Abstract

We investigate supercontinuum generation in photonic crystal fibers under femtosecond single and dual wavelength pumping experimentally and by numerical simulations. Details about the expansion of the blue but also the red side of the continuum due to cross-phase modulation (XPM) and transfer of energy to dispersive waves are revealed and experimentally confirmed. Additionally, simple guidelines are given to predicte the maximum bandwidth of supercontinuum generation only by the use of the dispersion curve of the fiber.

© 2005 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  26. T. V. Andersen, K. M. Hilligsøe, C. K. Nielsen, J. Thøgersen, K. P. Hansen, S. R. Keiding, and J. J. Larsen, "Continuous-wave wavelength conversion in a photonic crystal fiber with two zero-dispersion wavelengths," Opt. Express 12, 4113-4122 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4113">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4113</a>
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  28. S. M. Kobtsev and S. V. Smirnov, "Modelling of high-power supercontinuum generation in highly nonlinear, dispersion shifted fibers at CW pump," Opt. Express 13, 6912-6918 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6912">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6912</a>
    [CrossRef] [PubMed]

Adv. in Solid State Phys.

A. Tünnermann, T. Schreiber, M. Augustin, J. Limpert, M. Will, S. Nolte, H. Zellmer, R. Iliew, U. Peschel, and F. Lederer, �??Photonic crystal structures in ultrafast optics�?? in Adv. in Solid State Phys. (Editor: B. Kramer), 44, 117-132 (2004).
[CrossRef]

Appl. Phys. B

L. Tartara, I. Cristiani, and V. Degiorgio �??Blue light and infrared continuum generation by soliton fission in microstructured fibers,�?? Appl. Phys. B, 77, p. 307 (2003).
[CrossRef]

IEEE J. of Quantum Electron.

Y. Kodama, and A. Hasegawa, �??Nonlinear pulse propagation in a monomode dielectric guide,�?? IEEE J. of Quantum Electron. 23, 510-524 (1987).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

J. Phys. B

A. Tünnermann, T. Schreiber, F. Röser, A. Liem, S. Höfer, H. Zellmer, S. Nolte, and J. Limpert, �??The renaissance and bright future of fibre lasers,�?? J. Phys. B: At. Mol. Opt. Phys. 38, 681-693 (2005).
[CrossRef]

Opt. Commun.

T. Schreiber, J. Limpert, H. Zellmer, A. Tünnermann, and K. P. Hansen, �??High average power supercontinuum generation in photonic crystal fibers,�?? Opt. Commun. 228, 71-78 (2003).
[CrossRef]

Opt. Express

G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, "Spectral broadening of femtosecond pulses into continuum radiation in microstructured fibers," Opt. Express 10, 1083-1098 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1083">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-20-1083</a>
[PubMed]

N. Nishizawa and T. Goto, "Characteristics of pulse trapping by ultrashort soliton pulse in optical fibers across zerodispersion wavelength," Opt. Express 10, 1151-1160 (2002), <a href="http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-21-1151">http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-21-1151</a>
[PubMed]

I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124</a>
[CrossRef] [PubMed]

G. Genty, M. Lehtonen, H. Ludvigsen, and M. Kaivola, "Enhanced bandwidth of supercontinuum generated in microstructured fibers," Opt. Express 12, 3471-3480 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3471">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3471</a>
[CrossRef] [PubMed]

T. V. Andersen, K. M. Hilligsøe, C. K. Nielsen, J. Thøgersen, K. P. Hansen, S. R. Keiding, and J. J. Larsen, "Continuous-wave wavelength conversion in a photonic crystal fiber with two zero-dispersion wavelengths," Opt. Express 12, 4113-4122 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4113">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4113</a>
[CrossRef] [PubMed]

P. Champert, V. Couderc, P. Leproux, S. Février, V. Tombelaine, L. Labonté, P. Roy, C. Froehly, and P. Nérin, "White-light supercontinuum generation in normally dispersive optical fiber using original multiwavelength pumping system," Opt. Express 12, 4366-4371 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4366">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4366</a>
[CrossRef] [PubMed]

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]

M. H. Frosz, P. Falk, and O. Bang, "The role of the second zero-dispersion wavelength in generation of supercontinua and bright-bright soliton-pairs across the zero-dispersion wavelength," Opt. Express 13, 6181-6192 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6181">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-16-6181</a>
[CrossRef] [PubMed]

S. M. Kobtsev and S. V. Smirnov, "Modelling of high-power supercontinuum generation in highly nonlinear, dispersion shifted fibers at CW pump," Opt. Express 13, 6912-6918 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6912">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6912</a>
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

N. Akhmediev and M. Karlsson, �??Cherenkov radiation emitted by solitons in optical fibers,�?? Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, �??Temporal and spectral effects of cross-phase modulation on copropagating ultrashort pulses in optical fibers,�?? Phys. Rev. A 40, 5063�??5072 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. V. Husakou and J. Herrmann, �??Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,�?? Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, �??Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,�?? Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Science

D. G. Ouzounov, F. R. Ahmad, Dirk 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]

P. St. J. Russell, J.C. Knight, T.A. Birks, B.J. Mangan, and W.J. Wadsworth, �??Photonic crystal fibres,�?? Science 299, 358-362 (2003).
[CrossRef] [PubMed]

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, �??Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,�?? Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

Other

G. P. Agrawal, Nonlinear Fiber Optics, (Academic, New York 1995).

Supplementary Material (7)

» Media 1: AVI (531 KB)     
» Media 2: AVI (378 KB)     
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» Media 6: AVI (668 KB)     
» Media 7: AVI (1016 KB)     

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Figures (11)

Fig. 1.
Fig. 1.

Relative group delay for PCF1 (black) and PCF2 (blue).

Fig. 2.
Fig. 2.

Group delay matching (black∼PCF1, red∼PCF2) and phase matching of the dispersive wave according to Eq. (4) (gray∼PCF1, orange∼PCF2) in the anomalous dispersion region.

Fig. 3.
Fig. 3.

(a) Movie (532 kB) of XPM induced red shift using 150 fs, 100 pJ @ 1030 nm co-propagating with an initial delay of 5 ps to a 300fs, 100 fJ, 515 nm pulse in 1.4 m of PCF1, (b) movie (378 kB) exaggerated visible part in linear scale.

Fig. 4.
Fig. 4.

Movie (701 kB) of the XPM induced blue and red shift by a 300 fs, 200 pJ @ 1030 nm copropagating with an initial delay of 3 ps to a 300fs, 100 fJ, 515 nm pulse in 1.3 m of PCF1.

Fig. 5.
Fig. 5.

XPM induced blue and red shift compared to the initial spectrum (a) centered at a wavelength of 515 nm (black). Spectra after 1.5 m of PCF1 with initial 150 fs, 100pJ, Δτ=-8ps (b), 150 fs, 100pJ, Δτ=-5ps (c) and 300 fs, 150pJ, Δτ=-4ps (d). (e) same as (d) but propagated to 1.8 m.

Fig. 6.
Fig. 6.

Movies (430 kB, 549 kB, 669 kB) showing a 300fs pulse at 1030nm with a pulse energy of (a) 50pJ, (b) 100 pJ, (c) 150 pJ copropagating with an initial delay of 5 ps to a 300 fs, 100 fJ pulse at 515 nm in 1.5 m of PCF1.

Fig. 7.
Fig. 7.

Movie (0.99 MB) of the propagation of a 300 fs, 200 pJ pulse in PCF2 in a spectrographic view (a). The same propagation in a spectral view with higher dynamic range (b). In comparison, the initial evolution of a 300fs, 1 nJ pulse (c). Comparison of the spectra of the 200 pJ pulse after 60 cm and the 1 nJ pulse after 6 cm (d). (DWD - dispersive wave due to decay of the soliton, DWI -dispersive waves created by initial soliton fission process)

Fig. 8.
Fig. 8.

Experimental setup. ISO: Optical isolator, HWP: Half-wave-plate, PCF: Photonic crystal fiber, OSA: Optical spectrum analyzer.

Fig. 9.
Fig. 9.

Experimental spectral evolution with respect to increasing power (slice) in PCF1 (a,b,c) and PCF2 (d,e,f). (a) and (d) show the broadening of the infrared part without SH pumping. (b) and (d) show the evolution when a low power SH pulse is added with a specific (but constant) delay. In (c) selected slices from (b) highlight the spectral evolution for PCF1, when the power is right to only lead to a XPM red-shift (red curve - slice 7), increased to observe XPM red and blue shifts (blue curve - slice 8) and at the highest power in the infrared, where the maximum XPM blue shift is observed (black curve - slice 20). In (f) selected slices from (e) highlight the spectral evolution for PCF2 showing different amounts of XPM red-shift (red: slice 6, blue: slice 13, black: slice 18). (scale: oe-13-23-9556-i001)

Fig. 10.
Fig. 10.

Black curve shows the enhancement of the blue (a) and red side (b) of the XPM shifted SH signal. Green curve is the SH signal alone and the red curve is the infrared signal alone.

Fig. 11.
Fig. 11.

Spectrum at maximum pump power (100 mW) out of PCF2.

Tables (1)

Tables Icon

Table 1. Taylor series at 1030nm of the dispersion of the fiber used for the simulations.

Equations (9)

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A z + g 2 A gain / loss + ( n = 2 β n i n 1 n ! n T n ) A dispersion = i γ [ ( 1 f R ) ( A 2 A SPM i ω 0 T ( A 2 A ) self steepening ) + f R ( 1 + i ω 0 T ) ( A z T 0 h R ( τ ) A ( z , T τ ) 2 d τ ) delayed Raman response ]
P k = ( 2 N 2 k + 1 ) 2 N 2 P P , T k = T 0 2 N 2 k + 1
Δ ω SSFS ( z ) β 2 ( ω ) T k 4 z
Δ β = β ( ω S ) β ( ω D W ) ( ω S ω D W ) β 1 ( ω S ) + ( 1 f R ) γ P k = 0
d φ XPM = 2 γ A T z 2 d z
Δ ω XPM DW = ω XPM DW ω 0 DW = 2 γ 0 τ S ( τ ) 2 d τ β 1 ( ω XPM DW ) β 1 S
β 1 ( ω 0 DW ) β 1 S = ( β 1 ( ω XPM DW ) β 1 S )
Δ ω max XPM sec h 2 1.54 γ P 0 T 0 z I
z I = T 0 β 1 S β 1 DW

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