Abstract

We present detailed analytical and numerical results of the dispersion and nonlinear tolerances of RZ and Nyquist optical pulses in ultrahigh-speed TDM transmissions. From a Q-map analysis, i.e. by numerically calculating the Q-factor distribution as a function of transmission power and fiber dispersion, we found that Nyquist TDM transmission has a substantially larger Q margin as regards both dispersion and optical power thanks to ISI-free overlapped TDM. We also show that the optimum transmission power for Nyquist pulses is 2 dB lower than for RZ pulses. An analytical model is provided to explain the overlap-induced nonlinear impairments in Nyquist TDM transmission in a high power regime, which agrees well with numerical results.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  5. K. Harako, D. Seya, T. Hirooka, and M. Nakazawa, “640 Gbaud (1.28 Tbit/s/ch) optical Nyquist pulse transmission over 525 km with substantial PMD tolerance,” Opt. Express 21(18), 21062–21075 (2013).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2013 (2)

2012 (4)

2010 (1)

2009 (1)

2006 (1)

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

2000 (2)

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12(4), 392–394 (2000).
[Crossref]

1996 (1)

A. Sahara, H. Kubota, and M. Nakazawa, “Q-factor contour mapping for evaluation of optical transmission systems: soliton against NRZ against RZ pulse at zero group velocity dispersion,” Electron. Lett. 32(10), 915–916 (1996).
[Crossref]

Boerner, C.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Bononi, A.

Clausen, A. T.

Clausen, C. B.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12(4), 392–394 (2000).
[Crossref]

Ferber, S.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Futami, F.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Galili, M.

Grellier, E.

Guan, P.

Harako, K.

Hirooka, T.

Hu, H.

Inoue, T.

Jensen, J. B.

Jeppesen, P.

Kroh, M.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Kubota, H.

A. Sahara, H. Kubota, and M. Nakazawa, “Q-factor contour mapping for evaluation of optical transmission systems: soliton against NRZ against RZ pulse at zero group velocity dispersion,” Electron. Lett. 32(10), 915–916 (1996).
[Crossref]

Kumar, S.

Kurosu, T.

Ludwig, R.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Marembert, V.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Mecozzi, A.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12(4), 392–394 (2000).
[Crossref]

Mulvad, H. C. H.

Nakazawa, M.

K. Harako, D. Seya, T. Hirooka, and M. Nakazawa, “640 Gbaud (1.28 Tbit/s/ch) optical Nyquist pulse transmission over 525 km with substantial PMD tolerance,” Opt. Express 21(18), 21062–21075 (2013).
[Crossref] [PubMed]

T. Hirooka and M. Nakazawa, “Linear and nonlinear propagation of optical Nyquist pulses in fibers,” Opt. Express 20(18), 19836–19849 (2012).
[Crossref] [PubMed]

M. Nakazawa, T. Hirooka, P. Ruan, and P. Guan, “Ultrahigh-speed “orthogonal” TDM transmission with an optical Nyquist pulse train,” Opt. Express 20(2), 1129–1140 (2012).
[Crossref] [PubMed]

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

A. Sahara, H. Kubota, and M. Nakazawa, “Q-factor contour mapping for evaluation of optical transmission systems: soliton against NRZ against RZ pulse at zero group velocity dispersion,” Electron. Lett. 32(10), 915–916 (1996).
[Crossref]

Namiki, S.

Oxenløwe, L. K.

Peucheret, C.

Rossi, N.

Ruan, P.

Sahara, A.

A. Sahara, H. Kubota, and M. Nakazawa, “Q-factor contour mapping for evaluation of optical transmission systems: soliton against NRZ against RZ pulse at zero group velocity dispersion,” Electron. Lett. 32(10), 915–916 (1996).
[Crossref]

Schmidt-Langhorst, C.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Schubert, C.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Serena, P.

Seya, D.

Shahi, S. N.

Shtaif, M.

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12(4), 392–394 (2000).
[Crossref]

Tamura, K. R.

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

Tan, H. N.

Vacondio, F.

Watanabe, S.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Weber, H. G.

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

Yamamoto, T.

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

Yang, D.

Electron. Lett. (3)

M. Nakazawa, T. Yamamoto, and K. R. Tamura, “1.28 Tbit/s-70 km OTDM transmission using third- and fourth-order simultaneous dispersion compensation with a phase modulator,” Electron. Lett. 36(24), 2027–2029 (2000).
[Crossref]

H. G. Weber, S. Ferber, M. Kroh, C. Schmidt-Langhorst, R. Ludwig, V. Marembert, C. Boerner, F. Futami, S. Watanabe, and C. Schubert, “Single channel 1.28 Tbit/s and 2.56 Tbit/s DQPSK transmission,” Electron. Lett. 42(3), 178–179 (2006).
[Crossref]

A. Sahara, H. Kubota, and M. Nakazawa, “Q-factor contour mapping for evaluation of optical transmission systems: soliton against NRZ against RZ pulse at zero group velocity dispersion,” Electron. Lett. 32(10), 915–916 (1996).
[Crossref]

IEEE Photonics Technol. Lett. (1)

A. Mecozzi, C. B. Clausen, and M. Shtaif, “Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission,” IEEE Photonics Technol. Lett. 12(4), 392–394 (2000).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (7)

Other (3)

G. Baxter, S. Frisken, D. Abakoumov, H. Zhou, I. Clarke, A. Bartos, and S. Poole, “Highly programmable wavelength selective switch based on liquid crystal on silicon switching elements,” in Optical Fiber Communication Conference (OSA, 2006), paper OTuF2.
[Crossref]

H. Hu, D. Kong, E. Palushani, J. D. Andersen, A. Rasmussen, B. M. Sorensen, M. Galili, H. C. Hansen Mulvad, K. J. Larsen, S. Forchhammer, P. Jeppesen, and L. K. Oxenløwe, “1.28 Tbaud Nyquist signal transmission using time-domain optical Fourier transformation based receiver,” in CLEO: 2013 Postdeadline, OSA Postdeadline Paper Digest (online) (Optical Society of America, 2013), paper CTh5D.5.

D. O. Otuya, K. Harako, K. Kasai, T. Hirooka, and M. Nakazawa, “Single-channel 1.92 Tbit/s, 64 QAM coherent orthogonal TDM transmission of 160 Gbaud optical Nyquist pulses with 10.6 bit/s/Hz spectral efficiency,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2015), paper M3G.2.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Waveform (a) and spectrum (b) of Nyquist (α = 0 and 0.5) and Gaussian (0.8 and 0.6 ps) pulses for 640 Gbaud transmission.
Fig. 2
Fig. 2 Schematic configuration of a dispersion-managed fiber span.
Fig. 3
Fig. 3 Q maps for 640 Gbaud-525 km transmissions using a Nyquist pulse with α = 0 (a) and 0.5 (b).
Fig. 4
Fig. 4 Q maps for 640 Gbaud-525 km transmissions using a Gaussian pulse with Δτ = 0.8 ps (a) and 0.6 ps (b).
Fig. 5
Fig. 5 Q factor in Figs. 3 and 4 plotted as a function of transmission power when δD = 0.
Fig. 6
Fig. 6 Example of IXPM and IFWM contributions from Nyquist pulse overlap.
Fig. 7
Fig. 7 Relationship between Q factor and transmission power for Nyquist pulses in a 640 Gbaud-525 km transmission when δD = 0 ps/nm/km. The red curves show the analytical results obtained from Eqs. (3)-(11).
Fig. 8
Fig. 8 Individual contributions of IXPM and IFWM to the nonlinear impairments of Nyquist and Gaussian pulses.

Equations (11)

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i u z β 2 2 2 u t 2 +γ a 2 (z)|u | 2 u=0,
s ^ (f)={ T,0|f| 1α 2T T 2 { 1sin[ π 2α (2T|f|1) ] }, 1α 2T |f| 1+α 2T 0,|f| 1+α 2T ,
Δ u ^ (z,f)=i P p 3/2 l=N/2 N/2 m=N/2 N/2 n=N/2 N/2 a l a m a n * 0 z a 2 ( z ) X l,m,n ( z ,f) exp[ i β 2 z 2 (2πf) 2 ]d z
X l,m,n (z,f)= 1 2π| β 2 z| s ^ ( f lT 2π β 2 z ) s ^ ( f mT 2π β 2 z ) s ^ ( f+ nT 2π β 2 z )exp[ i β 2 z 2 (2πf) 2 +i lm T 2 β 2 z ]
ρ NL (f)= lim N 1 (N+1)T |γΔ u ^ (z,f) | 2 = γ 2 P p 3 lim N 1 (N+1)T l,m,n=N/2 N/2 l , m , n =N/2 N/2 a l a m a n * a l * a m * a n Y l,m,n (f) Y l , m , n * (f)
Y l,m,n (f)= 0 z a 2 ( z ) X l,m,n ( z ,f) exp[ i β 2 z 2 (2πf) 2 ]d z
σ 2 = σ ASE 2 + σ NL 2 = [ ρ ASE + ρ NL (f) ]H(f)df
σ NL 2 =( η SPM + η XPM + η FWM ) P av 3
η= η SPM + η XPM + η FWM = lim N γ 2 ( P p / P av ) 3 (N+1)T l,m,n=N/2 N/2 l , m , n =N/2 N/2 a l a m a n * a l * a m * a n Y l,m,n (f) Y l , m , n * (f)H(f)df
ρ NL (f)= γ 2 P p 3 T l,m=N/2 N/2 l , m =N/2 N/2 a l a m a l+m * a l * a m * a l + m Y l,m,l+m (f) Y l , m , l + m * (f)
η= γ 2 ( P p / P av ) 3 T l,m=N/2 N/2 l , m =N/2 N/2 a l a m a l+m * a l * a m * a l + m Y l,m,l+m (f) Y l , m , l + m * (f)H(f)df

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