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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 20 — Oct. 2, 2006
  • pp: 9238–9243
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Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber

A. Isomäki and O. G. Okhotnikov  »View Author Affiliations


Optics Express, Vol. 14, Issue 20, pp. 9238-9243 (2006)
http://dx.doi.org/10.1364/OE.14.009238


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Abstract

We demonstrate a solid-core ytterbium-doped photonic bandgap fiber laser passively mode-locked with a semiconductor saturable absorber. Gain and anomalous dispersion simultaneously provided by the photonic crystal fiber allow for a compact subpicosecond soliton oscillator. We also discuss the effect of higher-order dispersion in photonic bandgap fiber on laser performance.

© 2006 Optical Society of America

1. Introduction

To operate fiber lasers with λ≤1.3 µm in femtosecond pulse regime, normal dispersion of the laser cavity should be compensated by an appropriate cavity element with anomalous dispersion. Regular dispersion compensation based on diffraction gratings, however, violates an “all-fiber” nature of the laser. Recently, the dispersion compensators based on the photonic crystal fiber have been demonstrated resulting in compact all-fiber systems [1

1. H. Lim, F. ൦. Ilday, and F. W. Wise, “Femtosecond ytterbium fiber laser with photonic crystal fiber for dispersion control,” Opt. Express 10, 1497–1502 (2002) [PubMed]

, 2

2. A. Isomäki and O. G. Okhotnikov, “All-fiber ytterbium soliton mode-locked laser with dispersion control by solid-core photonic bandgap fiber,” Opt. Express 14, 4368–4373 (2006) [CrossRef] [PubMed]

]. Photonic crystal fibers with light guided by total internal reflection typically have a solid silica-based core surrounded by a silica-air photonic crystal cladding [3

3. J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003) [CrossRef] [PubMed]

]. Anomalous dispersion in this type of crystal fibers, however, could be generated with rather small core diameters. Although, the high nonlinearity of these fibers is widely used in supercontinuum generation, their poor mode matching with standard fibers results in high loss when using them as an intracavity dispersion compensator. An alternative solution is based on photonic bandgap (PBG) fibers [3

3. J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003) [CrossRef] [PubMed]

]. An all-solid PBG fiber [4

4. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594 (2002) [CrossRef]

, 5

5. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004) [CrossRef] [PubMed]

] made of a silica core and an array of higher index (e.g. Ge-doped) strands in the cladding has the advantage of a good mode matching with standard fibers. Furthermore, the all-solid structure exhibits no surface modes [5

5. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004) [CrossRef] [PubMed]

] and allows for high anomalous dispersion with low nonlinearity as compared with index guiding photonic crystal fibers. Another issue that makes these fibers particularly attractive for light emitting devices is the possibility to dope the silica core with rare-earth ions.

Er-and Yb-doped photonic crystal fibers first reported in [6

6. R. F. Cregan, J. C. Knight, P. St. J. Russell, and P. J. Roberts, “Distribution of spontaneous emission from an Er3+-doped photonic crystal fiber,” IEEE J. Lightwave. Technol. 17, 2138–2141 (1999) [CrossRef]

] and [7

7. W. J. Wadworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000) [CrossRef]

] have later been used in different types of lasers [8

8. K. Furusawa, T. M. Monro, P. Petropoulos, and D.J. Richardson, “Modelocked laser based on ytterbium doped holey fibre,” Electron. Lett. 37, 560–561 (2001) [CrossRef]

, 9

9. J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003) [CrossRef] [PubMed]

] and amplifiers [10

10. J. Limpert, A. Liem, M. Reich, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “Low-nonlinearity single-transverse-mode ytterbium-doped photonic crystal fiber amplifier,” Opt. Express 12, 1313–1319 (2004) [CrossRef] [PubMed]

]. More recently, Nd-doped photonic crystal fiber has been used as gain medium in a passively mode-locked fiber laser at 1.06 µm [11

11. M. Moenster, P. Glas, G. Steinmeyer, and R. Iliew, “Mode-locked Nd-doped microstructured fiber laser,’ Opt. Express 12, 4523–4528 (2004) [CrossRef] [PubMed]

, 12

12. M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, “Femtosecond Neodymium-doped microstructure fiber laser,” Opt. Express 13, 8671–8677 (2005) [CrossRef] [PubMed]

].

In this Letter, we report on the first demonstration of a mode-locked laser using an ytterbium-doped photonic bandgap (Yb-PBG) fiber as a gain medium and a dispersion compensator. Since the dispersion compensation is provided by the gain fiber, simple and compact femtosecond laser architecture can be realized. This approach offers potentially higher repetition rates when compared with the fiber lasers using standard Yb-doped fiber and a separate PBG fiber for dispersion compensation. We show that using a semiconductor saturable absorber mirror together with the Yb-PBG fiber allows for self-starting femtosecond mode-locked laser with repetition rate above 100 MHz around 1-µm wavelength range.

2. Photonic bandgap fiber laser characteristics

The experimental setup of the mode-locked laser is illustrated in Fig. 1. The fiber cavity is comprised of 0.27 m of ytterbium-doped PBG fiber and 0.47 m of standard single mode fiber. The free end of the Yb-doped PBG fiber is butt-coupled directly to a saturable absorber mirror. The laser output is taken from a variable coupler composed of a polarizing beam splitter and a half-wave plate placed in the free space section of the cavity. Throughout the study, the output coupling was maximized by rotating the half-wave plate. Depending on the cavity parameters, the optimal value of the output coupling that allowed for stable modelocked operation was ranged from 0.2 to 0.5. The laser was pumped with a single-mode grating-stabilized laser diode capable of delivering up to 300 mW of power at 980 nm.

Fig. 1. Laser setup with Yb-PBG fiber. PBS: polarizing beam splitter, λ/2: half-wave plate, WDM: pump/signal multiplexer, HR mirror: high reflectivity mirror.
Fig. 2. Dispersion of the whole fiber cavity and the transmission spectrum of the 2nd order bandgap of the Yb-PBG fiber. The inset shows the cross-sectional view of the fiber

Figure 2 shows the 2nd order transmission band of the Yb-PBG fiber recorded using a white-light source. The bandgap ranges from 980 to 1100 nm covering both the pump wavelength and the laser transition of the Yb-doped fiber. Although the transmission band shape of the PBG fiber is to certain extent affected by the high level of Yb doping, it is evident that the pump wavelength is located close to the short-wavelength edge of the band. The pump radiation is, therefore, weakly guided that in turn may decrease the overall pump efficiency. With optimization of the band spectral positioning, an improvement in the output power would be expected.

The inset in Fig. 2 shows a microscope image of the PBG fiber cross-section displaying 10 rings of Ge-doped inclusions with the refractive index of ~1.465 in pure silica background. The fiber diameter is 200 µm and the periodic structure has the spacing of 8.3 µm. The core was formed by replacing one inclusion in the middle with Yb-doped silica rod having the refractive index close to that of pure silica. The core’s numerical aperture is ~0.21 and it guides the fundamental mode with the field diameter of 9 µm. The mode size in the Yb-PBG fiber is slightly larger than the 6.4-µm mode diameter in the core of a standard fiber. It is expected, therefore, that optical nonlinearity of the Yb-PBG fiber would not dominate the total nonlinearity in the laser cavity. Owing to small mode mismatch between bandgap fiber and normal fiber, the splice loss was ~1 dB.

The measured round-trip group-velocity dispersion (GVD) of the laser cavity is seen in Fig 2. as well. The dichroic pump coupler made of standard single-mode fiber has a normal GVD of +0.024 ps2/m, while the PBG fiber exhibits anomalous GVD of-0.075 ps2/m at 1035 nm. Thus, the total cavity has an anomalous round-trip dispersion of-0.017 ps2 at 1035 nm corresponding to the signal wavelength of the experiments.

Another important feature of the Yb-PBG fiber is the spectral position of the zero-GVD wavelength. The anomalous waveguide dispersion due to the resonant-like PBG structure tends to shift the zero-GVD towards the short-wavelength edge of the transmission band [13

13. D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003) [CrossRef] [PubMed]

]. On the other hand, in case of an all-solid PBG fiber, the strong silica material dispersion at short wavelengths moves the zero-GVD to the opposite direction [5

5. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004) [CrossRef] [PubMed]

]. In case of the Yb-PBG fiber used here, the waveguide GVD is dominant over the material dispersion of silica at 1 µm wavelength range. We attribute this to the fact that the cutoff wavelength of the fundamental core mode is located at the band edge at 1094 nm. This gives rise to a rapid increase of dispersion at the long-wavelength edge and also shifts the zero-GVD to the short-wavelength side of the transmission band [14

14. J. Jasapara, T. H. Her, R. Bise, R. Windeler, and D. J. DiGiovanni, “Group-velocity dispersion measurements in a photonic bandgap fiber,” J. Opt. Soc. Am. B 20, 1611–1615 (2003) [CrossRef]

]. The effect is especially pronounced for the mode propagating in the secondary band instead of the fundamental one [15

15. C. Zhang, G. Kai, Z. Wang, T. Sun, C. Wang, Y. Liu, J. Liu, W. Zhang, S. Yuan, and X. Dong, “Design of tunable bandgap guidance in high-index filled microstructure fibers,” J. Opt. Soc. Am. B 23, 782–786 (2006) [CrossRef]

].

Fig. 3. Amplified spontaneous emission from the Yb-PBG fiber.
Fig. 4. Mode-locked pulse train (10 ns/div). The spikes at the end of the pulses are artifacts of detection electronics.

Figure 3 shows the spectrum of amplified spontaneous emission (ASE) from Yb-doped bandgap fiber for different pump powers. In these measurements, the lasing was avoided by blocking the laser mirrors. The figure illustrates that ASE spectrum matches closely the transmission band of the PBG fiber demonstrating an efficient filtering provided by the band spectral shape. This feature of the photonic bandgap structure was previously used to suppress undesired four-level transition in the Nd-doped fiber [16

16. A. Wang, A. K. George, and J. C. Knight, “Three-level neodymium fiber laser incorporating photonic bandgap fiber,” Opt. Lett. 31, 1388–1390(2006) [CrossRef] [PubMed]

].

3. Mode-locked operation

The laser exhibits self-starting mode-locked operation emitting the pulse train at the fundamental repetition rate of 117.5 MHz, as shown in Fig. 4. An average power of 3 mW at the output corresponds to the pulse energy of 25.5 pJ. As it was mentioned above, this characteristic is expected to advance with improving the guiding of the pump radiation. Fig. 5 shows the optical spectrum of the pulse with a spectral width of 4.0 nm. The corresponding intensity autocorrelation is shown in the inset of Fig. 4. A sech2-fit yields a pulse duration of 335 fs (FWHM), which gives a time-bandwidth product of 0.37 indicating a nearly transform limited pulse operation.

Although the Yb-PBG fiber shows a good performance in GVD compensation, it has significant dispersion of higher orders, particularly third-order dispersion (TOD). The TOD of the Yb-PBG fiber estimated from the measurements gives the value of 2.3 ps3/km at 1.04 µm. As a result, the dispersion is changed significantly across pulse spectrum. This exceptionally large value of TOD was found to affect the shape of soliton pulse spectrum and may set an ultimate limit for pulsewidth generated from photonic bandgap fiber lasers. Namely, the spectral sidebands in the pulse spectrum show notable asymmetry. Typically, we observe 2–3 soliton sidebands in the long-wavelength tail of the spectrum which corresponds to higher anomalous dispersion regime, while sidebands were never recorded at the short-wavelength wing of the spectrum, as seen from Fig. 6. The spectra have been obtained by changing the length of the fibers with normal and anomalous GVD. The dispersion values shown in Fig. 6 are measured at 1035 nm corresponding to the central wavelength of the pulse spectra. The asymmetric sideband formation was found from numerical simulation to be due to a high value of TOD in PBG fiber [17

17. R. Herda, A. Isomäki, and O. G. Okhotnikov, “Soliton sidebands in photonic bandgap fibre lasers,” Electron. Lett.42, (2006) [CrossRef]

]. Generally, these observations confirm a high immunity of the soliton pulses to higher order dispersion.

Fig. 5. Mode-locked pulse spectrum. Inset: measured intensity autocorrelation.
Fig. 6. Pulse spectra for different cavity dispersions. The lengths of the Yb-PBG fiber and the standard single mode fiber are (a) 0.35 m and 1.0 m, (b) 0.35 m and 0.8 m, (c) 0.27 m and 0.47 m, respectively. Some asymmetry in the soliton pulse spectra can be expected for different values of cavity dispersion, as discussed in the text. The difference in noise floor between the curves is due to variations in the sensitivity level of the optical spectrum analyzer. It should be noted that spectra are offset arbitrarily in respect of Y-axis for clarity.

4. Conclusion

We have demonstrated an environmentally stable soliton laser using ytterbium-doped all-solid photonic bandgap fiber providing both gain and dispersion compensation at 1 µm. The self-starting subpicosecond mode-locked operation is achieved by the semiconductor saturable absorber. We believe that this approach represent the new generation of ultrafast fiber oscillators operating with repetition rates above 100 MHz.

Acknowledgments

The authors acknowledge the financial support of the Academy of Finland (project GEMINI) and EU-FP6 URANUS project. Yb-doped photonic bandgap fiber was provided by Crystal Fibre A/S in the frame of the EU project. We acknowledge useful discussions with Claus Friis Pedersen from NKT Research.

References and links

1.

H. Lim, F. ൦. Ilday, and F. W. Wise, “Femtosecond ytterbium fiber laser with photonic crystal fiber for dispersion control,” Opt. Express 10, 1497–1502 (2002) [PubMed]

2.

A. Isomäki and O. G. Okhotnikov, “All-fiber ytterbium soliton mode-locked laser with dispersion control by solid-core photonic bandgap fiber,” Opt. Express 14, 4368–4373 (2006) [CrossRef] [PubMed]

3.

J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003) [CrossRef] [PubMed]

4.

N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594 (2002) [CrossRef]

5.

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004) [CrossRef] [PubMed]

6.

R. F. Cregan, J. C. Knight, P. St. J. Russell, and P. J. Roberts, “Distribution of spontaneous emission from an Er3+-doped photonic crystal fiber,” IEEE J. Lightwave. Technol. 17, 2138–2141 (1999) [CrossRef]

7.

W. J. Wadworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000) [CrossRef]

8.

K. Furusawa, T. M. Monro, P. Petropoulos, and D.J. Richardson, “Modelocked laser based on ytterbium doped holey fibre,” Electron. Lett. 37, 560–561 (2001) [CrossRef]

9.

J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express 11, 818–823 (2003) [CrossRef] [PubMed]

10.

J. Limpert, A. Liem, M. Reich, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “Low-nonlinearity single-transverse-mode ytterbium-doped photonic crystal fiber amplifier,” Opt. Express 12, 1313–1319 (2004) [CrossRef] [PubMed]

11.

M. Moenster, P. Glas, G. Steinmeyer, and R. Iliew, “Mode-locked Nd-doped microstructured fiber laser,’ Opt. Express 12, 4523–4528 (2004) [CrossRef] [PubMed]

12.

M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, “Femtosecond Neodymium-doped microstructure fiber laser,” Opt. Express 13, 8671–8677 (2005) [CrossRef] [PubMed]

13.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003) [CrossRef] [PubMed]

14.

J. Jasapara, T. H. Her, R. Bise, R. Windeler, and D. J. DiGiovanni, “Group-velocity dispersion measurements in a photonic bandgap fiber,” J. Opt. Soc. Am. B 20, 1611–1615 (2003) [CrossRef]

15.

C. Zhang, G. Kai, Z. Wang, T. Sun, C. Wang, Y. Liu, J. Liu, W. Zhang, S. Yuan, and X. Dong, “Design of tunable bandgap guidance in high-index filled microstructure fibers,” J. Opt. Soc. Am. B 23, 782–786 (2006) [CrossRef]

16.

A. Wang, A. K. George, and J. C. Knight, “Three-level neodymium fiber laser incorporating photonic bandgap fiber,” Opt. Lett. 31, 1388–1390(2006) [CrossRef] [PubMed]

17.

R. Herda, A. Isomäki, and O. G. Okhotnikov, “Soliton sidebands in photonic bandgap fibre lasers,” Electron. Lett.42, (2006) [CrossRef]

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(140.3510) Lasers and laser optics : Lasers, fiber
(260.2030) Physical optics : Dispersion
(320.7090) Ultrafast optics : Ultrafast lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 25, 2006
Revised Manuscript: September 18, 2006
Manuscript Accepted: September 18, 2006
Published: October 2, 2006

Citation
A. Isomäki and Oleg G. Okhotnikov, "Femtosecond soliton mode-locked laser based on ytterbium-doped photonic bandgap fiber," Opt. Express 14, 9238-9243 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-20-9238


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References

  1. H. Lim, F. Ö. Ilday, and F. W. Wise, "Femtosecond ytterbium fiber laser with photonic crystal fiber for dispersion control," Opt. Express 10, 1497-1502 (2002) [PubMed]
  2. A. Isomäki and O. G. Okhotnikov, "All-fiber ytterbium soliton mode-locked laser with dispersion control by solid-core photonic bandgap fiber," Opt. Express 14, 4368-4373 (2006) [CrossRef] [PubMed]
  3. J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003) [CrossRef] [PubMed]
  4. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002) [CrossRef]
  5. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004) [CrossRef] [PubMed]
  6. R. F. Cregan, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Distribution of spontaneous emission from an Er3+-doped photonic crystal fiber," IEEE J. Lightwave. Technol. 17, 2138-2141 (1999) [CrossRef]
  7. W. J. Wadworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, "Yb3+-doped photonic crystal fibre laser," Electron. Lett. 36, 1452-1454 (2000) [CrossRef]
  8. K. Furusawa, T. M. Monro, P. Petropoulos, and D.J. Richardson, "Modelocked laser based on ytterbium doped holey fibre," Electron. Lett. 37, 560-561 (2001) [CrossRef]
  9. J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, "High-power air-clad large-mode-area photonic crystal fiber laser," Opt. Express 11, 818-823 (2003) [CrossRef] [PubMed]
  10. J. Limpert, A. Liem, M. Reich, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, "Low-nonlinearity single-transverse-mode ytterbium-doped photonic crystal fiber amplifier," Opt. Express 12, 1313-1319 (2004) [CrossRef] [PubMed]
  11. M. Moenster, P. Glas, G. Steinmeyer, and R. Iliew, "Mode-locked Nd-doped microstructured fiber laser," Opt. Express 12, 4523-4528 (2004) [CrossRef] [PubMed]
  12. M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, "Femtosecond Neodymium-doped microstructure fiber laser," Opt. Express 13, 8671-8677 (2005) [CrossRef] [PubMed]
  13. D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003) [CrossRef] [PubMed]
  14. J. Jasapara, T. H. Her, R. Bise, R. Windeler, and D. J. DiGiovanni, "Group-velocity dispersion measurements in a photonic bandgap fiber," J. Opt. Soc. Am. B 20, 1611-1615 (2003) [CrossRef]
  15. C. Zhang, G. Kai, Z. Wang, T. Sun, C. Wang, Y. Liu, J. Liu, W. Zhang, S. Yuan, and X. Dong, "Design of tunable bandgap guidance in high-index filled microstructure fibers," J. Opt. Soc. Am. B 23, 782-786 (2006) [CrossRef]
  16. A. Wang, A. K. George, and J. C. Knight, "Three-level neodymium fiber laser incorporating photonic bandgap fiber," Opt. Lett. 31, 1388-1390 (2006) [CrossRef] [PubMed]
  17. R. Herda, A. Isomäki, and O. G. Okhotnikov, "Soliton sidebands in photonic bandgap fibre lasers," Electron. Lett. 42, (2006) [CrossRef]

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