Optical Spectral Processing / All-Order PMD Technology: Compensation, Sensing, Emulation

Transcription

1 PMD Compensation at Ultra-High Bit Rates or Optical Spectral Processing / All-Order PMD Technology: Compensation, Sensing, Emulation A.M. Weiner Purdue University amw@ecn.purdue.edu Funding:

2 Outline Introduction to PMD (focus on all-order PMD) Optical spectral processing (pulse shaping etc.) Sub-ps pulse all-order PMD compensation experiments Extending to DWDM via hyperfine-resolution spectral dispersers Spectral polarization sensor (parallel sensing at under 1 ms) All-order PMD emulation (generation)

3 Polarization Mode Dispersion (PMD) Anatomy of a real fiber Poole and Nagel, in Optical Fiber Telecommunications IIIA, Academic Press (1997). See also Kogelnik, Jopson, and Nelson, in Optical Fiber Telecommunications IVB, Academic Press (2002). Δτ For broadband inputs, random birefringences lead to wavelengthdependent polarization scrambling and wavelength- and polarization-dependent delays.

4 1 st Order PMD: Small distortion Small bandwidth limit First Order PMD Narrowband inputs Differential group delay (DGD) ŝ S (ω2) 3 ŝ ŝ (ω3) (ω1) θ Poincare sphere Ω (ω2) S 2 Poole and Giles, Opt. Lett. 13, 155 (1988) S 1 sˆ out =Ω sˆ out ω PSP( ω ) =Ω( ω )/ Ω( ω ) DGD( ) ( ) θ ω 2 = Ω ω2 ω 3 ω 1 Fiber characterized by two principal states of polarization (PSPs), in general elliptical For input light launched along a PSP, output SOP is constant to first order in ω Two PSPs have a differential group delay (DGD) Maxwellian distribution Valid only for small DGD (compared to pulse width)

5 M. Duelk and P. Winzer, IEEE High Speed Study Group, Nov. 2006

6 M. Duelk and P. Winzer, IEEE High Speed Study Group, Nov Appropriate modulation format and FEC suggests impressive inroads against PMD For very speed systems or higher PMD fibers, PMD issues likely to remain important

7 PMD Compensation Electrical compensation Impairment resistant modulation format Optical compensation (bit-rate and format independent) Distorted input Polarization splitter Polarization combiner First-order optical compensator Polarization controller Compensated output Split into PSPs, delay, and recombine! (or similar) Adjustable delay Applies only to small DGD less than a few tenths of pulse duration for RZ less than a few tenths of bit period for NRZ Already challenging in view of: time-dependent, random PMD variations requirements for low outage probability (e.g., <10-5 )

8 Limitations to First Order PMD Approximation B PMD 0.64 DGD The autocorrelation bandwidth of the PSP vectors is inversely proportional to the mean differential group delay. Shtaif, Mecozzi, and Nagel, IEEE Phot. Tech. Lett. 12, 53 (2000). Foschini, Jopson, Nelson, and Kogelnik, Journal of Lightwave Technology 17, 1560 (1999)

9 All-Order PMD Effects 800 fs pulse distorted by PMD emulator with mean DGD ~ 5.5 ps H. Miao, et, Opt. Lett. 32, 2360 (2007) Complicated frequency-dependent polarization scrambling Frequency- and polarization-dependent delays Will occur whenever the distortion approaches the pulse width or bit period

10 All-Order Optical PMD Compensation Complex frequency-dependent vector field - Generate frequency-dependent inverse matrix? - Operate on frequency-dependent vector field? TX Link Compensator RX All-order PMD (frequency-dependent complex transfer matrix) Sensor Controller - Spectral polarimetry? - Frequency-dependent delay or phase? -Complexity? -Requirements on TX? - Compensator synthesis in the time-domain (digital filter approach) - Compensator synthesis in the optical frequency domain

11 All-Order Optical PMD Compensation Digital filter (time-domain) approach C.K. Madsen, Opt. Lett. 25, 878 (2000) Cascaded all-pass filter elements e.g., cascaded first-order compensator elements Examples - Cascaded polarization mode coupling in birefringent LiNbO 3 R. Noe, et al, Elec. Lett. 35, 652 (1999) [Univ. Paderborn] - Cascaded ring resonators in silica PLCs - C.K. Madsen, et al, JLT 22, 1041 (2004) [Lucent] Challenges - Large number of stages for all-order PMD - Complexity of control problem grows with number of stages - Compensation of various orders of PMD is coupled and must be considered simultaneously

12 Parallel, Optical Spectral Processing -Pulse shaping -Dynamic spectral equalizers -Dynamic wavelength processing Spectral disperser Spectral combiner Broadband input - Ultrashort pulse - CW plus modulation - Multiple wavelengths Spatial light modulator Control of phase, intensity, polarization Frequency-by-frequency, independently, in parallel Processed output

13 Femtosecond Pulse Shaping Fourier synthesis via parallel spatial/spectral modulation A.M. Weiner, Rev. Sci. Instr. 71, 1929 (2000) Examples: Phase encoded O-CDMA waveform; square pulse Weiner et al, Opt. Lett. 15, 326 (1990); IEEE JQE 28, 908 (1992) Basic 4-f optical system, plus spectral masking: Long pulses (Nd:YAG), fixed mask: C. Froehly et al, Progress in Optics 20, 65 (1983) 100 fs pulses, fixed mask: Weiner, Heritage, and Kirschner, JOSA B 5, 1563 (1988) Liquid crystal modulator (LCM) arrays: Originally phase-only, then independent phase and intensity, now polarization Down to ~msec response, hundreds of pixels Diverse applications: fiber communications, coherent quantum control, few femtosecond pulse compression, nonlinear optical microscopy, RF photonics...

14 Pulse Shaping in WDM: Intensity Control Manipulation on a wavelength-by-wavelength basis No concern for phase or for coherence between channels Wavelength selective add-drop multiplexer (and wavelength selective switches) Ford et al, J. Lightwave Tech. 17, 904 (1999) [Lucent] Spectral gain equalizer Ford et al, IEEE JSTQE 10, 579 (2004) [Lucent]

15 Programmable Fiber Dispersion Compensation Using a Pulse Shaper: Subpicosecond Pulses Spectral phase equalizer Coarse dispersion compensation using matched lengths of SMF and DCF Fine-tuning and higher-order dispersion compensation using a pulse shaper as a programmable spectral phase equalizer Similar ideas apply to DWDM tunable dispersion compensation and few femtosecond pulse compression. A.M. Weiner, U.S. patent 6,879,426 ( ) τ ω = ψ ( ω) ω

16 Higher-Order Phase Equalization Using LCM Input pulse Input and output pulses from 3-km SMF-DCF-DSF link Output pulse (without phase correction) already compressed several hundred times Output pulse (with quadratic & cubic correction) Chang, Sardesai, and Weiner, Opt. Lett. 23, 283 (1998) No remaining distortion! Applied phase

17 Intensity cross-correlation (a.u.) 460 fs transmission over 50 km SMF Commercial DCF module (as is) with spectral phase equalizer without DC by pulse shaper second-order DC by pulse shaper both second- and thirdorder DC by pulse shaper Essentially distortion-free! Time (ps) Z. Jiang, Leaird, and Weiner, Opt. Lett. 30, 1449 (2005) Phase (rad) π π (A) (B) Pixel # ~ 5 ns after SMF 13.9 ps after DCF 470 fs after quadratic/cubic phase equalization

18 Pulse Shaping in WDM: Dispersion Compensation Research AWG pulse shaper and phase mask Grating pulse shaper and MEMS deformable mirror array Takenouchi, Goh and Ishii, OFC 2001 (NTT) ( ) τ ω = ψ ( ω) ω AWG pulse shaper and deformable mirror Sano et al, OFC 2003 (Sumitomo) VIPA pulse shaper and curved mirror Neilson et al, JLT 22, 101 (2004) [Lucent] Shirasaki and Cao, OFC 2001 (Fujitsu/Avanex) Either colorless dispersion compensation or independent fine-tuning of different channels

19 Frequency-Domain All-Order PMD Compensation (Principles and sub-ps pulse experiments) A.M. Weiner, U.S. Patent application (May 23, 2002)

20 (1) Distorted pulse: An All-Order Compensation Scheme Align Equalize Scalar field output spectral SOPs phase (1) (2) (3) Distorted input (vector field) State-of-polarization shaper { } E ( ω) = E ( ω) a( ω)ˆ α+ b( ω)ˆ β PMD (2) Sense and correct full spectrally dependent state of polarization in { } E( ω) = Ein( ω)exp jψ( ω) yˆ (3) Sense and compensate full spectral phase (generalized chromatic dispersion) E( ω) = E ( ω)ˆ y in Phase shaper Restored pulse

21 All-Order PMD-Compensator Implementation ( nm) (~576 fs pulse width) (16-piece PM fiber) (Cross correlation with 72 fs reference pulse; or FROG) New sensor New LCM configuration (7.6 db insertion loss) (4.5 db insertion loss) Concatenated polarization and phase pulse shapers Wavelength-parallel polarimeter for control of polarization pulse shaper Ultrashort pulse measurement approach for control of phase shaper M. Akbulut, et al, Opt. Lett. 29, 1129 (2004); Opt. Lett. 30, 2691 (2005); OFC 2005 (post-deadline); JLT 24, 251 (2006)

22 State-of-polarization (SOP) Control Two liquid crystal layers, aligned at 90 /45 Rotate ARBITRARY POLARIZATION STATE into a FIXED LINEAR STATE LCM Second Layer Operation LCM First Layer Operation RHCP SOP for a single wavelength (OR a single LCM pixel) Birefringence axis of LCM First Layer Birefringence axis of LCM Second Layer In an array in a pulse shaper configuration, many frequency components can be SOP-rotated independently and in parallel M. Akbulut, et al, Opt. Lett. 29, 1129 (2004)

23 Phase and Partial Polarization Control Two liquid crystal layers, aligned at ±45 Two LC layers successively rotate SOP about 45 o point Polarization rotation depends on arc length (retardance) difference together with a polarizer, this gives amplitude control (as in a spectral gain equalizer) Phase modulation depends on total arc length (total retardance) Poincare sphere

24 Pure Phase Control Liquid crystal layers at ± 45 With equal retardances, rotations by two LC layers are equal and opposite Output SOP = input SOP: no polarization rotation (independent of input SOP) Phase modulation depends on total arc length (independent of input SOP) Poincare sphere

25 Spectral Phase Retrieval: 1 st method Various ultrafast measurement techniques available Here we use the Gerchberg-Saxton algorithm Uses I(t), measured via cross-correlation, and power spectrum Use initial guess to start algorithm FFT -1 j ( ) I( ω) e β ω Et () j () t e α Apply power spectrum Typically iterations Apply intensity data E( ω) j ( ) e β ω FFT j It () e α () t (Iterated G-S algorithm) Measure new intensity profile Improved pulse Apply phase to shaper

26 All-Order Compensation Experiment (1) PMD Distorted SOP Spectrum Corrected SOP Spectrum 600 fs input pulse through PMD emulator (16 section PM fiber, mean DGD ~1.3 ps) Frequency-dependent polarization correction adds frequency-dependent phase Input Pulse (575.7 fs) PMD Distorted Pulse After SOP correction Recovered Pulse (630.8 fs) Time (ps) Time (ps) Time (ps) Time (ps) M. Akbulut, et al, Opt. Lett. 30, 2691 (2005); OFC 2005 (post-deadline); JLT 24, 251 ( 2006)

27 All-Order Compensation Experiment (2) PMD Distorted SOP Spectrum Corrected SOP Spectrum 800 fs input pulse through PMD emulator (16 section PM fiber, mean DGD ~1.3 ps) Frequency-dependent polarization correction adds frequency-dependent phase Input Pulse (791.8 fs) PMD Distorted Pulse After SOP correction Recovered Pulse (696.3 fs) Time (ps) Time (ps) Time (ps) Time (ps) M. Akbulut, et al, Opt. Lett. 30, 2691 (2005); OFC 2005 (post-deadline); JLT 24, 251 ( 2006)

28 Spectral Phase Retrieval: 2 nd method Second-Harmonic Generation (SHG) Frequency-Resolved Optical Gating (FROG) Two-dimensional data set Iterative retrieval (much more robust than G-S) Innovations: extremely high sensitivity using A-PPLN waveguides; polarization insensitive measurement operation 2-D Spectrogram with respect to frequency and delay R. Trebino, Frequency resolved optical gating, KAP, 2000 H. Miao, et al, OFC 2007; Opt. Lett. 32, 424 ( 2007); Opt. Lett. 32, 874 ( 2007)

29 Phase Sensing via FROG Pulses measured after SOP correction, before phase correction 600 fs pulse through PMD emulator with mean DGD ~1.4 ps) 22 nw coupled fundamental power, FROG error=0.007 Measured pulse after SOP correction, but before phase correction. H. Miao, et al, OFC 2007

30 Phase Sensing via FROG Pulses measured after both SOP and phase correction 600 fs pulse through PMD emulator with mean DGD ~1.4 ps) 22 nw coupled fundamental power, FROG error= fs Measured pulse after SOP and phase correction Robust: comparable results in several different experiments H. Miao, et al, OFC 2007

31 All-Frequency PMD Compensator in Feedforward Scheme P. B. Phua, Hermann A. Haus, and E. P. Ippen Frequencydependent PSP vector via Poincare arc method with polarization switching Isotropic dispersion compensation Depiction of PSP vectors Rotate PSP vector to common direction Frequency-dependent DGD compensation Proposal and analysis, with some suggestions for implementation Sensing via launch polarization switching; differentiation of spectral polarimetry data Phua, Haus, and Ippen, JLT 22, 1280 (2004)

32 Wavelength-Parallel Jones Matrix Correction Chromatic dispersion ( ) j e ψ ω U f PMD part ( ) β ( ω) * * ( ) ( ) α ω = β ω α ω Jones space: Full Jones matrix jψ( ω) E ω = T ω E ω T ( ω ) = e U f ( ω ) out ( ) ( ) ( ) in All-Order PMD Compensation Correcting U f to a frequency-independent matrix Wavelength-parallel Jones matrix sensing - Sensing via launch polarization switching and spectral polarimetry data (no differentiation of polarimetry data) Wavelength-by-wavelength Jones matrix correction H. Miao, et, Opt. Lett. 32, 2360 (2007)

33 Wavelength-Parallel Jones Matrix Sensing Broadband Signal U f Spectral Polarimeter Fast wavelength-parallel polarimeter for SOP sensing, ms responding time 0 Linear Input SOP Broadband Signal U f Spectral Polarimeter RHC Input SOP H. Miao, et al. CLEO 2007 S. X. Wang, et al, JLT., vol. 24, , 2006 Determines Jones matrix, not PSP vector Polarimetry data processed via standard matrix inversion (no differentiation) (+) - Less susceptible to measurement noise, reduced demands on spectral resolution Switching between known polarizations, as in standard Jones matrix methods (-)

34 Modified Wavelength-Parallel Jones Matrix Sensing Works for arbitrary input polarization Broadband Signal with frequency independent SOP 4 SOPs FLC FLC (0, 45 ) (45, 90 ) Ferroelectric liquid crystals (switchable wave plates) U f Broadband Polarimeter U = U U f 4 Output SOP Spectra const Processing algorithm Select two output SOP spectra with angular separation closest to 90 (60 ~120 ) Calculate cross product of selected SOP spectra Associate one selected SOP spectrum, and cross-product spectrum, with 0 and 45 linear input SOP, respectively Matrix inversion gives U(ω)=U f (ω)u const, where U const is an unimportant frequencyindependent rotation matrix Compensating U f (ω) constitutes all-order PMD compensation (plus simple frequency-independent polarization rotation) H. Miao, et, Opt. Lett. 32, 2360 (2007)

35 U α β Jones matrix β α = * * ( jθ ) Jones matrix of a 0 linear retarder Jones Matrix Correction Each frequency sensed and compensated independently U jφ jψ cosθe sinθe = jψ jφ sinθe cosθe ( jθ ) U exp 0 cosθ j sinθ exp 0 Jones matrix inverted = 0 exp( jθ 3) j sinθ2 cosθ 2 0 exp( jθ1) with Jones matrix of a 45 linear retarder ( ) ( ) θ = ϕ+ ψ 2 + π 4, θ = θ, and θ = ϕ ψ 2 π layer LCM configuration: U LCM Compare matrix of a liquid crystal retarder (difference leads to extra isotropic phase; taken out with layers 3&4) Jones matrix of a 0 linear retarder 1 0 = 0 exp ( jθ ( V) )

36 Compensation Experiments Custom 4-layer, 128-pixel liquid crystal modulator array Pixel spacing: 11.6 GHz H. Miao, et, Opt. Lett. 32, 2360 (2007)

37 Experimental Results (Distorted SOP Spectra) 800 fs pulse distorted by PMD emulator with mean DGD ~ 5.5 ps H. Miao, et, Opt. Lett. 32, 2360 (2007)

38 Distorted and Restored Pulses Intensity cross-correlation measurements 826 fs 828 fs H. Miao, et, Opt. Lett. 32, 2360 (2007)

39 Extension to Parameters Suitable For DWDM (e.g., 40 Gb/s systems)

40 Hyperfine Resolution Wavelength Demux Virtually Imaged Phased Array (VIPA) R r Fiber Collimator Cylindrical Lens VIPA λ 1 λ2 λ 3 Virtual Source Array Introduced by Shirasaki, Opt. Lett. (1996) Offers high spectral resolution, as in a Fabry-Perot But acts as spectral disperer, with large spectral dispersion arising from multiple beam interference in side-entrance etalon geometry Why? τ θ k x ω Bor et al, Opt. Commun. 59, 229 (1985) Angular dispersion is fundamentally linked to delay gradient across a beam.

41 8-Channel Hyperfine Demux (~700 MHz linewidth, ~3 GHz channel spacing, 50 GHz FSR) Cylindrical Lenses VIPA Cylindrical Lens Collimator (input) Receiving Fiber Array (output) VIPA spectral disperser (Parts donated by ) Xiao and Weiner, IEEE PTL 17, 372 (2005)

42 Programmable Hyperfine Resolution VIPA Pulse Shaper Tunable Dispersion Compensation at 10 Gb/s over 240 km SMF A.M. Weiner, U.S. patent 6,879,426 Circulator Collimator λ 1 λ n B2B ( ) τω= CYL ψ( ω) ω VIPA CYL SLM + Mirror Apply quadratic phase 20 km, 40 km SMF 240km uncompensated Compensated (shaper only, no DCF) G.-H. Lee, S. Xiao, and A.M. Weiner, OFC 2006 (paper OTHE5); IEEE PTL 18, 1819 (2006)

43 PMD Compensation with VIPA Pulse Shaper Pulse widths compatible with 40 Gb/s systems Optical Pulses PC 15 ps nm 50 MHz Polarimeter Photo Detector & Sampling Scope FLC FLC Cylindrical Lens PMD ~42 ps mean DGD Collimator 200 GHz VIPA Lens Flipper Mirror LCM 4-layer LCM 1.6 GHz/pixel 13.8 db insertion loss Jones matrix sensing and compensation, as before, but scaled to finer spectral resolution and larger time aperture H. Miao, et al, OFC 2008 (OThG2)

44 Compensation Results Continues to work while input polarization is switching (enables continuous, real-time sensing) Initial pulse, FLC stable PMD distorted pulse FLC switching at 20 Hz PMD distorted pulse FLC switching at 2 khz Restored pulse FLC switching at 2 khz H. Miao, et al, OFC 2008 (OThG2)

45 Wavelength-Parallel Polarimetry Requirement to sense frequency-dependent polarization data in milliseconds! A.M. Weiner and X. Wang, U.S. patent 7,116,419

46 Current Practice: Single-Channel Polarimetry Example: serial configuration adjustable wave-plates detector source fixed polarizer To achieve frequency (wavelength) resolution: Multiple polarimeters (expensive) or Frequency-swept measurements (slow)

47 Fast Wavelength-Parallel Polarization Sensor Broadband optical source Fast switching FLC retarders Polarizer (fixed) Spectral disperser (grating/lens) InGasAs detector array FLC controller and data processing State 1 State 2 State 1 State 2 Configured for: 256 channels 0.4 nm (50 GHz) spacing < 3 polarization error < 1 ms read-out time Wang et al, Opt. Lett. 29, 923 (2004); JLT 24, 3982 (2006)

48 High Resolution Spectral Polarimeter Now able to resolve polarization variations within 10 Gb/s channel ~1GHz / pixel spacing ~1GHz 3dB resolution <1 ms read-out time < 3 polarization error WDM channel 0 polarizer FLC switching λ/4 retarder pair 50 GHz VIPA lens InGaAs linescan camera SOP string spectral SOP points Laboratory tests showing tight correlation between SOP string length and PMDinduced power penalty Live 10 Gb/s traffic in AT&T central office 10 GHz Wang, Weiner, Boroditsky and Brodsky, IEEE PTL 18, 1753 (2006); Wang, Weiner, Foo, Bownass, Moyer, O Sullivan, Birk, and Borodistsky, JLT 24, 4120 (2006)

49 2D Fast Wavelength Parallel Polarization Sensor Application to PMD sensing and compensation Multiple λ s in single instrument! 2D wavelength demux VIPA direction 50 GHz Grating dispersion direction High resolution 2D configuration: 32.8 nm span 1500 channels 2.8 GHz channel spacing (<20 db crosstalk) 5 ms read-out time (potential) 1520 nm nm Wang, Xiao, and Weiner, Opt. Express 13, 2005

50 All-Order PMD Emulation (Generation)

51 Traditional PMD Emulators L. Yan, et. al., JLT, vol. 24, , 2006 A new approach Spectral Processor PMD pulse shaper Wang et al, IEEE PTL 19, 1203 (2007); Opt. Express 15, 2127 (2007); Miao et al, IEEE PTL, in press.

52 All-Order Emulation Experimental Setup Generate 0 linear and RHC input SOP for PMD sensing For SOP Sensing 4-layer LCM programmed according to target PMD (Jones matrix) profile Müller Matrix Method (MMM) is used for PMD characterization Miao et al, IEEE PTL, in press.

53 All-Order Emulation Experimental Results Simple case: emulation of two concatenated fibers PSP target All-order example: programmed according to computer generated target with 5 ps mean DGD data target data DGD Miao et al, IEEE PTL, in press

54 Independently programmable multi-channel DGD emulation - Hyperfine resolution VIPA shaper - Accommodates 4 WDM channels at 50 GHz spacing - High-order DGD with fixed PSP (this example) Broadband source Fast scope ( 12dB) f=75mm cylindrical lens 200 GHz VIPA f=500mm achromatic 2-layer lens 128-element LCM + mirror Frequency dependent DGD profiles CH1 CH2 CH3 CH4 Wang et al, IEEE PTL 19, 1203 (2007); Opt. Express 15, 2127 (2007)

55 Summary Optical spectral processing applied to all-order PMD First reported all-order PMD compensation experiment (sub-ps pulses) Wavelength-parallel polarization sensor (parallel sensing at under 1 ms) All-order PMD generation Extension towards DWDM compatible implementations Future challenges, questions, opportunities Systems tests Endless all-order compensation Elucidation of compensation limits, outage probabilities 2D spectral disperser geometry with potential for compensation/ sensing/emulation of multiple DWDM channels within a single box H. Miao M. Akbulut X. Wang Li Xu Purdue Thanks to D.E. Leaird G.-H. Lee S. Xiao Z. Jiang P. Miller and L. Mirkin (CRI) M. Boroditsky and M. Brodsky (AT&T) C.Lin (Avanex) M. Fejer (Stanford)