In-service PMD monitoring and compensation

Univ. Paderborn R. Noé 1 In-service PMD monitoring and compensation Reinhold Noé, David Sandel University of Paderborn Electrical Engineering and Information Technology Optical Communication and High-Frequency Engineering D-3395 Paderborn Acknowledgements: V. Mirvoda, S. Bhandare, S. Hinz, S. Chotchidjoum, A. Fauzi, F. Wüst, H. Zhang, H. Herrmann, H. Suche, W. Sohler, Deutsche Forschungsgemeinschaft, Infineon Technologies, www.work-gmbh.com, Siemens ICN Most of this material can also be found in R. Noé et al., PMD in High-Bit-Rate Transmission and Means for Its Mitigation, IEEE JSTQE 1(24)2, pp. 341-355, and its references.

Univ. Paderborn R. Noé 2 Overview Introduction Electrical PMD compensation PMD detection 1st-order PMD detection Higher-order PMD detection Polarization scrambling Optical PMD compensation Polarization division multiplex Limits due to fiber nonlinearity Coherent optical systems Higher-order PMD description Conclusions

Introduction Univ. Paderborn R. Noé 3 Input field for unchirped, small-signal ( a << 1) intensity modulation: E in ( jω t j ( ) ( ) t j ( ) ( ) t ) e ω + ω ω ω + a 4 e + a 4 e e in = Output field after transfer through medium with transfer function/matrix J : Definition of intensity (normalized optical power, photocurrent): I = E Optical distortions can only partly be recovered in the electrical domain! Intensity transfer through medium: I E in out = Small-signal intensity modulation transfer function of a linear lossless optical medium ( jω t j ( ) ( ) ( ) t j ( ) ( ) ( ) t ( )) e ω + ω ω ω J ω + a 4 e J ω + ω + a 4 e J ω ω e in = 1+ a cosωt = 1+ a Re H m ( jωt ) e E/O Ein optical medium Eout I out O/E = 1+ a Re + + + ( ω ) = ( 1 2) J ( ω ) J( ω + ω ) + J ( ω ω ) J( ω ) e ( ) in in 2 ( jωt ( ) ) H ω e e m

Introduction Univ. Paderborn R. Noé 4 What is polarization mode dispersion (PMD)? Unitary Jones matrix: J 1 2 2 2 ( ω + ω ) = u + u 1 * * 1 2 = u 2 u1 u u PMD vector Ω : = Ω τ = n A 2 Re Im B B A B = j( u = j( u * ' 1u1 * ' 2u1 + u u 2 * 1 u * ' 2 ' 2) u ) Principal state-of-polarization (PSP) Differential group delay (DGD) Modulation transfer function for ω : H m ± jωτ 2 ( ω) ~ cosωτ 2 + jω S sin ωτ 2 H m ( ω ) ~ e T n in PMD effect scales with bit rate. 1st derivative of output polarization with respect to optical frequency vanishes for PSPs (Poole/Wagner, 1986)! S in = ± Ω n

Introduction Univ. Paderborn R. Noé 5 Pure 1st-order PMD Eye diagrams (DGD = 3T/8): laser Fiber is birefringent due to unwanted core ellipticity! DGD Fast PSP laser Eye closure τ 2 difficult to detect for small τ Both PSPs excited with equal powers = worst case

Electrical PMD compensation Univ. Paderborn R. Noé 6 Electrical PMD compensation by quantized feedback eye diagram subdiagrams with preceding 1 1 + = or + + + = optimum decision point Due to negative binomial or χ 2 noise from optical amplifiers, system penalty is larger than subdiagram opening penalty.

Electrical PMD compensation Univ. Paderborn R. Noé 7 Calculated sensitivity penalty vs. normalized DGD 12 1 Penalty [db] 8 without QF with QF 6 4 2 Degreesof-freedom: 128 32 8.2.4.6.8 τ T 1 Calculation fundamentals: R. Noé, Electrical Engineering 83(11), pp. 15-2

Electrical PMD compensation Univ. Paderborn R. Noé 8 However Experiments have shown smaller penalties. Reasons: Noise is not purely negative binomial or χ 2. Finite extinction and unavoidable patterning penalties generally mask the first ~1...2dB of PMD penalty. More elaborate equalizers may improve matters. Electrical equalizer can help also against other distortions. Much cheaper than optical PMD compensators. Electrical PMD compensation is an attractive compromise for any bit rate where it can be implemented!

Experiment performed with Siemens ICN Univ. Paderborn R. Noé 9 PMD penalty detection by spectral analysis PRBS 1 Gb/s transmitter 4 Gb/s attenuator PT PMF PT 2ps PMD simulator PMF 1ps Univ. Paderborn / Siemens, 1998 PMF 1ps automatic PT PMF 1ps automatic PT PMF 1ps automatic PT PMD compensator receiver 4 Gb/s BER 1 Gb/s 2 4 2 GHz 1 GHz controller (PC) 5 GHz Simple realization: Bandpass (or highpass) filter, followed by square-law power detector Essentially, the opening is being maximized. Example: Filter bandwidth = 4 GHz, initial filter output SNR = db, integration over 1 μs yields final SNR = 46 db. Is this sufficent?

1st-order PMD detection Univ. Paderborn R. Noé 1 Performance of spectral analysis PMD penalty detectors (Measured at 1Gb/s, but could be scaled to any bit rate.) 1 BPF.125/T BPF.25/T BPF.5/T HPF 1. 2. DGD / T 3. 5 GHz bandpass filter or 4... 1 GHz highpass filter detects PMD most sensitively. Unambiguous readout until 4 ps of 1st-order DGD by 2.5 and 1.25 GHz filters Switching between, and linear combination of different signals

1st-order PMD detection Univ. Paderborn R. Noé 11 PMD detection for DPSK signals using an electrical highpass filter 1.8 Highpass output.6 power (a.u.).4.2 CSRZ-DPSK NRZ-DPSK.5 1 DGD/T For small DGDs, highpass output power drops with the square of the DGD. Small DGDs are difficult to detect. Ambiguous readout

1st-order PMD detection Polarization modulation causes arrival time variations in the presence of PMD Univ. Paderborn R. Noé 12 4Gbit/s eye diagrams (triggered from TX) TX fiber with PMD ps TX TX scrambler One polarization scrambler may be shared by many wavelength channels. arrival time variation Δtˆ () t 2ps 5.5ps 19ps

1st-order PMD detection Univ. Paderborn R. Noé 13 PMD detection in 4Gbit/s transmission system Clock recovery PLL in receiver tracks arrival time variations. Arrival time clock phase integral of VCO input signal TX 4Gbit/s Differential group delay (DGD) arrival time variations Bit rate scalablity If you can demultiplex the signal using a clock PLL, then arrival time detection is also possible. PLL may even include OTDM demultiplexer at high data rates. polarization scrambler a.u. 1-1 fiber PMD Δtˆrms @ 77fs of DGD rms VCO decision circuitry Δtˆ ( t) -2 5 1 15 2 25 μs PI data out

1st-order PMD detection Univ. Paderborn R. Noé 14 4Gbit/s PMD compensation with arrival time detection 33km DSF DFB laser 13km SSMF MOD 4Gbit/s DCF PMD compensator 63km SSMF polarization scrambler 51km DSF M 5km DSF motorized endless polarization transformer Vertical broadening of ones is due to slow PDL. M controller VCO PI PT DGD 6ps PT DGD 6ps decision circuitry data out LiNbO 3 polarization transformers

1st-order PMD detection Univ. Paderborn R. Noé 15 Prescaled clock spectra in the presence of a 19 ps DGD dbm -2-3 -4-5 -6-7 -8 ~3 db without PMD compensation -9-1 9952 9953 9954 MHz 9955 with 1 ps + 8.5 ps PMD compensator 1 min persistence, rotating emulator

1st-order PMD detection Univ. Paderborn R. Noé 16 Root mean square arrival time variation vs. differential group delay for tennis ball polarization scrambler 1 Δtˆrms best case 1 worst case.1 1 1 Δtˆrms (ps) + σ < Δtˆ rms(sensitivity) σ.88 ps or 1.35 ps sensitivity DGD [ps] 2.4 μs measurement interval (417kHz scrambling frequency)

Chromatic dispersion detection Univ. Paderborn R. Noé 17 Chromatic dispersion detection at 4Gbit/s using synchronous arrival time detection DFB laser 5MHz FM & AM modulation NRZ / CS-RZ 4Gbit/s data in FM: 224MHz(rms) AM: 1.2%(rms) CD fiber with CD ref. phase trimmer decision circuitry VCO PI arrival time data out Small pump current modulation of TX laser at 5MHz If there is chromatic dispersion (CD), FM modulates arrival time, detectable in RX at VCO input. CD [a.u.] 4-4 NR Z CS- RZ Operable over more than one eye closure 1 attoseconds or 5 fs/nm accuracy 2 ps/nm longterm drift Parasitic AM provides reference for synchronous (lock-in) detection of arrival time modulation. -8-2 2 ps/nm

1st-order PMD detection 3-Dimensional DOP-Evaluation Univ. Paderborn R. Noé 18 courtesy Rosenfeldt et al., ECOC 21

1st-order PMD detection Univ. Paderborn R. Noé 19 Polarimetric PMD detection Scalable to any bit rate! DOP measurement introduced by N. Kikuchi, S. Sasaki, ECOC 1999. Improvement by scrambler and by making use of the measured polarization states (H. Rosenfeldt et al., OFC21). Allows for direct control of PMD compensator (but only if polarization transformations between polarimeter and PMD compensator are known and stable!) Higher-order PMD detection is likewise possible. Drawbacks: Cost, ambiguity (for RZ) Possible remedies: Grating-based spectral polarimeters (P. Westbrook et al., OFC22, WK5) Extra optical filters

1st-order PMD detection Univ. Paderborn R. Noé 2 Minimum DOP vs. DGD for different pulse shapes 1 min. DOP pulse shape -2-1 1 2 time, DGD 1-2 -1 1 2 time, DGD 1-2 -1 1 2 time, DGD Readout is proportional to DGD, but only if pulses edges are shorter than DGD!

1st-order PMD detection Univ. Paderborn R. Noé 21 How to detect 1st-order PMD Measurement of eye opening power spectral density (or autocorrelation funct.) arrival time detection polarimetric methods Polarization scrambler needed Extra optics in each WDM channel no no yes no** no no no no** Extra RF electronics yes yes no no n Readout is DGD, n = 2 2 1 1* Speed slow fast fast fast** * as long as pulse rise and fall times are shorter than DGD ** in principle Arrival time detection is easily realized with commercially available technology.

Higher-order PMD detection Univ. Paderborn R. Noé 22 Slope steepness difference indicates higher-order PMD Assuming perfect arrival time detection, resulting DGD profile of fiber and PMD compensator will most likely form a loop. As a function of optical frequency, sections with given constant DGDs twist, thereby sliding loop endpoint on a parabola P. Projection PQM of quadratic motion QM (parabola ordinate) along input polarization causes eye diagram shear. Slope steepness difference variations always exists due to scrambling..2 Ω3 / Τ.2 Ω2 / Τ -.2 LM QM P Ω1 / Τ PQM.2 photodiode d/dt maximum > + + minimum < slope steepness difference

Higher-order PMD detection Univ. Paderborn R. Noé 23 Effects of DGD loop on 4Gbit/s eye diagram Back-to-back Input polarization parallel to linear motion of DGD profile endpoint. Curvature difference (like for chromatic dispersion) always exists. Measurement: maximum > photodiode d/dt d/dt + + minimum < curvature difference Input polarization parallel to quadratic motion of DGD profile endpoint.

Higher-order PMD detection Univ. Paderborn R. Noé 24 4Gbit/s transmission experiment with PMD compensation TX 4Gbit/s tennis ball scrambler SMF d/dt Mechanical Electrooptic PMD PMD emulator compensator M1 M2 + + E1 E2 controller slope steepness difference clock and data recovery VCO arrival time PI data out

Higher-order PMD detection Univ. Paderborn R. Noé 25 Results 1 slope steepness difference [a.u.] 1 1 back-toback, no PDL back-to-back, with PDL with maximized area proportional readout with minimized area DGD sections Loop area +++ps, no PDL ps 2 +++ps, with PDL ps 2 2.2+4+4+2.2ps 8.8 ps 2 6.25+4+4+6.25ps 25 ps 2 6.25+6.25+6.25+6.25ps 39 ps 2 6.25+19+22.8+6.25ps 261 ps 2 1 1 Maximized DGD profile loop area [ps 2 ] Measurement interval 2.4 μs

Higher-order PMD detection Univ. Paderborn R. Noé 26 Typical eye patterns for various polarizations at the input of a DGD profile loop, with stopped polarization scrambler back-to-back 1 6.25+6.25+6.25+6.25ps 1 1

Higher-order PMD detection Univ. Paderborn R. Noé 27 Detectability of square-shaped DGD loop vs. section length 1-1 1-2 1-3 1/32 slope steepness difference eye closure 1/16 curvature difference 1/8 DGD per section / T input polarization parallel to QM LM 1/4 Slope steepness difference is most sensitive for small DGDs. Readout is proportional to DGD loop area. Polarization scrambling is required but this may have been implemented for 1storder PMD detection anyway.

Higher-order PMD detection Univ. Paderborn R. Noé 28 Measurement of How to detect DGD loop for any input polarization n eye opening highpass output power Detects PMD of order 1, 2, 3 1, 2, and, with wrong sign, 3 Readout is DGD, n = 3 ambiguous readout (see above) curvature difference slope steepness difference 2, 3 3 3 2 Hardware effort highest low higher low Speed slow fast fast fast Patterning strong weak Polarization scrambler needed? Influence of fiber chromatic dispersion (CD) no polarization-dependent addition of 2nd-order PMD and fiber CD yes decreases readout Slope steepness difference (+ highpass output power) measurement is attractive.

Polarization scrambling Univ. Paderborn R. Noé 29 Electrooptic tennis ball polarization scrambler: Measured output Stokes parameter trajectories and spectra S 2 DFB laser input polarization setting rms ampl..4 S1 S2 S3 Only 3 harmonics! polarimeter scrambler (1 waveplate).2 S1 S2 S 1 S 3 S 3 1 2 3 4 5 6 7 n S 1 S 2 Circular input polarization S = ( 1+ 1 3) 2 cosωt ( 1 1 3) ( 1+ 1 2 sinωt + ( 1 1 3) 2 3 cos 2ωt 2 cos3ωt 2 sin 3ωt Eigenvalues of Stokes vector covariance matrix: 1/3 ±.55

Polarization scrambling Univ. Paderborn R. Noé 3 Eigenvalues of normalized Stokes vector covariance matrix for tennis ball polarization scrambler.4.3 Convergence speed of optical PMD compensation with arrival time detection depends on eigenvalues. Variations are permissible as long as minimum convergence speed (for most infavorable polarization setting) is sufficiently fast..2 152 154 156 158 λ [nm] at least 4THz usable bandwidth

Polarization scrambling Univ. Paderborn R. Noé 31 Covariance matrix eigenvalues of polarization-independent independent 2-waveplate 2 polarization scrambler DFB laser scan of input polarization scrambler 8 polarimeter occurrences 4 histogram for 51 equispaced input polarizations smallest eigenvalue largest eigenvalue Higher harmonic content than tennis ball scrambler!.25.3.35

Polarization scrambling Univ. Paderborn R. Noé 32 Covariance matrix eigenvalues of polarization-independent independent 2-waveplate 2 polarization scrambler.4 largest eigenvalue Values taken for scan over 51 equidistributed input polarizations.3 smallest eigenvalue.2 152 154 156 158 λ [nm] ~4THz usable bandwidth

Optical PMD compensation Univ. Paderborn R. Noé 33 Measured differential group delay profiles and ideal PMD compensation ~ PMD vector of two cascaded DGD sections: Ω = Ω + R Can be generalized by induction. DGD profile: concatenated local backtransformed PMD vectors 1 1 1 Ω 2 22ps + 6ps ϕ 1 Same as for a fiber plus a perfect PMD compensator, which returns on fiber DGD profile until origin! Ω 1 origin overall PMD vector 2ps end point 1 back-to-back end point Ω 2 Inverse scattering theory proposed by L. Möller -1 Ω 1 [ps] origin -2-4 -6 Ω 2 [ps]

Polarization fundamentals and polarization control Univ. Paderborn R. Noé 34 Electrooptic waveplate, usable for endless polarization control Noé et al., 1987/1988 SiO 2 Au V 1 V 1 V 2 Y, TE Z Plane of normalized voltages: -1 V 2 /V 2,π 1 1 V 1 /V 1,π LiNbO 3 7 μm X-cut, Z-propagation LiNbO 3 V 1 alone: horizontal/vertical birefringence V 2 alone: 45 / 45 linear birefringence Both effects combined: Ti:LiNbO3 X, TM Waveplate with adjustable retardation and orientation Eigenmodes in S 1 -S 2 plane Uninterrupted, endless transformation of circular polarization into any state or vice versa. For circular input polarization the output polarization is obtained by an azimuthal equidistant projection onto Poincaré sphere: S 3 S 2-1 S 1

Polarization fundamentals and polarization control Univ. Paderborn R. Noé 35 In-phase and quadrature, periodic mode conversion in birefringent waveguide for endless polarization control: Soleil-Babinet analog (SBA) Differential group delay ~.26 ps/mm Spatially periodic, X-directed (vertical) electric field perturbs local eigenmodes. Example: Horizontal input polarization x E y Mode conversion: in phase quadrature Output signal: * 2 Re( ) * 2 = E x Ey S3 = 2 Im E x Ey Eigenmodes of a spatial period Λ: circular ±45 linear S ( ) [ 1 ] T E = 1, =, S = Eigenmodes of nλ long section can be anywhere on S 2 -S 3 great circle V 1 V 2 S 3 X, TM LiNbO 3 Z, TE Y 3Λ/4 Λ Λ/4 Λ = TE-TM beat length, ~21μm at 155nm wavelength S 2 S 1

Optical PMD compensation Fabricated by Prof. Sohler, Univ. Paderborn Distributed PMD compensator in X-cut, Y-propagation LiNbO 3 Univ. Paderborn R. Noé 36 in-phase ground ground quadrature Λ = 21μm Optical bandwidth 3 THz Thermal tuning 1 GHz/K Voltages <8V 73 electrode pairs ( 1.25 mm) on 93 mm long substrate Combined differential group delay of 2 units: 43 ps

Optical PMD compensation Univ. Paderborn R. Noé 37 Speed problem of equalizers with more than one variable DGD section Scenario: additional DGD of 52 ps to be inserted in equalizer 1st possibility: DGD change... 52 ps = 1, λ. At least one subsequent joint (polarization transformer) must rotate 1, times with 1... 1 steps/turn. Speed problem! No PMD compensation with more than 1 section is possible with variable DGD sections! 2nd possibility: two fixed 26 ps DGD sections unfold ~1, times faster ps... 52 ps ps... 52 ps 1, turns DGD section joints 1, turns (ERRORS!)... unless joint(s) turn 1, times

Optical PMD compensation Univ. Paderborn R. Noé 38 Measured differential group delay profiles of distributed PMD compensator -3 1 origin Ω 1 [ps] 2ps 7 Ω 3 [ps] end point Ω 3 [ps] 4 origin end point 4 Ω 2 [ps] -4 Ω 1 [ps] 14-6 Ω 2 [ps]

Optical PMD compensation Univ. Paderborn R. Noé 39 Advantages of LiNbO 3 over other polarization transformers Speed Availability of 2 kinds of birefringence (in-phase and quadrature mode conversion, or phase shift and mode conversion) Advantages of distributed X-cut, Y-propagation PMD compensator over X-cut, Z-propagation LiNbO 3 polarization transformers Low-loss integration of DGD sections and polarization transformers on one chip. Multi-section PMD compensators must have fixed DGD sections anyway (Noé et al., JLT 1999). DGD of ~26ps/1mm is perfect at 4...8Gbit/s! First and higher-order PMD compensation on one chip! Higher electrooptic coefficient Polarization transformers are optimally oriented with respect to DGD sections! (Endless polarization transformation from any polarization to linear in only one X-cut, Z-propagation LiNbO 3 waveplate is practically impossible.) No, or at least a substantially reduced DC drift!

Optical PMD compensation Univ. Paderborn R. Noé 4 Polarization control results 1 5 1.2.4.6.8.1.12.14 Continuous, endless polarization tracking on the 3 most critical great circles of the Poincaré sphere crossing the TE/TM poles. All other cases are better behaved. Corresponding misalignment angle distribution, number of hits vs. angle in rad. Tracking speed:.12 rad/iteration

Optical PMD compensation Univ. Paderborn R. Noé 41 Practical problem Long term (days to months) DC drift is a big problem in X-cut, Z-prop. LiNbO 3 polarization transformers due to the static field required to tune out residual waveguide birefringence. Although there is no static field in X-cut, Y-prop. LiNbO 3 a susceptibility to DC drift can not be ruled out. Drive device with zero-mean signals to reduce/avoid DC drift!

Optical PMD compensation Univ. Paderborn R. Noé 42 DGD profile of a PMDC subject to DC drift, and 3 DGD profile Characterization and calibration results instantiations of a PMDC protected against DC drift Full mode conversion SBA with rotating orientation added at PMDC input. DGD profile is twisted. DC drift is avoided. ψ ψ 2 DGD profile origin DGD profile endpoint ψ ψ ψ Static case, subject to DC drift.

Experiment performed with Siemens ICN TX 2 Gbit/s photodiode motorized endless polarization transformers M DGD 1ps M PMD compensator, 43ps DGD 2ps control -2-4 -6-8 Univ. Paderborn R. Noé 43 2Gbit/s PMD compensation with distributed PMD compensator on log(ber) off -1 1 2 3 4 5 6 1 on off clock & data recovery ( ) 2 ( ) 2 data out controller.5.5 power @ 1GHz 1 2 3 4 5 6 1 power @ 5GHz 1 2 3 4 5 6 time [min] back-to-back compensator alone 3 ps compensated 3 ps, compensator off

Experiment performed with Siemens ICN 4 Gbit/s eye diagrams with LiNbO 3 distributed PMD compensator Univ. Paderborn R. Noé 44 back-to-back equalizer not working equalizer working

Optical PMD compensation Univ. Paderborn R. Noé 45 4 Gbit/s CSRZ-DPSK transmission setup with distributed PMD compensation DFB 33km DSF DPSK 4Gbit/s DGD CSRZ 2GHz 1km SSMF scrambler 417 khz DGD LiNbO 3 PMDC AWG DEMUX MZI lock-in controller arrival time integrator clock signal clock and data recovery VCO PI data out clock phase error signal

Univ. Paderborn R. Noé 46 Arrival time detection of PMD for 4 Gbit/s CSRZ-DPSK 1 rms arrival time signal [a.u.] 1 highest readout lowest readout 1 ±σ sensitivity: 1.2ps.1.5 1 1 DGD [ps] Measurement interval: 2.4 μs Sensitivity: ~1.2 ps

Optical PMD compensation Univ. Paderborn R. Noé 47 Spectra at integrator output with PMD compensator stopped or running power [dbm] -2-4 PMDC stopped PMDC running -6-8 1 2 3 MHz

Optical PMD compensation Univ. Paderborn R. Noé 48 Q factors measured for various configurations 26 24 Q [db] 22 2 18 back-toback + of fiber 4+4 + PMDC + 34km scrambler + 2 DGD sections [ps] 6.6+6.2 6.6+8.6 13.6+8.6 or +6.2 +6.6ps, w/o fiber

Polarization division multiplex Univ. Paderborn R. Noé 49 Motivation for polarization division multiplex transmission Doubled fiber capacity 2 4Gbit/s NRZ polarization division multiplex tolerates more PMD than 8Gbit/s NRZ single-channel transmission, and much more than polarization-interleaved 4Gbit/s NRZ single-channel transmission with halved frequency spacing and polarizer at RX. 2 4Gbit/s PolDM tolerates more chromatic dispersion than 8Gbit/s. Distributed PMD compensator is able to output any desired polarization state Either polarization division multiplex or PMD compensation come at a fairly low incremental cost.

Polarization division multiplex Univ. Paderborn R. Noé 5 Polarization division multiplex (PolDM): Principle and effect of polarization crosstalk in receiver DFB laser i i 1 2 b 1 b 1 modulator 1 modulator 2 cos sin 2 2 ψ ψ polarization combiner 2 + b 2 + b 2 2 sin cos fiber 2 2 ψ ψ 2 + b b 1 2 b b polarization transformer control: HOW? 1 2 2 cosϕ sinψ cosϕ sinψ polarization splitter photoreceivers measured 2x1Gbit/s data signals without polarization control Information Photocurrents bits Polarization mismatch Interchannel phase difference Interchannel interference causes penalty ψ, not just ψ 2, and should be used as an error signal.

Polarization division multiplex Univ. Paderborn R. Noé 51 Polarization division multiplex transmission using interference detection scheme TX 1 Gbit/s FM 5kHz polarization combiner 25 ns motorized endless polarization transformer LiNbO 3 M polarization transformer fiber controller polarizer ( ) 2 clock & data recovery data out 1...2MHz FM and interchannel delay generate differential phase modulation to randomize interference. Extrapolated BER: 1-72 ~1ms signal acquisition time and up to 1 rad/s endless polarization tracking speed demonstrated. DSP can make control at least 1 times faster. data output signal and its eye diagram

Polarization division multiplex Univ. Paderborn R. Noé 52 Interference causes Bessel spectrum of photocurrent Even vs. odd Bessel line powers fluctuate as a function of mean interchannel phase difference. Suitable power weighting makes signal independent of phase fluctuations and, to first order, of differential phase modulation index η πδf τ 4.2. ~ peak peak = 54MHz 25ns -3 dbm -5-7 -9 detected worst case after automatic polarization adjustment.5 1 1.5 2 MHz 2.5 J1 J2 J3 J4 J5

Polarization division multiplex Univ. Paderborn R. Noé 53 PMD tolerance of polarization division multiplex vs. 2-IM Non-interleaved NRZ PolDM supports same capacity fiber length product. RZ and phase-shaped PolDM transmission reduce PMD tolerance. Note: System penalty [db] 2 eye closure penalty [db] 1 8 interleaved = worst case eye closure penalty [db] (FWHM=.34T) 1 8 eye closure penalty [db] non-interleaved = best case 6 4 2 non-interleaved = best case PolDM RZ 2-IM RZ 6 4 2 interleaved = worst case PolDM NRZ 2-IM NRZ.2.4.6.8 DGD/T.2.4.6.8 DGD/T

Polarization division multiplex Univ. Paderborn R. Noé 54 Arrival time variation for RZ polarization division multiplex transmission PMD with PSPs equal to, 9 cause uncritical static arrival time difference between polarization channels. If single ones exite both principal states-of-polarization the arrival time of double ones depends dynamically on phase difference between the two polarizations: PSPs: +45, -45 retardation = n 2π 45 o fiber with PMD -45 o arrival time variation

Polarization division multiplex Univ. Paderborn R. Noé 55 Root mean square arrival time variation vs. DGD at 4Gbit/s 1 2 dynamic a.u. A.U. 1 1 ±σ static 11.1 1-1 1 1 1 1 DGD [ps] sensitivity 15fs, measured in 4.8μs

Polarization division multiplex Univ. Paderborn R. Noé 56 FM 2 4Gbit/s, 212km polarization division multiplex transmission with endless polarization control and PMD compensation 1541.6 nm 1544.8 nm 33km DSF 15km SSMF DCF CS-RZ 2GHz MOD 4Gbit/s 63km SSMF MUX 51km DSF motorized endless polarization transformer M 5km DSF ERRORS without PMDC M polarization & PMD controller PT DGD 4ps PT arrival time interference polarizer VCO decision circuitry PI data out NO ERRORS with PMDC

Polarization division multiplex Univ. Paderborn R. Noé 57 RZ polarization division multiplex signals in the presence of interchannel phase modulation Polarization crosstalk interference detection PMD arrival time detection A similar scheme exists also for NRZ polarization division multiplex.

Limits due to fiber nonlinearity Univ. Paderborn R. Noé 58 Setup for demonstration of cross channel-induced nonlinear PMD in WDM system, L. Möller, L. Boivin, S. Chandrasekhar and L.L. Buhl, ELECTRONICS LETTERS, Vol. 37, No. 5, (36-38), March 21 PMD affected signal after PMDE Demultiplexed PMD affected signal after PMDE, SMF, PMDC in linear propagation Demultiplexed PMD affected WDM signal after PMDE, SMF, PMDC in nonlinear propagation (+6.5 dbm launched power, 198.6 ps DGD+XPMIPS) Demultiplexed non-pmd affected WDM signal after SMF in non-linear propagation (+6.5 dbm launched power, DGD + XPMIPS) Single channel PMD affected signal after PMDE, SMF, PMDC in non-linear propagation (+9.5 dbm launched power, 198.6 ps DGD)

Limits due to fiber nonlinearity Univ. Paderborn R. Noé 59 Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems, B.C. Collings, L. Boivin, Photonics Technology Letters, Vol. 12, No. 11, 2, pp. 1582-1584

Coherent optical transmission Univ. Paderborn R. Noé 6 Principle of coherent optical transmission optical transmitter S fiber local oscillator laser coupler balanced or differential photoreceiver jω t j t () S ω t = E e E () t j e LO E = E P I = S, LO ELO, + 2 ( je E ) E 1 2 1 = 2 E1,2 ES ± 2 Re LO S + 2 4 1,2 LO electrical output, I(t) + + jω t () t = R( P P ) = R Re( je E ) = R Re( E E e IF ) = 2R ω 1 1 1 () t ( ES jelo ) E 2() t ( jes + ELO ) IF = 2 P S = ω S 1 P LO ω 2 cos LO ( ψ 2) cos( ω t + ϕ ) cos( ψ 2) ϕ IF LO IF = arg S IF + 1 2 ( E E ) P = E LO, = 2 S, LO, S, = S, LO E E + LO, S, 2 E E S, LO, S, LO Operation point of the photodiodes is transferred from the apex of the parabolic field detection characteristic to a steeper part. Interference term provides linear electric field detection! Intermediate frequency... ω IF 1/(2T) Heterodyne ω IF = Homodyne 1/T >> ω IF Intradyne, needs I&Q or 3-phase optical receiver. With asynchronous detection: phase diversity Polarization matching required! ψ = angle on Poincaré sphere

Coherent optical transmission Univ. Paderborn R. Noé 61 Phase diversity, polarization diversity, polarization division multiplex, electronic polarization control, PMD, PDL and CD compensation E LO,x Re(X 1 ) 9 hybrid E S E LO PBS E S,x Multiplication by Jones matrices cascaded with DGD sections, which together represent inverse DGD profile of fiber: Im(X 1 ) 45 PBS E S,y 9 hybrid Complete purely electronic polarization control, PMD, PDL and CD compensation Re(X 2 ) Im(X 2 ) E LO,y

Higher-order PMD description Univ. Paderborn R. Noé 62 PMD definition and categorization Taylor series expansion of PMD vector is unphysical because PMD changes quasi periodically as a function of frequency. If Taylor series is used: Categorize various orders of PMD depending on their relation to the input polarization. order parallel to input polarization perpendicular to input polarization: mix of opposed parallel cases 1 delay symmetric eye closure 2 (2nd-order) CD, adds to fiber CD, symmetric overshoot, curvature difference.2 -.2.2 -.2.5 (depends on fiber CD).3.2.1 -.1 -.2 -.3 5-5 -.4 -.2.2.4 3 3rd-order CD, slope steepness difference, asymmetric overshoot.15.1.5 -.5 -.1 -.15-55 -.5.5 vertically asymmetric, horizontally symmetric eye closure.15.1.5 -.5 -.1 -.15.5 -.5-5.5

Higher-order PMD description Univ. Paderborn R. Noé 63 Fourier expansion of mode coupling (FEMC) A frequency-independent mode conversion at the fiber input. This is described by 2 parameters, for example retardation and orientation of an SBA. A total DGD. A frequency-independent mode conversion at the fiber output. In the general case a mode conversion (2 parameters, as at the input) and a differential phase shift (one more parameter) are needed. In total this means that there is a frequencyindependent elliptical retarder at the output. Complex Fourier coefficients F k of mode coupling along the birefringent medium, which exhibits the above total DGD only in the absence of mode conversion. Soleil-Babinet analog (SBA) retardation orientation (= bend angle) (= bend orientation) F k ( z) jψ ( z) = L j2πk z L e e dϕ dz dz

Higher-order PMD description Univ. Paderborn R. Noé 64 Order and number of real parameters in higher-order PMD definition methods Method (below) and its order (right) 1 2 3 4 Taylor expansion of PMD vector (TEPV, Jones matrix given by Heismann) 3 6 9 12 Exponential Jones matrix expansion (EMTY = Eyal, Marshall, Tur, Yariv) 3 6 9 12 Sequence of DGD sections (SDGD) 3 5 7 9 Fourier expansion of mode coupling (FEMC) 3 5 9 13 1st-order PMD, identical for all methods F, uniform bending of DGD profile F 2, F 1, F 1, F, F 1, more complicated bending of DGD profile F, F 1, F 2 3 extra parameters are needed for all methods if frequency-independent output polarization transformation needs also to be described.

Higher-order PMD description PMD device to be characterized Univ. Paderborn R. Noé 65 DGD profile of an exemplary PMD structure, cascaded with inverted FEMC structures cascaded with inverted 1st-order structure cascaded with inverted 2nd-order FEMC structure cascaded with inverted 3rd-order FEMC structure

Higher-order PMD description Univ. Paderborn R. Noé 66 Extinction of cross polarization at output of PMD device cascaded with inverted 3rd-order FEMC structure db -2-4 co-polarized input pulse 37.2 db cross-polarized -6-4 -2 2 4 time [DGD units] Gaussian input pulse width is chosen equal to total DGD of FEMC structure after convergence of search algorithm. Search algorithm maximizes cross polarization extinction. Ideal PMD description would result in infinite cross polarization extinction. (Time is rescaled by factor 16 compared to previous viewgraph.)

Higher-order PMD description Univ. Paderborn R. Noé 67 Suppression of cross polarization by equalizers (= inverted structures) defined by higher-order PMD definition methods Method order Gaussian input pulse width [a.u.] Taylor expansion of PMD vector (TEPV) Exponential Jones matrix expansion (EMTY) Fourier expansion of mode coupling (FEMC) 1.3 db 1.3 db 1.3 db 14.8 db 12.6 db 21.6 db db and pulse width values are averaged over 75 PMD examples. 19.9 db 16.1 db 35.5 db Pulse widths are chosen equal for all methods, using the value obtained after convergence of FEMC for one particular order. Part of extinction improvement of high method orders is due to broader pulses. Extinction improvement of higher-order FEMC over 1st-order PMD seems to be 2 times larger (in db) than that of TEPV or EMTY! Reason: FEMC (and SDGD) are closely related to natural PMD, unlike higher-order TEPV and EMTY. Drawback: Finding FEMC coefficients is a numerical optimization process more research is needed. 1 5.6 2 7.2 3 9.5

Conclusions Univ. Paderborn R. Noé 68 Conclusions (1): My PMD compensation philosophy Electrical compensation: Low-cost compromise, to be used at 1 Gbit/s. Electrical detection: Low-cost, high performance. Arrival time detection (example: 2.4μs, sensitivity ~1 ps @ 4 Gbit/s) Slope steepness detection Polarization scrambler is needed or may be useful. Optical detection is probably not required. If it is to be used, a shared polarization spectrometer is needed to bring cost down. Optical compensation: High performance. Distributed PMD compensator in X-cut, Y-prop. LiNbO 3 has various advantages over other PMD compensators: Polarization transformers and DGD sections are integrated on one chip. Endless polarization transformations of any polarization state into PSP of DGD section DC drift is much less problematic than in X-cut, Z-prop. LiNbO 3 polarization transformers.

Conclusions Univ. Paderborn R. Noé 69 Conclusions (2): Difficulties in implementing PMD compensation Fast endless polarization control = 6% PMD and polarization mismatch detection = 3% PMD theory = 1% Go or no go: XPM-induced polarization modulation is dangerous in the case of intensity-modulation or NRZ signalling. RZ-DPSK is tempting. 1%? 6%? Number of publications Most of this material can also be found in R. Noé et al., PMD in High-Bit-Rate Transmission and Means for Its Mitigation, IEEE JSTQE 1(24)2, pp. 341-355, and its references. Yet more theory :-( Fourier expansion of mode coupling (FEMC) improves higher-order PMD description.