Abstract

Supercontinuum generation can be achieved in the continuous-wave regime with a few watts of pump power launched into kilometer-long fibers. High power spectral density broadband light sources can be obtained in this way. Using a generalized nonlinear Schrödinger equation model and an ensemble averaging procedure that takes into account the partially-coherent nature of the pump laser, we fully explain for the first time the spectral broadening mechanisms underlying this process. Our simulations and experiments confirm that continuous-wave supercontinuum generation involve Raman soliton dynamics and dispersive waves in a way akin to pulsed supercontinua. The Raman solitons are however generated with a wide distribution of parameters because they originate from the random phase and intensity fluctuations associated with the pump incoherence. This soliton distribution is averaged out by experimental measurements, which explains the remarkable smoothness of experimental continuous-wave supercontinuum spectra.

© 2005 Optical Society of America

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References

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Appl. Phys. B (1)

J. W. Nicholson, A. K. Abeeluck, C. Headley, M. F. Yan, and C. G. Jørgensen, �??Pulsed and continuous-wave supercontinuum generation in highly nonlinear, dispersion-shifted fibers,�?? Appl. Phys. B B77, 211�??218 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

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]

Electron. Lett. (2)

T. Morioka, K. Mori, and M. Saruwatari, �??More than 100-wavelength-channel picosecond optical pulse generation from single laser source using supercontinuum in optical fibres,�?? Electron. Lett. 29, 862�??864 (1993).
[CrossRef]

H. Takara, T. Ohara, and K. Sato, �??Over 1000 km DWDM transmission with supercontinuum multi-carrier source,�?? Electron. Lett. 39, 1078�??1079 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, �??Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,�?? IEEE J. Quantum Electron. QE-23, 1938�??1946 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. N. Islam, �??Raman amplifiers for telecommunications,�?? IEEE J. Sel. Top. Quantum Electron. 8, 548�??559 (2002).
[CrossRef]

J. Opt. Soc. Am. B (6)

JETP Lett. (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel�??makh, and A. A. Fomichev, �??Stimulated Raman conversion of multisoliton pulses in quartz optical fibers,�?? Zh. Eksp. Teor. Fiz. 41, 242�??244 (1985) JETP Lett. 41, 294�??297 (1985)].

Opt. Commun. (1)

M. González-Herráez, S. Martín-López, P. Corredera, M. L. Hernanz, and P. R. Horche, �??Supercontinuum generation using a continuous-wave Raman fiber laser,�?? Opt. Commun. 226, 323�??328 (2003).
[CrossRef]

Opt. Express (4)

Opt. Lett. (11)

D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, �??Study of an ultrahigh-numerical-aperture fiber continuum generation source for optical coherence tomography,�?? Opt. Lett. 27, 2010�??2012 (2002).
[CrossRef]

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).
[CrossRef] [PubMed]

M. González-Herráez, L. Thévenaz, and P. Robert, �??Distributed measurement of chromatic dispersion by four-wave mixing and brillouin optical-time-domain analysis,�?? Opt. Lett. 28, 2210�??2212 (2003).
[CrossRef]

F. Vanholsbeeck, S. Coen, Ph. Emplit, C. Martinelli, and T. Sylvestre, �??Cascaded Raman generation in optical fibers : Influence of chromatic dispersion and Rayleigh backscattering,�?? Opt. Lett. 29, 998�??1000 (2004).
[CrossRef] [PubMed]

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]

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]

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O�??Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, �??Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,�?? Opt. Lett. 27, 1174�??1176 (2002).
[CrossRef]

J. M. Dudley and S. Coen, �??Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,�?? Opt. Lett. 27, 1180�??1182 (2002).
[CrossRef]

D. Monzón-Hernández, A. N. Starodumov, Y. O. Barmenkov, I. Torres-Gómez, and F. Mendoza-Santoyo, �??Continuous-wave measurement of the fiber nonlinear refractive index,�?? Opt. Lett. 23, 1274�??1276 (1998).
[CrossRef]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, �??Supercontinuum generation in tapered fibers,�?? Opt. Lett. 25, 1415�??1417 (2000).
[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, 25�??27 (2000).
[CrossRef]

Optics Letters (1)

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, �??Incoherent modulation instability in instantaneous nonlinear Kerr media,�?? to be published in Optics Letters.

Phys. Rev. A (1)

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, �??Noise amplification in dispersive nonlinear media,�?? Phys. Rev. A 51, 4086�??4092 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S.Windeler, R. Holzwarth, Th. Udem, and T. W. Hänsch, �??Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb,�?? Phys. Rev. Lett. 84, 5102�??5105 (2000).
[CrossRef] [PubMed]

A. V. Husakou and J. Herrmann, �??Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,�?? Phys. Rev. Lett. 87, 203901/1�??4 (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, 173901/1�??4 (2002).
[CrossRef] [PubMed]

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, �??Fundamental noise limitations to supercontinuum generation in microstructure fiber,�?? Phys. Rev. Lett. 90, 113904/1�??4 (2003).
[CrossRef] [PubMed]

Science (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S.Windeler, J. L. Hall, and S. T. Cundiff, �??Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,�?? Science 288, 635�??639 (2000).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, Optics and Photonics Series, 3rd ed. (Academic Press, San Diego, 2001).

Supplementary Material (1)

» Media 1: AVI (2366 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

SC spectrum with different pump powers at room temperature (≃ 20 °C). All the curves have been normalized to the same peak value. Inset shows how increasing pump power leads to a stronger pump depletion.

Fig. 2.
Fig. 2.

(a) Temporal intensity profile of the cw input beam used in the simulations for one particular realization of the random initial spectral phase (shown here with an average power of 1.7 W). (b) Intensity autocorrelation of the RFL output at 2.1 W.

Fig. 3.
Fig. 3.

(a) Numerical output spectra for various pump power levels and (b) temporal intensity output at P p = 1.7 W for the initial condition shown in Fig. 2(a). (c) Measured intensity autocorrelation of the SC at P p = 1.7 W.

Fig. 4.
Fig. 4.

Results of five identical simulations differing only by the random initial spectral phase and performed with a pump power P p = 1.7 W. (a) represents the initial field intensities while (b) shows the corresponding generated spectra. A movie of the simulation can be seen by clicking on the figure. [Media 1]

Fig. 5.
Fig. 5.

Comparison of experimental and simulated SC spectra obtained for a pump power of (a) P p = 0.72 W and (b) P p = 1.7 W. The numerical results have been averaged over an ensemble of 100 simulations differing only by the random initial spectral phase.

Equations (2)

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E z = α 2 E i β 2 2 2 E t 2 + β 3 6 3 E t 3 + + iγE ( t R ( t ' ) E ( z , t t ' ) 2 d t ' + i Γ R ( z , t ) ) .
Γ R ( Ω , z ) Γ R * ( Ω ' , z ' ) = ( 2 f R ħ ω 0 γ ) Im h R ( Ω ) [ n th ( Ω ) + U ( Ω ) ] δ ( z z ' ) δ ( Ω Ω ' )

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