m winter d kroushkov and k petermann ieee summer topicals july 2010 n.
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Cross-Polarization Modulation in Polarization-Multiplexed Systems

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M. Winter, D. Kroushkov, and K. Petermann IEEE Summer Topicals July 2010. Cross-Polarization Modulation in Polarization-Multiplexed Systems. typical DWDM system with a nonlinearity probe. ► CW probe is unaffected by linear effects / SPM ► other channels are 10 Gbps OOK in 50 GHz grid.

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typical DWDM system with a nonlinearity probe

► CW probe is unaffected by linear effects / SPM

► otherchannelsare 10 Gbps OOK in 50 GHz grid


► basics

cross-polarization modulation (XPolM)

► statistical models

► XPolM and polarization multiplex

► experiments


nonlinear polarization effects known since at least 1969 ► e.g. Kerr shutter (Duguay and Hansen, APL, pp. 192+, 1969)

XPolM first described in its „current version“ in 1995 ► Stokes space Manakov equation ► collision of two solitons ► Mollenauer et al., Optics Letters, pp. 2060+, 1995

many-channel formulation in 2006 ► Menyuk and Marks, JLT, pp. 2806+, 2006


Poincaré sphere

probe channel

DWDM interferers

Stokes vector sum

nonlinear rotation


► length (intensity) varies due to walk-off►(interferer and probe group velocity differs)

► direction (SOP) varies due to PMD► (interferer and probe birefringence differs)

► both effects are random

various models have been proposed to describe this behavior

(interferer) Stokes vectors are not constant


► Karlsson‘s statistical model (JLT, pp. 4127+, 2006)

► influence on PMD compensation ► mostly two-channel system, no PMD dependence

► diffusion model (Winter et al., JLT, pp. 3739+, 2009)

► SOPs evolve as random walk ► ensemble mean values only

► carousel model (Bononi et al., JLT, pp. 1903+, 2003)

► pump and probe rotate when both carry a mark ► two-channel system, no PMD

dwdm power channel threshold for mean probe dop 0 97
DWDM power/channel threshold for mean probe DOP=0.97

► resonant dispersion map, 10 × 10 Gbps OOK interferers► @ 50 GHz spacing

depolarization of probe vs number of 3 dbm interferers
depolarization of probe vs. number of 3 dBm interferers

► difficult to simulate, expensive to measure► saturates at about 20


a typical PolDM system

► selective upgrade: 10G NRZ » 100G PolDM RZ-QPSK

► fits into 50 GHz grid


detected field at y-Rx:

► otherwise crosstalk occurs from x to y and vice versa

► crosstalk increases with misalignment angle and with►length of field vector

polarization DEMUX must be aligned to PolDM subchannels

(visualization in Jones space)


XPolM causes symbol-to-symbol fluctuations around mean SOP

► cannot be compensated (again like XPM)

modern coherent receivers can handle subchannel SOP changes with PMD time constants

► DCF abuse with a screwdriver: 280 µrad/ns(Krummrich and Kotten, OFC 2004, FI3)


field amplitude at y-Rx

aligned subchannels

interleaved subchannels


► crosstalk is never zero because pulses at Rx are no longer RZ

(accumulated GVD, PMD, noise)

interleaving RZ-shaped symbols minimizes crosstalk generation


10 × 10G NRZ interferers w/ 100G PolDM-RZ-QPSK probe

► 256 ps/nm RDPS, 10 interferers, SSMF, no PMD

► power/channel threshold is reduced by up to 2 dB


the statistical ensemble (mean DOP = 0.975)

► DOPs and ROSNRs spread over large range

► for DOPs < 0.98 (0.97), ROSNR penalties become significant


Xie showed how PolDM interferers can cause negligible XPolM compared to single-polarization (PTL, pp. 274+, 2009)

► requires RZ pulse shape and subchannel interleaving

► neighboring half-symbol slots have orthogonal polarization states

► probe SOP oscillates but rotation does not accumulate


► onset of nonlinear penalties at much lower powers

► (near) saturation of penalties for large channel spacing

(van den Borne et al., ECOC, 2004, Mo 4.5.5)


► saturation of penalties for large number of interferers

(Renaudier et al., PTL, pp. 1816+, 2009)


► benefit of PolDM vs. OOK interferers

(Bertran-Pardo et al., OFC, 2008, OTuM5)


► XPolM in DWDM systems causes depolarization

► diffusion model correctly predicts simulated behavior

► depolarization creates detrimental PolDM crosstalk

► can be reduced by interleaving PolDM subchannels

slides available at http://www.marcuswinter.de/publications/ST2010