Abstract

We propose a scheme for multilevel (nine or more) amplitude regeneration based on a nonlinear optical loop mirror (NOLM) and demonstrate through numerical modeling its efficiency and cascadability on circular 16-, 64-, and 256-symbol constellations. We show that the amplitude noise is efficiently suppressed. The design is flexible and enables variation of the number of levels and their positioning. The scheme is compatible with phase regenerators. Also, compared to the traditional single-NOLM configuration scheme, new features, such as reduced and sign-varied power-dependent phase shift, are available. The model is simple to implement, as it requires only two couplers in addition to the traditional NOLM, and offers a vast range of optimization parameters.

© 2014 Optical Society of America

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  1. P. J. Winzer and R.-J. Essiambre, J. Lightwave Technol. 24, 4711 (2006).
    [CrossRef]
  2. M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
    [CrossRef]
  3. O. Leclerc, U. E. Desurvire, and O. Audouin, Opt. Fiber Technol. 3, 97 (1997).
    [CrossRef]
  4. S. Boscolo, S. K. Turitsyn, and K. J. Blow, Opt. Fiber Technol. 14, 299 (2008).
    [CrossRef]
  5. M. Matsumoto, IEEE J. Sel. Top. Quantum Electron. 18, 738 (2012).
    [CrossRef]
  6. K. S. Turitsyn and S. K. Turitsyn, Opt. Lett. 37, 3600 (2012).
    [CrossRef]
  7. M. A. Sorokina and S. K. Turitsyn, “Shannon capacity of nonlinear regenerative channels,” arXiv:1305.1537 (2013).
  8. T. Umeki, M. Asobe, H. Takara, Y. Miyamoto, and H. Takenouchi, Opt. Express 21, 18170 (2013).
    [CrossRef]
  9. N. J. Doran and D. Wood, Opt. Lett. 13, 56 (1988).
    [CrossRef]
  10. A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
    [CrossRef]
  11. T. I. Lakoba and M. Vasilyev, Opt. Express 15, 10061 (2007).
    [CrossRef]
  12. T. Roethlingshoefer, G. Onishchukov, B. Schmauss, and G. Leuchs, IEEE Photon. Technol. Lett. 26, 556 (2014).
    [CrossRef]
  13. F. Seguineau, B. Lavigne, D. Rouvillain, P. Brindel, L. Pierre, and O. Leclerc, Proceedings of the Optical Fiber Communication Conference (2004), paper WN4.
  14. A. Gray, Z. Huang, I. Khrushchev, and I. Bennion, Electron. Lett. 40, 498 (2004).
    [CrossRef]
  15. M. A. Sorokina, S. Sygletos, and S. K. Turitsyn, Opt. Lett. 38, 4378 (2013).
    [CrossRef]
  16. G. J. Foschini, N. J. Holmdel, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. 22, 28 (1974).
    [CrossRef]
  17. Z. H. Peric, I. B. Djordjevic, S. M. Bogosavljevic, and M. C. Stefanovic, 9th Mediterranean Electrotechnical Conference (1998), Vol. 2, pp. 866–869.
  18. R. Dischler, Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh3B.2.
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    [CrossRef]
  20. J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
    [CrossRef]
  21. G. Hesketh and P. Horak, Opt. Lett. 38, 5357 (2013).
    [CrossRef]

2014

T. Roethlingshoefer, G. Onishchukov, B. Schmauss, and G. Leuchs, IEEE Photon. Technol. Lett. 26, 556 (2014).
[CrossRef]

2013

2012

K. S. Turitsyn and S. K. Turitsyn, Opt. Lett. 37, 3600 (2012).
[CrossRef]

M. Matsumoto, IEEE J. Sel. Top. Quantum Electron. 18, 738 (2012).
[CrossRef]

2011

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

2008

S. Boscolo, S. K. Turitsyn, and K. J. Blow, Opt. Fiber Technol. 14, 299 (2008).
[CrossRef]

2007

2006

2005

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
[CrossRef]

2004

A. Gray, Z. Huang, I. Khrushchev, and I. Bennion, Electron. Lett. 40, 498 (2004).
[CrossRef]

1997

O. Leclerc, U. E. Desurvire, and O. Audouin, Opt. Fiber Technol. 3, 97 (1997).
[CrossRef]

1991

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

1988

1974

G. J. Foschini, N. J. Holmdel, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. 22, 28 (1974).
[CrossRef]

Asobe, M.

Audouin, O.

O. Leclerc, U. E. Desurvire, and O. Audouin, Opt. Fiber Technol. 3, 97 (1997).
[CrossRef]

Bennion, I.

A. Gray, Z. Huang, I. Khrushchev, and I. Bennion, Electron. Lett. 40, 498 (2004).
[CrossRef]

Blow, K. J.

S. Boscolo, S. K. Turitsyn, and K. J. Blow, Opt. Fiber Technol. 14, 299 (2008).
[CrossRef]

Bogosavljevic, S. M.

Z. H. Peric, I. B. Djordjevic, S. M. Bogosavljevic, and M. C. Stefanovic, 9th Mediterranean Electrotechnical Conference (1998), Vol. 2, pp. 866–869.

Bogris, A.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Boscolo, S.

S. Boscolo, S. K. Turitsyn, and K. J. Blow, Opt. Fiber Technol. 14, 299 (2008).
[CrossRef]

Brindel, P.

F. Seguineau, B. Lavigne, D. Rouvillain, P. Brindel, L. Pierre, and O. Leclerc, Proceedings of the Optical Fiber Communication Conference (2004), paper WN4.

Cvecek, K.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
[CrossRef]

Desurvire, U. E.

O. Leclerc, U. E. Desurvire, and O. Audouin, Opt. Fiber Technol. 3, 97 (1997).
[CrossRef]

Dischler, R.

R. Dischler, Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh3B.2.

Djordjevic, I. B.

Z. H. Peric, I. B. Djordjevic, S. M. Bogosavljevic, and M. C. Stefanovic, 9th Mediterranean Electrotechnical Conference (1998), Vol. 2, pp. 866–869.

Doran, N. J.

Ellis, A. D.

Essiambre, R.-J.

Foschini, G. J.

G. J. Foschini, N. J. Holmdel, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. 22, 28 (1974).
[CrossRef]

Gitlin, R.

G. J. Foschini, N. J. Holmdel, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. 22, 28 (1974).
[CrossRef]

Gray, A.

A. Gray, Z. Huang, I. Khrushchev, and I. Bennion, Electron. Lett. 40, 498 (2004).
[CrossRef]

Gruner-Nielsen, L.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Hesketh, G.

Holmdel, N. J.

G. J. Foschini, N. J. Holmdel, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. 22, 28 (1974).
[CrossRef]

Horak, P.

Huang, Z.

A. Gray, Z. Huang, I. Khrushchev, and I. Bennion, Electron. Lett. 40, 498 (2004).
[CrossRef]

Kakande, J.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Khrushchev, I.

A. Gray, Z. Huang, I. Khrushchev, and I. Bennion, Electron. Lett. 40, 498 (2004).
[CrossRef]

Kubota, H.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Lakoba, T. I.

Lavigne, B.

F. Seguineau, B. Lavigne, D. Rouvillain, P. Brindel, L. Pierre, and O. Leclerc, Proceedings of the Optical Fiber Communication Conference (2004), paper WN4.

Leclerc, O.

O. Leclerc, U. E. Desurvire, and O. Audouin, Opt. Fiber Technol. 3, 97 (1997).
[CrossRef]

F. Seguineau, B. Lavigne, D. Rouvillain, P. Brindel, L. Pierre, and O. Leclerc, Proceedings of the Optical Fiber Communication Conference (2004), paper WN4.

Leuchs, G.

T. Roethlingshoefer, G. Onishchukov, B. Schmauss, and G. Leuchs, IEEE Photon. Technol. Lett. 26, 556 (2014).
[CrossRef]

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
[CrossRef]

Matsumoto, M.

M. Matsumoto, IEEE J. Sel. Top. Quantum Electron. 18, 738 (2012).
[CrossRef]

Meissner, M.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
[CrossRef]

Miyamoto, Y.

Nakazawa, M.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Onishchukov, G.

T. Roethlingshoefer, G. Onishchukov, B. Schmauss, and G. Leuchs, IEEE Photon. Technol. Lett. 26, 556 (2014).
[CrossRef]

Parmigiani, F.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Peric, Z. H.

Z. H. Peric, I. B. Djordjevic, S. M. Bogosavljevic, and M. C. Stefanovic, 9th Mediterranean Electrotechnical Conference (1998), Vol. 2, pp. 866–869.

Petropoulos, P.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Phelan, R.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Pierre, L.

F. Seguineau, B. Lavigne, D. Rouvillain, P. Brindel, L. Pierre, and O. Leclerc, Proceedings of the Optical Fiber Communication Conference (2004), paper WN4.

Richardson, D. J.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Roethlingshoefer, T.

T. Roethlingshoefer, G. Onishchukov, B. Schmauss, and G. Leuchs, IEEE Photon. Technol. Lett. 26, 556 (2014).
[CrossRef]

Rouvillain, D.

F. Seguineau, B. Lavigne, D. Rouvillain, P. Brindel, L. Pierre, and O. Leclerc, Proceedings of the Optical Fiber Communication Conference (2004), paper WN4.

Schmauss, B.

T. Roethlingshoefer, G. Onishchukov, B. Schmauss, and G. Leuchs, IEEE Photon. Technol. Lett. 26, 556 (2014).
[CrossRef]

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
[CrossRef]

Seguineau, F.

F. Seguineau, B. Lavigne, D. Rouvillain, P. Brindel, L. Pierre, and O. Leclerc, Proceedings of the Optical Fiber Communication Conference (2004), paper WN4.

Slavik, R.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Sorokina, M.

Sorokina, M. A.

M. A. Sorokina, S. Sygletos, and S. K. Turitsyn, Opt. Lett. 38, 4378 (2013).
[CrossRef]

M. A. Sorokina and S. K. Turitsyn, “Shannon capacity of nonlinear regenerative channels,” arXiv:1305.1537 (2013).

Sponsel, K.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
[CrossRef]

Stefanovic, M. C.

Z. H. Peric, I. B. Djordjevic, S. M. Bogosavljevic, and M. C. Stefanovic, 9th Mediterranean Electrotechnical Conference (1998), Vol. 2, pp. 866–869.

Striegler, A. G.

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
[CrossRef]

Suzuki, K.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Sygletos, S.

Syvridis, D.

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Takara, H.

Takenouchi, H.

Turitsyn, K. S.

Turitsyn, S.

Turitsyn, S. K.

M. A. Sorokina, S. Sygletos, and S. K. Turitsyn, Opt. Lett. 38, 4378 (2013).
[CrossRef]

K. S. Turitsyn and S. K. Turitsyn, Opt. Lett. 37, 3600 (2012).
[CrossRef]

S. Boscolo, S. K. Turitsyn, and K. J. Blow, Opt. Fiber Technol. 14, 299 (2008).
[CrossRef]

M. A. Sorokina and S. K. Turitsyn, “Shannon capacity of nonlinear regenerative channels,” arXiv:1305.1537 (2013).

Umeki, T.

Vasilyev, M.

Weinstein, S.

G. J. Foschini, N. J. Holmdel, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. 22, 28 (1974).
[CrossRef]

Winzer, P. J.

Wood, D.

Yamada, E.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Electron. Lett.

M. Nakazawa, E. Yamada, H. Kubota, and K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

A. Gray, Z. Huang, I. Khrushchev, and I. Bennion, Electron. Lett. 40, 498 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Matsumoto, IEEE J. Sel. Top. Quantum Electron. 18, 738 (2012).
[CrossRef]

IEEE Photon. Technol. Lett.

T. Roethlingshoefer, G. Onishchukov, B. Schmauss, and G. Leuchs, IEEE Photon. Technol. Lett. 26, 556 (2014).
[CrossRef]

A. G. Striegler, M. Meissner, K. Cvecek, K. Sponsel, G. Leuchs, and B. Schmauss, IEEE Photon. Technol. Lett. 17, 639 (2005).
[CrossRef]

IEEE Trans. Commun.

G. J. Foschini, N. J. Holmdel, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. 22, 28 (1974).
[CrossRef]

J. Lightwave Technol.

Nat. Photonics

J. Kakande, R. Slavik, F. Parmigiani, A. Bogris, D. Syvridis, L. Gruner-Nielsen, R. Phelan, P. Petropoulos, and D. J. Richardson, Nat. Photonics 5, 748 (2011).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

O. Leclerc, U. E. Desurvire, and O. Audouin, Opt. Fiber Technol. 3, 97 (1997).
[CrossRef]

S. Boscolo, S. K. Turitsyn, and K. J. Blow, Opt. Fiber Technol. 14, 299 (2008).
[CrossRef]

Opt. Lett.

Other

F. Seguineau, B. Lavigne, D. Rouvillain, P. Brindel, L. Pierre, and O. Leclerc, Proceedings of the Optical Fiber Communication Conference (2004), paper WN4.

M. A. Sorokina and S. K. Turitsyn, “Shannon capacity of nonlinear regenerative channels,” arXiv:1305.1537 (2013).

Z. H. Peric, I. B. Djordjevic, S. M. Bogosavljevic, and M. C. Stefanovic, 9th Mediterranean Electrotechnical Conference (1998), Vol. 2, pp. 866–869.

R. Dischler, Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh3B.2.

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Figures (4)

Fig. 1.
Fig. 1.

Scheme of the coupled NOLM.

Fig. 2.
Fig. 2.

(a) TF for the dimensionless power P¯=PγL/2 and (b) associated phase shift for parameters α=0.267; Δϕ=3π/2; κ=β/(1β)=0.014 (solid curves). By changing parameters to α=1α, one can achieve sign-reversed phase shift, and the amplitude levels will be shifted (dashed curves).

Fig. 3.
Fig. 3.

Constellation diagrams (normalized to signal power S=1) for circular 16- (row 1), 64- (row 2), and 256- (row 3) QAM after transmission without (column a) and with 10 (column b) and 20 (column c) equidistantly placed amplitude regenerators [see Fig. 1 with γL=2W1; α=0.24, κ=0.03 (rows 1 and 2) and α=0.267, κ=0.014 (row 3)], with an OPC placed in the middle of the transmission line. In the absence of regeneration, the respective linear system has SNR=20dB (row 1), SNR=25dB (row 2), and SNR=30dB (row 3).

Fig. 4.
Fig. 4.

Constellation diagrams (normalized to signal power S=1) for circular 16- (row a) and 32- (row b) QAM after transmission with 10 PSAs (column 1) and 10, 20, and 30 (columns 2–4, respectively) phase and amplitude regenerators equidistantly placed along the line (with parameters γL=2W1, α=0.24, κ=0.03). In the absence of regeneration, the respective linear system has SNR=15dB (row a) and SNR=20dB (row b).

Equations (6)

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

C^1=12(1ii1).
N^(Pin2)=[(1α)ei(1α)γLPin/2+αeiαγLPin/2]Pin2,
C^2=(1βiβiβ1β),
Aout=Poutei(φ+δϕ)=([1+iκ(1α)ei(1α)γLPin/2+αeiαγLPin/2])Pineiφ.
Pout=Pin(1+κ2((1α)2+α2)2κ2(1α)αcos[(12α)ψ]+2κ[(1α)sin[(1α)ψ]αsin[αψ]]),ψ=γLPin2,δϕ=arctan(ακcos(αψ)(1α)κcos((1α)ψ)1ακsin(αψ)+(1α)κsin((1α)ψ)).
Pouteiφout=Pineiφ(1+meiMφ).

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