Abstract

We theoretically study broadband supercontinuum generation in photonic crystal fibers exhibiting two zero dispersion wavelengths and under continuous-wave pumping. We show that when the pump wavelength is located in between the zero-dispersion wavelengths, a wide and uniform spectral broadening is achieved through modulation instability, generation of both blue-shifted and red-shifted dispersive waves and subsequently through soliton self-frequency shift. This supercontinuum is therefore bounded by these two dispersive waves which allow the control of its bandwidth by a suitable tuning of the fiber dispersion. As a relevant example, we predict that broadband (1050–1600 nm) continuous-wave light can be generated in short lengths of microstructured fibers pumped by use of a 10-W Ytterbium fiber laser.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  8. A. Mussot, T. Sylvestre, L. Provino, and H. Maillotte, "Generation of a broadband single-mode supercontinuum in a conventional dispersion-shifted fiber by use of a subnanosecond microchiplaser," Opt. Lett. 28, 1820-1822 (2003) http://www.opticsinfobase.org/abstract.cfm?URI=ol-28-19-1820
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. M. Koshiba and K. Saitoh, "Applicability of classical optical fiber theories to holey fibers," Opt. Lett. 29, 1739-1741 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=ol-29-15-1739
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  23. B. Barviau, S. Randoux, and P. Suret, "Spectral broadening of a multimode continuous-wave optical field propagating in the normal dispersion regime of a fiber," Opt. Lett. 31, 1696-1698 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-11-1696
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. C. H. Henry,"Theory of the linewidth of SC Lasers," IEEE J. Quantum Electron. 18, 259-264 (1982).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  28. Note that Fig. 3(e) represents the evolution of the SC spectrum versus the fiber length in logarithm scale. In order to obtain a clear figure, it is plotted from smoothed SC spectra by using the method described in Ref. [29]. One example of this smoothing method is represented in green on Fig. 3(d).
  29. http://www.nrbook.com/a/bookcpdf/c14-8.pdf
  30. D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
    [CrossRef] [PubMed]

2006 (4)

2005 (3)

2004 (5)

2003 (3)

2002 (3)

2000 (2)

T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1417 (2000) http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-19-1415
[CrossRef]

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, 27-27 (2000). http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-1-25
[CrossRef]

1999 (1)

1995 (2)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, "Noise amplification in dispersive nonlinear media", Phys. Rev. A 51, 4086-4092 (1995). http://dx.doi.org/10.1103/PhysRevA.51.4086
[CrossRef] [PubMed]

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602-2607 (1995).
[CrossRef] [PubMed]

1989 (1)

1982 (1)

C. H. Henry,"Theory of the linewidth of SC Lasers," IEEE J. Quantum Electron. 18, 259-264 (1982).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. H. Henry,"Theory of the linewidth of SC Lasers," IEEE J. Quantum Electron. 18, 259-264 (1982).
[CrossRef]

J. Opt. Soc. Am. B (3)

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

A. V. Husakou and J. Herrmann, "Supercontinuum generation, four wave mixing, and fission of higher-order solitons in photonic-crystal fibers," J. Opt. Soc. Am. B.,  19, 2171-2182 (2002).
[CrossRef]

Opt. Express (7)

Opt. Lett. (9)

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) http://www.opticsinfobase.org/abstract.cfm?URI=ol-29-18-2163
[CrossRef] [PubMed]

T. Sylvestre, A. Vedadi, H. Maillotte, F. Vanholsbeeck, and S. Coen, "Supercontinuum generation using continuous-wave multiwavelength pumping and dispersion management," Opt. Lett. 31, 2036-2038 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-13-2036
[CrossRef] [PubMed]

A. V. Avdokhin, S. V. Popov, and J. R. Taylor, "Continuous-wave, high-power, Raman continuum generation in holey fibers, " Opt. Lett. 28, 1353-1355 (2003) http://www.opticsinfobase.org/abstract.cfm?URI=ol-28-15-1353
[CrossRef] [PubMed]

T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1417 (2000) http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-19-1415
[CrossRef]

A. Mussot, T. Sylvestre, L. Provino, and H. Maillotte, "Generation of a broadband single-mode supercontinuum in a conventional dispersion-shifted fiber by use of a subnanosecond microchiplaser," Opt. Lett. 28, 1820-1822 (2003) http://www.opticsinfobase.org/abstract.cfm?URI=ol-28-19-1820
[CrossRef] [PubMed]

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, 27-27 (2000). http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-1-25
[CrossRef]

W. Drexler, U. Morgner, F. X. Krtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, "Invivo ultrahigh-resolution optical coherence tomography," Opt. Lett. 24, 1221-1223 (1999) http://www.opticsinfobase.org/abstract.cfm?URI=ol-24-17-1221
[CrossRef]

M. Koshiba and K. Saitoh, "Applicability of classical optical fiber theories to holey fibers," Opt. Lett. 29, 1739-1741 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=ol-29-15-1739
[CrossRef] [PubMed]

B. Barviau, S. Randoux, and P. Suret, "Spectral broadening of a multimode continuous-wave optical field propagating in the normal dispersion regime of a fiber," Opt. Lett. 31, 1696-1698 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-11-1696
[CrossRef] [PubMed]

Phys. Rev. A (2)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, "Noise amplification in dispersive nonlinear media", Phys. Rev. A 51, 4086-4092 (1995). http://dx.doi.org/10.1103/PhysRevA.51.4086
[CrossRef] [PubMed]

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602-2607 (1995).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

J. Dudley, G. Genty and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135 (2006). http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=RMPHAT000078000004001135000001&idtype=cvips&gifs=yes&citing=sci
[CrossRef]

Science (1)

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

Other (5)

Note that Fig. 3(e) represents the evolution of the SC spectrum versus the fiber length in logarithm scale. In order to obtain a clear figure, it is plotted from smoothed SC spectra by using the method described in Ref. [29]. One example of this smoothing method is represented in green on Fig. 3(d).

http://www.nrbook.com/a/bookcpdf/c14-8.pdf

G. P.  Agrawal, Nonlinear Fiber Optics, 3rd ed., (Academic Press, San Diego, CA, USA, 2001).

O. V. Sinkin, R. Holzlöhner, J. Zweck, and C. R. Menyuk, "Optimization of the Split-Step Fourier Method in Modeling Optical-Fiber Communications Systems," J. Lightwave Technol. 21, 61- (2003) http://www.opticsinfobase.org/abstract.cfm?URI=JLT-21-1-61
[CrossRef]

J. C. Travers, S. V. Popov, J. R. Taylor, H. Sabert, and B. Mangan, "Extended Bandwidth CW-Pumped Infra-Red Supercontinuum Generation in Low Water-Loss PCF," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CFO4. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CFO4

Supplementary Material (1)

» Media 1: MOV (2902 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

(a). Dispersion curves and (b) effective areas of PCF1, PCF2 and PCF3.

Fig. 2.
Fig. 2.

(a). Spectrum of the input pump and (b) initial field intensities. The dashed red line represents the mean pump power.

Fig. 3.
Fig. 3.

(a).-3 (e). Power spectrum for different fiber lengths. The green curve is an averaging of the spectrum by using the smoothing method described in Ref. [29]. (f) Evolution of the power spectrum versus the fiber length from 0 to 20 m in logarithm scale with the average spectra. A movie of the SC dynamics can be viewed by cliquing on Fig. 3. [Media 1]

Fig. 3.
Fig. 3.

(a). Numerical filtering of the SC in PCF2 at L=7.34 m [Fig. 3(c)]. (b) Fourier transform of the SC (blue) and of the filtered SC (red).

Fig. 4.
Fig. 4.

Center wavelengths of the DWs as a function of the pump wavelength from Eq. 2. (b) averaged output spectrum in PCF2 with SRS [green, Fig. 3(d)] and without SRS (blue).

Fig. 5.
Fig. 5.

(a). Center wavelengths of the DW as a function of the pump wavelength for PCF1,2 and 3 in green, blue and red respectively. (b) PSD in PCF1,2 and 3 for L=20 m and P=10 W. Vertical dashed lines represents the second ZDW of each fiber.

Fig. 6.
Fig. 6.

Results for four identical simulations with different initial spectral phase of the pump in PCF2 (P=10 W). (a), (b), (c) and (d) represent the initial field intensities and (e) the output spectra.

Tables (2)

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Table 1 geometrical PCF parameters and ZDWs.

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Table 2. Dispersion orders for PCF1, 2 and 3.

Equations (2)

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E z = i m 2 m = 12 i m β m m ! m E τ m + i γ ( ω 0 ) [ 1 + i ω 0 τ ] × [ E ( z , τ ) + R ( τ ) E ( z , τ τ ) 2 d τ ]
Δ β = β ( ω P ) β ( ω DW ) = ( 1 f R ) γ ( ω P ) P P n 2 n = 12 ( ω DW ω P ) n n ! β n ( ω P ) = 0

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