Abstract

We show that Kerr nonlinearity induced intermodal power transfer in a particular mode group of a multimode fiber can be formulated by the same type of equation used to describe the effect of cross polarization modulation in single-mode fibers.

© 2013 Optical Society of America

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References

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  1. P. J. Winzer and G. J. Foschini, Opt. Express 19, 16680 (2011).
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    [CrossRef]
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2012

2011

2009

2008

1995

1974

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Antonelli, C.

Bunge, C.-A.

Dirac, P. A. M.

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Clarendon, 1958).

Foschini, G. J.

Gordon, J. P.

Hall, B. C.

B. C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Springer, 2003).

Heismann, F.

Horak, P.

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Mecozzi, A.

Mollenauer, L. F.

Petermann, K.

G. Rademacher, S. Warm, and K. Petermann, IEEE Photon. Technol. Lett. 24, 1929 (2012).
[CrossRef]

M. Winter, C.-A. Bunge, D. Setti, and K. Petermann, J. Lightwave Technol. 27, 3739 (2009).
[CrossRef]

Poletti, F.

Rademacher, G.

G. Rademacher, S. Warm, and K. Petermann, IEEE Photon. Technol. Lett. 24, 1929 (2012).
[CrossRef]

Setti, D.

Shtaif, M.

Warm, S.

G. Rademacher, S. Warm, and K. Petermann, IEEE Photon. Technol. Lett. 24, 1929 (2012).
[CrossRef]

Winter, M.

Winzer, P. J.

IEEE Photon. Technol. Lett.

G. Rademacher, S. Warm, and K. Petermann, IEEE Photon. Technol. Lett. 24, 1929 (2012).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Sov. Phys. JETP

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Other

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Clarendon, 1958).

B. C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Springer, 2003).

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Figures (3)

Fig. 1.
Fig. 1.

XPolM: (a)–(c) The input polarization state (a) of the low power channel at wavelength λa is rotated by the high power pump at 45° (b) to the output state (c). XMM: (d)–(f) The input mode LP11a,x (d) with low power is rotated by the high power pump (LP11a,x+LP11b,x) (e) to the output LP11b,x mode (f). The rotation corresponds to an accumulated nonlinear phase shift of π.

Fig. 2.
Fig. 2.

Evolution of the modes on the Poincaré sphere. The input state of the low power channel at wavelength λa is rotated by an angle of π to the antipodal point on the sphere.

Fig. 3.
Fig. 3.

Power distribution in the x polarization of the LP11a mode at the probe wavelength λa for a pump power of 29 dBm. As is predicted by the analytical theory, there is permanent power exchange along the link due to the nonlinearity induced phase shift. Circles are simulated values; each one corresponds to a different link realization. The intermediate points are interpolated. In the ideal case, illustrated by the diamonds connected with a dashed line, the inflection points (corresponding to an accumulated phase shift multiple of π/2) lie on the middle line. The extrema (corresponding to integer multiples of π) are the points where the probe is completely translated either to the LP11a mode (maxima) or to the LP11b mode (minima).

Equations (7)

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|Ez=β|Etiβ22|Et2+iγκE|E|E.
|az=iγκ(a|a|a+b|b|a+|bb|aXMM)|bz=iγκ(b|b|b+a|a|b+|aa|b),
Az=iγκ[B,A]=iγκ[A+B,A]Bz=iγκ[A,B]=iγκ[A+B,B].
A(z)=eiγκz(A+B)A(0)eiγκz(A+B)=eiγκzadA+BA(0)B(z)=eiγκz(A+B)B(0)eiγκz(A+B)=eiγκzadA+BB(0),
eX(z)/z=eX(z){X/z12![X,X/z]+13![X,[X,X/z]]},
A(z)=eiγκ0zb|bB^A(0)eiγκ0zb|bB^=eiγκ0zb|badB^A(0).
σ1=(1001)σ2=(0110)σ3=(0ii0),

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