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Phase-Conjugated Twin Waves for Communication beyond

the Kerr Nonlinearity Limit

Xiang Liu*, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. ChandrasekharBell Labs, Alcatel-Lucent, 791 Holmdel-Keyport Road, Holmdel, New Jersey 07733, USA

*email: xiang.liu@alcatel-lucent.com

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Additional experimental resultsWe have reported the experimental results obtained when the phase-conjugated twin waves are synchronously

transmitted, i.e., there is no time delay between them during transmission. It can be seen from Eq. (2) of the main

text that the cross-polarization nonlinear interaction (the 2nd

term on the R.H.S. of the equation) can only be

cancelled out, upon the coherent superposition of the PCTW, when the twin waves are synchronously transmitted. Itis of interest to experimentally verify this. We thus repeat the experiment shown in Fig. 3 of the main text and

introduce a large time delay between the twin waves during the transmission (

txy). The time delay is chosen to be50 times the modulation symbol duration (s) or 10 nanoseconds, sufficient to de-correlate the twin waves in termsof their cross-polarization nonlinear interactions. Figure 1 shows the measured signal quality (defined as 1/2),

before and after coherent superposition of the PCTW, as a function of signal launch power into each fiber span (Pin).

In the nearly linear transmission regime (P in-4 dBm), the performance of the asynchronous PCTW is only slightly worse (by ~ 1dB) than that of the

synchronous PCTW before the coherent superposition. This could be explained as the avoidance of the worst-case

signal patterns, i.e., those of consecutive identical modulated symbols on both polarizations, in the case of

synchronous PCTW. After the coherent superposition, the performance of the asynchronous PCTW is noticeably

worse (by 2~3 dB) than that of the synchronous PCTW, supporting the earlier expectation that the synchronous

PCTW provides more complete cancellation of the nonlinear interactions that the asynchronous PCTW.

Note also that the asynchronous PCTW transmission with sufficient time between the two polarization

components is physically identical to conventional polarization-division multiplexed quadrature phase-shift-keying(PDM-QPSK) transmission. It can be seen that the improvement of the optimum signal Q factor obtained by the

coherent superposition of the synchronous PCTW is ~5.7 dB, which is referred to in the main text when estimating

the overall benefit of the PCTW-based transmission.

It is of value to discuss the noise distributions before and after a given noise reduction technique. For dispersion-unmanaged transmission, the nonlinear distortion distribution was found to be Gaussian-like

1,2. Most of the residual

nonlinear distortions after PCTW-based nonlinear cancellation may come from imperfect matching of the

transmission characteristics of the twin waves, due to effects such as polarization-mode dispersion and polarization-

dependent loss. It is expected that the residual noise distribution would also be Gaussian-like. To confirm this, wefurther process the experimental data, and plot the probability density function (pdf) of the phase deviations caused

by the signal distortions (Figure 2). The pdf is normalized to its peak value. We plot the pdf as a function of phase

deviation rather than amplitude deviation because phase deviation is more responsible for the bit error-ratio (BER)

performance of the QPSK signal in our experiments. As shown in Fig. 2, the pdf before the coherent superposition

of the twin waves is Gaussian-like down to ~510-3

, but there are floor-like non-Gaussian deviations at lowerprobabilities. Remarkably, the pdf after the coherent superposition of the twin waves is much more Gaussian-like

down to ~10-3

, and the maximum deviation from the Gaussian distribution is reduced by about 4-fold. In modern

communication systems, forward-error correction (FEC) is applied, and pdf distributions at low probabilities (e.g.,

lower than 10-3

) are of less importance, so the quality factor used here (1/2) could serve as a useful measure toquantify the performance improvement of PCTW. For the experiment shown in Fig. 6 of the main text, BER is used

to quantify the signal quality after transmission. Furthermore, high-coding-gain soft-decision FEC is applied and it

has been confirmed that the raw bit errors are correctable as expected (Fig. 6c of the main text).

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHOTON.2013.109

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-8 -7 -6 -5 -4 -3 -2 -1 06

8

10

12

14

16

18

20

Pin

(dBm)

1/2

(dB)

Before superposition of PCTW, txy

/s=0

After superposition of PCTW, txy

/s=0

Before superposition of PCTW, txy

/s=50

After superposition of PCTW, txy

/s=50

Figure 1 | Experimentally measured signal quality factor (1/2) as a function of signal launch power into each fiber

span (Pin) without and with time delay (txy) between the PCTW during transmission. s: Modulation symbol

duration.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 210

-4

10-3

10-2

10-1

100

Phase deviation (rad.)

Normalizedprob

abilitydensityfunction

Before superposition,experiment

Before superposition,Gaussian fit

After superposition,experiment

After superposition,Gaussian fit

Figure 2 | Experimentally measured probability density functions of the angular signal distortions after 3200-kmfiber transmission before and after the coherent superposition of the twin waves. The transmission link is the same

as that described in the main text (Fig. 1a) and the signal launch power is -2 dBm.

1. Splett, A., Kurzke, C. & Petermann K. Ultimate transmission capacity of amplified optical fiber communication systems taking into accountfiber nonlinearities, in Proceedings of the 1993 European Conference on Optical Communications, MoC2.4.

2. Carena, A., Bosco, G., Curri, G. V., Poggiolini, P., Tapia Taiba, M. & Forghieri, F. Statistical characterization of PM-QPSK signals afterpropagation in uncompensated fiber links, in Proceedings of the 2010 European Conference on Optical Communication , P4.07.

2 NATURE PHOTONICS | www.nature.com/naturephotonics

SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHOTON.2013.109