Abstract

We present the theory of Raman amplification in long multimode optical fibers, where strong random mode coupling within groups of quasi-degenerate modes is unavoidable. In such fibers, the signal components in modes that belong to the same strongly coupled group experience the same Raman amplification, where the differential gain is linearly dependent on the aggregate powers of the pump in each of the mode groups. The equations that we derive significantly facilitate the numerical and analytical study of Raman amplification in long multimode fibers.

© 2013 Optical Society of America

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References

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2012 (4)

2011 (2)

2009 (1)

2008 (1)

2004 (1)

M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604 (2004).
[CrossRef]

2003 (1)

Q. Lin and G. P. Agrawal, J. Opt. Soc. Am. 20, 1616 (2003).
[CrossRef]

1995 (1)

1975 (1)

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. 11, 964 (1975).
[CrossRef]

Agrawal, G. P.

Q. Lin and G. P. Agrawal, J. Opt. Soc. Am. 20, 1616 (2003).
[CrossRef]

Antonelli, C.

Bolle, C.

Burrows, E. C.

Cherlow, J.

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. 11, 964 (1975).
[CrossRef]

Cirigliano, M.

Dougherty, D. J.

Esmaeelpour, M.

Essiambre, R.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, J. Lightwave Technol. 30, 521 (2012).
[CrossRef]

R. Ryf, R. Essiambre, J. von Hoyningen-Huene, and P. Winzer, Proceedings of Optical Fiber Communications Conference (OFC) (Optical Society of America, 2012), paper OW1D.2.

Ferrario, M.

Foschini, G. J.

Gnauck, A. H.

Haus, H. A.

Hellwarth, R.

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. 11, 964 (1975).
[CrossRef]

Ho, K-P.

Horak, P.

Ippen, E. P.

Kahn, J. M.

Kärtner, F. X.

Kolesik, M.

M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Lin, Q.

Q. Lin and G. P. Agrawal, J. Opt. Soc. Am. 20, 1616 (2003).
[CrossRef]

Lingle, R.

Marazzi, L.

Martelli, P.

Martinelli, M.

McCurdy, A. H.

Mecozzi, A.

Moloney, J. V.

M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Mumtaz, S.

Peckham, D. W.

Poletti, F.

Randel, S.

Rottwitt, K.

K. Rottwitt and A. J. Stenz, Optical Fiber Telecommunications IV A, I. P. Kaminow and T. Li, eds., (Academic, 2002), Chap. 5, p. 213.

Ryf, R.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, J. Lightwave Technol. 30, 521 (2012).
[CrossRef]

R. Ryf, R. Essiambre, J. von Hoyningen-Huene, and P. Winzer, Proceedings of Optical Fiber Communications Conference (OFC) (Optical Society of America, 2012), paper OW1D.2.

Shtaif, M.

Sierra, A.

Stenz, A. J.

K. Rottwitt and A. J. Stenz, Optical Fiber Telecommunications IV A, I. P. Kaminow and T. Li, eds., (Academic, 2002), Chap. 5, p. 213.

von Hoyningen-Huene, J.

R. Ryf, R. Essiambre, J. von Hoyningen-Huene, and P. Winzer, Proceedings of Optical Fiber Communications Conference (OFC) (Optical Society of America, 2012), paper OW1D.2.

Winzer, P.

R. Ryf, R. Essiambre, J. von Hoyningen-Huene, and P. Winzer, Proceedings of Optical Fiber Communications Conference (OFC) (Optical Society of America, 2012), paper OW1D.2.

Winzer, P. J.

Yang, T.-T.

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. 11, 964 (1975).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

Q. Lin and G. P. Agrawal, J. Opt. Soc. Am. 20, 1616 (2003).
[CrossRef]

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

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. (1)

R. Hellwarth, J. Cherlow, and T.-T. Yang, Phys. Rev. 11, 964 (1975).
[CrossRef]

Phys. Rev. E (1)

M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Other (2)

K. Rottwitt and A. J. Stenz, Optical Fiber Telecommunications IV A, I. P. Kaminow and T. Li, eds., (Academic, 2002), Chap. 5, p. 213.

R. Ryf, R. Essiambre, J. von Hoyningen-Huene, and P. Winzer, Proceedings of Optical Fiber Communications Conference (OFC) (Optical Society of America, 2012), paper OW1D.2.

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Equations (20)

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E(r,t)=n0dω2{En(z,ω)Fn(x,y,ω)Nn(ω)exp(iωt)+c.c.},
En(z,ω)z=iω4Nn(ω)dxdyFn*·P˜R,
PR(r,t)=ϵ0χ(3)dτ[h(tτ)|E(r,τ)|2E(r,t)+g(tτ)E(r,t)·E(r,τ)E(r,τ)],
E(r,t)=12[Asexp(iωst)+Apexp(iωpt)+c.c.,],
Aα(r)=nFn(x,y,ωα)Nn(ωα)En(α)(z),
PR=ϵ0χ(3)8(exp(iωst){2h˜*(Δω)Ap(As·Ap*)+g˜*(Δω)[As|Ap|2+Ap*(As·Ap)]}+exp(iωpt){2h˜(Δω)As(Ap·As*)+g˜(Δω)[Ap|As|2+As*(As·Ap)]}+c.c.),
En(p)z=iωpκhkmfnhkm(p)Eh(s)Ek(p)Em(s)*,
En(s)z=iωsκhkmfnhkm(s)Eh(p)Ek(s)Em(p)*,
fnhkm(p)=h˜(Δω)×Qnhkm(p)+g˜(Δω)2(Rnhkm(p)+Tnhkm(p)),
fnhkm(s)=h˜*(Δω)×Qnhkm(s)+g˜*(Δω)2(Rnhkm(s)+Tnhkm(s)).
Qnhkm(p)=ε02c2121Nn(ωp)Nh(ωs)Nk(ωp)Nm(ωs)[Fn*(ωp)·Fh(ωs)][Fk(ωp)·Fm*(ωs)]dxdy,
Eu(p)z=iωpκ(j=1M(s)ru,j(p)|Ej(s)|2)Eu(p),
Ev(s)z=iωsκ(j=1M(p)rj,v(s)|Ej(p)|2)Ev(s),
rj,k(α)=14NjNkhj,nkfnhnh(α).
Eu(p)z=iωpκnuhkmfnhkm(p)Eh(s)Ek(p)Em(s)*e^n,
iωpκnuhkmfnhkm(p)E[Em(s)*Eh(s)]E[En(p)*Ek(p)],
iωpκj=1M(s)hj,nufnhnh(p)|Ej(s)|22Nj|Eu(p)|22Nu.
iωpκj=1M(s)ru,j(p)|Ej(s)|2|Eu(p)|2.
Pu(p)z=ωpκj=1M(s)2Im{ru,j(p)}Pj(s)Pu(p),
Pv(s)z=ωsκj=1M(p)2Im{rv,j(s)}Pj(p)Pv(s),

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