1. Page 1 T.I. Lakoba, October 2003 Using phase modulation to suppress ghost pulses in high-speed optical transmission Taras I. Lakoba Department of Mathematics and Statistics University of Vermont * Acknowledgement: Anatoly Marhelyuk (Agere Systems) * This work was completed when the author was with Lucent Technologies, Holmdel, NJ

2. Page 2 T.I. Lakoba, October 2003 Introduction Ghost pulses (GP) and intra-channel timing jitter are the major nonlinearity-induced impairments in quasi-linear transmission. GP are small, parasitic pulses which are created via the interplay of nonlinearity and pulse overlap at the locations of logical ZEROs:  ONEs in bits k, l, m create a GP in bit k + l - m via Intra-Channel Four Wave Mixing:  Ψ GP = Ψ k + Ψ l - Ψ m [ Essiambre et al, 1999; Mamyshev & Mamysheva, 1999 ]. Apart from the phase matching condition, GP are known to critically depend on parameter [ precompensation + ½ (accumulated dispersion) ]

3. Page 3 T.I. Lakoba, October 2003 Key idea Generation of GP is a highly coherent effect : In a bit sequence 11…11011…11 ( N ONES on each side of ZERO), there are N 2 triplets of ONES creating a GP at ZERO. If all Ψ k are the same  all individual Ψ GP are the same  they add in-phase and create a GP with power ~ (N 2 ) 2 = N 4. Destroy, at Tx, the phase coherence of ONES contributing to largest GP  phases of GPs created by different triplets of ONES will differ  the GP (= sum of individual GPs) will be much reduced. To destroy phase coherence, apply sinusoidal phase modulation (PM) to input signal. Amplitude and period of PM must be chosen in a special way:  to make the GP suppression efficient and  to minimize collateral distortions to the data (i.e., to ONEs). This was realized and done in [ Forzati, Martensson, Berntson, Djupsjobacka, Johannisson, 2002 ]. Their scheme required synchronization between PM’s and data’s timings. In this work: Find PM’s parameters such that the above synchronization is NOT required  cheaper and more reliable Tx.

4. Page 4 T.I. Lakoba, October 2003 Implementation of key idea (1) Transmitter: Sinusoidal PM can be created by the same pulse carver which produces the pulses:  the phase of the pulses is determined by the sum of the voltages driving the two arms of the MZI,  the power profile of pulses is determined by the voltages’ difference.  Independent control of the phase and the power profile of the pulses. Alternative: Use a single phase modulator located after the optical multiplexer (since the timing of the PM is not synchronized with that of the data signal)

5. Page 5 T.I. Lakoba, October 2003 Implementation of key idea (2) Algorithm for finding parameters of PM = A PM sin(2  t/T PM +  PM ): Given arbitrary bit sequence 11…11011..11 with M and N ONES on sides of GP, simple MATLAB code calculates the interference field at bit # 0 (location of GP): By inspection, find such values of the A PM and T PM that the interference field is minimized for all values of  PM : 0<  PM < 2 . Different contours correspond to different  PM 

6. Page 6 T.I. Lakoba, October 2003 Ghost pulses in SSMF SSMF is chosen because GP suppression in it is most pronounced. In TWRS or LEAF effect is less due to smaller local dispersion. D SSMF ~ -20 ps 2 /km at 1550 nm  13-ps pulse (50% duty ratio, 40 Gb/s) broadens by ~20 in 50km of SSMF  it spreads over ~10 bits  worst GP is produced in bit sequence (10 x ONEs, ZERO, 10 x ONEs). Any shorter sequence of ONEs will produce a smaller GP, any longer sequence will produce almost the same GP (no extra overlap). In (2 7 -1)-PRBS the “worst” bit sequence is (6 x ONEs, ZERO, 5 x ONEs). For it, the algorithm yields: 1.2 < A PM < 1.4, T bit /0.35 < T PM < T bit /0.20 to achieve optimum GP suppression. Direct numerical simulations are required to confirm these quick estimates.

7. Page 7 T.I. Lakoba, October 2003 To proceed, we need: Simulation parameters: –20x80 km of SSMF; –Precompensation is -500 ps/nm, which is the optimum value for given distance and path-average dispersion. –Postcompensation is such that total accumulated dispersion is near zero; –All-Raman amplification (~25% forward pumping, ~75% backward pumping); –Receiver has: optical BW ~ 80 GHz, electrical BW ~ 25 GHz. Performance metric: –the required OSNR in 0.1 nm for a given value of BER (e.g., 10 -9 ); –this metric uniquely characterizes nonlinear degradation of signal (i.e., it is independent of the amount of accumulated ASE); –the higher the required OSNR, the worse the system performance; –transmission penalty = (Req. OSNR at output) – (Req. OSNR b2b).

8. Page 8 T.I. Lakoba, October 2003 Baseline case: no PM Optical eye  (optimal postcompensation) Req. OSNR at BER=10 -9 after transmission Back-to-back req. OSNR in 0.1 nm at BER= 10 - 9 : ~ 22.5 dB. Transmission penalty : 30 dB - 22.5 dB = 7.5 dB Back-to-back req. OSNR in 0.1 nm at BER= 10 - 9 : ~ 22.5 dB. Transmission penalty : 30 dB - 22.5 dB = 7.5 dB

9. Page 9 T.I. Lakoba, October 2003 Effect of PM : A PM =1.0  Min. max. penalty = 3.5 dB T PM =T bit / 0.35T PM =T bit / 0.30 T PM =T bit / 0.25 T PM =T bit / 0.50T PM =T bit / 0.45T PM =T bit / 0.40 Different colors correspond to different ϕ PM with step 0.2 π

10. Page 10 T.I. Lakoba, October 2003 Effect of PM : A PM =1.2  Min. max. penalty = 2.5 dB T PM =T bit / 0.35T PM =T bit / 0.30T PM =T bit / 0.25 T PM =T bit / 0.50T PM =T bit / 0.45T PM =T bit / 0.40

11. Page 11 T.I. Lakoba, October 2003 T PM =T bit / 0.35T PM =T bit / 0.30T PM =T bit / 0.25 T PM =T bit / 0.50T PM =T bit / 0.45T PM =T bit / 0.40 Effect of PM : A PM =1.4  Min. max. penalty = 2.5 dB

12. Page 12 T.I. Lakoba, October 2003 T PM =T bit / 0.35T PM =T bit / 0.30T PM =T bit / 0.25 T PM =T bit / 0.50T PM =T bit / 0.45T PM =T bit / 0.40 Effect of PM : A PM =1.6  Min. max. penalty = 3.0 dB

13. Page 13 T.I. Lakoba, October 2003 Examples of optical eyes: PM with optimum T PM =T bit /0.35, A PM =1.4, but “worst” phase  PM. before transmissionafter transmission

14. Page 14 T.I. Lakoba, October 2003 Conclusions PM can reduce transmission penalty from 7.5 to 2.5 dB (at 10 -9 BER). Period and amplitude of PM should be rather tightly controlled: T bit / 0.40 < T PM < T bit / 0.30, 1.2 < A PM < 1.6. The best performance is found near the centers of these ranges. However, phase (timing) of PM relative to that of data does NOT need to be controlled  cheaper and more reliable Tx. Very high penalties due to GP, observed in simulations, may exaggerate actual penalties in transmission experiments. Possible reason is related to the discussed mechanism of GP suppression: real transmitters always have “parasitic phase modulation” (chirp). (Another reason can be the timing jitter of the input data.)