Abstract

Conventional and advanced modulation formats that simultaneously modulate two or more of the optical attributes of phase, amplitude, and polarization and/or utilize observation intervals longer than two chips (time slots) are designed by using a unified interpretation as signaling by means of generalized Stokes parameters. In particular, the new paradigm is applied to the recently introduced multichip extension of optical differential phase shift keying.

© 2006 Optical Society of America

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References

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  1. A. H. Gnauk, P. J. Winzer, J. Lightwave Technol. 23, 115 (2005).
    [CrossRef]
  2. T. Koonen, G. Morthier, J. Jennen, H. de Waardt, P. Demeester, in Proceedings of the European Conference on Optical Communications (ECOC’01) (2001), Vol. 4, pp. 608–609.
  3. M. Nazarathy, E. Simony, IEEE Photon. Technol. Lett. 17, 1133 (2005).
    [CrossRef]
  4. Y. Yadin, A. Bilenca, M. Nazarathy, IEEE Photon. Technol. Lett. 17, 2001 (2005).
    [CrossRef]
  5. S. Benedetto, P. Poggiolini, IEEE Trans. Commun. 40, 708 (1992).
    [CrossRef]
  6. S. Betti, F. Curti, G. De Marchis, E. Iannone, J. Lightwave Technol. 8, 1127 (1990).
    [CrossRef]
  7. J. Comellas, J. M. Gene, J. Prat, IEEE Photon. Technol. Lett. 16, 1766 (2004).
    [CrossRef]
  8. C. W. Chow, H. K. Tsang, in 10th OptoElectronics and Communications Conference (OECC) (2005), p. 6A3.
  9. M. Nazarathy, E. Simony, “Generalized Stokes parameters shift keying: a new perspective on optimal detection over electrical and optical vector incoherent channels,” IEEE Trans. Commun. (to be published).
  10. M. Nazarathy, E. Simony, “Stokes space optimal detection of polarization and differential phase shift-keying modulation,” J. Lightwave Technol. (to be published).

2005

A. H. Gnauk, P. J. Winzer, J. Lightwave Technol. 23, 115 (2005).
[CrossRef]

M. Nazarathy, E. Simony, IEEE Photon. Technol. Lett. 17, 1133 (2005).
[CrossRef]

Y. Yadin, A. Bilenca, M. Nazarathy, IEEE Photon. Technol. Lett. 17, 2001 (2005).
[CrossRef]

2004

J. Comellas, J. M. Gene, J. Prat, IEEE Photon. Technol. Lett. 16, 1766 (2004).
[CrossRef]

1992

S. Benedetto, P. Poggiolini, IEEE Trans. Commun. 40, 708 (1992).
[CrossRef]

1990

S. Betti, F. Curti, G. De Marchis, E. Iannone, J. Lightwave Technol. 8, 1127 (1990).
[CrossRef]

Benedetto, S.

S. Benedetto, P. Poggiolini, IEEE Trans. Commun. 40, 708 (1992).
[CrossRef]

Betti, S.

S. Betti, F. Curti, G. De Marchis, E. Iannone, J. Lightwave Technol. 8, 1127 (1990).
[CrossRef]

Bilenca, A.

Y. Yadin, A. Bilenca, M. Nazarathy, IEEE Photon. Technol. Lett. 17, 2001 (2005).
[CrossRef]

Chow, C. W.

C. W. Chow, H. K. Tsang, in 10th OptoElectronics and Communications Conference (OECC) (2005), p. 6A3.

Comellas, J.

J. Comellas, J. M. Gene, J. Prat, IEEE Photon. Technol. Lett. 16, 1766 (2004).
[CrossRef]

Curti, F.

S. Betti, F. Curti, G. De Marchis, E. Iannone, J. Lightwave Technol. 8, 1127 (1990).
[CrossRef]

De Marchis, G.

S. Betti, F. Curti, G. De Marchis, E. Iannone, J. Lightwave Technol. 8, 1127 (1990).
[CrossRef]

de Waardt, H.

T. Koonen, G. Morthier, J. Jennen, H. de Waardt, P. Demeester, in Proceedings of the European Conference on Optical Communications (ECOC’01) (2001), Vol. 4, pp. 608–609.

Demeester, P.

T. Koonen, G. Morthier, J. Jennen, H. de Waardt, P. Demeester, in Proceedings of the European Conference on Optical Communications (ECOC’01) (2001), Vol. 4, pp. 608–609.

Gene, J. M.

J. Comellas, J. M. Gene, J. Prat, IEEE Photon. Technol. Lett. 16, 1766 (2004).
[CrossRef]

Gnauk, A. H.

Iannone, E.

S. Betti, F. Curti, G. De Marchis, E. Iannone, J. Lightwave Technol. 8, 1127 (1990).
[CrossRef]

Jennen, J.

T. Koonen, G. Morthier, J. Jennen, H. de Waardt, P. Demeester, in Proceedings of the European Conference on Optical Communications (ECOC’01) (2001), Vol. 4, pp. 608–609.

Koonen, T.

T. Koonen, G. Morthier, J. Jennen, H. de Waardt, P. Demeester, in Proceedings of the European Conference on Optical Communications (ECOC’01) (2001), Vol. 4, pp. 608–609.

Morthier, G.

T. Koonen, G. Morthier, J. Jennen, H. de Waardt, P. Demeester, in Proceedings of the European Conference on Optical Communications (ECOC’01) (2001), Vol. 4, pp. 608–609.

Nazarathy, M.

M. Nazarathy, E. Simony, IEEE Photon. Technol. Lett. 17, 1133 (2005).
[CrossRef]

Y. Yadin, A. Bilenca, M. Nazarathy, IEEE Photon. Technol. Lett. 17, 2001 (2005).
[CrossRef]

M. Nazarathy, E. Simony, “Generalized Stokes parameters shift keying: a new perspective on optimal detection over electrical and optical vector incoherent channels,” IEEE Trans. Commun. (to be published).

M. Nazarathy, E. Simony, “Stokes space optimal detection of polarization and differential phase shift-keying modulation,” J. Lightwave Technol. (to be published).

Poggiolini, P.

S. Benedetto, P. Poggiolini, IEEE Trans. Commun. 40, 708 (1992).
[CrossRef]

Prat, J.

J. Comellas, J. M. Gene, J. Prat, IEEE Photon. Technol. Lett. 16, 1766 (2004).
[CrossRef]

Simony, E.

M. Nazarathy, E. Simony, IEEE Photon. Technol. Lett. 17, 1133 (2005).
[CrossRef]

M. Nazarathy, E. Simony, “Stokes space optimal detection of polarization and differential phase shift-keying modulation,” J. Lightwave Technol. (to be published).

M. Nazarathy, E. Simony, “Generalized Stokes parameters shift keying: a new perspective on optimal detection over electrical and optical vector incoherent channels,” IEEE Trans. Commun. (to be published).

Tsang, H. K.

C. W. Chow, H. K. Tsang, in 10th OptoElectronics and Communications Conference (OECC) (2005), p. 6A3.

Winzer, P. J.

Yadin, Y.

Y. Yadin, A. Bilenca, M. Nazarathy, IEEE Photon. Technol. Lett. 17, 2001 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Nazarathy, E. Simony, IEEE Photon. Technol. Lett. 17, 1133 (2005).
[CrossRef]

Y. Yadin, A. Bilenca, M. Nazarathy, IEEE Photon. Technol. Lett. 17, 2001 (2005).
[CrossRef]

J. Comellas, J. M. Gene, J. Prat, IEEE Photon. Technol. Lett. 16, 1766 (2004).
[CrossRef]

IEEE Trans. Commun.

S. Benedetto, P. Poggiolini, IEEE Trans. Commun. 40, 708 (1992).
[CrossRef]

M. Nazarathy, E. Simony, “Generalized Stokes parameters shift keying: a new perspective on optimal detection over electrical and optical vector incoherent channels,” IEEE Trans. Commun. (to be published).

J. Lightwave Technol.

M. Nazarathy, E. Simony, “Stokes space optimal detection of polarization and differential phase shift-keying modulation,” J. Lightwave Technol. (to be published).

S. Betti, F. Curti, G. De Marchis, E. Iannone, J. Lightwave Technol. 8, 1127 (1990).
[CrossRef]

A. H. Gnauk, P. J. Winzer, J. Lightwave Technol. 23, 115 (2005).
[CrossRef]

Other

T. Koonen, G. Morthier, J. Jennen, H. de Waardt, P. Demeester, in Proceedings of the European Conference on Optical Communications (ECOC’01) (2001), Vol. 4, pp. 608–609.

C. W. Chow, H. K. Tsang, in 10th OptoElectronics and Communications Conference (OECC) (2005), p. 6A3.

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Figures (2)

Fig. 1
Fig. 1

Poincaré sphere representation of the 6-ary DPSK modulation format. The constellation points are equispaced on a grand circle of the sphere.

Fig. 2
Fig. 2

(Color online) Stokes receiver (for equi-energy transmitted signals): the vector of GSPs is extracted out of the observed waveform and correlated against each of the transmitted Stokes vectors. Finally, the detected transmission index is identified as the index of the largest correlation.

Equations (14)

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

S 00 A ̰ x 2 + A ̰ y 2 , S 11 A ̰ x 2 A ̰ y 2 ,
S 01 2 Re A ̰ x A ̰ y * , S 10 2 Im A ̰ x A ̰ y * .
S l m = 2 Re J l m , l < m , S l m = 2 Im J l m , l > m .
r ̰ = A ̰ ( α ) e j θ + n ̰ , 0 α M 1 ,
α ̂ = arg max α S ( α ) S r ̰ ,
S 01 ( α ) J 01 ( α ) = A k A k 1 = A k 1 s k A k 1 = s k ,
S 12 ( α ) J 12 ( α ) = A k 1 A k 2 = S 01 ( α ) [ k 1 ] = s k 1 ,
S 02 ( α ) J 02 ( α ) = A k A k 2 = s k A k 1 A k 2 = s k s k 1 A k 2 A k 2 = s k s k 1 .
S ( α ) = [ S 01 ( α ) , S 12 ( α ) , S 02 ( α ) ] = [ s k , s k 1 , s k s k 1 ]
S ( + 1 , + 1 ) = [ 1 , 1 , 1 ] , S ( + 1 , 1 ) = [ 1 , 1 , 1 ] ,
S ( 1 , + 1 ) = [ 1 , 1 , 1 ] , S ( 1 , 1 ) = [ 1 , 1 , 1 ] .
S 01 r ̰ = 2 1 2 Re J 01 r Re r ̰ k r ̰ k 1 * q T r e [ k ] ,
S 12 r ̰ = 2 1 2 Re J 12 r Re r ̰ k 1 r ̰ k 2 * q T r e [ k 1 ] ,
S 02 r ̰ = 2 1 2 Re J 02 r Re r ̰ k r ̰ k 2 * q 2 T r e [ k ] .

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