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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 13 — Jun. 18, 2012
  • pp: 13769–13776
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Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control

Kana Iwakuni, Hajime Inaba, Yoshiaki Nakajima, Takumi Kobayashi, Kazumoto Hosaka, Atsushi Onae, and Feng-Lei Hong  »View Author Affiliations


Optics Express, Vol. 20, Issue 13, pp. 13769-13776 (2012)
http://dx.doi.org/10.1364/OE.20.013769


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Abstract

We have developed an optical frequency comb using a mode-locked fiber ring laser with an intra-cavity waveguide electro-optic modulator controlling the optical length in the laser cavity. The mode-locking is achieved with a simple ring configuration and a nonlinear polarization rotation mechanism. The beat note between the laser and a reference laser and the carrier envelope offset frequency of the comb were simultaneously phase locked with servo bandwidths of 1.3 MHz and 900 kHz, respectively. We observed an out-of-loop beat between two identical combs, and obtained a coherent δ-function peak with a signal to noise ratio of 70 dB/Hz.

© 2012 OSA

1. Introduction

2. Outline of a comb system using a high-speed servo controllable mode-locked fiber ring laser

Figure 1
Fig. 1 Setup for a comb with a fiber-coupled waveguide EOM and four-branch configuration. Thick solid lines and curves represent optical fiber; O.I., optical isolator; O.C., output coupler; WDM, wavelength division multiplexing coupler; Q, quarter wave plate; H, half wave plate; P, polarizer; TEC, thermo-electric cooler; EDF, erbium-doped fiber; HNLF, highly nonlinear fiber; PPLN, periodically-poled lithium niobate; PD, photo diode.
shows a mode-locked fiber laser system with an intra-cavity wg-EOM and four output branches. The cavity design is based on that reported by Tamura et al. [17

17. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080–1082 (1993). [CrossRef] [PubMed]

]. The gain medium, an erbium-doped fiber (EDF), is pumped backwards by a 1480-nm laser diode via a wavelength division multiplexing (WDM) coupler. The repetition rate is set at 43 MHz, which is favorable for starting the mode-locking operation and for broadening the comb spectrum with a highly nonlinear fiber (HNLF). An output coupler consumes 30% of the intra-cavity power, and the output power is approximately 4 mW. The pump power is typically 80 mW for the oscillator, and the spectral width Δλ is approximately 24 nm.

An intra-cavity wg-EOM, namely a lithium-niobate-based phase modulator for 1.55 μm, is also inserted for fast control of the cavity length. The operating voltage (Vπ) is less than 5.0 V, and so a high-voltage amplifier is not required. The insertion loss and polarization extinction ratio are less than 5 dB and more than 20 dB, respectively. Wg-EOMs usually have a polarization-maintaining fiber (PMF) on the input side, which often makes it difficult to start the mode-locking utilizing a polarization-rotation mechanism. We attribute the difficulty in the mode-locking to back reflection at the spliced point between the SMF and PMF. Therefore, in this study, we employ a wg-EOM with SMFs on the input and output sides. However, it is still a question as to whether the mode-locking can be maintained whenever the voltage applied to the EOM is widely varied because the input polarization cannot be expected to be linear. For example, if the input is circularly polarized, the output is in a linear polarization state when Vπ is applied to the EOM. However, in practice the mode-locking remains stable at any operating voltage between –10 and 10 V. Therefore, we are able to use the mode-locked laser for the comb experiment.

The right half of Fig. 1 shows four branches, some of which contain an erbium-doped fiber amplifier (EDFA) and HNLF for spectral broadening. The output power is equally distributed into the four branches, amplified by the EDFA, and broadened by the HNLF if necessary. The chirp of the optical pulses is optimally managed for effective amplification and spectral broadening [18

18. Y. Nakajima, H. Inaba, F. L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008). [CrossRef]

]. The three branches employed in this study are used to detect a CEO beat, a beat note with a 1064-nm laser, and a beat note with another comb, respectively.

The frequencies of all the comb modes are stabilized when two of the comb modes are frequency-stabilized. In this study, we stabilize the carrier envelope offset frequency (fCEO) and the frequency of the comb mode at 1064 nm. We use a 1064 nm Nd:YAG laser stabilized to an ultrastable cavity as the 1064 nm reference. The fCEO and the beat frequency between the laser and the comb (fbeat) are individually phase-locked at 30 MHz.

3. High-speed servo control of fiber based frequency comb

3.1 Phase-locking of carrier envelope offset beat

Figure 2
Fig. 2 PLL systems for fCEO, and beat note between the comb and a reference laser. Thick solid lines represent optical fiber, and a thin solid line represents a beam in space. Broken lines represent electric wire. PD, photo detector; BPF, electrical band pass filter; PPLN, periodically-poled lithium niobate.
shows the feedback control system of the fCEO schematically. The CEO beat was detected with an InGaAs photo detector at 1020 nm using a common path f-2f interferometer. The beat note was filtered and amplified at 30 MHz, and then frequency divided to 3 MHz. A double-balanced mixer was used to detect the phase difference between the signal and a hydrogen-maser-based microwave reference (3 MHz). The output of the mixer was added to the injection current of the pump laser as the feedback signal via a loop filter. To achieve a broad servo bandwidth, we undertook the following; (1) the feedback current signal was directly added to the cathode of the pumping laser diode without a bias-T; (2) we eliminated low-pass filters from the phase lock loop as far as we could; (3) we used a relatively broad bandpass filter (center: 30 MHz, 3dB bandwidth: 10 MHz) to ensure the bandwidth; (4) we optimized the parameter of the loop filter experimentally; and (5) we adjusted the intracavity polarization state to maximize the injection current sensitivity against the fCEO. In addition, in this experiment, a differential control was effective in increasing the bandwidth.

Figure 3
Fig. 3 (a) Spectrum and (b) spectral power density of phase noise of the in-loop CEO beat. RBW, resolution bandwidth.
shows an in-loop CEO beat and the spectral density of the residual phase noise. We obtained a coherent δ-function peak with a signal to noise ratio of 70 dB/Hz and a servo bandwidth of more than 900 kHz, which we estimated from the servo bumps in the in-loop spectrum and the spectral density of the phase noise. To the best of our knowledge, this is the broadest servo bandwidth for fCEO locking yet achieved when fbeat is simultaneously locked. The broad bandwidth also enables us to increase the proportional-integration corner frequency in the loop filter to 50 kHz, which indicates successful locking with a broad servo bandwidth. An unexpected bump appears at 600 kHz in the in-loop beat spectrum for simultaneous locking with an fbeat.

As regards fCEO locking in rare-earth doped lasers, it has been a generally accepted opinion that the servo bandwidth is limited due to the long lifetime of the laser level in the gain medium [22

22. B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond fiber laser,” Opt. Express 13(26), 10622–10633 (2005). [CrossRef] [PubMed]

]. We overcome the conventional limitation and consider it to be a sufficiently broad servo bandwidth for a narrow linewidth comb.

3.2 Phase-locking of beat note between comb and a cw laser using an intracavity, waveguide electro-optic modulator

PZTs have been used to control the cavity length of mode-locked lasers. However, the phase locking of a beat frequency with a reference laser (fbeat) using PZTs is often difficult because fbeat contains large and fast phase noise during free running operation, and in most cases their servo bandwidths are limited to less than a few tens of kHz. For phase locking with a broad servo bandwidth, it is possible to use a transducer with broad and flat frequency response characteristics. In this study, we employ an intracavity wg-EOM to control the cavity length (fbeat) [15

15. E. Baumann, F. R. Giorgetta, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “High-performance, vibration-immune, fiber-laser frequency comb,” Opt. Lett. 34(5), 638–640 (2009). [CrossRef] [PubMed]

, 16

16. Y. Nakajima, H. Inaba, K. Iwakuni, K. Hosaka, A. Onae, K. Minoshima, and F. L. Hong, “All-fiber-based frequency comb with an intra-cavity waveguide electro-optic modulator,” Conference on Lasers and Electro-Optics (CLEO), San Jose (2010).

].

Figure 2 also shows a schematic of the phase-locking for the beat note between the comb and the reference laser. The beat note was detected with an InGaAs photo detector at 1064 nm. The detected signal was filtered and amplified at 30 MHz, and mixed using a double-balanced mixer with a hydrogen maser based frequency reference (30 MHz). The output of the mixer was fed back via a loop filter as applied voltage to the intracavity wg-EOM.

With the fbeat locking, we made a similar effort to that employed for the above-mentioned fCEO locking. In our experiment, differential control enabled us to achieve a broad servo bandwidth exceeding 1 MHz although it is not needed to achieve locking.

Figure 4
Fig. 4 (a) Spectrum and (b) spectral power density of phase noise of the in-loop beat between the comb and the 1064 nm reference laser. RBW, resolution bandwidth.
shows the spectrum of an in-loop beat and the spectral density of the residual phase noise. We obtained a coherent δ-function peak with a signal to noise ratio of 75-80 dB/Hz and a servo bandwidth of 1.3 MHz reproducibly. The servo bandwidth was estimated from the frequency at the servo bumps. Unexpected bumps appear at around 600 kHz in the in-loop beat spectrum for simultaneous locking with an fCEO.

4. Evaluation of out-of-loop beat of two comb systems using mode-locked fiber lasers

5. Conclusion

We developed a mode-locked fiber laser with an intra-cavity waveguide EOM for an optical frequency comb with a narrow linewidth. The laser has a simple ring cavity and is based on a nonlinear polarization rotation mechanism for mode locking. We attempted to increase the fCEO servo bandwidth. As a result, we achieved broad servo bandwidths for the fCEO and the fbeat simultaneously to narrow the relative linewidths of all the comb modes. Furthermore, we observed an out-of-loop beat between two identical comb systems to evaluate the performance of the combs.

This simple and robust laser with simultaneous and high-speed two phase locking offers high-performance and practicality, which could support applications requiring high precision and reliability such as optical clocks. In addition, it will become a mainstream high-speed-controllable optical frequency comb since it has a broad bandwidth, mechanical stability, a simple configuration, and commercially available components.

Acknowledgments

We are grateful to M. Onishi, T. Sasaki, T. Okuno and M. Hirano of Sumitomo Electronics Inc. for helpful discussions on optical fiber. We are also grateful to K. Kawasaki of Mitsutoyo Corp. for his help with system fabrication. This work is supported by the “Grant for Industrial Technology Research” program of the New Energy and Industrial Technology Development Organization (NEDO), and also by the “Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST)”.

References and links

1.

K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000). [CrossRef] [PubMed]

2.

K. M. Yamada, A. Onae, F.-L. Hong, H. Inaba, H. Matsumoto, Y. Nakajima, F. Ito, and T. Shimizu, “High precision line profile measurements on C-13 acetylene using a near infrared frequency comb spectrometer,” J. Mol. Spectrosc. 249(2), 95–99 (2008). [CrossRef]

3.

Q. Quraishi, M. Griebel, T. Kleine-Ostmann, and R. Bratschitsch, “Generation of phase-locked and tunable continuous-wave radiation in the terahertz regime,” Opt. Lett. 30(23), 3231–3233 (2005). [CrossRef] [PubMed]

4.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321(5894), 1335–1337 (2008). [CrossRef] [PubMed]

5.

F. Adler, P. Masłowski, A. Foltynowicz, K. C. Cossel, T. C. Briles, I. Hartl, and J. Ye, “Mid-infrared Fourier transform spectroscopy with a broadband frequency comb,” Opt. Express 18(21), 21861–21872 (2010). [CrossRef] [PubMed]

6.

C. Wang and P. Sahay, “Breath analysis using laser spectroscopic techniques: Breath biomarkers, spectral fingerprints, and detection limits,” Sensors (Basel Switzerland) 2009, 8231–8262 (2009).

7.

A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29(10), 1081–1083 (2004). [CrossRef] [PubMed]

8.

W. C. Swann, J. J. McFerran, I. Coddington, N. R. Newbury, I. Hartl, M. E. Fermann, P. S. Westbrook, J. W. Nicholson, K. S. Feder, C. Langrock, and M. M. Fejer, “Fiber-laser frequency combs with subhertz relative linewidths,” Opt. Lett. 31(20), 3046–3048 (2006). [CrossRef] [PubMed]

9.

T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevicius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics 2(6), 355–359 (2008). [CrossRef]

10.

M. J. Martin, S. M. Foreman, T. R. Schibli, and J. Ye, “Testing ultrafast mode-locking at microhertz relative optical linewidth,” Opt. Express 17(2), 558–568 (2009). [CrossRef] [PubMed]

11.

Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F. L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express 18(2), 1667–1676 (2010). [CrossRef] [PubMed]

12.

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008). [CrossRef] [PubMed]

13.

T. C. Briles, D. C. Yost, A. Cingöz, J. Ye, and T. R. Schibli, “Simple piezoelectric-actuated mirror with 180 kHz servo bandwidth,” Opt. Express 18(10), 9739–9746 (2010). [CrossRef] [PubMed]

14.

D. D. Hudson, K. W. Holman, R. J. Jones, S. T. Cundiff, J. Ye, and D. J. Jones, “Mode-locked fiber laser frequency-controlled with an intracavity electro-optic modulator,” Opt. Lett. 30(21), 2948–2950 (2005). [CrossRef] [PubMed]

15.

E. Baumann, F. R. Giorgetta, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “High-performance, vibration-immune, fiber-laser frequency comb,” Opt. Lett. 34(5), 638–640 (2009). [CrossRef] [PubMed]

16.

Y. Nakajima, H. Inaba, K. Iwakuni, K. Hosaka, A. Onae, K. Minoshima, and F. L. Hong, “All-fiber-based frequency comb with an intra-cavity waveguide electro-optic modulator,” Conference on Lasers and Electro-Optics (CLEO), San Jose (2010).

17.

K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett. 18(13), 1080–1082 (1993). [CrossRef] [PubMed]

18.

Y. Nakajima, H. Inaba, F. L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun. 281(17), 4484–4487 (2008). [CrossRef]

19.

F. L. Hong, K. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, “Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser,” Opt. Lett. 28(17), 1516–1518 (2003). [CrossRef] [PubMed]

20.

L. Nugent-Glandorf, T. A. Johnson, Y. Kobayashi, and S. A. Diddams, “Impact of dispersion on amplitude and frequency noise in a Yb-fiber laser comb,” Opt. Lett. 36(9), 1578–1580 (2011). [CrossRef] [PubMed]

21.

J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian f (ceo) phase excursions,” Appl. Phys. B 86(2), 219–227 (2007). [CrossRef]

22.

B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond fiber laser,” Opt. Express 13(26), 10622–10633 (2005). [CrossRef] [PubMed]

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(140.4050) Lasers and laser optics : Mode-locked lasers
(320.7090) Ultrafast optics : Ultrafast lasers

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: April 18, 2012
Manuscript Accepted: May 17, 2012
Published: June 5, 2012

Citation
Kana Iwakuni, Hajime Inaba, Yoshiaki Nakajima, Takumi Kobayashi, Kazumoto Hosaka, Atsushi Onae, and Feng-Lei Hong, "Narrow linewidth comb realized with a mode-locked fiber laser using an intra-cavity waveguide electro-optic modulator for high-speed control," Opt. Express 20, 13769-13776 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-13769


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References

  1. K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt.39(30), 5512–5517 (2000). [CrossRef] [PubMed]
  2. K. M. Yamada, A. Onae, F.-L. Hong, H. Inaba, H. Matsumoto, Y. Nakajima, F. Ito, and T. Shimizu, “High precision line profile measurements on C-13 acetylene using a near infrared frequency comb spectrometer,” J. Mol. Spectrosc.249(2), 95–99 (2008). [CrossRef]
  3. Q. Quraishi, M. Griebel, T. Kleine-Ostmann, and R. Bratschitsch, “Generation of phase-locked and tunable continuous-wave radiation in the terahertz regime,” Opt. Lett.30(23), 3231–3233 (2005). [CrossRef] [PubMed]
  4. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science321(5894), 1335–1337 (2008). [CrossRef] [PubMed]
  5. F. Adler, P. Masłowski, A. Foltynowicz, K. C. Cossel, T. C. Briles, I. Hartl, and J. Ye, “Mid-infrared Fourier transform spectroscopy with a broadband frequency comb,” Opt. Express18(21), 21861–21872 (2010). [CrossRef] [PubMed]
  6. C. Wang and P. Sahay, “Breath analysis using laser spectroscopic techniques: Breath biomarkers, spectral fingerprints, and detection limits,” Sensors (Basel Switzerland)2009, 8231–8262 (2009).
  7. A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett.29(10), 1081–1083 (2004). [CrossRef] [PubMed]
  8. W. C. Swann, J. J. McFerran, I. Coddington, N. R. Newbury, I. Hartl, M. E. Fermann, P. S. Westbrook, J. W. Nicholson, K. S. Feder, C. Langrock, and M. M. Fejer, “Fiber-laser frequency combs with subhertz relative linewidths,” Opt. Lett.31(20), 3046–3048 (2006). [CrossRef] [PubMed]
  9. T. R. Schibli, I. Hartl, D. C. Yost, M. J. Martin, A. Marcinkevicius, M. E. Fermann, and J. Ye, “Optical frequency comb with submillihertz linewidth and more than 10 W average power,” Nat. Photonics2(6), 355–359 (2008). [CrossRef]
  10. M. J. Martin, S. M. Foreman, T. R. Schibli, and J. Ye, “Testing ultrafast mode-locking at microhertz relative optical linewidth,” Opt. Express17(2), 558–568 (2009). [CrossRef] [PubMed]
  11. Y. Nakajima, H. Inaba, K. Hosaka, K. Minoshima, A. Onae, M. Yasuda, T. Kohno, S. Kawato, T. Kobayashi, T. Katsuyama, and F. L. Hong, “A multi-branch, fiber-based frequency comb with millihertz-level relative linewidths using an intra-cavity electro-optic modulator,” Opt. Express18(2), 1667–1676 (2010). [CrossRef] [PubMed]
  12. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett.100(1), 013902 (2008). [CrossRef] [PubMed]
  13. T. C. Briles, D. C. Yost, A. Cingöz, J. Ye, and T. R. Schibli, “Simple piezoelectric-actuated mirror with 180 kHz servo bandwidth,” Opt. Express18(10), 9739–9746 (2010). [CrossRef] [PubMed]
  14. D. D. Hudson, K. W. Holman, R. J. Jones, S. T. Cundiff, J. Ye, and D. J. Jones, “Mode-locked fiber laser frequency-controlled with an intracavity electro-optic modulator,” Opt. Lett.30(21), 2948–2950 (2005). [CrossRef] [PubMed]
  15. E. Baumann, F. R. Giorgetta, J. W. Nicholson, W. C. Swann, I. Coddington, and N. R. Newbury, “High-performance, vibration-immune, fiber-laser frequency comb,” Opt. Lett.34(5), 638–640 (2009). [CrossRef] [PubMed]
  16. Y. Nakajima, H. Inaba, K. Iwakuni, K. Hosaka, A. Onae, K. Minoshima, and F. L. Hong, “All-fiber-based frequency comb with an intra-cavity waveguide electro-optic modulator,” Conference on Lasers and Electro-Optics (CLEO), San Jose (2010).
  17. K. Tamura, E. P. Ippen, H. A. Haus, and L. E. Nelson, “77-fs pulse generation from a stretched-pulse mode-locked all-fiber ring laser,” Opt. Lett.18(13), 1080–1082 (1993). [CrossRef] [PubMed]
  18. Y. Nakajima, H. Inaba, F. L. Hong, A. Onae, K. Minoshima, T. Kobayashi, M. Nakazawa, and H. Matsumoto, “Optimized amplification of femtosecond optical pulses by dispersion management for octave-spanning optical frequency comb generation,” Opt. Commun.281(17), 4484–4487 (2008). [CrossRef]
  19. F. L. Hong, K. Minoshima, A. Onae, H. Inaba, H. Takada, A. Hirai, H. Matsumoto, T. Sugiura, and M. Yoshida, “Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser,” Opt. Lett.28(17), 1516–1518 (2003). [CrossRef] [PubMed]
  20. L. Nugent-Glandorf, T. A. Johnson, Y. Kobayashi, and S. A. Diddams, “Impact of dispersion on amplitude and frequency noise in a Yb-fiber laser comb,” Opt. Lett.36(9), 1578–1580 (2011). [CrossRef] [PubMed]
  21. J. J. McFerran, W. C. Swann, B. R. Washburn, and N. R. Newbury, “Suppression of pump-induced frequency noise in fiber-laser frequency combs leading to sub-radian f (ceo) phase excursions,” Appl. Phys. B86(2), 219–227 (2007). [CrossRef]
  22. B. R. Washburn, W. C. Swann, and N. R. Newbury, “Response dynamics of the frequency comb output from a femtosecond fiber laser,” Opt. Express13(26), 10622–10633 (2005). [CrossRef] [PubMed]

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