Abstract

A technique to realize an effective negative Kerr nonlinear coefficient using two highly nonlinear fibers is presented. This technique is used compensate the fiber nonlinearity in optical backpropagation.

© 2011 Optical Society of America

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  1. D. M. Pepper and A. Yariv, Opt. Lett. 5, 59 (1980).
    [CrossRef] [PubMed]
  2. I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.
  3. L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.
  4. E. Ip and J. Kahn, J. Lightwave Technol. 26, 3416(2008).
    [CrossRef]
  5. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, Opt. Express 16, 880 (2008).
    [CrossRef] [PubMed]
  6. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007), Chaps. 2, 6, 7, and 11.

2008 (2)

1980 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007), Chaps. 2, 6, 7, and 11.

Boffi, P.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Brener, I.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Burkett, W.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Chaban, E. E.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Chen, X.

Chou, M. H.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Cristiani, I.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Degiorgio, V.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Fejer, M. M.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Ferrario, M.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Goldfarb, G.

Harel, R.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Ip, E.

Kahn, J.

Kim, I.

Kosinski, A.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Langrock, C.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Li, G.

Li, X.

Marazzi, L.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Martelli, P.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Martinelli, M.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Mateo, E.

Mikkelsen, B.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Minzioni, P.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Parameswaran, K.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Parolari, P.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Pepper, D. M.

Philen, D. L.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Pusino, V.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Raybon, G.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Righetti, A.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Rottwitt, K.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Siano, R.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

Stark, J. B.

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

Yaman, F.

Yariv, A.

J. Lightwave Technol. (1)

Opt. Express (1)

Opt. Lett. (1)

Other (3)

I. Brener, B. Mikkelsen, K. Rottwitt, W. Burkett, G. Raybon, J. B. Stark, K. Parameswaran, M. H. Chou, M. M. Fejer, E. E. Chaban, R. Harel, D. L. Philen, and A. Kosinski, in Optical Fiber Communication Conference, 2000 (IEEE, 2000), Vol.  4, p. 266.

L. Marazzi, P. Parolari, P. Martelli, R. Siano, P. Boffi, M. Ferrario, A. Righetti, M. Martinelli, V. Pusino, P. Minzioni, I. Cristiani, V. Degiorgio, C. Langrock, and M. M. Fejer, in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2009), paper JWA44.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007), Chaps. 2, 6, 7, and 11.

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Figures (4)

Fig. 1
Fig. 1

(a) Block diagram of a fiber-optic link with OBP. (b) Block diagram of the NLC. TX, transmitter; G, amplifier, RX, receiver; y-pol., y-polarization; x-pol, x-polarization.

Fig. 2
Fig. 2

Real part of the optical field envelope versus normalized time. T s , symbol interval; distance = 800 km , and n sp = 0 . Tx, transmitter

Fig. 3
Fig. 3

BER versus launch power to the fiber-optic link. Transmission distance = 800 km .

Fig. 4
Fig. 4

BER versus transmission reach.

Equations (17)

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u / z = i [ D ( t ) + N ( t , z ) ] u ( t , z ) ,
D ( t ) = β 2 2 2 t 2 , N ( t , z ) = γ a 2 ( z ) | u ( t , z ) | 2 ,
a 2 ( z ) = exp [ mod ( z , L a ) α ] .
u ( t , L tot ) = M u ( t , 0 ) ,
M = e i 0 L tot [ D ( t ) + N ( t , s ) ] d s .
u OBP , out ( t ) = M 1 u ( t , L tot ) = u ( t , 0 ) .
M 1 = e i 0 L tot [ D ( t ) + N ( t , s ) ] d s .
M 1 A ( t , 0 , Δ z / 2 ) · B ( t , Δ z ) · A ( t , Δ z / 2 , 3 Δ z / 2 ) · B ( t , 2 Δ z ) B ( t , L tot ) · A ( t , L tot Δ z / 2 , L tot ) ,
A ( t , x , y ) = exp [ i D ( t ) ( y x ) ] ,
B ( t , x ) = exp [ i x Δ z x a 2 ( z ) | u ( t , z ) | 2 d z ] .
B ( t , x ) = exp { i γ Δ z eff exp [ mod ( x , L a ) α ] | u ( t , x ) | 2 } ,
Δ z eff = m [ 1 e α L a ] α + 1 e mod ( Δ z , L a ) α α ,
B ( t , x ) = e i γ m [ 1 exp ( α L a ) ] | u ( t , x ) | 2 / α .
u p 1 ( t , L 1 ) = u p 1 ( t , 0 ) e i g 1 | u s ( t ) | 2 + i θ 1 + i Ω t ,
u p 2 ( t , L 2 ) = u p 2 ( t , 0 ) e i g 2 | u s ( t ) + u p 1 ( t , L 1 ) | 2 + i θ 2 + i Ω t ,
u p 2 ( t , L ) u p 2 ( t , 0 ) e i θ 2 { [ 1 + i g 2 ( | u s | 2 + | u p ( t , 0 ) | 2 ) ] e i Ω t + i g 2 u s u p 1 ( t , 0 ) e i g 1 | u s ( t ) | 2 i θ 1 + i g 2 u s u p 1 ( t , 0 ) e i [ g 1 | u s ( t ) | 2 + 2 Ω t + θ 1 ] } .
u out = K u s ( t ) exp [ i g 1 | u s ( t ) | 2 ] ,

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