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Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 21 — Oct. 17, 2005
  • pp: 8625–8633
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Supercontinuum generation in large mode-area microstructured fibers

G. Genty, T. Ritari, and H. Ludvigsen  »View Author Affiliations


Optics Express, Vol. 13, Issue 21, pp. 8625-8633 (2005)
http://dx.doi.org/10.1364/OPEX.13.008625


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Abstract

Supercontinuum generation in large mode-area microstructured fibers is demonstrated by launching into the fiber ns pulses from a passively Q-switched Nd:YAG laser. The special properties of these fibers open the way to compact, single-mode, high-power supercontinuum sources with a low divergence of the output beam. The nonlinear phenomena leading to the formation of the broad spectrum are also described.

© 2005 Optical Society of America

1. Introduction

With the rapid development of microstructured fibers (MFs), supercontinuum (SC) generation has been the focus of intense research over the past years [1

1 . See for instance Nonlinear optics of photonic crystals, Special issue of J. Opt. Soc. Am. B 19 , 1961 – 2296 ( 2002 ) or Supercontinuum generation, Special issue of Appl. Phys. B 77 , 143 – 376 ( 2003 ).

]. The interest for this type of ultra-broadband sources originates from the wide range of potential applications in various fields such as sensors, characterization of optical components, interferometry or optical coherence tomography [2–5

2 . T. M. Monro , W. Belardi , K. Furusawa , J. C. Baggett , N. G. R. Broderick , and D. J. Richardson , “ Sensing with microstructured optical fibres ,” Meas. Sci. Technol. 12 , 854 – 858 ( 2001 ). [CrossRef]

]. Typically, supercontinua have been generated in short lengths of narrow-core MFs by pumping with femtosecond laser pulses [6

6 . J. K. Ranka , R. S. Windeler , and A. J. Stentz , “ Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm ,” Opt. Lett. 25 , 25 – 27 ( 2000 ). [CrossRef]

] or in several meter-long MFs employing picosecond or nanosecond pulsed sources [7–9

7 . S. Coen , A. Hing Lun Chau , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber ,” Opt. Lett. 26 , 1356 – 1358 ( 2001 ). [CrossRef]

]. Lately, SC generation has also been reported in highly nonlinear, dispersion-shifted fibers pumped by continuous wave sources such as cascaded Raman fiber lasers and Raman-amplified laser diodes [10–11

10 . A. K. Abeeluck , C. Headley , and C. G. Jørgensen , “ High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser ,” Opt. Lett. 29 , 2163 – 2165 ( 2004 ). [CrossRef] [PubMed]

]. Narrow-core MFs possess high numerical aperture resulting in a large divergence of the output beam, which requires additional optics in order to couple the SC light into standard fibers or optical components. Furthermore, the dimension of the core on the order of a micron yields a high local intensity and large attenuation at wavelengths larger than the core size, thereby limiting the maximum output power and infrared bandwidth obtainable. Narrow-core MFs may also exhibit multi-mode behavior, which is detrimental to SC applications.

On the other hand, large mode-area microstructured fibers (LMA-MFs) can combine a large core size and a low numerical aperture while still allowing only the fundamental mode to propagate at all wavelengths [12–14

12 . J. C. Knight , T. A. Birks , R. F. Cregan , P. St. J. Russell , and J. P. de Sandro , “ Large mode area photonic crystal fibre ,” Electron. Lett. 34 , 1347 – 1348 ( 1998 ). [CrossRef]

]. In addition, the long-wavelength cut-off of LMA-MFs is located at longer wavelengths than in the case of narrow-core MFs. Furthermore, the larger dimensions allow for a better control of the microstructure during the manufacturing process and fibers with almost perfectly symmetrical microstructures, thus eliminating birefringence, have been reported [15

15 . T. Ritari , T. Niemi , M. Wegmuller , N. Gisin , J. R. Folkenberg , A. Pettersson , and H. Ludvigsen , “ Polarization-mode dispersion of large mode-area photonic crystal fibers ,” Opt. Commun. 226 , 233 – 239 ( 2003 ). [CrossRef]

]. This may prove to be useful if no polarization dependence of the generated supercontinuum is desired. Moreover, as the absorption of the water peak decreases for larger core dimensions, LMA-MFs exhibit low losses compared to narrow-core MFs at 1390 nm.

In this paper, we investigate the generation of supercontinuum in different LMA-MFs employing a compact, diode-pumped nanosecond laser. This type of source may be particularly useful in applications requiring broadband sources with low numerical aperture where, e.g., a high brightness, large depth of focus or circular beam is needed. Moreover, the relatively large core-size of LMA-MFs allows for direct insertion of a FC/PC output connector or easy splicing to standard single-mode fibers leading the route to fully compact and functional sources.

2. Experiments

The fibers used in the experiments are three large mode-area MFs with a triangular microstructured cladding [15

15 . T. Ritari , T. Niemi , M. Wegmuller , N. Gisin , J. R. Folkenberg , A. Pettersson , and H. Ludvigsen , “ Polarization-mode dispersion of large mode-area photonic crystal fibers ,” Opt. Commun. 226 , 233 – 239 ( 2003 ). [CrossRef]

]. The core diameter of the three fibers referred to as LMA-10, LMA-15 and LMA-20, are equal to 10.8, 14.8 and 19.4 μm, respectively. Microscope images of the cross section of LMA-10 and LMA-15 are displayed in Fig. 1. Note that the scaling is different for the two images.

Fig. 1. Optical microscope images of LMA-10 and LMA-15. Remark: not to scale.

Table 1. Characteristics of the fibers. λZD: zero-dispersion wavelength, γ: nonlinear coefficient (given at 1064 nm), and NA: numerical aperture (given at 1064 nm).

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Fig. 2. (a) Dispersion profile of the LMA-MFs. The black, red and blue lines correspond to LMA-10, LMA-15 and LMA-20, respectively. (b) Experimental setup. MO: microscope objective and OSA: optical spectrum analyzer.

A schematic of the experimental setup is illustrated in Fig. 2(b). In order to generate the continuum, the light emitted from a passively Q-switched Nd:YAG laser at the wavelength of 1064 nm was launched into the LMA-MFs. The spectrum and temporal profile of the pulses measured at the output of the laser are plotted in Fig. 3. The laser operates at a repetition rate of 25 kHz and produces pulses with a temporal width of ~3 ns. The maximum average output power of the laser is 180 mW, corresponding to a peak power of ca. 1.7 kW. Note that, for each LMA-MF, the pump wavelength is located in the normal dispersion region. The output of the laser was not polarized and no attempt was made to obtain linear polarization as this would only result in a decrease of available power. Furthermore, accurate characterization of the polarization properties of these fibers showed a small residual birefringence compared to narrow-core MFs [15

15 . T. Ritari , T. Niemi , M. Wegmuller , N. Gisin , J. R. Folkenberg , A. Pettersson , and H. Ludvigsen , “ Polarization-mode dispersion of large mode-area photonic crystal fibers ,” Opt. Commun. 226 , 233 – 239 ( 2003 ). [CrossRef]

] and no polarization dependence is therefore expected for the continuum. Coupling to the LMA-MFs was achieved with a simple ×10 microscope objective (Zeiss CP-Achromat ×10). The spectrum at the output of the fibers was monitored with an optical spectrum analyzer (Ando AQ6315B).

Fig. 3. Spectrum (a) and time trace (b) of the pump pulses. Note the slight offset of the OSA wavelength axis. The resolution of the OSA was set to 0.05 nm.

The supercontinuum spectrum generated in LMA-10 is shown in Fig. 4 for increasing average power. For maximum power coupled into the fiber, the SC spectrum covers more than an optical octave (from 600 nm to beyond 1800 nm) with a relatively good smoothness in the infrared region. Note that despite the length of the fiber, the OH absorption peak at around 1390 nm is rather weak here in contrast to SC generated in narrow-core MFs. This is readily explained by the fact that the OH-losses are strongly enhanced for reduced core diameters. All the spectral components were found to propagate in the fundamental mode. The photograph of the SC output mode observed in the far-field at a wavelength of 630 nm (see inset in Fig. 4) clearly illustrates single-mode propagation. Note that the peak at 800 nm corresponds to the remain of the diode used to pump the Q-switched laser.

Fig. 4. Supercontinuum generated in LMA-10. Pav: avarage power measured at the fiber output. Inset: Output mode at λ ≈630 nm (taken with a digital camera). The dashed line marks the location of the zero-dispersion wavelength. The peak at 800 nm corresponds the remain of the diode employed to pump the Nd:YAG crystal. The resolution of the OSA was set to 10 nm.

The experiment was subsequently repeated for LMA-15. The development of the spectrum of the supercontinuum generated in this fiber as a function of average power is illustrated in Fig. 5. At maximum input power the -20 dB bandwidth of the spectrum extends from 1000 nm to 1750 nm. The evolution of the red side of the continuum as a function of power is nearly identical to Fig. 4. However, a substantial decrease appears on the blue side of the spectrum compared to the continuum generated in LMA-10. This decrease can be attributed to two factors, the lower magnitude of the nonlinear coefficient and the larger separation between the pump and the zero-dispersion wavelength, which reduces the efficiency of four-wave mixing processes between the Raman lines and the pump [22

22 . E.A. Golovchenko , P. V. Mamyshev , A. N. Pilipestskii , and E. M. Dianov , “ Mutual influence of the parametric effects ans stimulated Raman scattering in optical fibers ,” IEEE J. Quantum Electron. 26 , 1815 – 1820 ( 1990 ). [CrossRef]

]. The latter factor is most likely to play a greater role in the quasi-absence of blue spectral components since the broadening of the spectrum at lower power values is comparable for LMA-10 and LMA-15. The divergence of the infrared output beam was also observed to be less than with the LMA-10 fiber.

Fig. 5. Spercontinuum generated in LMA-15 and in a standard single-mode fiber (red). Pav: avarage power measured at the fiber output. The dashed lines mark the location of the zero-dispersion wavelength. For clarity, an arbitrary offset has been added to the SC spectrum of the standard single-mode fiber. The peak at 800 nm corresponds to the remain of the diode employed to pump the Nd:YAG crystal. The resolution of the OSA was set to 10 nm. SMF: single-mode fiber.

Generation of a supercontinuum could not be obtained in LMA-20 as the very low numerical aperture limited the maximum power coupled into the fiber to less than 40 mW using the same microscope objective. This power value is too low to generate a SC as the nonlinearity of LMA-20 is roughly two third that of LMA-15. Nevertheless, the utilization of appropriate optics should yield a broad continuum similar to that obtained with LMA-15 due to the similarity of the dispersion profiles of these two fibers. Indeed, simulations based on a simple model [19

19 . R. H. Stolen , C. Lee , and R. K. Jain , “ Development of the stimulated Raman spectrum in single-mode silica fibers ,” J. Opt. Soc. Am. B 1 , 652 – 657 ( 1984 ). [CrossRef]

] indicate that, with an input power of 80 mW, four Raman lines should be generated along the 90 m fiber, the last one falling into the anomalous dispersion region of LMA-20. Subsequent soliton formation and soliton self-frequency shift should then lead to a continuum spectrum resembling that formed along LMA-15. In our experiments, we were able to observe only the three first Raman lines located at around 1115, 1175 and 1237 nm as shown in Fig. 6. Due to the location of the zero-dispersion wavelength and as is the case with the single-mode fiber, the third Raman lines is generated at 1237 nm which is precisely located at 13.2 THz from the 1175 nm Raman line. This is in contrast with LMA-10 and LMA-15 where the third Raman lines falls into the anomalous dispersion region and its location is therefore strongly affected by four-wave mixing.

Fig. 6. Raman lines generated in LMA-20. Pav=35 mW. The dashed line marks the location of the zero-dispersion wavelength. The resolution of the OSA was set to 10 nm.

3. Conclusion

Acknowledgments

This work has been carried out within the project entitled “Photonic crystal based integrated optics” of the Future Electronics research program financed by the Academy of Finland (Project No: 205481). The graduate school of Modern Optics and Photonics is also acknowledged for financial support. We are also grateful to S. C. Buchter for the generous loan of the pump source. Crystal Fibre A/S is acknowledged for kindly providing the fiber samples.

References and links

1 .

See for instance Nonlinear optics of photonic crystals, Special issue of J. Opt. Soc. Am. B 19 , 1961 – 2296 ( 2002 ) or Supercontinuum generation, Special issue of Appl. Phys. B 77 , 143 – 376 ( 2003 ).

2 .

T. M. Monro , W. Belardi , K. Furusawa , J. C. Baggett , N. G. R. Broderick , and D. J. Richardson , “ Sensing with microstructured optical fibres ,” Meas. Sci. Technol. 12 , 854 – 858 ( 2001 ). [CrossRef]

3 .

I. Hartl , X. D. Li , C. Chudoba , R. K. Ghanta , T. H. Ko , J. G. Fujimoto , J. K. Ranka , and R. S. Windeler , “ Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber ,” Opt. Lett. 26 , 608 – 610 ( 2001 ). [CrossRef]

4 .

P. T. Rakich , H. Sotobayashi , J. T. Gopinath , S. G. Johnson , J. W. Sickler , C. W. Wong , J. D. Joannopoulos , and E. P. Ippen , “ Nano-scale photonic crystal microcavity characterization with an all-fiber based 1.2 – 2.0 μm supercontinuum ,” Opt. Express 13 , 821 – 825 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-821 [CrossRef] [PubMed]

5 .

M. Lehtonen , G. Genty , and H. Ludvigsen , “ Absorption and transmission spectral measurements of fiber-optic components using supercontinuum radiation ”, Appl. Phys. B 81 , 231 – 234 ( 2005 ). [CrossRef]

6 .

J. K. Ranka , R. S. Windeler , and A. J. Stentz , “ Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm ,” Opt. Lett. 25 , 25 – 27 ( 2000 ). [CrossRef]

7 .

S. Coen , A. Hing Lun Chau , R. Leonhardt , J. D. Harvey , J. C. Knight , W. J. Wadsworth , and P. St. J. Russell , “ White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber ,” Opt. Lett. 26 , 1356 – 1358 ( 2001 ). [CrossRef]

8 .

W. J. Wadsworth , N. Joly , J. C. Knight , T. A. Birks , F. Biancalana , and P. St. J. Russell , “ Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres ,” Opt. Express 12 , 299 – 309 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299 [CrossRef] [PubMed]

9 .

J. M. Dudley , L. Provino , N. Grossard , H. Maillotte , R. S. Windeler , B. J. Eggleton , and S. Coen , “ Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping ,” J. Opt. Soc. Am. B 19 , 765 – 771 ( 2002 ). [CrossRef]

10 .

A. K. Abeeluck , C. Headley , and C. G. Jørgensen , “ High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser ,” Opt. Lett. 29 , 2163 – 2165 ( 2004 ). [CrossRef] [PubMed]

11 .

A. K. Abeeluck and C. Headley , “ Supercontinuum growth in a highly nonlinear fiber with a low-coherence semiconductor laser diode ,” Appl. Phys. Lett. 85 , 4863 – 4865 ( 2004 ). [CrossRef]

12 .

J. C. Knight , T. A. Birks , R. F. Cregan , P. St. J. Russell , and J. P. de Sandro , “ Large mode area photonic crystal fibre ,” Electron. Lett. 34 , 1347 – 1348 ( 1998 ). [CrossRef]

13 .

M. D. Nielsen , C. Jacobsen , N. A. Mortensen , J. R. Folkenberg , and H. R. Simonsen , “ Low-loss photonic crystal fibers for transmission systems and their dispersion properties ,” Opt. Express 12 , 1372 – 1376 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1372 [CrossRef] [PubMed]

14 .

M. D. Nielsen , J. R. Folkenberg , N. A. Mortensen , and A. Bjarklev , “ Bandwidth comparison of photonic crystal fibers and conventional single-mode fibers ,” Opt. Express 12 , 430 – 435 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-430 [CrossRef] [PubMed]

15 .

T. Ritari , T. Niemi , M. Wegmuller , N. Gisin , J. R. Folkenberg , A. Pettersson , and H. Ludvigsen , “ Polarization-mode dispersion of large mode-area photonic crystal fibers ,” Opt. Commun. 226 , 233 – 239 ( 2003 ). [CrossRef]

16 .

M. D. Nielsen and N. A. Mortensen , “ Photonic crystal fiber design based on the V-parameter ,” Opt. Express 11 , 2762 – 2768 ( 2003 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2762 [CrossRef] [PubMed]

17 .

D. Yevick and B. Hermansson , “ Efficient beam propagation techniques ,” IEEE J. Quantum Electron. 26 , 109 – 112 ( 1990 ). [CrossRef]

18 .

T. Sylvestre , H. Maillote , E. Lantz , and P. Tchofo Dinda , “ Raman-assisted parametric frequency conversion in a normally dispersive single-mode fiber ,” Opt. Lett. 24 , 1561 – 1563 ( 1999 ). [CrossRef]

19 .

R. H. Stolen , C. Lee , and R. K. Jain , “ Development of the stimulated Raman spectrum in single-mode silica fibers ,” J. Opt. Soc. Am. B 1 , 652 – 657 ( 1984 ). [CrossRef]

20 .

A. K. Abeeluck and C. Headley , “ Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation ,” Opt. Lett. 30 , 61 – 63 ( 2005 ). [CrossRef] [PubMed]

21 .

N. Bloembergen and Y. R. Shen , “ Coupling between vibrations and light waves in Raman laser media ,” Phys. Rev. Lett. 12 , 504 – 507 ( 1964 ). [CrossRef]

22 .

E.A. Golovchenko , P. V. Mamyshev , A. N. Pilipestskii , and E. M. Dianov , “ Mutual influence of the parametric effects ans stimulated Raman scattering in optical fibers ,” IEEE J. Quantum Electron. 26 , 1815 – 1820 ( 1990 ). [CrossRef]

23 .

G. Genty , M. Lehtonen , and H. Ludvigsen , “ Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub-30 fs pulses ,” Opt. Express 12 , 4614 – 4624 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4614 [CrossRef] [PubMed]

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(230.3990) Optical devices : Micro-optical devices
(290.5860) Scattering : Scattering, Raman

ToC Category:
Research Papers

History
Original Manuscript: July 26, 2005
Revised Manuscript: September 14, 2005
Published: October 17, 2005

Citation
G. Genty, T. Ritari, and H. Ludvigsen, "Supercontinuum generation in large mode-area microstructured fibers," Opt. Express 13, 8625-8633 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-21-8625


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References

  1. See for instance Nonlinear optics of photonic crystals, Special issue of J. Opt. Soc. Am. B 19, 1961-2296 (2002) or Supercontinuum generation, Special issue of Appl. Phys. B 77, 143-376 (2003).
  2. T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, �??Sensing with microstructured optical fibres,�?? Meas. Sci. Technol. 12, 854-858 (2001). [CrossRef]
  3. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, R. S. Windeler, �??Ultrahigh-resolution optical coherence tomography using continuum generation in an air silica microstructure optical fiber,�?? Opt. Lett. 26, 608-610 (2001). [CrossRef]
  4. P. T. Rakich, H. Sotobayashi, J. T. Gopinath, S. G. Johnson, J. W. Sickler, C. W. Wong, J. D. Joannopoulos, and E. P. Ippen, �??Nano-scale photonic crystal microcavity characterization with an all-fiber based 1.2 �?? 2.0 µm supercontinuum,�?? Opt. Express 13, 821-825 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-821">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-821</a> [CrossRef] [PubMed]
  5. M. Lehtonen, G. Genty, and H. Ludvigsen, �??Absorption and transmission spectral measurements of fiber-optic components using supercontinuum radiation�??, Appl. Phys. B 81, 231-234 (2005). [CrossRef]
  6. J. K. Ranka, R. S. Windeler, and A. J. Stentz, �??Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,�?? Opt. Lett. 25, 25-27 (2000). [CrossRef]
  7. S. Coen, A. Hing Lun Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, �??White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,�?? Opt. Lett. 26, 1356-1358 (2001). [CrossRef]
  8. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St. J. Russell, �??Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,�?? Opt. Express 12, 299-309 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299</a> [CrossRef] [PubMed]
  9. J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, �??Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,�?? J. Opt. Soc. Am. B 19, 765-771 (2002). [CrossRef]
  10. A. K. Abeeluck, C. Headley, and C. G. Jørgensen, �??High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,�?? Opt. Lett. 29, 2163- 2165 (2004). [CrossRef] [PubMed]
  11. A. K. Abeeluck and C. Headley, �??Supercontinuum growth in a highly nonlinear fiber with a low-coherence semiconductor laser diode,�?? Appl. Phys. Lett. 85, 4863-4865 (2004). [CrossRef]
  12. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, �??Large mode area photonic crystal fibre,�?? Electron. Lett. 34, 1347-1348 (1998). [CrossRef]
  13. . M. D. Nielsen, C. Jacobsen, N. A. Mortensen, J. R. Folkenberg, and H. R. Simonsen, �??Low-loss photonic crystal fibers for transmission systems and their dispersion properties,�?? Opt. Express 12, 1372-1376 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1372">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1372</a> [CrossRef] [PubMed]
  14. M. D. Nielsen, J. R. Folkenberg, N. A. Mortensen, and A. Bjarklev, �??Bandwidth comparison of photonic crystal fibers and conventional single-mode fibers,�?? Opt. Express 12, 430-435 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-430">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-430</a> [CrossRef] [PubMed]
  15. T. Ritari, T. Niemi, M. Wegmuller, N. Gisin, J. R. Folkenberg, A. Pettersson, and H. Ludvigsen, �??Polarization-mode dispersion of large mode-area photonic crystal fibers,�?? Opt. Commun. 226, 233-239 (2003). [CrossRef]
  16. M. D. Nielsen and N. A. Mortensen, �??Photonic crystal fiber design based on the V-parameter,�?? Opt. Express 11, 2762-2768 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2762">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2762</a> [CrossRef] [PubMed]
  17. D. Yevick and B. Hermansson, �??Efficient beam propagation techniques,�?? IEEE J. Quantum Electron. 26, 109-112 (1990). [CrossRef]
  18. T. Sylvestre, H. Maillote, E. Lantz, and P. Tchofo Dinda, �??Raman-assisted parametric frequency conversion in a normally dispersive single-mode fiber,�?? Opt. Lett. 24, 1561-1563 (1999). [CrossRef]
  19. R. H. Stolen, C. Lee, and R. K. Jain, �??Development of the stimulated Raman spectrum in single-mode silica fibers,�?? J. Opt. Soc. Am. B 1, 652-657 (1984). [CrossRef]
  20. A. K. Abeeluck and C. Headley, �??Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,�?? Opt. Lett. 30, 61-63 (2005). [CrossRef] [PubMed]
  21. N. Bloembergen and Y. R. Shen, �??Coupling between vibrations and light waves in Raman laser media,�?? Phys. Rev. Lett. 12, 504-507 (1964). [CrossRef]
  22. E.A. Golovchenko, P. V. Mamyshev, A. N. Pilipestskii, and E. M. Dianov, �??Mutual influence of the parametric effects ans stimulated Raman scattering in optical fibers,�?? IEEE J. Quantum Electron. 26, 1815-1820 (1990). [CrossRef]
  23. G. Genty, M. Lehtonen, and H. Ludvigsen, "Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub-30 fs pulses," Opt. Express 12, 4614-4624 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4614">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4614</a> [CrossRef] [PubMed]

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