Abstract

The parametric gain range of a degenerate four-wave mixing process is determined in the undepleted pump regime. The gain range is considered with and without taking the mode field distributions of the four-wave mixing components into account. It is found that the mode field distributions have to be included to evaluate the parametric gain correctly in dispersion-tailored speciality fibers and that mode profile engineering can provide a way to increase the parametric gain range.

© 2014 Optical Society of America

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References

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2014 (1)

2013 (1)

2012 (2)

2011 (1)

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, Opt. Commun. 284, 5208 (2011).
[CrossRef]

2009 (1)

2008 (1)

2002 (1)

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

1998 (1)

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Alkeskjold, T.

Andrekson, P.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Bang, O.

Broeng, J.

Chen, Y.

Coscelli, E.

Demas, J.

Du, C.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, Opt. Commun. 284, 5208 (2011).
[CrossRef]

Hansryd, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Hedekvist, P.-O.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Jauregui, C.

Jørgensen, M.

Lægsgaard, J.

Laurila, M.

Li, J.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Limpert, J.

Luo, J.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, Opt. Commun. 284, 5208 (2011).
[CrossRef]

Milam, D.

Petersen, S.

Poli, F.

Ramachandran, S.

Rasmussen, P.

Ruan, S.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, Opt. Commun. 284, 5208 (2011).
[CrossRef]

Shu, J.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, Opt. Commun. 284, 5208 (2011).
[CrossRef]

Steinmetz, A.

Steinvurzel, P.

Tai, B.

Tünnermann, A.

Wei, H.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, Opt. Commun. 284, 5208 (2011).
[CrossRef]

Westlund, M.

J. Hansryd, P. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002).
[CrossRef]

Yan, L.

Yan, P.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, Opt. Commun. 284, 5208 (2011).
[CrossRef]

Zhao, J.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, Opt. Commun. 284, 5208 (2011).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Image of the hybrid photonic crystal fiber. The inner cladding consists of airholes with hole-to-hole spacing Λ; one row of airholes has been replaced with high-index Germanium-doped silica rods of two different diameters, giving an asymmetric design. The outer cladding is an airclad. (b) The effective area, Aeff, of the fundamental mode (FM) and the two orientations of the LP11 mode (HOM11 and HOM12) polarized along the Germanium-doped silica rods. Spatial field distributions at 1056 nm for the FM and HOM11 and at 1050 nm for HOM12 are seen in the legend.

Fig. 2.
Fig. 2.

Intramodal parametric gain range and Δβ for the fundamental mode and a pump wavelength of 1056 nm (upper graph), for the LP11 mode named HOM11 and a pump wavelength of 1056 nm (middle graph), and for the LP11 mode named HOM12 and a pump wavelength of 1050 nm (lower graph). The gain range with and without the 1/Aeff-approximation is considered for a pump power of 150 kW.

Fig. 3.
Fig. 3.

Intramodal parametric gain for the fundamental mode and a pump wavelength of 1056 nm (top graph), for HOM11 and a pump wavelength of 1056 nm (middle graph), and for HOM12 and a pump wavelength of 1050 nm. The gain with and without the 1/Aeff-approximation is considered for a pump power of 150 kW.

Fig. 4.
Fig. 4.

Calculated mode field distributions at selected wavelengths of modes giving rise to parametric gain only without the 1/Aeff-approximation.

Equations (9)

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

dApdz=in2ωpcfpp|Ap|2Ap,
dAsdz=in2ωsc[2fsp|Ap|2As+fsippAp2Ai*eiΔβz],
dAidz=in2ωic[2fip|Ap|2Ai+fsippAp2As*eiΔβz],
fjk=|Fj|2|Fk|2|Fj|2|Fk|2,
fsipp=FsFiFpFp|Fs|2|Fi|2|Fp|2|Fp|2,
g=(n2ωpcPpfsipp)2(κ2)2,
κ=Δβ+2n2ωpcPp(fsp+fipfpp),
Δβ<2n2ωpPpc(fsippfspfip+fpp),Δβ>2n2ωpPpc(fsipp+fsp+fipfpp).
4n2ωpPpcAeff<Δβ<0.

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