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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 17 — Aug. 15, 2011
  • pp: 15879–15884
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Highly efficient femtosecond pulse stretching by tailoring cavity dispersion in erbium fiber lasers with an intracavity short-pass edge filter

Nan-Kuang Chen, Feng-Zhou Liu, Hsiu-Po Chuang, Yinchieh Lai, Shang-Da Yang, Jim-Wein Lin, Shien-Kuei Liaw, Yu-Chung Chang, Chen-Bin Huang, and Sien Chi  »View Author Affiliations


Optics Express, Vol. 19, Issue 17, pp. 15879-15884 (2011)
http://dx.doi.org/10.1364/OE.19.015879


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Abstract

We demonstrate highly efficient pulse stretching in Er3+-doped femtosecond mode-locked fiber lasers by tailoring cavity dispersion using an intracavity short-pass edge filter. The cavity dispersion is preset at around zero to obtain the shortest pulsewidth. When the cutoff wavelength of the short-pass edge filter is thermo-optically tuned to overlap the constituting spectral components of mode-locked pulses, large negative waveguide dispersion is introduced by the steep cutoff slope and the total cavity dispersion is moved to normal dispersion regime to broaden the pulsewidth. The time-bandwidth product of the mode-locked pulse increases with the decreasing temperature at the optical liquid surrounding the short-pass edge filter. Pulse stretch ratio of 3.53 (623.8fs/176.8fs) can be efficiently achieved under a temperature variation of 4°C.

© 2011 OSA

1. Introduction

Based on the above observation, in this work, we demonstrate an efficient pulse stretchable Er3+-doped FMLL, operating in a polarization additive-pulse mode-locking configuration [9

9. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8(10), 2068–2076 (1991). [CrossRef]

], by dispersionally stretching the mode-locked pulses. To facilitate the pulse stretching, the cavity dispersion of FMLL is intentionally tuned to close to the zero but still in the anomalous dispersion regime. The cavity dispersion and the Kerr nonlinearity are balanced and a shortest pulsewidth can be obtained. The pulse stretching is further achieved by incorporating a widely tunable fiber short-pass edge filter (SPEF) with a steep cutoff edge into the laser cavity, as shown in Fig. 1(a)
Fig. 1 (a) Experimental set-up of our pulse-stretchable Er3+-doped mode-locked fiber laser. WDM: wavelength division multiplexer, OSA: optical spectrum analyzer, RF: RF spectrum analyzer, AC: autocorrelator, SPEF: short-pass edge filter, EDF: erbium-doped fiber, PS: pulse shaper, PMT: photomultiplier tube, LIA: lock-in amplifier. (b) Spectral responses of a SPEF with an optical liquid (nD = 1.456) at different heating temperatures. (Res: 1 nm).
. The SPEF had been employed in achieving tunable CW fiber lasers as well as S-band erbium-doped fiber amplifiers by discretely suppressing the long-wavelength amplified spontaneous emission (ASE) noises [10

10. N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/24I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]

,11

11. N. K. Chen, K. C. Hsu, S. K. Liaw, Y. Lai, and S. Chi, “Influence of depressed-index outer ring on evanescent tunneling loss in tapered double-cladding fibers,” Opt. Lett. 33(15), 1666–1668 (2008). [CrossRef] [PubMed]

]. The SPEF has a steep cutoff slope, as shown in Fig. 1(b), due to the material dispersion discrepancy between the silica core and liquid cladding materials [10

10. N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/24I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]

,11

11. N. K. Chen, K. C. Hsu, S. K. Liaw, Y. Lai, and S. Chi, “Influence of depressed-index outer ring on evanescent tunneling loss in tapered double-cladding fibers,” Opt. Lett. 33(15), 1666–1668 (2008). [CrossRef] [PubMed]

]. The spectral characteristics become highly wavelength-dependent near the cutoff, which generates large negative waveguide dispersion (ps/nm/km). Thus, the waveguide dispersion of this highly dispersive composite waveguide structure is very strong compared with the material dispersion and the net cavity dispersion of FMLL is moved to normal dispersion regime to cause pulse stretching for mode-locked pulses. A fast switching between the shallow anomalous dispersion and deep normal dispersion regime is crucial to an efficient pulse stretching in FMLL. Consequently, a large negative dispersion must be rapidly and dynamically introduced into laser cavity. It is known that a large negative dispersion comes from the rapid power change from the core to the cladding [12

12. A. M. Vengsarkar and W. A. Reed, “Dispersion-compensating single-mode fibers: efficient designs for first- and second-order compensation,” Opt. Lett. 18(11), 924–926 (1993). [CrossRef] [PubMed]

,13

13. C. D. Poole, J. M. Weisenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994). [CrossRef]

] and can be available near the fundamental-mode (LP01 mode) cutoff wavelength in an optical fiber with a depressed-index inner cladding [12

12. A. M. Vengsarkar and W. A. Reed, “Dispersion-compensating single-mode fibers: efficient designs for first- and second-order compensation,” Opt. Lett. 18(11), 924–926 (1993). [CrossRef] [PubMed]

] or near the second-mode (LP11 mode) cutoff wavelength in multimode fiber [13

13. C. D. Poole, J. M. Weisenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994). [CrossRef]

]. Based on dispersion engineering technique through selecting suitable composite materials and waveguide structures in tapered fibers, a large negative dispersion [14

14. R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, “Group velocity dispersion of tapered fibers immersed in different liquids,” Opt. Express 12(8), 1700–1707 (2004). [CrossRef] [PubMed]

] or a large positive dispersion [15

15. M. Rusu, R. Herda, S. Kivistö, and O. G. Okhotnikov, “Fiber taper for dispersion management in a mode-locked ytterbium fiber laser,” Opt. Lett. 31(15), 2257–2259 (2006). [CrossRef] [PubMed]

] can be achieved. Accordingly, the SPEF can provide large negative dispersion near the cutoff wavelength. In the beginning, the cavity dispersion of fiber laser is preset around zero to obtain the shortest pulsewidth of ~176.8 fs. When the cutoff wavelength of intracavity SPEF is thermo-optically tuned to overlap the long-wavelength components of mode-locked pulses, the large negative waveguide dispersion is introduced into the laser cavity to broaden the mode-locked pulse. The pulse can be stretched from 176.8fs to 623.8fs (total pulsewidth stretching of 447fs) under a temperature variation of 4°C (from 36°C to 32°C) at the SPEF. This high efficient pulse-stretching scheme based on tunable waveguide dispersion is easier than changing the corresponding fiber length in laser cavity. It could also be promising for the high power stretched-pulse additive mode-locking lasers since the longer pulse duration, compared with the shorter pulse duration in soliton laser, can support much higher pulse energies before the Kerr nonlinearity is growing strong to cause multi-pulsing instability [16

16. E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE Photon. Technol. Lett. 47(5), 597–606 (2011). [CrossRef] [PubMed]

] or to damage the host glass material.

2. Fabrication and experiments

Figure 1(a) shows the experimental setup of the FMLL. The operation of the FMLL is based on polarization additive pulse mode-locking. A 3.5-m-long EDF (OFS: R37005) with a positive group velocity dispersion (GVD) parameter β 2 is used as the gain medium whereas the single-mode fiber (Corning: SMF-28) has a negative β 2 of about −20 ps2/km at 1.55 μm wavelength. The cavity dispersion is fine tuned by using a section of SMF-28 with proper length to make the net cavity dispersion in the anomalous dispersion regime but is quite close to the zero GVD. The polarization controller is used to generate the elliptically polarized light in the resonator. The horizontal and vertical components of the elliptically polarized light will suffer different nonlinear phase shifts, which leads to nonlinear polarization rotation. The nonlinear optical phenomenon comes from the nonlinear Kerr effect in fiber. Accordingly, the laser amplitude will be modulated at an extremely fast speed when the rotary polarization passing through a polarization-dependent isolator which actually plays as a saturable absorber in resonator. The FMLL based on the nonlinear polarization rotation method is called polarization additive pulse mode-locking [9

9. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8(10), 2068–2076 (1991). [CrossRef]

] and is the working principle of our FMLL. In order to tailor the cavity dispersion to enable the FMLL operating in the stretched-pulse regime for pulse stretching, a SPEF capable of providing large negative waveguide dispersion is implemented into the cavity between the output coupler and the waveplates, as shown in Fig. 1(a). It is known that a rapid power variation with wavelength from the core to the cladding can give rise to large negative waveguide dispersion [12

12. A. M. Vengsarkar and W. A. Reed, “Dispersion-compensating single-mode fibers: efficient designs for first- and second-order compensation,” Opt. Lett. 18(11), 924–926 (1993). [CrossRef] [PubMed]

]. When more optical powers quickly move into the cladding from the core, the group index and the group delay rapidly decreases with wavelength. Accordingly, the waveguide dispersion becomes highly negative when the wavelength is closing to a sharp fundamental-mode cutoff [10

10. N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/24I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]

,11

11. N. K. Chen, K. C. Hsu, S. K. Liaw, Y. Lai, and S. Chi, “Influence of depressed-index outer ring on evanescent tunneling loss in tapered double-cladding fibers,” Opt. Lett. 33(15), 1666–1668 (2008). [CrossRef] [PubMed]

] since the optical powers move to the outside from the tapered fiber abruptly. To design a SPEF with a sharp cutoff, the material dispersion discrepancy between the tapered fiber and the surrounding optical liquid must be carefully selected [10

10. N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/24I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]

]. The waveguide dispersion is also crucial to enhance the steepness of the fundamental-mode cutoff [11

11. N. K. Chen, K. C. Hsu, S. K. Liaw, Y. Lai, and S. Chi, “Influence of depressed-index outer ring on evanescent tunneling loss in tapered double-cladding fibers,” Opt. Lett. 33(15), 1666–1668 (2008). [CrossRef] [PubMed]

]. Since the thermo-optic coefficient of the Cargille® index liquid is high, the cutoff wavelength can be efficiently tunable [10

10. N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/24I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]

,11

11. N. K. Chen, K. C. Hsu, S. K. Liaw, Y. Lai, and S. Chi, “Influence of depressed-index outer ring on evanescent tunneling loss in tapered double-cladding fibers,” Opt. Lett. 33(15), 1666–1668 (2008). [CrossRef] [PubMed]

]. Thus, it is advantageous to produce the wavelength-tunable large negative waveguide dispersion to tailor the cavity dispersion of FMLL for pulse stretching in a controlled manner.

In fabrication, the SMF-28 was heated and stretched using a scanning hydrogen flame fiber-tapering workstation until the diameter of tapered waist is approaching 30 μm. The length of uniform waist is about 1.5 cm and is crucial to the cutoff slope [10

10. N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/24I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]

]. The tapered fiber was then glued into a U-groove engraved on a glass substrate and an optical dispersive Cargille® index liquid (nD = 1.456) was used to surround the tapered region. Since the silica tapered fiber has a higher dispersion slope than that of the Cargille index liquid, their refractive index dispersion curves will cross each other at a cutoff point [10

10. N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/24I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]

,11

11. N. K. Chen, K. C. Hsu, S. K. Liaw, Y. Lai, and S. Chi, “Influence of depressed-index outer ring on evanescent tunneling loss in tapered double-cladding fibers,” Opt. Lett. 33(15), 1666–1668 (2008). [CrossRef] [PubMed]

]. This point separates the stopband and passband wavelengths and can be movable when the index liquid is heating up or cooling down by a thermoelectric cooler (TE-cooler). The tapered waist diameter was intentionally selected to be around 30 μm to obtain the steepest cutoff slope as well as the largest attenuation for stopband, so that the large negative waveguide dispersion can be introduced into FMLL to stretch the mode-locked pulses. The SPEF so made can be tuning over 1250-1650 nm with the rejection efficiency above 45 dB and the cutoff slope of higher than −1.0 dB/nm. The spectral responses, measured by an optical spectrum analyzer (OSA) under the resolution (RES) of 1 nm, within the temperature variation of 6 °C (30-36°C) are shown in Fig. 1(b). The controlled temperature was stabilized to within 0.1°C accuracy by a dual TE-cooler module and the cutoff wavelength can be tuned at a speed of a few tens of milliseconds for 1 nm wavelength-shift while the spectral shape is always the same [17

17. N. K. Chen, S. Chi, and S. M. Tseng, “Wideband tunable fiber short-pass filter based on side-polished fiber with dispersive polymer overlay,” Opt. Lett. 29(19), 2219–2221 (2004). [CrossRef] [PubMed]

]. This widely tunable SPEF was subsequently incorporated into an Er3+-doped FMLL, as shown in Fig. 1(a), to serve as the pulse stretcher when the polarization controller and the cavity dispersion are correctly controlled. A reflective 4-f pulse shaper with a dual-layer liquid crystal modulator [18

18. H. P. Chuang and C. B. Huang, “Generation and delivery of 1-ps optical pulses with ultrahigh repetition-rates over 25-km single mode fiber by a spectral line-by-line pulse shaper,” Opt. Express 18(23), 24003–24011 (2010). [CrossRef] [PubMed]

] is used to compensate the extra anomalous dispersion of the lead-out fiber of FMLL in obtaining the transform-limited pulsewidth. The photomultiplier tube and the lock-in amplifier are used to measure the autocorrelation trace of the output pulsewidth when the heating temperature of SPEF is changed. When the cutoff wavelength of SPEF starts to overlap the spectral components of the mode-locked pulses from the long-wavelength end, the large negative dispersion is introduced into the laser cavity. The FMLL is moving from the anomalous dispersion regime to normal dispersion regime. The dispersion and Kerr nonlinearity in FMLL cannot be balanced to maintain the fixed pulsewidth. Consequently, the mode-locked pulses are stretched and are not transform-limited. Also, the time-bandwidth product increases with the blue-shift of cutoff wavelength of SPEF.

3. Results and discussions

4. Conclusion

We have demonstrated pulse stretchable FMLL by incorporating a widely tunable SPEF into the laser ring cavity. The SPEF with a steep cutoff slope can introduce a large negative dispersion to tune the cavity dispersion from anomalous dispersion to normal dispersion regime. The corresponding pulsewidth of the output pulses can be stretched from 176.8fs to 623.8fs under a temperature variation of 4°C, without the need to change any fiber length. This approach enables the all-fiber femtosecond laser, to be efficiently pulse stretchable. This all-fiber scheme is simple, cost-effective, and wide-range tuning. The multistage intracavity SPEFs in laser cavity could be promising for achieving efficient pulse stretching to even large values for mode-locked fiber laser applications.

Acknowledgments

This work was supported in part by the R.O.C. National Science Council under Grants NSC 98-2221-E-239-001-MY2, NSC 100-2622-E-239-002-CC3, NSC 99-2628-E-018-013 and NSC 97-2923-E-011-001-MY3.

References and links

1.

N. Nishizawa, Y. Chen, P. Hsiung, E. P. Ippen, and J. G. Fujimoto, “Real-time, ultrahigh-resolution, optical coherence tomography with an all-fiber, femtosecond fiber laser continuum at 1.5 microm,” Opt. Lett. 29(24), 2846–2848 (2004). [CrossRef] [PubMed]

2.

D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33(7), 660–662 (2008). [CrossRef] [PubMed]

3.

Y. Zhao, Y. Liang, N. Zhang, M. Wang, and X. Zhu, “Pulse width effect in ultrafast laser ionization imaging,” Opt. Lett. 33(21), 2467–2469 (2008). [CrossRef] [PubMed]

4.

F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32(24), 3495–3497 (2007). [CrossRef] [PubMed]

5.

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25(2), 140–148 (2008). [CrossRef]

6.

V. P. Kalosha, L. Chen, and X. Bao, “Ultra-short pulse operation of all-optical fiber passively mode-locked ytterbium laser,” Opt. Express 14(11), 4935–4945 (2006). [CrossRef] [PubMed]

7.

M. E. Fermann, K. Sugden, and I. Bennion, “High-power soliton fiber laser based on pulse width control with chirped fiber Bragg gratings,” Opt. Lett. 20(2), 172–174 (1995). [CrossRef] [PubMed]

8.

F. Haxsen, D. Wandt, U. Morgner, J. Neumann, and D. Kracht, “Pulse characteristics of a passively mode-locked thulium fiber laser with positive and negative cavity dispersion,” Opt. Express 18(18), 18981–18988 (2010). [CrossRef] [PubMed]

9.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8(10), 2068–2076 (1991). [CrossRef]

10.

N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/24I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]

11.

N. K. Chen, K. C. Hsu, S. K. Liaw, Y. Lai, and S. Chi, “Influence of depressed-index outer ring on evanescent tunneling loss in tapered double-cladding fibers,” Opt. Lett. 33(15), 1666–1668 (2008). [CrossRef] [PubMed]

12.

A. M. Vengsarkar and W. A. Reed, “Dispersion-compensating single-mode fibers: efficient designs for first- and second-order compensation,” Opt. Lett. 18(11), 924–926 (1993). [CrossRef] [PubMed]

13.

C. D. Poole, J. M. Weisenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994). [CrossRef]

14.

R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, “Group velocity dispersion of tapered fibers immersed in different liquids,” Opt. Express 12(8), 1700–1707 (2004). [CrossRef] [PubMed]

15.

M. Rusu, R. Herda, S. Kivistö, and O. G. Okhotnikov, “Fiber taper for dispersion management in a mode-locked ytterbium fiber laser,” Opt. Lett. 31(15), 2257–2259 (2006). [CrossRef] [PubMed]

16.

E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE Photon. Technol. Lett. 47(5), 597–606 (2011). [CrossRef] [PubMed]

17.

N. K. Chen, S. Chi, and S. M. Tseng, “Wideband tunable fiber short-pass filter based on side-polished fiber with dispersive polymer overlay,” Opt. Lett. 29(19), 2219–2221 (2004). [CrossRef] [PubMed]

18.

H. P. Chuang and C. B. Huang, “Generation and delivery of 1-ps optical pulses with ultrahigh repetition-rates over 25-km single mode fiber by a spectral line-by-line pulse shaper,” Opt. Express 18(23), 24003–24011 (2010). [CrossRef] [PubMed]

19.

Y. F. Chen, S. W. Tsai, S. C. Wang, and J. Chen, “A diode-pumped high power Q-switched and self-mode-locked Nd:YVO4 laser with a LiF:F2saturable absorber,” Appl. Phys. B 73, 115–118 (2001). [CrossRef]

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(140.4050) Lasers and laser optics : Mode-locked lasers
(230.2035) Optical devices : Dispersion compensation devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 31, 2011
Revised Manuscript: July 1, 2011
Manuscript Accepted: July 3, 2011
Published: August 4, 2011

Citation
Nan-Kuang Chen, Feng-Zhou Liu, Hsiu-Po Chuang, Yinchieh Lai, Shang-Da Yang, Jim-Wein Lin, Shien-Kuei Liaw, Yu-Chung Chang, Chen-Bin Huang, and Sien Chi, "Highly efficient femtosecond pulse stretching by tailoring cavity dispersion in erbium fiber lasers with an intracavity short-pass edge filter," Opt. Express 19, 15879-15884 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-15879


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References

  1. N. Nishizawa, Y. Chen, P. Hsiung, E. P. Ippen, and J. G. Fujimoto, “Real-time, ultrahigh-resolution, optical coherence tomography with an all-fiber, femtosecond fiber laser continuum at 1.5 microm,” Opt. Lett. 29(24), 2846–2848 (2004). [CrossRef] [PubMed]
  2. D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33(7), 660–662 (2008). [CrossRef] [PubMed]
  3. Y. Zhao, Y. Liang, N. Zhang, M. Wang, and X. Zhu, “Pulse width effect in ultrafast laser ionization imaging,” Opt. Lett. 33(21), 2467–2469 (2008). [CrossRef] [PubMed]
  4. F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32(24), 3495–3497 (2007). [CrossRef] [PubMed]
  5. A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25(2), 140–148 (2008). [CrossRef]
  6. V. P. Kalosha, L. Chen, and X. Bao, “Ultra-short pulse operation of all-optical fiber passively mode-locked ytterbium laser,” Opt. Express 14(11), 4935–4945 (2006). [CrossRef] [PubMed]
  7. M. E. Fermann, K. Sugden, and I. Bennion, “High-power soliton fiber laser based on pulse width control with chirped fiber Bragg gratings,” Opt. Lett. 20(2), 172–174 (1995). [CrossRef] [PubMed]
  8. F. Haxsen, D. Wandt, U. Morgner, J. Neumann, and D. Kracht, “Pulse characteristics of a passively mode-locked thulium fiber laser with positive and negative cavity dispersion,” Opt. Express 18(18), 18981–18988 (2010). [CrossRef] [PubMed]
  9. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8(10), 2068–2076 (1991). [CrossRef]
  10. N. K. Chen, C. M. Hung, S. Chi, and Y. Lai, “Towards the short-wavelength limit lasing at 1450 nm over 4I13/2→4I15/2 transition in silica-based erbium-doped fiber,” Opt. Express 15(25), 16448–16456 (2007). [CrossRef] [PubMed]
  11. N. K. Chen, K. C. Hsu, S. K. Liaw, Y. Lai, and S. Chi, “Influence of depressed-index outer ring on evanescent tunneling loss in tapered double-cladding fibers,” Opt. Lett. 33(15), 1666–1668 (2008). [CrossRef] [PubMed]
  12. A. M. Vengsarkar and W. A. Reed, “Dispersion-compensating single-mode fibers: efficient designs for first- and second-order compensation,” Opt. Lett. 18(11), 924–926 (1993). [CrossRef] [PubMed]
  13. C. D. Poole, J. M. Weisenfeld, D. J. DiGiovanni, and A. M. Vengsarkar, “Optical fiber-based dispersion compensation using higher order modes near cutoff,” J. Lightwave Technol. 12(10), 1746–1758 (1994). [CrossRef]
  14. R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, “Group velocity dispersion of tapered fibers immersed in different liquids,” Opt. Express 12(8), 1700–1707 (2004). [CrossRef] [PubMed]
  15. M. Rusu, R. Herda, S. Kivistö, and O. G. Okhotnikov, “Fiber taper for dispersion management in a mode-locked ytterbium fiber laser,” Opt. Lett. 31(15), 2257–2259 (2006). [CrossRef] [PubMed]
  16. E. Ding, S. Lefrancois, J. N. Kutz, and F. W. Wise, “Scaling fiber lasers to large mode area: an investigation of passive mode-locking using a multi-mode fiber,” IEEE Photon. Technol. Lett. 47(5), 597–606 (2011). [CrossRef] [PubMed]
  17. N. K. Chen, S. Chi, and S. M. Tseng, “Wideband tunable fiber short-pass filter based on side-polished fiber with dispersive polymer overlay,” Opt. Lett. 29(19), 2219–2221 (2004). [CrossRef] [PubMed]
  18. H. P. Chuang and C. B. Huang, “Generation and delivery of 1-ps optical pulses with ultrahigh repetition-rates over 25-km single mode fiber by a spectral line-by-line pulse shaper,” Opt. Express 18(23), 24003–24011 (2010). [CrossRef] [PubMed]
  19. Y. F. Chen, S. W. Tsai, S. C. Wang, and J. Chen, “A diode-pumped high power Q-switched and self-mode-locked Nd:YVO4 laser with a LiF:F2−saturable absorber,” Appl. Phys. B 73, 115–118 (2001). [CrossRef]

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