Abstract

The effect of initial frequency chirp is investigated numerically to obtain efficient supercontinuum radiation in photonic crystal fibers (PCFs) with two closely spaced zero-dispersion wavelengths. The positive chirps,instead of zero or negative chirps, are recommended because self phase modulation and four-wave mixing can be facilitated by employing positive chirps. In contrast with the complicated and irregular spectrum generated by negative-chirped pulse, the spectrums generated by positive-chirped pulses are wider and much more regular. Moreover, the saturated length of the PCF,corresponding to the maximal spectrum width, can be shortened greatly and the efficiency of frequency conversion is also improved because of initial positive chirps. Nearly all the energy between the zero-dispersion wavelengths can be transferred to the normal dispersion region from the region within the two zero-dispersion wavelengths provided that the initial positive chirp is large enough.

© 2007 Optical Society of America

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References

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2006 (1)

2005 (1)

2004 (5)

2003 (3)

G. Chang, T. B. Norris, and H. G. Winful, "Optimization of supercontinuum generation in photonic crystal fibers for pulse compression," Opt. Lett. 28, 546-548 (2003), http://www.opticsexpress.org/abstract.cfm?id=80905.
[CrossRef] [PubMed]

P. S. J. Russell, "Appl. Phys.: Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

W. H. Reeves, D. V. Skryabin, and F. Biancalana,  et al., "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

2002 (3)

2000 (1)

Andersen, T. V.

Bang, O.

Biancalana, F.

W. H. Reeves, D. V. Skryabin, and F. Biancalana,  et al., "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Brown, T. G.

Chang, G.

Dudley, J. M.

Falk, P.

Frosz, M. H.

Fu, X.

X. Fu, L. Qian, and S. Wen,  et al., "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. Opt. A: Pure Appl. Opt. 6, 1012-1016 (2004).
[CrossRef]

Gaeta, A. L.

Genty, G.

Grossard, N.

Hilligsoe, K. M.

Lehtonen, M.

Ludvigsen, H.

Nielsen, C. K.

Norris, T. B.

Paulsen, H. N.

Provino, L.

Qian, L.

X. Fu, L. Qian, and S. Wen,  et al., "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. Opt. A: Pure Appl. Opt. 6, 1012-1016 (2004).
[CrossRef]

Ranka, J. K.

Reeves, W. H.

W. H. Reeves, D. V. Skryabin, and F. Biancalana,  et al., "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Russell, P. S. J.

P. S. J. Russell, "Appl. Phys.: Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Skryabin, D. V.

W. H. Reeves, D. V. Skryabin, and F. Biancalana,  et al., "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Stentz, A. J.

Wabnitz, S.

Wen, S.

X. Fu, L. Qian, and S. Wen,  et al., "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. Opt. A: Pure Appl. Opt. 6, 1012-1016 (2004).
[CrossRef]

Windeler, R. S.

Winful, H. G.

Zhu, Z.

J. Lightwave Technol. (1)

J. Opt. A: Pure Appl. Opt. (1)

X. Fu, L. Qian, and S. Wen,  et al., "Nonlinear chirped pulse propagation and supercontinuum generation in microstructured optical fibre," J. Opt. A: Pure Appl. Opt. 6, 1012-1016 (2004).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

W. H. Reeves, D. V. Skryabin, and F. Biancalana,  et al., "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (3)

Science (1)

P. S. J. Russell, "Appl. Phys.: Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear fiber optics (Academic Press, San Diego, 2001).

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Figures (6)

Fig. 1.
Fig. 1.

Dispersion profile of the sample PCF with two ZDWs, where the dashed lines and the dotted line indicate zero-dispersion wavelength and pump wavelength, respectively.

Fig.2.
Fig.2.

RMS spectrum width varied along with propagation distance for zero and positive chirps (a) and negative chirps (b).

Fig. 3.
Fig. 3.

Spectrum evolution along with propagation distance for initial chirp of C=10 (a) and C=-10 (b).

Fig. 4.
Fig. 4.

(a) Output spectrums of positive-chirped pulses, (b) temporal shapes of positive-chirped pulses, (c) output spectrums of negative-chirped pulses, (d) temporal shapes of negative-chirped pulses. The propagation distances are 15cm for positive chirps and 30cm for negative chirps, respectively.

Fig. 5.
Fig. 5.

The conversion efficiency for different positive (magenta curve) and negative (blue curve) chirps.

Fig. 6.
Fig. 6.

Calculated RMS spectrum width (a) and conversion efficiency (b) as a function of peak power P 0.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ξ u ( ξ , τ ) = i n = 2 N i n n ! L D 2 L D ( n ) sgn ( β n ) n τ n u ( ξ , τ ) + i N 2 ( 1 + i ω 0 τ p τ ) [ τ R ( τ ' ) u ( ξ , τ τ ' ) 2 d τ' ] u ( ξ , τ )
h R ( T ) = T 1 2 + T 2 2 T 1 T 2 2 exp ( T T 2 ) sin ( T T 2 ) ,
u ( 0 , τ ) = sech ( τ τ p ) exp ( i 2 τ p 2 )
Ω RMS 2 = ω 2 Ω c 2

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