Abstract

We show in theory and simulation that the supercontinuum generation from an initial continuous wave field in a highly nonlinear fiber operating near the zero-dispersion point can be significantly enhanced with the aid of dispersion management. We characterize the spectral broadening as a process initiated by modulational instability, but driven by the zero-dispersion dynamics of an N-soliton interacting with the asymmetric phase profile generated by the Raman effect, self-steepening effect, and/or higher-order dispersion. Higher N-soliton values lead to shorter pulses and a broader spectrum. This insight allows us to use dispersion management in conjunction with modulational instability to effectively increase the N value and greatly enhance the supercontiuum generation process.

© 2005 Optical Society of America

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References

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App. Phys. Lett.

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

IEEE J. Quant. Elec.

E. Golovchenko, P. Mamyshev, A. Pilipetskii, E. A. Dianov, �??Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,�?? IEEE J. Quant. Elec. 26, 1815-1820 (1990).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Comm.

A. Demircan and U. Bandelow, �??Supercontinuum generation by the modulation instability,�?? Opt. Comm. 244, 244-185 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

J. C. Bronski and J. N. Kutz, �??Numerical simulation of the semiclassical limit of the focusing nonlinear Schrodinger equation ,�?? Phys. Lett. A 254, 325 (1999).
[CrossRef]

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, G. Korn, �??Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,�?? Phys. Rev. Lett. 88, 173901 (2002)
[CrossRef] [PubMed]

Physica D

J. C. Bronski, �??Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem,�?? Physica D 97, 376-397 (1996)
[CrossRef]

Sov. Phys. JETP

V. E. Zakharov and A. B. Shabat, �??Exact theory of two-dimensional self-focusing and one-dimensional selfmodulation of waves in nonlinear media,�?? Sov. Phys. JETP 34, 62-69 (1972).

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd Ed., Academic Press, San Diego, 2001.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications, Oxford University Press, 1995.

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Figures (6)

Fig. 1.
Fig. 1.

Fundamental process of supercontinuum generation from a CW source. Here the MI induced instability is followed by the creation of an ultra-short (broadband) pulse train which is driven by the nonlinear interaction of the Raman effect in the zero-dispersion limit. As shown in Sec. 3, the introduction of the dispersion map helps to significantly broaden the spectrum.

Fig. 2.
Fig. 2.

Qualitative depiction of the eigenvalue distribution of the Zakharov-Shabat problem [20] without (a) and with (b) initial phase chirp [13] in arbitrary units. Note that the application of a large symmetric phase chirp splits the double eigenvalues of (a) as shown in (b) giving the Y-shaped zipper spectrum. Recall that the eigenvalue Zakharov-Shabat eigenvalues are given by λn =kn +n . Further, the real part of the eigenvalue kn determines the ejection velocity while the imaginary part ηn determines the ejected soliton pulse height and width.

Fig. 3.
Fig. 3.

Evolution of initial 5-soliton. The top figure shows the time-domain evolution and the ejected one-solitons due to the Raman response (TR =3 fs). The bottom figure shows the associated spectrum and the Raman red shift. Note the ejection of a≈150 fs pulse.

Fig. 4.
Fig. 4.

Onset of MI from an initial 800 mW CW wave (light line) for the dispersion values =0.1 ps/[km-nm] (top) and =1 ps/[km-nm] (bottom). The MI begins to grow substantially (bold lines) over a propagation distance of 1 km. The modulation cells, which are enclosed by the dotted lines, begin the ejection process illustrated in Fig. 3. The modulational cells for this example capture energies of ≈0.2 pJ (top) and ≈1.6 pJ (bottom) respectively.

Fig. 5.
Fig. 5.

Field propagation over 7 km from an initial 250 mW CW source showing the onset of MI followed pulse compression. Without dispersion management (top), the resulting FWHM pulse train is on the order of picoseconds which gives a spectrum of ≈60 nm for a =0.2 ps/[km-nm]. With dispersion management (5 km of =5 ps/[km-nm] fiber followed by 2 km of D̄=0.2 ps/[km-nm] fiber) gives more than four times the spectral broadening and results in a≈250 nm spectral width. The resulting pulse train (bottom) results in FWHM pulses on the order of femtoseconds.

Fig. 6.
Fig. 6.

Output spectrum after 7 km from an initial 250 mWCWsource. Without dispersion management (light line), the spectrum is ≈60 nm for a =0.2 ps/[km-nm]. Dispersion management (5 km of =5 ps/[km-nm] fiber followed by 2 km of =0.2 ps/[km-nm] fiber) gives more than four times the spectral broadening and results in a≈250 nm spectral width (bold line).

Equations (5)

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i Q Z + 1 2 2 Q T 2 + Q 2 Q τ Q ( Q 2 ) T = 0
( Q ( 0 , T ) 2 ) T = ( N 2 sech 2 T ) T = 2 N 2 sech 2 T tanh T .
Q = Q ( 0 , T ) exp [ i ( 2 τ N 2 sech 2 T tanh T ) Z ] .
Q n ( Z , T ) = 2 η n sech [ 2 η n ( T π κ n Z ) ] exp [ i 2 T + i π ( κ n 2 η 2 ) Z ] .
i Q Z + 1 2 2 Q T 2 + i β 3 Q T 3 + Q 2 Q τ Q ( Q 2 ) T + i σ ( Q 2 Q ) T + i Γ Q = 0

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