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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4889–4895
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Optical repetition rate stabilization of a mode-locked all-fiber laser

Steffen Rieger, Tim Hellwig, Till Walbaum, and Carsten Fallnich  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4889-4895 (2013)
http://dx.doi.org/10.1364/OE.21.004889


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Abstract

We designed an all-fiber mode-locked Erbium laser with optically stabilized repetition rate of 31.4 MHz. The stabilization was achieved by changing the refractive index of an Ytterbium-doped fiber in the resonator via optical pumping at a wavelength of 978 nm; and for long-term stability the local temperature of the fiber was additionally controlled with a thermo-electric element. The repetition rate was stabilized over 12 hours, and an Allan deviation of 2.5 × 10−12 for an averaging time of 1 s could be achieved.

© 2013 OSA

1. Introduction

Mode-locked fiber lasers are attractive sources for ultrashort light pulses in many applications. Fiber lasers are compact, reliable, cost-effective and offer possibilities for all-fiber concepts. Their applications cover many domains, e. g. in nonlinear microscopy [1

1. D. Träutlein, F. Adler, K. Moutzouris, A. Jeromin, A. Leitenstorfer, and E. Ferrando-May, “Highly versatile confocal microscopy system based on a tunable femtosecond Er:fiber source,” J. Biophotonics 1, 53–61 (2008). [CrossRef]

, 2

2. C. Cleff, J. Epping, P. Gross, and C. Fallnich, “Femtosecond OPO based on LBO pumped by a frequency-doubled Yb-fiber laser-amplifier system for CARS spectroscopy,” Appl. Phys. B 103, 795–800 (2011). [CrossRef]

] and the generation of optical frequency combs [3

3. G. G. Ycas, F. Quinlan, S. A. Diddams, S. Ostermann, S. Mahadevan, S. Redman, R. Terrien, L. Ramsey, C. F. Bender, B. Botzer, and S. Sigurdsson, “Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb,” Opt. Express 20, 6631–6643 (2012). [CrossRef] [PubMed]

]. For the latter application it is necessary to measure and control the carrier envelope offset (CEO) frequency as well as the laser repetition rate [4

4. H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002). [CrossRef]

].

The most common method of repetition rate control is a movable mirror in the free-space part of the laser cavity [5

5. W. Zhang, H. Han, Y. Zhao, Q. Du, and Z. Wei, “A 350MHz Ti:sapphire laser comb based on monolithic scheme and absolute frequency measurement of 729nm laser,” Opt. Express 17, 6059–6067 (2009). [CrossRef] [PubMed]

8

8. D. C. Heinecke, A. Bartels, and S. A. Diddams, “Offset frequency dynamics and phase noise properties of a self-referenced 10 GHz Ti:sapphire frequency comb,” Opt. Express 19, 18440–18451 (2011). [CrossRef] [PubMed]

], with the obvious disadvantage of a higher exposure to environmental influences, e. g. dust and mechanical perturbations. To avoid these disadvantages, an all-fiber setup is preferred, in which it is possible to use, e. g., pump power control of the gain fiber [9

9. N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321–324 (2004). [CrossRef]

, 10

10. H. Hundertmark, D. Wandt, C. Fallnich, N. Haverkamp, and H. R. Telle, “Phase-locked carrier-envelope-offset frequency at 1560 nm,” Opt. Express 12, 770–775 (2004). [CrossRef] [PubMed]

], which utilizes wavelength shifting as control mechanism. This may be undesirable for applications where a constant wavelength is needed. Furthermore, it significantly changes the pulse parameters. Another possibility is the stretching of fibers, e. g., by using a piezoelectric actuator [11

11. B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, and M. F. Yan, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett. 29, 250–252 (2004). [CrossRef] [PubMed]

, 12

12. J. Rauschenberger, T. M. Fortier, D. J. Jones, J. Ye, and S. T. Cundiff, “Control of the frequency comb from a mode-locked Erbium-doped fiber laser,” Opt. Express 10, 1404–1410 (2002). [CrossRef] [PubMed]

]. A well-approved design developed by our group [13

13. T. Walbaum, M. Löser, P. Gross, and C. Fallnich, “Mechanisms in passive synchronization of erbium fiber lasers,” Appl. Phys. B 102, 743–750 (2011). [CrossRef]

] uses about 40 cm of bend-insensitive fiber wound around a piezoelectric stretcher and offers a tuning range of the optical path length of approx. 100 μm. Other setups are capable of a geometric elongation of approx. 7 μm [11

11. B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, and M. F. Yan, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett. 29, 250–252 (2004). [CrossRef] [PubMed]

] or 1 μm and 10 μm in two stages [12

12. J. Rauschenberger, T. M. Fortier, D. J. Jones, J. Ye, and S. T. Cundiff, “Control of the frequency comb from a mode-locked Erbium-doped fiber laser,” Opt. Express 10, 1404–1410 (2002). [CrossRef] [PubMed]

]. Naturally, these devices consist of mechanical parts, which suffer from decreasing long-term performance due to abrasion and require the resonator to be opened when parts have to be exchanged.

A different approach to control the repetition rate is keeping the geometrical resonator length L fixed, but changing the optical length s = nL, with n being the refractive index. This can be accomplished via optical pumping of a dedicated active fiber, which changes the absorption at the pump wavelength and the gain at the respective emission wavelength. The change of absorption and gain is connected to a refractive index change Δn(λ) also for other wavelengths λ via the Kramers-Kronig relation [14

14. R. de L. Kronig, “On the theory of dispersion of X-rays,” J. Opt. Soc. Am. 12, 547–557 (1926). [CrossRef]

]. This effect has do be distinguished from the thermal refractive index change due to the absorption of pump power in the fiber, which has the same sign and similar order of magnitude but is significantly slower, in the order of hundredths of milliseconds instead of 0.85 ms [15

15. H. Tünnermann, J. Neumann, D. Kracht, and P. Weßels, “All-fiber phase actuator based on an erbium-doped fiber amplifier for coherent beam combining at 1064 nm,” Opt. Lett. 36, 448–450 (2011). [CrossRef] [PubMed]

]. In our setup fast actuation is needed and we therefore rely mostly on the fast refractive index change, which is well-described [16

16. M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, “Resonantly Enhanced Nonlinearity in Doped Fibers for Low-Power All-Optical Switching: A Review,” Opt. Fiber Technol. 3, 44–64 (1997). [CrossRef]

19

19. A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16, 12658–12663 (2008). [CrossRef] [PubMed]

] and used for coherent combining of continuous-wave (cw) Erbium amplifiers by Ytterbium fibers [20

20. A. A. Fotiadi, N. Zakharov, O. L. Antipov, and P. Mégret, “All-fiber coherent combining of Er-doped amplifiers through refractive index control in Yb-doped fibers,” Opt. Lett. 34, 3574–3576 (2009). [CrossRef] [PubMed]

] and vice versa [15

15. H. Tünnermann, J. Neumann, D. Kracht, and P. Weßels, “All-fiber phase actuator based on an erbium-doped fiber amplifier for coherent beam combining at 1064 nm,” Opt. Lett. 36, 448–450 (2011). [CrossRef] [PubMed]

]. However, the obvious step to use this technique for the repetition rate stabilization of a mode-locked laser can now be reported for the first time.

The crucial difference between these two applications is, that for pulsed lasers not the phase refractive index change Δn but the group refractive index change Δng is relevant. This applies similarly to the optical path length change Δs, where the group optical path length change Δsg = ngL is the important quantity for the propagation of pulses. Prior investigations as done in [19

19. A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16, 12658–12663 (2008). [CrossRef] [PubMed]

] were concentrated on Δs, using a probe beam emitted by a cw laser on a single wavelength. Therefore, it was necessary to evaluate the benefit of this method for the stabilization of a mode-locked laser by determining the maximum tuning range of Δsg and comparing it to environmental influences resulting from the thermo-optical effect.

2. Preinvestigations on the optically induced refractive index change

For the above purpose we used an interferometric measurement setup similar to the one described in [19

19. A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16, 12658–12663 (2008). [CrossRef] [PubMed]

] and placed an Ytterbium-doped fiber (Liekki Yb-1200-4/125, about 78 cm long) in one arm of a Mach-Zehnder interferometer. It was pumped by a laser diode at 978 nm emission wavelength connected to the Ytterbium-doped fiber via a wavelength division multiplexer (WDM). The probe beam was emitted by a cw Erbium fiber laser with tunable wavelength from 1500 nm to 1600 nm and 2 mW to 8 mW output power (depending on the wavelength). The pump-dependent phase change experienced by the light wave in the Ytterbium fiber interferometer arm was measured for pump powers up to 450 mW. The maximum possible optical path length change for this fiber was determined to be Δs = 3.5μm at λ = 1500nm linearly decreasing to Δs = 3.2μm at λ = 1600nm. These values are the limiting ones for the phase control as it is reported for coherent combining experiments [15

15. H. Tünnermann, J. Neumann, D. Kracht, and P. Weßels, “All-fiber phase actuator based on an erbium-doped fiber amplifier for coherent beam combining at 1064 nm,” Opt. Lett. 36, 448–450 (2011). [CrossRef] [PubMed]

, 20

20. A. A. Fotiadi, N. Zakharov, O. L. Antipov, and P. Mégret, “All-fiber coherent combining of Er-doped amplifiers through refractive index control in Yb-doped fibers,” Opt. Lett. 34, 3574–3576 (2009). [CrossRef] [PubMed]

].

In order to obtain the required information about Δsg, the assumption of a linear relation between Δn(λ) and λ was made, allowing to calculate the variation of the dispersion up to its first order. A maximum possible change of Δsg = 7.5μm could be obtained in the wavelength range of 1500 nm to 1600 nm. Interestingly, this is significantly higher than the corresponding phase path length change. It is also comparable to what can be achieved by using the common piezoelectric fiber stretchers mentioned above, but only sufficient for the stabilization of a laser in a well temperature-controlled laboratory. With the thermo-optical coefficient of a single mode fiber (α = 9.2 × 10−6/°C [21

21. S. Chang, C.-C. Hsu, T.-H. Huang, W.-C. Chuang, Y.-S. Tsai, J.-Y. Shieh, and C.-Y. Leung, “Heterodyne Interferometric Measurement of the Thermo-Optic Coefficient of Single Mode Fiber,” Chinese J. Phys. 38, 437–442 (2000).

]) and assuming a group index of ng = 1.468 [22

22. Corning SMF-28e+ Optical Fiber Product Information (2006).

], a resonator with a length of L = 6.59m (see below) will experience a temperature dependent change of its optical path length of ΔsgT = αngL = 89.0μm/°C with the temperature difference ΔT. Therefore, the locking range of the optical stabilization has to be extended to ensure operation in the presence of long-term temperature fluctuations.

In order to accomplish this extension, we built a module consisting of the highly Ytterbium-doped fiber (Liekki Yb-1200-4/125, in this case about 84 cm) placed on a thermo-electric element. The fiber was pumped by a laser diode at 978 nm wavelength and heated to approx. 57 °C. The temperature of the thermo-electric element was changed continuously by ±2°C with an influence of ΔsgT = 20μm/°C on the optical path length. This extended the effective locking range of the optical stabilization by Δsg = 80μm, which was sufficient to compensate the above mentioned environmental thermal variations.

3. Optical repetition rate stabilization

In the following, we present a mode-locked Erbium all-fiber laser with a repetition rate of 31.4 MHz, which could be stabilized via optical pumping of the above-mentioned Ytterbium fiber module within the laser cavity. The experimental setup is displayed in Fig. 1: it consisted of a fiber ring resonator containing the Erbium gain fiber, the Ytterbium fiber module with thermo-electric temperature control, WDMs to pump the active fibers with 978 nm laser diodes, an optical isolator and a combination of two polarization controllers (PCs) on both sides of a fiber-based polarizing beam splitter (PBS). The latter was used to achieve passive mode-locking via nonlinear polarization rotation (NPR) [23

23. K. R. Tamura, Additive Pulse Mode-Locked Erbium-Doped Fiber Lasers, PhD. thesis (Massachusetts Institute of Technology, 1994), http://hdl.handle.net/1721.1/11851.

]. The Erbium-doped fiber’s WDM additionally served as a filter for the amplified spontaneous emission (ASE) and the remaining pump light, which was emitted from the Ytterbium-doped fiber. This ensured the independence of the laser properties from the control fiber’s current pump power.

Fig. 1 Setup of the repetition-rate-controlled fiber laser. LD: laser diode; WDM: wavelength division multiplexer; RWDM: reflective wavelength division multiplexer; PBS: polarizing beam splitter; PC: polarization controller; ASE: amplified spontaneous emission.

The Erbium-doped gain fiber was a 65 cm long Liekki Er-80-8/125 fiber; this and all other used fibers were single-mode at 1570 nm. To compensate the high anomalous dispersion of the resonator, we added normally dispersive fiber to the resonator, titled “Dispersion Compensation” in Fig. 1. The setup lead to a total resonator length of 6.59 m and an average group velocity dispersion of D = 0.88fs/(m · nm), therefore the laser was operating in the slightly anomalous dispersive regime.

By pumping the Erbium-doped fiber with a power of 255 mW at 978 nm wavelength, an output power of 25 mW with a spectral width of 33 nm (FWHM) at a central wavelength of 1570 nm was obtained, and these values were independent of the pump power of the Ytterbium fiber. The pulse duration was measured by autocorrelation to be 1.7 ps assuming a squared hyperbolic secant pulse shape. The autocorrelation function showed a significant chirp, which suggests the possibility of compression. The bandwidth-limited pulse duration could be calculated from the spectrum using Fourier transformation to 130 fs.

The maximum repetition rate difference achievable by pumping the Ytterbium fiber with 450 mW could be determined to be 28 Hz. Under the assumption of a group index of 1.468 [22

22. Corning SMF-28e+ Optical Fiber Product Information (2006).

], this results in an optical path length change of 8.0 μm, which is (under consideration of the slightly different Ytterbium-fiber lengths) consistent with the interferometric measurement mentioned above.

The repetition rate was measured with an Agilent N9000A CXA radio frequency (RF) spectrum analyzer connected to a fast (2.5 GHz bandwidth) InGaAs photo detector at the laser output. The generation of the error signal for the stabilization was accomplished by a phase detector consisting of a frequency mixer (Mini-Circuits ZX05-153-S+), which generated a difference frequency signal between the reference frequency and the 176th harmonic of the repetition rate, which was gained from the amplified signal of the above-mentioned photo-detector. The 176th harmonic was used to enhance the phase detector’s sensitivity to repetition rate changes and to offer the possibility to use existing electronics. The available photo detector provided sufficient sensitivity at this hight frequency (however, this is a possibility for improvement). A reference signal of 461 MHz was provided by a signal generator (Rhode & Schwarz SMS 302.4012) and 12× frequency-multiplied to match the 176th harmonic of the repetition rate. After applying a low pass filter with a cut-off frequency below the repetition rate, the output voltage U of the phase detector was proportional to the sine of the phase difference φerr of the two input signals: U = Kd sinφerr. The proportionality constant Kd was obtained from the amplitude of the sine signal with disabled stabilization. With enabled stabilization the phase difference was sufficiently small (φerr ≈ 0) and the expression could be approximated to U = Kd φerr. Then the output voltage could be used for the controller as an error signal proportional to the phase difference [24

24. R. E. Best, Phase-Locked Loops: Design, Simulation, and Applications, 6th ed. (McGraw-Hill, 2007).

].

The error signal was processed by an analog proportional-integral-derivative (PID) controller acting on a current sink. The current sink was connected parallel to the laser diode of the Ytterbium-doped fiber as an actuator for fast reduction of the laser diode current proportional to the controller output voltage. In this way, the pump power for the Ytterbium-doped fiber was varied between zero and 450 mW. Additionally, the controller output served as an error signal for a second proportional controller, which raised or lowered the temperature of the Ytterbium fiber module depending on the long-term repetition rate drift, as mentioned above. The bandwidth of this setup was limited by the life-time of the Ytterbium ion’s excited state, which is 0.85 ms (corresponding to 1.18 kHz). However, if faster control was needed, it would be possible to further extend this limitation with a special controller [20

20. A. A. Fotiadi, N. Zakharov, O. L. Antipov, and P. Mégret, “All-fiber coherent combining of Er-doped amplifiers through refractive index control in Yb-doped fibers,” Opt. Lett. 34, 3574–3576 (2009). [CrossRef] [PubMed]

].

The stability of the repetition rate was monitored over 12 hours with the RF spectrum analyzer in locked as well as in free-running mode by measuring the peak position of the 89th harmonic with a sweep time of 200 ms and a resolution bandwidth of 9.1 Hz. The significant improvement of the repetition rate stability can be seen in Fig. 2. Without stabilization, there is a repetition rate drift of 600 Hz, which is supposed to originate in the heating-up of the laboratory due to running electrical devices and the outside temperature. The two jumps may be results of disturbances from ongoing work in the laboratory, e. g., a slamming lab door. The drift was reduced to small residual fluctuations with a standard deviation of σ = 22mHz with enabled stabilization. Similar results were obtained with all-optical and disabled thermal control over time scales of 30 minutes.

Fig. 2 Fluctuations of the repetition rate in stabilized (a), as well as in free-running mode (b).

In order to quantify the repetition rate stability, the output signal of the phase detector U(t) was measured over 12 hours with a storage oscilloscope (Tektronix DPO 7254) and the overlapping Allan deviation σy[25

25. IEEE-SA Standards Board, “IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology – Random Instabilities,” IEEE Std1139–2008.

, 26

26. D. W. Allan, “Statistics of Atomic Frequency Standards,” Proc. IEEE 54, 221–230 (1966). [CrossRef]

] was calculated. To do this, the phase fluctuations x(t) had to be determined from x(t) = U(t)/2πKdfrepmh with mh being the order number of the observed harmonic. Then σy(τ) was obtained as described in [25

25. IEEE-SA Standards Board, “IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology – Random Instabilities,” IEEE Std1139–2008.

] and the results are shown in Fig. 3 depending on the averaging time τ. Values of σy = 1 × 10−9 for τ = 3ms to σy = 1.4 × 10−16 for τ = 2 × 104 s were obtained with this stabilization. A line with a τ−1 slope was added to the diagram, which indicates that the remaining noise resulted from white phase modulation or flicker phase modulation [25

25. IEEE-SA Standards Board, “IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology – Random Instabilities,” IEEE Std1139–2008.

].

Fig. 3 Overlapping Allan deviation of the laser’s repetition rate in stabilized operation. The solid line is a τ−1 slope for comparison.

4. Conclusion

In conclusion, we developed a new method to stabilize the repetition rate of an all-fiber mode-locked Erbium laser via optical pumping of an Ytterbium fiber in the resonator. It was shown that our device was capable of tuning the optical resonator length by up to 8 μm. Additional temperature variation of the Ytterbium fiber led to an increased stabilization range of over 80 μm, which ensured independence of environmental temperature changes on longer time scales. The Allan deviation of the repetition rate was determined to be comparable to the ones of other reported investigations. In contrast to mechanical methods, the optical control of the repetition rate provides advantages to applications where for instance mechanical abrasion is a problem or high reliability is mandatory, and finally reveals new opportunities for the control of light by light.

Acknowledgment

We acknowledge support by the Deutsche Forschungsgemeinschaft and the Open Access Publication Fond of the University of Muenster.

References and links

1.

D. Träutlein, F. Adler, K. Moutzouris, A. Jeromin, A. Leitenstorfer, and E. Ferrando-May, “Highly versatile confocal microscopy system based on a tunable femtosecond Er:fiber source,” J. Biophotonics 1, 53–61 (2008). [CrossRef]

2.

C. Cleff, J. Epping, P. Gross, and C. Fallnich, “Femtosecond OPO based on LBO pumped by a frequency-doubled Yb-fiber laser-amplifier system for CARS spectroscopy,” Appl. Phys. B 103, 795–800 (2011). [CrossRef]

3.

G. G. Ycas, F. Quinlan, S. A. Diddams, S. Ostermann, S. Mahadevan, S. Redman, R. Terrien, L. Ramsey, C. F. Bender, B. Botzer, and S. Sigurdsson, “Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb,” Opt. Express 20, 6631–6643 (2012). [CrossRef] [PubMed]

4.

H. R. Telle, B. Lipphardt, and J. Stenger, “Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements,” Appl. Phys. B 74, 1–6 (2002). [CrossRef]

5.

W. Zhang, H. Han, Y. Zhao, Q. Du, and Z. Wei, “A 350MHz Ti:sapphire laser comb based on monolithic scheme and absolute frequency measurement of 729nm laser,” Opt. Express 17, 6059–6067 (2009). [CrossRef] [PubMed]

6.

F. Adler, K. Moutzouris, A. Leitenstorfer, H. Schnatz, B. Lipphardt, G. Grosche, and F. Tauser, “Phase-locked two-branch erbium-doped fiber laser system for long-term precision measurements of optical frequencies,” Opt. Express 12, 5872–5880 (2004). [CrossRef] [PubMed]

7.

J. A. Cox, A. H. Nejadmalayeri, J. Kim, and F. X. Kärtner, “Complete characterization of quantum-limited timing jitter in passively mode-locked fiber laser,” Opt. Lett. 35, 3522–3524 (2010). [CrossRef] [PubMed]

8.

D. C. Heinecke, A. Bartels, and S. A. Diddams, “Offset frequency dynamics and phase noise properties of a self-referenced 10 GHz Ti:sapphire frequency comb,” Opt. Express 19, 18440–18451 (2011). [CrossRef] [PubMed]

9.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B 78, 321–324 (2004). [CrossRef]

10.

H. Hundertmark, D. Wandt, C. Fallnich, N. Haverkamp, and H. R. Telle, “Phase-locked carrier-envelope-offset frequency at 1560 nm,” Opt. Express 12, 770–775 (2004). [CrossRef] [PubMed]

11.

B. R. Washburn, S. A. Diddams, N. R. Newbury, J. W. Nicholson, and M. F. Yan, “Phase-locked, erbium-fiber-laser-based frequency comb in the near infrared,” Opt. Lett. 29, 250–252 (2004). [CrossRef] [PubMed]

12.

J. Rauschenberger, T. M. Fortier, D. J. Jones, J. Ye, and S. T. Cundiff, “Control of the frequency comb from a mode-locked Erbium-doped fiber laser,” Opt. Express 10, 1404–1410 (2002). [CrossRef] [PubMed]

13.

T. Walbaum, M. Löser, P. Gross, and C. Fallnich, “Mechanisms in passive synchronization of erbium fiber lasers,” Appl. Phys. B 102, 743–750 (2011). [CrossRef]

14.

R. de L. Kronig, “On the theory of dispersion of X-rays,” J. Opt. Soc. Am. 12, 547–557 (1926). [CrossRef]

15.

H. Tünnermann, J. Neumann, D. Kracht, and P. Weßels, “All-fiber phase actuator based on an erbium-doped fiber amplifier for coherent beam combining at 1064 nm,” Opt. Lett. 36, 448–450 (2011). [CrossRef] [PubMed]

16.

M. J. F. Digonnet, R. W. Sadowski, H. J. Shaw, and R. H. Pantell, “Resonantly Enhanced Nonlinearity in Doped Fibers for Low-Power All-Optical Switching: A Review,” Opt. Fiber Technol. 3, 44–64 (1997). [CrossRef]

17.

J. W. Arkwright, P. Elango, G. R. Atkins, T. Whitbread, and M. J. F. Digonnet, “Experimental and Theoretical Analysis of the Resonant Nonlinearity in Ytterbium-Doped Fiber,” J. Lightwave Technol. 16, 798–806 (1998). [CrossRef]

18.

S. C. Fleming and T. J. Whitley, “Measurement and Analysis of Pump-Dependent Refractive Index and Dispersion Effects in Erbium-Doped Fiber Amplifiers,” IEEE J. Quantum Electron. 32, 1113–1121 (1996). [CrossRef]

19.

A. A. Fotiadi, O. L. Antipov, and P. Mégret, “Dynamics of pump-induced refractive index changes in single-mode Yb-doped optical fibers,” Opt. Express 16, 12658–12663 (2008). [CrossRef] [PubMed]

20.

A. A. Fotiadi, N. Zakharov, O. L. Antipov, and P. Mégret, “All-fiber coherent combining of Er-doped amplifiers through refractive index control in Yb-doped fibers,” Opt. Lett. 34, 3574–3576 (2009). [CrossRef] [PubMed]

21.

S. Chang, C.-C. Hsu, T.-H. Huang, W.-C. Chuang, Y.-S. Tsai, J.-Y. Shieh, and C.-Y. Leung, “Heterodyne Interferometric Measurement of the Thermo-Optic Coefficient of Single Mode Fiber,” Chinese J. Phys. 38, 437–442 (2000).

22.

Corning SMF-28e+ Optical Fiber Product Information (2006).

23.

K. R. Tamura, Additive Pulse Mode-Locked Erbium-Doped Fiber Lasers, PhD. thesis (Massachusetts Institute of Technology, 1994), http://hdl.handle.net/1721.1/11851.

24.

R. E. Best, Phase-Locked Loops: Design, Simulation, and Applications, 6th ed. (McGraw-Hill, 2007).

25.

IEEE-SA Standards Board, “IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology – Random Instabilities,” IEEE Std1139–2008.

26.

D. W. Allan, “Statistics of Atomic Frequency Standards,” Proc. IEEE 54, 221–230 (1966). [CrossRef]

27.

K. Sugiyama, A. Onae, T. Ikegami, S. Slyusarev, F.-L. Hong, K. Minoshima, H. Matsumoto, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Frequency control of a chirped-mirror-dispersion-controlled mode-locked Ti:Al2O3 laser for comparison between microwave and optical frequencies,” Proc. SPIE 4269, 95–104 (2001). [CrossRef]

28.

C. Ye, J. J. Montiel, i Ponsoda, A. Tervonen, and S. Honkanen, “Refractive index change in ytterbium-doped fibers induced by photodarkening and thermal bleaching,” Appl. Opt. 49, 5799–5805 (2010). [CrossRef] [PubMed]

29.

M. Engholm, P. Jelger, F. Laurell, and L. Norin, “Improved photodarkening resistivity in ytterbium-doped fiber lasers by cerium codoping,” Opt. Lett. 34, 1285–1287 (2009). [CrossRef] [PubMed]

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(140.3510) Lasers and laser optics : Lasers, fiber
(140.4050) Lasers and laser optics : Mode-locked lasers
(230.1150) Optical devices : All-optical devices
(140.3425) Lasers and laser optics : Laser stabilization

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: December 6, 2012
Revised Manuscript: January 11, 2013
Manuscript Accepted: January 11, 2013
Published: February 20, 2013

Citation
Steffen Rieger, Tim Hellwig, Till Walbaum, and Carsten Fallnich, "Optical repetition rate stabilization of a mode-locked all-fiber laser," Opt. Express 21, 4889-4895 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4889


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References

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