Impact evaluation of third-order dispersion in strongly DM-WDM soliton transmission systems

Depto. De Teoría de la Señal y Comunicaciones

Impact evaluation of third-order dispersion in strongly DM-WDM soliton transmission

systems

Francisco J. Díaz-OteroUniversity of Vigo, Spain

Pedro Chamorro-PosadaUniversity of Valladolid, Spain

Francisco J. Diaz Otero

Impact evaluation of third-order dispersion in strongly DM-WDM soliton transmission systems

LENCOS 2009Sevilla (Spain) July 14-17, 2009

ContentsContents

IntroductionVariational MethodResultsDiscussion

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IntroductionVariational methodResultsDiscussion

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I n t r o

Introduction

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Solitons: Adequate for optical ultra-long distance WDM transmission systems.

However, nonlinear interactions degrade the system performance and causes intra and interchannel crosstalk.

Why DM?: Less penalties: Gordon-Haus timing jitter, four-wave

mixing (FWM) and residual frequency shifts. Better SNR. DM soliton systems are a good choice for Gb/s/channel

WDM systems. But, a potential problem may arise due to TOD for high bit

rates, even for a single channel.





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V a r i a t i ona l

Variational Method

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Dispersion Managed Soliton

L. Mollenauer, J. P. Gordon “Solitons in optical fibers Fundamental and applications” Elsevier Academic Press 2006 pp.24




V a r i a t i ona l

Variational Method

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Pulse shape essentially Gaussian

Reduce the GNLS to a system of coupled ODE equations

Using Lagrangian approximation

Yielding the main parameters of the pulse: inverse of the pulse width, linear chirp, centre frequency, centre position and phase of the pulse

Powerful Tool !!




V a r i a t i ona l

Variational Method

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GNLS for a strong management two-pulse amplified transmission system with SPM and XPM neglecting the phase-dependent terms

Gaussian ansatz for the pulses shapes

Lagrangian density S. Mookherjea and A. Yariv, Hamiltonian dynamics of breathers with third-order dispersion, Journal of the Optical Society of America B 18, 8, 1150 (2001).




V a r i a t i ona l

Variational Method

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ODE equations including loss and amplification with TOD. This model is only valid in the strong dispersion management regime (|D>10|) due to the fast oscillating movement of both pulses.





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Re su l t s

Results

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TOD effects

Prototypical Model with two pulses. Normalized map with Z+=Z−=0.5 Average value Dav=1. We consider p(0)=1 pulses. We set E2=0 and solve the above ODE equations keeping only

the results of the parameters for the l=1 pulse. Correction of the effective dispersion as:

Transverse velocity of the pulse changes to:




Re su l t s

Results

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TOD effects

Intrachannel effect: Collision takes place faster; loss of simmetry in the pulse displacement. No significant effect as we introduce TOD by means of δ in terms of energy and/or chirp.

Interchannel effect:a. > 0 E increase for the < 0 channel and decrease

for the > 0 channel. No change in chirp.b. Changes become significant as D.c. Assume 1 ≃ − ≃ −2 the symmetry in the

movement of the two solitons is lost ( V1 ≠ V2 ) d. Nevertheless for any value of V1,2=V1-V2=-2

Strength of nonlinear interaction (XPM) not affected




Re su l t s

Results

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TOD effects- Measuring parameter??

Intrachannel: The simultaneous presence of two pulses produces a shift of their center frequencies displacement of their center positions due to group velocity dispersion in the transmission medium. These two closely adjacent pulses attract each other and collide.

We can measure this effect in terms of the interaction distance: T1 – T2 = 0.5.

Interaction distance:Decrease with TOD(6%-47%)




Re su l t s

Results

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TOD effects- Measuring parameter?? Interchannel: Zigzag motion of both pulses induced by the

change of the sign of dispersion Fast local collisions Residual Frequency shift

H. Sugahara, H. Kato, T. Inoue, A. Maruta and Y. Kodama, “Optimal dispersion management for a wavelength división multiplexed optical soliton transmisión system”, Journal of Ligthwave Technology, vol. 17, 9, pp. 1547-1559 (1999).




Re su l t s

Results

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“Sinc-like” profile of the residual frequency shiftResidual frequency shift:Decrease or increase with channel position

(6%-50%)




Re su l t s

Results

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TOD effects

Interchannel effects:




Re su l t s

Results

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Loss and amplification effects - Changing the amplifier location: Pulse Energy

• Midpoint of the anomalous dispersion map, Za=0.125, highest value of initial pulse energy with regard to the lossless system.

•At this point the situation turns over The energy gets smaller between Za=[0.4-0.6]. •From this point the situation evolves in a symmetrical way.•The energy gets a new minimum at Za= 0.875.•From this point on, the situation reverses until Za=1.




Re su l t s

Results

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Loss and amplification effects - Changing the amplifier location: Chirp

• Midpoint of the anomalous dispersion map, Za=0.125, lowest value of chirp with regard to the lossless system.

•At this point the situation turns over The chirp gets higher until we reach Za=0.6. • From this point on, the situation reverses in a symmetrical way until Za=1.




Re su l t s

Results

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Loss and amplification effects - Changing the amplifier location: Trajectories in the phase-plane

Both these effects change the Poincaré Map in a highly non symmetrical way.




Re su l t s

Results

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Loss and amplification effects in WDM: Fixed amplifier location Za=1

Francisco J. Diaz-Otero, Pedro Chamorro-Posada, “Interchannel soliton collisions in periodic dispersion maps in the presence of third-order dispersion with loss and amplification'‘”International Conference on Advanced Optoelectronics and Lasers (CAOL) Proceedings 2008.

The location of the chirp-free points is no longer at the midpoint of the anomalous dispersion fiber segment.

The evolution of the pulse parameters is not symmetrical about the line C=0.

Although the pulse has a non-zero chirp at the midpoint of the anomalous segment, it becomes zero at some particular point inside the map.

“Zero” frequency shifts move to ΔD=8n+6.




Re su l t s

Results

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Pulse Energy:Pulse energy for which the solution is periodic

Two-step dispersion managed profile Z+=Z-=0.1 ; Average dispersion Dav=1 Uniform nonlinearity ; Initital pulse width p=1T1=-22.2,T2=22.2, w1=-17.75, w2=17.75ΔB=35.5 (Δλ=8nm) Initial pulse separation and freq. shift in acordance with H. Sugahara, H. Kato, T. Inoue, A. Maruta and Y. Kodama, “Optimal dispersion management for a wavelength división multiplexed optical soliton transmisión system”, Journal of Ligthwave Technology, vol. 17, 9, pp. 1547-1559 (1999).




Re su l t s

Results

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Trajectories in the phase-plane:Phase-plane dynamics for lossless (left) and lossy (right) DM

transmission in the l = -17.75 channel for different values of TOD parameter




Re su l t s

Results

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Residual frequency shift: Residual frequency shift vs. dispersion difference in a periodic DM map with parameters as described in the text both for lossless (left) and lossy (right) cases




Re su l t s

Results

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Loss and amplification effects in single channel: Interaction distance

Increase in the interaction distance as we place an amplifier at specific positions of the dispersion map period for some values of the dispersion difference, as we can see in the inset, for amplifiers located at Za>0.07 and D>20 with Z+=Z−=0.5.




Re su l t s

Results

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Loss and amplification effects in single channel: Interaction distance

We also find that TOD can substantially reduce the interaction distance regardless the amplifier location (Za =0.1).




Re su l t s

Results

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Loss and amplification effects - Changing the amplifier location: Residual frequency shift

• The classic oscillatory profile disappears and new local minima appear showing a behavior with no characteristic remarks.

• Za = 0.25, absolute minimum of residual frequency shift.• Za = 0.50, oscillatory profile but with local minimum instead

of maximum at D = 8n + 6.




Re su l t s

Results

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Loss and amplification effects - Changing the amplifier location: Delta effects

• The main effect of TOD is to decrease (increase) the residual frequency shift for the l=1 (l=2) channel, while maintaining both the characteristic oscillatory profile along the dispersion difference axis and the positions of the local minima, as in the lossless system. (Za=0.05)




Re su l t s

Results

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Loss and amplification effects - Changing the amplifier location: PDE-ODE Comparison

Excellent agreement is found between the results obtained from the integration of the ODE system and the numerical integration

of the PDE using the split-step Fourier method




Re su l t s

Results

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References

[1] L.F. Mollenauer and J.P. Gordon, Solitons in optical fibers: fundamentals and applications. Elsevier/Academic Press (2006).

[2] T. Inoue, H. Sugahara, A. Maruta and Y. Kodama: Interactions BetweenDispersion Managed Solitons in Optical-Time-Division-Multiplexed Systems.IEEE Photon. Technol. Lett. 12 (2000) 299.[3] D. Anderson: Variational approach to nonlinear pulse propagation in

optical fibers. Phys. Rev. A 27 (1983) 3135.[4] F. J. Diaz-Otero and P. Chamorro-Posada: Interchannel soliton collisions

in periodic dispersion maps in the presence of third order dispersion. XVII International Conference on Nonlinear Evolution Equations and Dynamical Systems (NEEDS 2007). J. Nonlinear Math. Phys., 15 Supp.3 (2008) 137–143.

[5] F. J. Diaz-Otero, P. Chamorro-Posada and J.C. Garcia-Escartin: Dispersion-managed soliton interactions in the presence of third-order dispersion. II International Conference on Advanced Optoelectronics and Lasers (CAOL 2005). CAOL Proceedings, (2005) 153–155.

Localized Excitations in Nonlinear Complex Systems (LENCOS)Sevilla (Spain) July 14-17, 2009

Depto. De Teoría de la Señal y Comunicaciones

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Impact evaluation of third-order dispersion in strongly DM-WDM soliton transmission systems

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