Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX olarization-Multiplexed System Outage due to Nonlinearity- Induced Depolarization Marcus Winter, Dimitar Kroushkov, and Klaus Petermann ECOC MMX / Th.10.E.3 P

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX inter-channel nonlinear polarization effects 2

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 3 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

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 4 SOP evolution back-to-back (fully polarized)

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX SOP evolution (without amplifier noise) 5 significant nonlinear depolarization rapid (symbol-to-symbol) fluctuations of the SOP can we model this and can this become a problem?

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 6 cross-polarization modulation (XPolM) ► basics ► statistical models ► XPolM and polarization multiplex ► open questions

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX XPolM basics 7

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 8 XPolM is closely related to XPM nonlinear variation of the refractive indexrefractive index difference proportional to sum of interfering channels‘ powers (polarization-dependent) Stokes vectors results in the modulation of signal phasepolarization (phase difference)

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 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 , 1995 many-channel formulation in 2006 ► Menyuk and Marks, JLT, pp , 2006 ► Karlsson and Sunnerud, JLT, pp ,

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 10 Poincaré sphere probe channel DWDM interferers Stokes vector sum nonlinear rotation

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX statistical models 11

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX (interferer) Stokes vectors are not constant 12 ► 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

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX ► carousel model (Bononi et al., JLT, pp , 2003) ► pump and probe rotate when both carry a mark ► two-channel system, no PMD 13 ► diffusion model (Winter et al., JLT, pp , 2009) ► SOPs evolve as random walk ► ensemble mean values only ► Karlsson‘s statistical model (JLT, pp , 2006) ► influence on PMD compensation ► mostly two-channel system, no PMD dependence

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX SOP distribution resembles diffusion 14

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX DWDM power/channel threshold for mean probe DOP=0.97 ► resonant dispersion map, 10 × 10 Gbps OOK interferers 50 GHz spacing 15

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 16 depolarization of probe vs. number of 3 dBm interferers ► difficult to simulate, expensive to measure ► saturates at about 20

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX XPolM and polarization multiplex 17

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 18 ► selective upgrade: 10G NRZ » 100G PolDM RZ-QPSK ► fits into 50 GHz grid a typical PolDM system

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX polarization DEMUX must be aligned to PolDM subchannels (visualization in Jones space) 19 ► otherwise crosstalk occurs from x to y and vice versa ► crosstalk increases with misalignment angle and with ► length of field vector detected field at y-Rx:

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 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) 20 XPolM causes symbol-to-symbol fluctuations around mean SOP ► cannot be (fully) compensated (again like XPM)

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX interleaving RZ-shaped symbols minimizes crosstalk generation 21 time 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, filtering) ► synchonized sampling necessary at Rx

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX × 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

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 23 the statistical ensemble (mean DOP = 0.975) ► DOPs and ROSNRs spread over large range ► for DOPs < 0.98 (0.97), ROSNR penalties become significant

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX open problems 24

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX outage probability ► progress made when defining outage via DOP ► (see proceedings paper, figure shows probability) ► outage via ROSNR much more interesting / relevant 25

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX influence of CMA (polarization demux) window length ► SOP correlation over several symbols possible ► systems with little or no inline GVD compensation ► correlation can be used to reduce crosstalk ► fast algorithms needed 26

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX dispersion map / interferer modulation format ► especially uncompensated spans ► GVD pulse distortion no longer negligible ► PSK formats no longer ideal 27

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX regimes of dominance ► SPM vs. XPM vs. XPolM ► depends on many factors ► (dispersion map, modulation format, PMD, GVD, …) ► first results by Bononi 28

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX summary 29

Winter et al.: XPolM in PolDM Systems, Th.10.E.3, ECOC MMX 30 ► XPolM in DWDM systems causes depolarization ► diffusion model correctly predicts simulated behavior ► in many situations ► depolarization creates detrimental PolDM crosstalk slides available at ► there are still many open questions about XPolM