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In this section it is proposed and experimentally verified that a pump-probe measurement o f XPM can be used to predict the XPM-induced Q-factor reduction through comparison with direct BER measurements. The experimental set-up shown in Fig. 5.12 was used for single and 2-channel transmission over up to 12 post-compensated spans o f SSMF. Q-factor measurements were performed at lOGbit/s using 2*^-1 PRBS sequences and pump-probe experiments were carried out to measure ctxpm as a function o f transmission distance [THIOOb]. The experimental verification was performed in three steps:

A M easuring XPM distortion

• The CW probe channel was tuned to AA = 0.4nm from the modulated pump channel. Fig. 5.21(a) shows a typical averaged trace o f the XPM -distorted CW probe after 6 spans. • The XPM index Cxpm, normalised to the average probe power, was calculated as shown in

Fig. 5.21(b). To increase the accuracy, 256bits o f the PRBS sequence were used to calculate (Txpm- As a result, the statistical error o f the estimated Cxpm caused by considering a short sequence length was avoided.

(^xpM reached 0.09 after 5 spans, in good agreement with the results o f split-step simulations using an adaptive step-size to reduce the calculation time for multi-span links. In the simulation o f the pump-probe measurements the EDFAs were assumed to be simple gain elements since the effect o f ASE noise was eliminated in the time-averaged traces o f the experiment. After a single span the distortion was lower than in the previous single span measurements in Fig. 5.7 due to the reduced launch power o f lOdBm/channel. For comparison, the analytical expression APX^»)) ^ F^((o)7^;,((o) described in section 2.3.8 was used to estimate ctxpm for the probe channels s [KILOOb]. The calculated and experimentally obtained values agreed closely for 1 span (8% accuracy). However, for longer distances the build-up o f distortion was overestimated (81% error for 7 spans) due to the assumption o f an undistorted pump waveform, which is inaccurate due to SPM -induced pulse broadening. For an undistorted pump and exactly compensated spans a linear increase is expected indicated by the dotted line in Fig. 5.21(b). The calculation was repeated, using the distorted pump channel waveforms at the input o f each span obtained in single channel simulations and more accurate results were obtained.

Chapter 5: Q-factor measurements 150 rô 3 E o Fig. 5.21 1.4 1.2 1.0 0.8 0.6 1 ns/dlv 0.2 0 .1 6 S 0.12 Q. 0 .0 8 0 .0 4 0 1 2 3 4 5 6 7 Number of sp an s

(a) Measured trace o f XPM -distorted CW probe channel after 6 spans.

(b) Standard deviation o f m easured distortion ( • ) , split-step Fourier simulation (solid line), analytical results assuming un distorted pum p (dotted line) and SPM distorted pump (dashed line).

B Using axpM to predict Q-factor reduction due to XPM

The experimentally measured values o f Gxpm in Fig. 5.21(b) were used to predict the Q-factor reduction due to XPM caused by an interfering channel at ts.X= 0.4nm, with both channels m odulated at lOGbit/s.

• At first, wide channel spacing was used, so that the XPM distortion was negligible due to the large walk-off d^p = D AX. In this case, the standard deviation o f the ‘1’-level was dominated by ASE noise and SPM. The values o f were found from measurements o f the BER as a function o f the decision voltage.

• Using equation (5.5), the values for Gxpm and were used to calculate O] with AX= 0.4nm channel spacing. The resulting BER values used for this analysis are plotted as solid lines in Fig. 5.22(a)-(b) after 3 and 5 recirculations.

To confirm the results o f the calculations, the BER measurements were repeated, now with 0.4nm channel spacing. Good agreement between predicted and actual BER values can be seen in Fig. 5.22. The signal was degraded by XPM at AA=0.4nm, and this is reflected in the significant variation o f the ‘1’-level with AX. On the contrary, the ‘0 ’-level rem ained almost unchanged for both AX since ob was least affected by nonlinearities. This indicates that, for NRZ signal formats, XPM penalties can be accurately estimated from the distortion o f the ‘ 1’- level alone. The error-free interval, the range o f decision voltage with BER< 10'^, narrows down to zero for A2.=1.6nm when the link length increased to 5 spans in Fig. 5.22(b), and for A/l=0.4nm the minimum BER increased to 10'^ due to XPM-induced distortion.

Chapter 5: Q-factor measurements 151 cr LU CD o

'O' level

'T level

'T level

'O' level

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Decision voltage (V)

_{Decision voltage (V)}

Fig. 5.22 BER curves for 2 channels, lOGbit/s recirculating loop experiment, SSM F+DCF spans, lOdBm/channel, receiver power: -33dBm (O ): AX,= 1.6nm, (■ ): A2=0.4nm, (— ): calculated using experimental results for Oxpm, (a) after 3 recirculations, (b) after 5 recirculations

C Comparison with direct measurement of Q

Fig. 5.23 shows the Q-factors predicted from the measurements o f oâpm, together with the values obtained from the measured BER curves. The data points represent the direct Q-factor measurements for wide and narrow channel spacing. A continuous decrease o f Q with transmission distance was observed due to ASE noise, SPM and XPM distortion. After transmission over 5 spans the Q-faetor was reduced by 1.5dB when the channels were tuned from wide spacing to 0.4nm. Excellent agreement between calculated and measured values for AA=0.4nm, with only +0.2dB overestimation o f the Q-factor reduction for 5 spans, demonstrates the validity o f using pump-probe characterisation to estimate XPM-indueed penalties. ■D o

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Q-factor as a function o f distance for m ultiple spans o f SSM F+DCF, lOGbit/s PRBS 2 '^ -l, (O ): AA=1.6nm, (■ ): A/l=0.4nm, (— ): Q calculated using measured (Jxpm, Q (dB)=20-/og(Q)

Chapter 5: Q-factor measurements 152

Finally, the error-free transmission distance was extended by placing an additional EDFA before the DCF. This configuration, shown in Fig. 5.24(a), increased the optical SNR, reducing the build-up o f ASE noise with distance due to the loop loss o f 28dB. As a result, the error-free transmission distance could be increased to 12 recirculations.

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(a) modified post-compensated span inserting additional loop ED FA before DCF,

(b) Q-factor vs. for n=6 and n = \2 recirculations, (•): direct m easurem ent o f Q-factor, (— ): obtained from analytically calculated values o f ctxpm

As shown in Fig. 5.24(b) the XPM -induced penalty AQ increased from 1.5dB at n=6 to approximately 2.2dB at n=l2. Due to the lower launch power into the SSMF in this modified span the transmission remained error-free for all AT at n=6. However, the Q-factor was reduced to Q<15.5dB for AT<0.6 after 12 recirculations, corresponding to BER>10"^. The direct measurements o f the Q-factor for 2-channel transmission agree well with the combined results obtained from a single channel measurement and the analytically calculated contribution <Jxpm-

In summary, a pump-probe characterisation o f a W DM link was used for the first time to make accurate predictions o f the impact o f XPM on BER. This is one o f the main contributions o f this thesis linking transmission experiments and the more fundamental pump- probe experiments. Results o f analytical calculations o f XPM-induced distortion were found

Chapter 5: Q-factor measurements 153

to be in good agreement with experimental results, although the effects o f SPM and dispersion on the pump channel waveform must be taken into account to ensure accuracy for longer distances.

5.4 Summary

In this chapter, the impact o f XPM on multi-channel WDM transmission was systematically investigated. The Q-factor was determined as a function o f these key transmission parameters: channel spacing, num ber o f channels, power per channel and distance. Initially, the Q-factor was m easured for a single fibre span and found to be inversely proportional to A/l. The variation o f Q with AÀ, resulting from XPM occurring in the transmission link, increased with launch power and number o f channels. In contrast, the span length and linear dispersion compensation were found to change Q independent o f the particular wavelength spacing. Using the recirculating loop, the Q-factor was studied as a function o f distance in post­ compensated links. The error-free distance was limited by ASE due to the 28dB loop loss but could be increased adding a second loop amplifier. The impact o f channel num ber on XPM was investigated for WDM transmission. In this thesis the analysis was divided into two separate cases: firstly, keeping the power per channel constant the Q-factor decreased with the num ber o f channels since more XPM distortion was introduced. The variances o f separate channels could be used to obtain the total distortion. Secondly, assuming a constant launch pow er into the link the optical SNR o f each channel depends on the total channel number. For large channel num bers transmission is limited by ASE noise. In the case o f fewer channels, the m easured effects o f XPM and SPM were found to degrade Q significantly.

For the first time, Q-factor measurements were quantitatively related to pump-probe experiments. X PM distortion was shown to accurately estimate the Q-factor for multi-channel transmission. This technique was successfully demonstrated in two cases:

The penalty due to XPM was investigated as a function o f distance. Measurements and analytical calculation o f XPM distortion for the same link allowed to estimate the Q- factor for 2-channel transmission. A comparison with directly m easured Q-factors showed that this technique was accurate within 0.2dB after 5 recirculations.

For a constant num ber o f spans, the Q-factor was initially measured for a single channel. The Q-factor for 2-channel transmission for a range o f AÀ was calculated by combining the single channel Q-factors and o^pa/obtained in pump-probe experiments, and shown to give good agreement with the direct Q-factor measurements.

Chapter 6: OTDM experiments 154

Chapter 6