation of China (NSFC), Nos. 61235010, 61177048 and 61307054), and the Beijing University of Technology, China.
References and links
1. S. Kameyama, T. Ando, K. Asaka, Y. Hirano, and S. Wadaka, “Compact all-fiber pulsed coherent Doppler lidar system for wind sensing,” Appl. Opt. 46(11), 1953–1962 (2007). [CrossRef] [PubMed]
2. C. G. Carlson, P. D. Dragic, R. K. Price, J. J. Coleman, and G. R. Swenson, “A narrow-linewidth, Yb fiber-amplifier-based upper atmospheric Doppler temperature lidar,” IEEE J. Sel. Top. Quantum Electron. 15(2), 451–461 (2009). [CrossRef]
3. H. S. Margolis, “Metrology: Lattice clocks embrace ytterbium,” Nat. Photonics 3(10), 557–558 (2009). [CrossRef]
4. M. Seimetz, “Laser Linewidth Limitations for Optical Systems with High-Order Modulation Employing Feed Forward Digital Carrier Phase Estimation,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2008), paper OTuM2. [CrossRef]
5. T. Wu, X. Peng, W. Gong, Y. Zhan, Z. Lin, B. Luo, and H. Guo, “Observation and optimization of 4He atomic polarization spectroscopy,” Opt. Lett. 38(6), 986–988 (2013). [CrossRef] [PubMed]
6. S. S. Sané, S. Bennetts, J. E. Debs, C. C. N. Kuhn, G. D. McDonald, P. A. Altin, J. D. Close, and N. P. Robins, “11 W narrow linewidth laser source at 780 nm for laser cooling and manipulation of Rubidium,” Opt. Express 20(8), 8915–8919 (2012). [CrossRef] [PubMed]
7. B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari, V. B. Adya, C. Affeldt, M. Agathos, K. Agatsuma, N. Aggarwal, O. D. Aguiar, L. Aiello, A. Ain, P. Ajith, B. Allen, A. Allocca, P. A. Altin, S. B. Anderson, W. G. Anderson, K. Arai, M. A. Arain, M. C. Araya, C. C. Arceneaux, J. S. Areeda, N. Arnaud, K. G. Arun, S. Ascenzi, G. Ashton, M. Ast, S. M. Aston, P. Astone, P. Aufmuth, C. Aulbert, S. Babak, P. Bacon, M. K. Bader, P. T. Baker, F. Baldaccini, G. Ballardin, S. W. Ballmer, J. C. Barayoga, S. E. Barclay, B. C. Barish, D. Barker, F. Barone, B. Barr, L. Barsotti, M. Barsuglia, D. Barta, J. Bartlett, M. A. Barton, I. Bartos, R. Bassiri, A. Basti, J. C. Batch, C. Baune, V. Bavigadda, M. Bazzan, B. Behnke, M. Bejger, C. Belczynski, A. S. Bell, C. J. Bell, B. K. Berger, J. Bergman, G. Bergmann, C. P. Berry, D. Bersanetti, A. Bertolini, J. Betzwieser, S. Bhagwat, R. Bhandare, I. A. Bilenko, G. Billingsley, J. Birch, R. Birney, O. Birnholtz, S. Biscans, A. Bisht, M. Bitossi, C. Biwer, M. A. Bizouard, J. K. Blackburn, C. D. Blair, D. G. Blair, R. M. Blair, S. Bloemen, O. Bock, T. P. Bodiya, M. Boer, G. Bogaert, C. Bogan, A. Bohe, P. Bojtos, C. Bond, F. Bondu, R. Bonnand, B. A. Boom, R. Bork, V. Boschi, S. Bose, Y. Bouffanais, A. Bozzi, C. Bradaschia, P. R. Brady, V. B. Braginsky, M. Branchesi, J. E. Brau, T. Briant, A. Brillet, M. Brinkmann, V. Brisson, P. Brockill, A. F. Brooks, D. A. Brown, D. D. Brown, N. M. Brown, C. C. Buchanan, A. Buikema, T. Bulik, H. J. Bulten, A. Buonanno, D. Buskulic, C. Buy, R. L. Byer, M. Cabero, L. Cadonati, G. Cagnoli, C. Cahillane, J. C. Bustillo, T. Callister, E. Calloni, J. B. Camp, K. C. Cannon, J. Cao, C. D. Capano, E. Capocasa, F. Carbognani, S. Caride, J. C. Diaz, C. Casentini, S. Caudill, M. Cavaglià, F. Cavalier, R. Cavalieri, G. Cella, C. B. Cepeda, L. C. Baiardi, G. Cerretani, E. Cesarini, R. Chakraborty, T. Chalermsongsak, S. J. Chamberlin, M. Chan, S. Chao, P. Charlton, E. Chassande-Mottin, H. Y. Chen, Y. Chen, C. Cheng, A. Chincarini, A. Chiummo, H. S. Cho, M. Cho, J. H. Chow, N. Christensen, Q. Chu, S. Chua, S. Chung, G. Ciani, F. Clara, J. A. Clark, F. Cleva, E. Coccia, P. F. Cohadon, A. Colla, C. G. Collette, L. Cominsky, M. Constancio, A. Conte, L. Conti, D. Cook, T. R. Corbitt, N. Cornish, A. Corsi, S. Cortese, C. A. Costa, M. W. Coughlin, S. B. Coughlin, J. P. Coulon, S. T. Countryman, P. Couvares, E. E. Cowan, D. M. Coward, M. J. Cowart, D. C. Coyne, R. Coyne, K. Craig, J. D. Creighton, T. D. Creighton, J. Cripe, S. G. Crowder, A. M. Cruise, A. Cumming, L. Cunningham, E. Cuoco, T. D. Canton, S. L. Danilishin, S. D’Antonio, K. Danzmann, N. S. Darman, C. F. Da Silva Costa, V. Dattilo, I. Dave, H. P. Daveloza, M. Davier, G. S. Davies, E. J. Daw, R. Day, S. De, D. DeBra, G. Debreczeni, J. Degallaix, M. De Laurentis, S. Deléglise, W. Del Pozzo, T. Denker, T. Dent, H. Dereli, V. Dergachev, R. T. DeRosa, R. De Rosa, R. DeSalvo, S. Dhurandhar, M. C. Díaz, L. Di Fiore, M. Di Giovanni, A. Di Lieto, S. Di Pace, I. Di Palma, A. Di Virgilio, G. Dojcinoski, V. Dolique, F. Donovan, K. L. Dooley, S. Doravari, R. Douglas, T. P. Downes, M. Drago, R. W. Drever, J. C. Driggers, Z. Du, M. Ducrot, S. E. Dwyer, T. B. Edo, M. C. Edwards, A. Effler, H. B. Eggenstein, P. Ehrens, J. Eichholz, S. S. Eikenberry, W. Engels, R. C. Essick, T. Etzel, M. Evans, T. M. Evans, R. Everett, M. Factourovich, V. Fafone, H. Fair, S. Fairhurst, X. Fan, Q. Fang, S. Farinon, B. Farr, W. M. Farr, M. Favata, M. Fays, H. Fehrmann, M. M. Fejer, D. Feldbaum, I. Ferrante, E. C. Ferreira, F. Ferrini, F. Fidecaro, L. S. Finn, I. Fiori, D. Fiorucci, R. P. Fisher, R. Flaminio, M. Fletcher, H. Fong, J. D. Fournier, S. Franco, S. Frasca, F. Frasconi, M. Frede, Z. Frei, A. Freise, R. Frey, V. Frey, T. T. Fricke, P. Fritschel, V. V. Frolov, P. Fulda, M. Fyffe, H. A. Gabbard, J. R. Gair, L. Gammaitoni, S. G. Gaonkar, F. Garufi, A. Gatto, G. Gaur, N. Gehrels, G. Gemme, B. Gendre, E. Genin, A. Gennai, J. George, L. Gergely, V. Germain, A. Ghosh, A. Ghosh, S. Ghosh, J. A. Giaime, K. D. Giardina, A. Giazotto, K. Gill, A. Glaefke, J. R. Gleason, E. Goetz, R. Goetz, L. Gondan, G. González, J. M. Castro, A. Gopakumar, N. A. Gordon, M. L. Gorodetsky, S. E. Gossan, M. Gosselin, R. Gouaty, C. Graef, P. B. Graff, M. Granata, A. Grant, S. Gras, C. Gray, G. Greco, A. C. Green, R. J. Greenhalgh, P. Groot, H. Grote, S. Grunewald, G. M. Guidi, X. Guo, A. Gupta, M. K. Gupta, K. E. Gushwa, E. K. Gustafson, R. Gustafson, J. J. Hacker, B. R. Hall, E. D. Hall, G. Hammond, M. Haney, M. M. Hanke, J. Hanks, C. Hanna, M. D. Hannam, J. Hanson, T. Hardwick, J. Harms, G. M. Harry, I. W. Harry, M. J. Hart, M. T. Hartman, C. J. Haster, K. Haughian, J. Healy, J. Heefner, A. Heidmann, M. C. Heintze, G. Heinzel, H. Heitmann, P. Hello, G. Hemming, M. Hendry, I. S. Heng, J. Hennig, A. W. Heptonstall, M. Heurs, S. Hild, D. Hoak, K. A. Hodge, D. Hofman, S. E. Hollitt, K. Holt, D. E. Holz, P. Hopkins, D. J. Hosken, J. Hough, E. A. Houston, E. J. Howell, Y. M. Hu, S. Huang, E. A. Huerta, D. Huet, B. Hughey, S. Husa, S. H. Huttner, T. Huynh-Dinh, A. Idrisy, N. Indik, D. R. Ingram, R. Inta, H. N. Isa, J. M. Isac, M. Isi, G. Islas, T. Isogai, B. R. Iyer, K. Izumi, M. B. Jacobson, T. Jacqmin, H. Jang, K. Jani, P. Jaranowski, S. Jawahar, F. Jiménez-Forteza, W. W. Johnson, N. K. Johnson-McDaniel, D. I. Jones, R. Jones, R. J. Jonker, L. Ju, K. Haris, C. V. Kalaghatgi, V. Kalogera, S. Kandhasamy, G. Kang, J. B. Kanner, S. Karki, M. Kasprzack, E. Katsavounidis, W. Katzman, S. Kaufer, T. Kaur, K. Kawabe, F. Kawazoe, F. Kéfélian, M. S. Kehl, D. Keitel, D. B. Kelley, W. Kells, R. Kennedy, D. G. Keppel, J. S. Key, A. Khalaidovski, F. Y. Khalili, I. Khan, S. Khan, Z. Khan, E. A. Khazanov, N. Kijbunchoo, C. Kim, J. Kim, K. Kim, N. G. Kim, N. Kim, Y. M. Kim, E. J. King, P. J. King, D. L. Kinzel, J. S. Kissel, L. Kleybolte, S. Klimenko, S. M. Koehlenbeck, K. Kokeyama, S. Koley, V. Kondrashov, A. Kontos, S. Koranda, M. Korobko, W. Z. Korth, I. Kowalska, D. B. Kozak, V. Kringel, B. Krishnan, A. Królak, C. Krueger, G. Kuehn, P. Kumar, R. Kumar, L. Kuo, A. Kutynia, P. Kwee, B. D. Lackey, M. Landry, J. Lange, B. Lantz, P. D. Lasky, A. Lazzarini, C. Lazzaro, P. Leaci, S. Leavey, E. O. Lebigot, C. H. Lee, H. K. Lee, H. M. Lee, K. Lee, A. Lenon, M. Leonardi, J. R. Leong, N. Leroy, N. Letendre, Y. Levin, B. M. Levine, T. G. Li, A. Libson, T. B. Littenberg, N. A. Lockerbie, J. Logue, A. L. Lombardi, L. T. London, J. E. Lord, M. Lorenzini, V. Loriette, M. Lormand, G. Losurdo, J. D. Lough, C. O. Lousto, G. Lovelace, H. Lück, A. P. Lundgren, J. Luo, R. Lynch, Y. Ma, T. MacDonald, B. Machenschalk, M. MacInnis, D. M. Macleod, F. Magaña-Sandoval, R. M. Magee, M. Mageswaran, E. Majorana, I. Maksimovic, V. Malvezzi, N. Man, I. Mandel, V. Mandic, V. Mangano, G. L. Mansell, M. Manske, M. Mantovani, F. Marchesoni, F. Marion, S. Márka, Z. Márka, A. S. Markosyan, E. Maros, F. Martelli, L. Martellini, I. W. Martin, R. M. Martin, D. V. Martynov, J. N. Marx, K. Mason, A. Masserot, T. J. Massinger, M. Masso-Reid, F. Matichard, L. Matone, N. Mavalvala, N. Mazumder, G. Mazzolo, R. McCarthy, D. E. McClelland, S. McCormick, S. C. McGuire, G. McIntyre, J. McIver, D. J. McManus, S. T. McWilliams, D. Meacher, G. D. Meadors, J. Meidam, A. Melatos, G. Mendell, D. Mendoza-Gandara, R. A. Mercer, E. Merilh, M. Merzougui, S. Meshkov, C. Messenger, C. Messick, P. M. Meyers, F. Mezzani, H. Miao, C. Michel, H. Middleton, E. E. Mikhailov, L. Milano, J. Miller, M. Millhouse, Y. Minenkov, J. Ming, S. Mirshekari, C. Mishra, S. Mitra, V. P. Mitrofanov, G. Mitselmakher, R. Mittleman, A. Moggi, M. Mohan, S. R. Mohapatra, M. Montani, B. C. Moore, C. J. Moore, D. Moraru, G. Moreno, S. R. Morriss, K. Mossavi, B. Mours, C. M. Mow-Lowry, C. L. Mueller, G. Mueller, A. W. Muir, A. Mukherjee, D. Mukherjee, S. Mukherjee, N. Mukund, A. Mullavey, J. Munch, D. J. Murphy, P. G. Murray, A. Mytidis, I. Nardecchia, L. Naticchioni, R. K. Nayak, V. Necula, K. Nedkova, G. Nelemans, M. Neri, A. Neunzert, G. Newton, T. T. Nguyen, A. B. Nielsen, S. Nissanke, A. Nitz, F. Nocera, D. Nolting, M. E. Normandin, L. K. Nuttall, J. Oberling, E. Ochsner, J. O’Dell, E. Oelker, G. H. Ogin, J. J. Oh, S. H. Oh, F. Ohme, M. Oliver, P. Oppermann, R. J. Oram, B. O’Reilly, R. O’Shaughnessy, C. D. Ott, D. J. Ottaway, R. S. Ottens, H. Overmier, B. J. Owen, A. Pai, S. A. Pai, J. R. Palamos, O. Palashov, C. Palomba, A. Pal-Singh, H. Pan, Y. Pan, C. Pankow, F. Pannarale, B. C. Pant, F. Paoletti, A. Paoli, M. A. Papa, H. R. Paris, W. Parker, D. Pascucci, A. Pasqualetti, R. Passaquieti, D. Passuello, B. Patricelli, Z. Patrick, B. L. Pearlstone, M. Pedraza, R. Pedurand, L. Pekowsky, A. Pele, S. Penn, A. Perreca, H. P. Pfeiffer, M. Phelps, O. Piccinni, M. Pichot, M. Pickenpack, F. Piergiovanni, V. Pierro, G. Pillant, L. Pinard, I. M. Pinto, M. Pitkin, J. H. Poeld, R. Poggiani, P. Popolizio, A. Post, J. Powell, J. Prasad, V. Predoi, S. S. Premachandra, T. Prestegard, L. R. Price, M. Prijatelj, M. Principe, S. Privitera, R. Prix, G. A. Prodi, L. Prokhorov, O. Puncken, M. Punturo, P. Puppo, M. Pürrer, H. Qi, J. Qin, V. Quetschke, E. A. Quintero, R. Quitzow-James, F. J. Raab, D. S. Rabeling, H. Radkins, P. Raffai, S. Raja, M. Rakhmanov, C. R. Ramet, P. Rapagnani, V. Raymond, M. Razzano, V. Re, J. Read, C. M. Reed, T. Regimbau, L. Rei, S. Reid, D. H. Reitze, H. Rew, S. D. Reyes, F. Ricci, K. Riles, N. A. Robertson, R. Robie, F. Robinet, A. Rocchi, L. Rolland, J. G. Rollins, V. J. Roma, J. D. Romano, R. Romano, G. Romanov, J. H. Romie, D. Rosińska, S. Rowan, A. Rüdiger, P. Ruggi, K. Ryan, S. Sachdev, T. Sadecki, L. Sadeghian, L. Salconi, M. Saleem, F. Salemi, A. Samajdar, L. Sammut, L. M. Sampson, E. J. Sanchez, V. Sandberg, B. Sandeen, G. H. Sanders, J. R. Sanders, B. Sassolas, B. S. Sathyaprakash, P. R. Saulson, O. Sauter, R. L. Savage, A. Sawadsky, P. Schale, R. Schilling, J. Schmidt, P. Schmidt, R. Schnabel, R. M. Schofield, A. Schönbeck, E. Schreiber, D. Schuette, B. F. Schutz, J. Scott, S. M. Scott, D. Sellers, A. S. Sengupta, D. Sentenac, V. Sequino, A. Sergeev, G. Serna, Y. Setyawati, A. Sevigny, D. A. Shaddock, T. Shaffer, S. Shah, M. S. Shahriar, M. Shaltev, Z. Shao, B. Shapiro, P. Shawhan, A. Sheperd, D. H. Shoemaker, D. M. Shoemaker, K. Siellez, X. Siemens, D. Sigg, A. D. Silva, D. Simakov, A. Singer, L. P. Singer, A. Singh, R. Singh, A. Singhal, A. M. Sintes, B. J. Slagmolen, J. R. Smith, M. R. Smith, N. D. Smith, R. J. Smith, E. J. Son, B. Sorazu, F. Sorrentino, T. Souradeep, A. K. Srivastava, A. Staley, M. Steinke, J. Steinlechner, S. Steinlechner, D. Steinmeyer, B. C. Stephens, S. P. Stevenson, R. Stone, K. A. Strain, N. Straniero, G. Stratta, N. A. Strauss, S. Strigin, R. Sturani, A. L. Stuver, T. Z. Summerscales, L. Sun, P. J. Sutton, B. L. Swinkels, M. J. Szczepańczyk, M. Tacca, D. Talukder, D. B. Tanner, M. Tápai, S. P. Tarabrin, A. Taracchini, R. Taylor, T. Theeg, M. P. Thirugnanasambandam, E. G. Thomas, M. Thomas, P. Thomas, K. A. Thorne, K. S. Thorne, E. Thrane, S. Tiwari, V. Tiwari, K. V. Tokmakov, C. Tomlinson, M. Tonelli, C. V. Torres, C. I. Torrie, D. Töyrä, F. Travasso, G. Traylor, D. Trifirò, M. C. Tringali, L. Trozzo, M. Tse, M. Turconi, D. Tuyenbayev, D. Ugolini, C. S. Unnikrishnan, A. L. Urban, S. A. Usman, H. Vahlbruch, G. Vajente, G. Valdes, M. Vallisneri, N. van Bakel, M. van Beuzekom, J. F. van den Brand, C. Van Den Broeck, D. C. Vander-Hyde, L. van der Schaaf, J. V. van Heijningen, A. A. van Veggel, M. Vardaro, S. Vass, M. Vasúth, R. Vaulin, A. Vecchio, G. Vedovato, J. Veitch, P. J. Veitch, K. Venkateswara, D. Verkindt, F. Vetrano, A. Viceré, S. Vinciguerra, D. J. Vine, J. Y. Vinet, S. Vitale, T. Vo, H. Vocca, C. Vorvick, D. Voss, W. D. Vousden, S. P. Vyatchanin, A. R. Wade, L. E. Wade, M. Wade, S. J. Waldman, M. Walker, L. Wallace, S. Walsh, G. Wang, H. Wang, M. Wang, X. Wang, Y. Wang, H. Ward, R. L. Ward, J. Warner, M. Was, B. Weaver, L. W. Wei, M. Weinert, A. J. Weinstein, R. Weiss, T. Welborn, L. Wen, P. Weßels, T. Westphal, K. Wette, J. T. Whelan, S. E. Whitcomb, D. J. White, B. F. Whiting, K. Wiesner, C. Wilkinson, P. A. Willems, L. Williams, R. D. Williams, A. R. Williamson, J. L. Willis, B. Willke, M. H. Wimmer, L. Winkelmann, W. Winkler, C. C. Wipf, A. G. Wiseman, H. Wittel, G. Woan, J. Worden, J. L. Wright, G. Wu, J. Yablon, I. Yakushin, W. Yam, H. Yamamoto, C. C. Yancey, M. J. Yap, H. Yu, M. Yvert, A. Zadrożny, L. Zangrando, M. Zanolin, J. P. Zendri, M. Zevin, F. Zhang, L. Zhang, M. Zhang, Y. Zhang, C. Zhao, M. Zhou, Z. Zhou, X. J. Zhu, M. E. Zucker, S. E. Zuraw, J. Zweizig, and LIGO Scientific Collaboration and Virgo Collaboration, “Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116(6), 061102 (2016). [PubMed]
8. N. Chiodo, K. Djerroud, O. Acef, A. Clairon, and P. Wolf, “Lasers for coherent optical satellite links with large dynamics,” Appl. Opt. 52(30), 7342–7351 (2013). [CrossRef] [PubMed]
9. G. A. Cranch, “Frequency noise reduction in erbium-doped fiber distributed-feedback lasers by electronic feedback,” Opt. Lett. 27(13), 1114–1116 (2002). [CrossRef] [PubMed]
10. Z. Feng, C. Li, S. Xu, C. Yang, S. Mo, D. Chen, M. Peng, and Z. Yang, “Suppression of the low frequency intensity noise of a single-frequency Yb3+-doped phosphate fiber laser at 1083 nm,” Laser Phys. 24(6), 065106 (2014). [CrossRef]
11. A. Wang, H. Ming, F. Li, L. Xu, L. Lv, H. Gui, J. Huang, and J. Xie, “Single-frequency, single-polarization ytterbium-doped fiber laser by self-injection locking,” Chin. Opt. Lett. 2(4), 223–225 (2004).
12. Q. Zhao, S. Xu, K. Zhou, C. Yang, C. Li, Z. Feng, M. Peng, H. Deng, and Z. Yang, “Broad-bandwidth near-shot-noise-limited intensity noise suppression of a single-frequency fiber laser,” Opt. Lett. 41(7), 1333–1335 (2016). [CrossRef] [PubMed]
13. Y. Zhao, Q. Wang, J. Chang, J. Ni, C. Wang, Z. Sun, P. Wang, G. Lv, and G. Peng, “Suppression of the intensity noise in distributed feedback fiber lasers by self-injection locking,” Laser Phys. Lett. 9(10), 739–743 (2012). [CrossRef]
14. C. Li, S. Xu, X. Huang, Y. Xiao, Z. Feng, C. Yang, K. Zhou, W. Lin, J. Gan, and Z. Yang, “All-optical frequency and intensity noise suppression of single-frequency fiber laser,” Opt. Lett. 40(9), 1964–1967 (2015). [CrossRef] [PubMed]
15. P. Goldberg, P. W. Milonni, and B. Sundaram, “Theory of the fundamental laser linewidth,” Phys. Rev. A 44(3), 1969–1985 (1991). [CrossRef] [PubMed]
16. K. J. Weingarten, B. Braun, and U. Keller, “In situ small-signal gain of solid-state lasers determined from relaxation oscillation frequency measurements,” Opt. Lett. 19(15), 1140–1142 (1994). [CrossRef] [PubMed]
17. O. Svelto, Principles of Lasers (Plenum Press, 1998)
18. R. Q. Hui, Fiber Optic Measurement Techniques (Academic, 2008).
19. S. Foster, A. Tikhomirov, and M. Milnes, “Fundamental Thermal Noise in Distributed Feedback Fiber Lasers,” Quantum Electron. 43(5), 378–384 (2007). [CrossRef]
20. E. Rønnekleiv, “Frequency and Intensity Noise of Single Frequency Fiber Bragg Grating Lasers,” Opt. Fiber Technol. 7(3), 206–235 (2001). [CrossRef]
21. S. Foster, “Fundamental limits on 1/f frequency noise in rare-earth-metal-doped fiber lasers due to spontaneous emission,” Phys. Rev. A 78(1), 013820 (2008). [CrossRef]
