Making A Many-Colored Processing Engine: Signal Processing with - PowerPoint PPT Presentation

Making A Many-Colored Processing Engine: Signal Processing with Optical Filters Christi K. Madsen Texas A&M University cmadsen@ee.tamu.edu Outline: • The Toolbox … Optical filter theory & architectures • The Engine … Practical implementations • The Road … High-bitrate System Applications

A Bandwidth Perspective … over 10 Orders of Magnitude! Voice, kb/s Intra-channel modems (e.g. per-channel) Cable & Wireless <5 kHz Inter-channel MHz (e.g. mux/demux) Wavelength Division Optical Multiplexing (WDM) GHz Fiber Per channel rate limits: • electronics >50 THz • mux/demux • impairments

Filter Applications in Optical Fiber Systems Gain Dispersion Add/Drop Equalizer Compensator Demultiplexer Demultiplexer Multiplexer Multiplexer τ(λ) A/D Amplifier Fiber dBm Tx Rx 1530 1560 2.5 → 10 → 40 Gb/s →160 100’s 1000’s km channels

Wavelength-Agile Optical Networks λ -Router λ -Router λ -Router λ -Router λ -Router λ -Router Tunable Optical Bandwidth Processing!

Interference ⇔ Digital Filters Optical Filters Split → Delay → Weight → Combine b 0 X(z) Y(z) Splitter Combiner ∆ L + z -1 b 1 Directional Couplers X(z) Y(z) + Γ z -1 a 1 partial reflectors a unit Z transform z − 1 ~ delay − β − ⇒ j L 1 e z

A Simple Splitter ( ) θ cos Directional Y Coupler X 1 1 θ=κ c L c where X Y 2 2 ( ) − θ j sin L O M O L b g b g PL M O θ − θ Y cos j sin X M P = P 1 1 b g b g N Q N Q N Q − θ θ Y j sin cos X 2 2 Coherent Interference Field transmission coefficients.

Mach-Zehnder Interferometer Feed-forward interference ⇒ single-stage FIR φ − = − All-zero 1 ∆ L H c c z s s − 1 2 1 2 transfer c h − x = − 1 + H j c s z s c functions 1 2 1 2 Free Spectral Range c = path length FSR ∆ difference n L g normalized frequency

Single-stage Optical IIR Filters Fabry-Perot etalon Ring resonator R=L/2 π partial reflectors Unit Delay = T n L / c g Free Spectral Range = FSR 1 / T normalized frequency

Optical Allpass Filters Optical Allpass Filters Ring Resonator Gires-Tournois Interferometer L=2 π R L / 2 φ R − j κ ρ 1 < ρ 0 ≅ 1 1 Free Spectral Range ρ = − 1 k Unit Delay = = FSR 1 / T − j k T n L / c g For a lossless filter, magnitude response = 1 (allpass!)

Phase and Group Delay Response Phase and Group Delay Response ρ = − 1 k − j k Scaling: physical Scaling: physical τ 2 d   T Dispersion = g = −  D c D  n λ λ d  

Dispersion via Taylor Series Expansion b g b g 1 1 β Ω + ∆Ω ≈ β Ω + β ′ ∆Ω + β ′′ ∆Ω + β ′′′ ∆Ω + 2 3 � c c 2 ! 3 ! Cubic Quadratic Delay Phase dispersion dispersion Φ d Φ = − β L τ ≡− Ω g d τ d Dispersion ≡ g D (ps/nm) λ d

Bandwidth Utilization in WDM Systems Channel spacing Signal bandwidth filter Power response 10% 40% 80% spectral efficiency Frequency Typical: 50 or 100 GHz grid Hi Spectral Efficiency → Challenging Filters

Single → Multi-stage Filter Architectures 2x2 FIR Lattice Filter φ φ ∆ L ∆ L Jinguji, JLT (1995) Generalized Mach-Zehnder (optical phased array) 1xN NxN

Arrayed Waveguide Grating (AWG) Ideally Dispersion-free! G. Lenz G. Lenz Vellekoop and Smit, JLT (1991) Takahashi, EL (1990) Dragone, PTL (1991)

IIR Multi-stage Filter Architectures Single-pole filter - Marcatili, BSTJ, p. 2103, 1969 Arbitrary pole locations - Orta, et al., PTL, p.1447, 1995 - Madsen & Zhao, JLT, p. 437, 1996 - Little, et al, JLT, p. 998, 1997 φ 1r φ 2r φ 3r φ 4r Arbitrary pole & zero locations κ 1r κ 2r κ 3r κ 4r κ 1t κ 2t κ 3t κ 4t κ 0t - Jinguji, JLT, p. 1882, 1996 φ 1t φ 2t φ 3t φ 4t φ 1 φ 2 φ 3 κ 1 κ 2 κ 3 Simplified pole/zero filter κ =0.5 κ =0.5 - Madsen, PTL, 1998 κ 2 κ 1 κ 3 Use allpass filter decomposition to realize optimal bandpass designs φ 2 φ 3 φ 1 * * * efficiently!

Multi-stage Filter Synthesis Design: Desired Frequency Response → Filter Parameters • Approximation problem (Taylor series, least squares, min-max) • Choose filter class, architecture, number of stages, FSR Bandpass filter cutoff=0.1

Building the engine … In theory, there is no difference between theory and practice. But, in practice, there is. -- Jan L.A. van de Snepscheut

Optical versus Digital filters Property Digital Filters Optical Filters • Gain - expensive and adds noise Gain/Loss Gain is free • Loss changes filter response • Fabrication variations Coefficient quantization • Wavelength, polarization, sensitivity errors temperature, aging use real Real vs. coefficients to complex coefficients complex avoid complex are easily realized coefficients computations

Allpass Filter Magnitude Response Allpass Filter Magnitude Response • For a lossless filter, magnitude response = 1 (allpass!) • With loss, magnitude response depends on ρ φ L=2 π R R κ X Y ρ = − κ 1 − → − γ 1 1 z z − b g = ρ − γ 1 z H z − ρ γ − 1 1 z

Silica Planar Waveguides Lucent Technologies Bell Labs Innovations Very low loss! Mature fabrication processes! – Large-volume manufacturable – Large-scale integration – Realize complex filter and switch architectures – Low-loss thermo-optic tuning for dynamic optical routing & adaptive processing – Excellent platform for hybrid integration Collaborators: M. Cappuzzo, E. Chen, L. Gomez, A. Griffin, E. Laskowski, and A. Wong-foy

Silica-on-Silicon Planar Waveguides

heater Cross-Section and upper cladding Definitions core lower cladding Si substrate Phase shifter Cladding Waveguide Waveguide core − n n ∆ ≡ core clad 2 + n n core clad Substrate

Mach-Zehnder interferometer Vary phase in one arm relative to the other Variable coupler Variable attenuator 1x2 and 2x2 switch M. Earnshaw M. Earnshaw

Planar Waveguide Design: Bend Radius Phase Shifter • Large FSR ⇒ Large ∆ ! c φ r = • Precise coupling ratios FSR n L R g κ r L C • Fiber-waveguide FSR L coupling loss ↑ (GHz) (mm) • thermal 8 25 crosstalk ↑ 12.5 16 25 8 50 4 100 2 = π + L 2 R 2 L C

Micro-ring Resonator Filters SEM of Gap Higher Order Filters Tunable 5 th Order µ ring filter 5 th Order Little, OFC’03

Common Material Systems for Integrated Optics Index of Typical waveguide Loss (dB/cm) refraction cross section @ 1550 nm @ 1550 nm P:SiO 2 SiO 2 1.45 0.02 Silica (SiO 2 ) Waveguide Si mode InP InGaAsP Indium phosphide (InP) 3.2 0.2, 2 InP , ... , Ti:LiNbO 3 2.3 0.5 LiNbO 3 Lithium niobate (LiNbO 3 ) Si 3.5 0.1 SiO 2 Silicon-on-insulator (SOI) Si 1.5 0.1 Polymer Polymer Si C. Doerr C. Doerr

Common phase shifters Mechanism Chrome Temp. dependence of Silica (SiO 2 ) refractive index Thermooptic Gold Forward bias: p Carrier density change Polyimide Indium phosphide (InP) i Reverse bias: Carrier density change Electrooptic n n , & Pockels Gold Lithium niobate (LiNbO 3 ) Pockels Electrooptic Silicon (Si) Current Injection C. Doerr C. Doerr

Chromatic Dispersion Tolerance 10Gb/s NRZ Eye Diagram inter-symbol interference (ISI) 0 km tolerance scales 0 ps/nm as 1/(bitrate)^2 Example: ~1dB system penalty 50 km 850 ps/nm 10 Gb/s D=±800 ps/nm 40 Gb/s D=±50 ps/nm! 160 Gb/s D=±3 ps/nm!!! 100 km 1700 ps/nm ⇒ Tunable dispersion compensation Fiber +17 ps/nm/km

Test Drive … Tunable Dispersion Compensators Periodic Delay Constant Dispersion Across Passband 100GHz 80GHz key for λ -agile networks! (per channel, any channel)

Multi-Stage Group Delay Phase φ 1 φ Ν Shifter κ 1 κ N In ... Out Nonlinear design optimization • bandwidth utilization • dispersion • group delay ripple Favors High Spectral Efficiency! Theoretically lossless Precisely tune two variables/stage Madsen & Lenz, PTL ‘98 US Patent 6289151

Tunable Allpass Filter Architecture Basic Design Phase Shifter φ r R ρ = 1 − κ r κ r In Out Tunable Design Asymmetric MZI Symmetric MZI φ m φ m φ r φ r Phase Shifter b g = a f b g a f ϕ ρ φ ρ ϕ λ j j ρ φ λ = ρ λ e , e m m

Tunable Ring Dispersion Compensators Tunable constant Tunable constant Tunable Allpass Designs Fabrication tolerances Fabrication tolerances φ m dispersion or dispersion or greatly reduced greatly reduced φ m Phase Shifter dispersion slope dispersion slope (insensitive to (insensitive to κ κ compensators compensators coupling ratios) coupling ratios) κ κ φ r φ r Dispersion Constant Dispersion Slope Madsen, et al, IPR’99

40Gb/s Compensator* with 280 ps/nm Tuning CSRZ Passband=60 GHz FSR=75 GHz N=4, BWU=80% Back-to-back NRZ back-to-back TDC=0 ps/nm Fiber=+100 TDC=0 TDC=+100 ps/nm Fiber=+100 TDC=-115 TDC=-100 ps/nm *with 50 GHz bandlimiting filter Madsen, et al, OFC’02 PD