Open Access
Add to BibSonomyAbstract
We report a fiber laser noise reduction method by locking it to an actively stabilized optical delay line, specifically a fiber-based Mach–Zehnder interferometer with a 10 km optical fiber spool. The fiber spool is used to achieve large arm imbalance. The heterodyne signal of the two arms converts the laser noise from the optical domain to several megahertz, and it is used in laser noise reduction by a phase-locked loop. An additional phase-locked loop is induced in the system to compensate the phase noise due to environmentally induced length fluctuations of the optical fiber spool. A major advantage of this structure is the efficient reduction of out-of-loop frequency noise, particularly at low Fourier frequency. The frequency noise reaches −30 dBc/Hz at 1 Hz, which is reduced by more than 90 dB compared with that of the laser in its free-running state.
© 2017 Optical Society of America
1. Introduction
Low-phase noise continuous-wave (CW) lasers are key requirements for applications such as high-resolution spectroscopy [1], optical atomic clocks [2], low-noise interferometric sensors [3], optical frequency transfer via fiber link [4–11], and many others. The commercial lasers, such as Erbium-doped fiber distributed-feedback lasers, typically exhibit optical linewidths between 1 kHz and 10 kHz It is still insufficient for many of these applications.
For long term frequency stabilization, the laser frequency is often locked to either the side or the peak of the narrow saturated absorption features of a kind of atomic [12]. While for short term stabilization, the frequency noise and linewidth of CW lasers are usually reduced by the Pound-Drever-Hall method [13–16]. Then the laser noise can be measured by analysing the beat frequency of two identical system [17–19]. In this method, a linewidth of sub-40 mHz has been achieved for a CW laser [16], and the fractional frequency stability of the stabilized laser has been reduced to 1 × 10−15 at 1 s [14]. However, this scheme requires a fine alignment of free-space optical components, tight polarization adjustment, and spatial mode matching. Moreover, the cavity has to be housed in a high-vacuum enclosure with thermal radiation shielding to avoid air-index fluctuations and improve thermal control and stability. Therefore, the system is usually bulky, fragile, and expensive, and it is difficult to adopt this laser stabilization method outside of the laboratory, such as for portable interferometric sensors.
An alternative approach to reduce the phase noise of the laser is to measure it via a fixed relative time delay line [20, 21] and to subsequently compensate it using a phase-locked loop. The structure can also be used in the mode-locked laser system [22]. The fixed relative time delay can be obtained by a two-arm interferometer such as Mach–Zehnder interferometer (MZI). It converts the laser frequency excursion of the optical frequency (νopt) into phase error (ϕerr (f)) in the radio frequency domain with a transfer function
where τ is the fiber delay time. The bandwidth of the laser stabilization system is proportional to 1/τ. When the imbalance arm is 10 km, the bandwidth equals 20 kHz. f is the Fourier frequency. For f ≪ 1/τ, HMZI (f) ≈ 2πτ.As presented in Fig. 1, if the arm imbalance of the interferometer is 1 km, 1 Hz frequency excursion in the optical domain will convert into an approximately 31.4 μrad phase signal; if the arm imbalance is 10 km, 1 Hz frequency excursion in the optical domain will convert into an approximately 314 μrad phase signal. In order to obtain a sufficient frequency discriminator sensitivity, a relatively large arm imbalance is required. Optical fiber is an excellent material to achieve such a large path imbalance. It can lead to a more robust, more compact, and cheaper device than the ultrastable cavity. However, the time delay induced by an optical fiber would fluctuate as the optical length of the fiber is sensitive to environmentally induced acoustic, mechanical, and thermal perturbations. These perturbations can significantly degrade phase noise reduction of the CW laser, particularly at low Fourier frequency. Usually, air-sealed chambers or vacuum chambers are used to passively isolate the interferometer from the influence of temperature and vibration [23–28].
In this letter, an acousto-optic modulator (AOM) is used in order to actively compensate environmentally induced phase noise in the fiber-based MZI. The stabilized MZI is used for extracting the intrinsic frequency excursion of a fiber laser (Koheras ADJUSTIK E15, NKT Photonics). The scheme is not only portable but also robust to the environment. In our experiment, the arm imbalance of the MZI is 10 km. Its bandwidth is 20 kHz, and its quality factor theoretically equals to that of a 10 cm Fabry–Perot cavity with a finesse of 330000. When the MZI is actively stabilized, the out-of-loop frequency noise of the stabilized laser is reduced by more than 45 dB at low Fourier frequency compared to that when the MZI has not been stabilized. This implies that the frequency noise performance of the laser can be efficiently reduced by this laser stabilization scheme.
2. Theoretical analysis
A fiber-based optical delay line is used to compensate the laser noise, which is shown in Fig. 2. The laser signal cos(2πνt+Φ0) is launched into an MZI and becomes cos(2π(ν+Δν)t+Θ0+δΘ(t)) and cos(2π(ν+νs)t+Θ0), which are due to the fiber delay and an optical frequency shifter, respectively, where Δν equals ν(t+Δt)−νt, and Δt is the light transfer time in the optical fiber. When the signals from the two arms recombine, they are detected by a photodiode. The frequency of the detected signal after a low-pass filter is cos(2π(νs-Δν)t−δΘ(t)).
Δν is due to the laser noise and δΘ(t) is due to length fluctuations of the optical fiber. If there was no environmentally induced noise in the fiber in the optical delay line system, the extracted error signal would only come from the laser. The detected signal would be cos(νst−Δνt). It can be used to reduce the laser noise with a feedback loop within a bandwidth of 1/Δt. However, owing to the existence of environmentally induced noise δΘ(t), the extracted error signal is not only from the laser noise but also from the optical delay line. The ideal result of the compensation systems should reduce both noises simultaneously.
Even though the laser noise exists in the range from low Fourier frequency to high Fourier frequency while the noise from the optical delay line only dominates at low Fourier frequency, it is impossible to compensate the laser noise and the noise in the optical delay line separately. Therefore, we adjust the two noise reduction loops simultaneously. While adjusting the proportional-integral (PI) parameters of the two noise reduction loops, a signal analyzer and an oscilloscope are used to monitor the out-of-loop phase noise of the laser by analyzing the beat frequency of the laser. First, we compensate the noise of the laser approximately such that the frequency noise at high Fourier frequency is significantly reduced. Then, we begin to compensate the noise in the optical delay line. In this process, we attempt to minimize the laser noise at low Fourier frequency. We obtain a relatively low laser noise at low Fourier frequency by adjusting the bandwidth of the loop filter and the PI parameters.
3. Experimental setup and result
The frequency noise reduction scheme of the laser is shown in Fig. 3. Frequency noise reduction is based on the extracted error signal from a frequency-shifted MZI. The frequency-shifted MZI converts the optical frequency fluctuation into a phase error signal in the radio frequency domain. The carrier signal of the phase error is the center frequency of the AOM. The input optical wave is split between the two arms of the MZI by a 50/50 fiber coupler (Coupler-1). The first arm of the MZI consists of an AOM (AOM2) and the fiber spool. The AOM is used to shift the frequency of the laser signal thereby generating a heterodyne signal between the signals propagating in the two arms. It is also used to compensate environmentally induced phase fluctuations in the MZI. The second arm of the MZI consists of a polarization controller. By adjusting the polarization controller, light waves in the two arms of the MZI will share the same state of polarization, which leads to a maximum beat-note signal amplitude. From the beat-note, the frequency noise of the laser and environmentally induced phase noise in the interferometer can be extracted.
Fig. 3 Frequency noise reduction scheme of the CW laser. CW: CW laser, AOM: acousto-optic modulator, AMP: amplifier, VCO: voltage-controlled oscillator, PI-Con: PI controller, BPF: band-pass filter, LPF: low-pass filter, Frq.Source: frequency source, Frq. Analyzer: frequency analyzer, P.C.: polarization controller, and PD: photodetector. The couplers are all polarization insensitive. The signal detected by the photodetector after Coupler-2 is used to stabilize the interferometer and reduce the laser noise. The signal detected by the photodiode after coupler-4 is used to compensate environmentally induced phase fluctuations in the fiber spool and monitor the out-of-loop phase noise of the laser.
The optical power seeded into the interferometer is 3 dBm. The optical power loss in the first arm is approximately 12 dB due to the loss in the couplers, AOM2, and the fiber spool. The optical power loss in the second arm is approximately 7 dB due to the loss in the two couplers and polarization controller. The beat signal of the two arms is photodetected at the output port of Coulper-2. The detected radio signal contains a carrier signal, which is centered at fAOM2. This radio signal is phase-modulated by Δνt + δΘ(t) + Δθrf, where Δθrf is the local oscillator phase shift, Δνt is frequency noise of the laser, and δΘ(t) is environmentally induced phase noise in the MZI. In order to minimize the interference between Δνt and δΘ(t), the laser phase noise reduction and the interferometer stabilization process will be controlled by different PI controllers. Before the error signal is sent into the PI controller, it is amplified and filtered. The bandwidth of the low-pass filter for the interferometer stabilization loop is below 100 Hz because the environmental influence is predominant at low Fourier frequencies [24]. The bandwidth of the low-pass filter for the laser phase noise reduction is 20 kHz owing to the bandwidth of the MZI. However, it is not enough to achieve the minimum frequency noise for the laser. More importantly, the proportional and integral parameters of the PI controllers for the laser noise reduction and interferometer stabilization should be adjusted together based on the out-of-loop phase noise of the laser.
The out-of-loop phase noise of the laser is monitored by another MZI [17, 21]. An AOM (AOM3) is used to shift the frequency of the laser signal in the arm of the MZI that has a 10 km-long fiber spool. The analysis MZI is placed in a chamber to avoid vibration. During the out-of-loop noise measurement, an error signal is also feedback to the AOM to further stabilize the MZI. The optical power photodetected at the output port of Coulper-4 contains a radio frequency, which is centered at fAOM3. The signal is phase-modulated by the out-of-loop phase noise of the laser. By adjusting the proportional and integral parameters of the laser stabilization loop and its interferometer stabilization loop, the lowest out-of-loop frequency noise below −30 dBc/Hz is achieved for the Fourier frequency at 1 Hz. A signal source analyzer (FSUP-26, Rohde & Schwarz) is used to analyze the frequency noise of the output beat signal. Figure 4 illustrates the out-of-loop frequency noises of the laser under different states. The frequency noise is reduced by more than 90 dB for the Fourier frequency at approximately 1 Hz compared to that of the free-running laser. Furthermore, the phase noise of the laser is reduced by approximately 45 dB for the Fourier frequency at 1 Hz compared to that when the MZI, which is used for laser stabilization, has not been stabilized yet. This illustrates that the environmental influence on the MZI is great at low Fourier frequency and is reduced efficiently. However, it is still difficult to completely eliminate the interference between intrinsic laser noise and environmentally induced noise of the fiber.
Fig. 4 Out-of-loop frequency noise of the stabilized laser. The noise floor is in-loop measurement without the 10 km fiber spool.
In order to further test the laser stabilization performance, we built two sets of laser stabilization systems, which are illustrated in Fig. 5. The two laser stabilization system were constructed with separate fiber Michelson interferometer mounted on independent vibration isolation platforms with separate electronics and optical devices. However, the two systems are identical and their contributions to the measurements can be considered the same. The output of the laser is splitted 50/50 into the two systems and then stabilized respectively. The beat signal of the two systems is detected by a broadband photodiode, measured by FSUP-26. and presented as the yellow dashed curve in Fig. 4. The curves presents the relative frequency noise between the two identical laser stabilization systems [18]. The frequency noise of the two lasers should be below this curve if their noise are fully independent from each other.
Fig. 5 Test of the laser stabilization performance with two sets of identical stabilization systems. The isolator (iso) is used to reduce the back-reflection signal. The fiber after the coupler (cp-1) is used for de-correlation.
4. Conclusion
In conclusion, we demonstrated a noise reduction method for a CW laser by locking it to an actively stabilized MZI with an arm imbalance of 10 km. The frequency noise of the laser is reduced significantly by actively stabilizing the MZI, particularly at low Fourier frequency. The frequency noise is approximately 45 dB lower compared to that when the laser is stabilized without stabilizing the MZI at low Fourier frequency. This improvement is due to the efficient active reduction of environmentally induced phase noise of the MZI. Previously, the environmental influence was isolated using air-sealed chambers, vacuum chambers or other passive protection method. However, these methods make the laser stabilization scheme bulky. Compared to such methods, our scheme is both portable and more immune to environmental influence. It provides a more compact, robust, and flexible alternative to the ultrastable cavity-locking method with an all-fiber system.
Funding
National Natural Science Foundation of China (NSFC) (61535001,61371074) and Program of International S&T Cooperation (2016YFE0100200).
Acknowledgments
The authors thank Yunfeng Zhang and Yaolin Zhang for technical discussions.
References and links
1. R. de Groote, I. Budinčević, J. Billowes, M. Bissell, T. Cocolios, G. Farooq Smith, V. Fedosseev, K. Flanagan, S. Franchoo, R. G. Ruiz, H. Heylen, R. Li, K. M. Lynch, B. A. Marsh, G. Neyens, R. E. Rossel, S. Rothe, H. H. Stroke, K. D. A. Wendt, S. G. Wilkins, and X. Yang, “Use of a continuous wave laser and pockels cell for sensitive high-resolution collinear resonance ionization spectroscopy,” Phys. Rev. Lett. 115, 132501 (2015). [CrossRef] [PubMed]
2. Y. Jiang, A. Ludlow, N. Lemke, R. Fox, J. Sherman, L.-S. Ma, and C. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011). [CrossRef]
3. R. X. Adhikari, “Gravitational radiation detection with laser interferometry,” Rev. Mod. Phys. 86, 121 (2014). [CrossRef]
4. L.-S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett. 19, 1777–1779 (1994). [CrossRef] [PubMed]
5. N. Newbury, P. Williams, and W. Swann, “Coherent transfer of an optical carrier over 251 km,” Opt. Lett. 32, 3056–3058 (2007). [CrossRef] [PubMed]
6. O. Terra, G. Grosche, and H. Schnatz, “Brillouin amplification in phase coherent transfer of optical frequencies over 480 km fiber,” Opt. Express 18, 16102–16111 (2010). [CrossRef] [PubMed]
7. M. Fujieda, M. Kumagai, S. Nagano, A. Yamaguchi, H. Hachisu, and T. Ido, “All-optical link for direct comparison of distant optical clocks,” Opt. Express 19, 16498–16507 (2011). [CrossRef] [PubMed]
8. O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the internet fiber network,” Opt. Express 20, 23518–23526 (2012). [CrossRef] [PubMed]
9. D. Li, D. Hou, E. Hu, and J Zhao, “Phase conjugation frequency dissemination based on harmonics of optical comb at 10−17 instability level,” Opt. Lett. 39, 5058–5061 (2014). [CrossRef] [PubMed]
10. D. Calonico, E. Bertacco, C. Calosso, C. Clivati, G. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. Sutyrin, G. Tino, ME. Zucco, and F. Levi, “High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117, 979–986 (2014). [CrossRef]
11. F. Stefani, O. Lopez, A. Bercy, W.-K. Lee, C. Chardonnet, G. Santarelli, P.-E. Pottie, and A. Amy-Klein, “Tackling the limits of optical fiber links,” J. Opt. Soc. Am. B 32, 787–797 (2015). [CrossRef]
12. K.B. MacAdam, A. Steinbach, and Carl Wieman, “A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb,” Am. J. Phys. 60, 1098–1111 (1992) [CrossRef]
13. R. Drever, J. L. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983). [CrossRef]
14. A. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette, S. Foreman, M. Boyd, S. Blatt, and J. Ye, “Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1×10–15,” Opt. lett. 32, 641–643 (2007). [CrossRef] [PubMed]
15. S. Webster, M. Oxborrow, S. Pugla, J. Millo, and P. Gill, “Thermal-noise-limited optical cavity,” Phys. Rev. A 77, 033847 (2008). [CrossRef]
16. T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. Martin, L. Chen, and J. Ye, “A sub-40-mhz-linewidth laser based on a silicon single-crystal optical cavity,” Nat. Photonics 6, 687–692 (2012). [CrossRef]
17. H. Ludvigsen, M. Tossavainen, and M. Kaivola, “Laser linewidth measurements using self-homodyne detection with short delay,” Opt. Commun. 155, 180–186 (1998). [CrossRef]
18. R. Scott, C. Langrock, and B. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7, 641–655 (2001). [CrossRef]
19. D. Hou, C.-C. Lee, Z. Yang, and ST.R. chibli, “Timing jitter characterization of mode-locked lasers with Hz resolution using a simple optical heterodyne technique,” Opt. Lett. 40, 2985–2988 (2015). [CrossRef] [PubMed]
20. Y. T. Chen, “Use of single-mode optical fiber in the stabilization of laser frequency,” Appl. Opt. 28, 2017–2021 (1989). [CrossRef] [PubMed]
21. G. Cranch, “Frequency noise reduction in erbium-doped fiber distributed-feedback lasers by electronic feedback,” Opt. Lett. 27, 1114–1116 (2002). [CrossRef]
22. K. Jung and J. Kim, “All-fibre photonic signal generator for attosecond timing and ultralow-noise microwave,” Sci. Rep. 5, 16250 (2015). [CrossRef]
23. B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Opt. 45, 8491–8499 (2006). [CrossRef] [PubMed]
24. F. Kéfélian, H. Jiang, P. Lemonde, and G. Santarelli, “Ultralow-frequency-noise stabilization of a laser by locking to an optical fiber-delay line,” Opt. Lett. 34, 914–916 (2009). [CrossRef] [PubMed]
25. H. Jiang, F. Kéfélian, P. Lemonde, A. Clairon, and G. Santarelli, “An agile laser with ultra-low frequency noise and high sweep linearity,” Opt. Express 18, 3284–3297 (2010). [CrossRef] [PubMed]
26. T. G. McRae, S. Ngo, D. A. Shaddock, M. T. Hsu, and M. B. Gray, “Frequency stabilization for space-based missions using optical fiber interferometry,” Opt. Lett. 38, 278–280 (2013). [CrossRef] [PubMed]
27. T. G. McRae, S. Ngo, D. A. Shaddock, M. T. Hsu, and M. B. Gray, “Digitally enhanced optical fiber frequency reference,” Opt. Lett. 39, 1752–1755 (2014). [CrossRef] [PubMed]
28. J. Dong, Y. Hu, J. Huang, M. Ye, Q. Qu, T. Li, and L. Liu, “Subhertz linewidth laser by locking to a fiber delay line,” Appl. Opt. 54, 1152–1156 (2015). [CrossRef] [PubMed]
