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 …

• ver 10 Orders of Magnitude!

Voice, kb/s modems <5 kHz MHz Cable & Wireless >50 THz Optical Fiber Intra-channel (e.g. per-channel) Inter-channel (e.g. mux/demux) Per channel rate limits:

• electronics
• mux/demux
• impairments

Wavelength Division Multiplexing (WDM) GHz

Filter Applications in Optical Fiber Systems

Fiber Amplifier

Multiplexer Multiplexer Demultiplexer Demultiplexer

100’s channels

Rx Add/Drop A/D

Tx

1000’s km

1530 1560

dBm

Gain Equalizer

2.5→10→40 Gb/s→160

τ(λ)

Dispersion Compensator

Wavelength-Agile Optical Networks

λ-Router λ-Router λ-Router λ-Router λ-Router λ-Router

Tunable Optical Bandwidth Processing!

Digital Filters ⇔ Optical Filters Interference

Split → Delay → Weight → Combine

Splitter Combiner Directional Couplers ∆L + z-1 a1 X(z) Y(z) Γ + z-1 b0 b1 Y(z) X(z) partial reflectors

z−1

a unit delay Z transform

e z

j L − −

⇒

β 1

~

A Simple Splitter

1

X

2

X

1

Y

2

Y

θ=κcLc

( )

θ cos

( )

θ sin j −

where

Directional Coupler

Y Y j j X X

1 2 1 2

L N M O Q P =

− −

L N M O Q PL N M O Q P

cos sin sin cos θ θ θ θ

b g b g b g b g

Coherent Interference Field transmission coefficients.

Mach-Zehnder Interferometer

Feed-forward interference ⇒ single-stage FIR

normalized frequency

∆L φ

H j c s z s c

x = −

+

− 1 2 1 1 2

c h

H c c z s s

− −

= −

1 2 1 1 2

FSR c n L

g

= ∆

path length difference

Free Spectral Range All-zero transfer functions

Single-stage Optical IIR Filters

Fabry-Perot etalon Ring resonator

partial reflectors

R=L/2π

normalized frequency

Unit Delay

c L n T

g

/ = T FSR / 1 =

Free Spectral Range

Optical Allpass Filters Optical Allpass Filters

Gires-Tournois Interferometer Ring Resonator

c L n T

g

/ =

Unit Delay

φ

L=2πR

R

− j κ

−j k

ρ = − 1 k

ρ1 1 < ρ0 1 ≅

L / 2

T FSR / 1 =

Free Spectral Range

For a lossless filter, magnitude response = 1 (allpass!)

Phase and Group Delay Response Phase and Group Delay Response

−j k

ρ = − 1 k

2 g n

d T D c D d τ λ λ   = = −    

Scaling: physical Scaling: physical

Dispersion

Dispersion via Taylor Series Expansion

Delay

g

d d τ Φ ≡− Ω

Dispersion (ps/nm)

g

d D d τ λ ≡

Quadratic dispersion

β β β β β Ω ∆Ω Ω ∆Ω ∆Ω ∆Ω

c c

+ ≈ + ′ + ′′ + ′′′ +

b g b g

1 2 1 3

2 3

! !

• Φ = −βL

Phase Cubic dispersion

Bandwidth Utilization in WDM Systems

filter response

Power

40% 10% 80% spectral efficiency Signal bandwidth Channel spacing

Frequency Typical: 50 or 100 GHz grid

Hi Spectral Efficiency → Challenging Filters

Single → Multi-stage Filter Architectures 2x2 FIR Lattice Filter

∆L φ ∆L φ

Jinguji, JLT (1995)

Generalized Mach-Zehnder (optical phased array)

1xN NxN

Arrayed Waveguide Grating (AWG)

• G. Lenz
• G. Lenz

Ideally Dispersion-free!

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

κ 0t κ 1t κ 1r φ 1t φ 1r κ 2t κ 2r φ 2t φ 2r κ 3t κ 3r φ 3t φ 3r κ 4t κ 4r φ 4t φ 4r

Arbitrary pole & zero locations

• Jinguji, JLT, p. 1882, 1996

Simplified pole/zero filter

• Madsen, PTL, 1998

κ=0.5 κ=0.5

κ 1 κ 2 κ 3

κ 1

κ 2 κ 3

φ 1

*

φ 2

*

φ 3

*

φ 1 φ 2 φ 3

Use allpass filter decomposition to realize optimal bandpass designs 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/Loss Gain is free

• Gain - expensive and adds noise
• Loss changes filter response

Coefficient sensitivity quantization errors

• Fabrication variations
• Wavelength, polarization,

temperature, aging Real vs. complex coefficients use real coefficients to avoid complex computations complex coefficients are easily realized

Allpass Filter Magnitude Response Allpass Filter Magnitude Response

• For a lossless filter, magnitude response = 1 (allpass!)
• With loss, magnitude response depends on ρ

ρ κ = − 1

X

κ

Y

φ

L=2πR

R

1 1 − − →

z z γ

H z z z

b g =

− −

− −

ρ γ ρ γ

1 1

1

Lucent Technologies

Bell Labs Innovations

Silica Planar Waveguides 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

• ptical 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

Si substrate lower cladding upper cladding heater core

Cross-Section and Definitions

clad core clad core

2 n n n n + − ≡ ∆

Substrate Waveguide core Waveguide Phase shifter Cladding

Mach-Zehnder interferometer

Vary phase in one arm relative to the other

• M. Earnshaw
• M. Earnshaw

Variable coupler Variable attenuator 1x2 and 2x2 switch

Planar Waveguide Design: Bend Radius

κr φr

Phase Shifter

R

FSR c n L

g

=

LC

• Large FSR ⇒ Large ∆!
• Precise coupling ratios
• Fiber-waveguide

coupling loss↑

• thermal

crosstalk↑ FSR (GHz) L (mm) 8 25 12.5 16 25 8 50 4 100 2

L R LC = + 2 2 π

Micro-ring Resonator Filters

SEM of Gap 5th Order Tunable 5th Order µring filter Little, OFC’03

Higher Order Filters

Common Material Systems for Integrated Optics

InP InP InGaAsP SiO2 P:SiO2

, ...

Waveguide mode

Index of refraction @ 1550 nm Loss (dB/cm) @ 1550 nm Typical waveguide cross section 1.45 0.02 Silica (SiO2)

Si

Indium phosphide (InP) Lithium niobate (LiNbO3) Silicon-on-insulator (SOI) 3.2 2.3 3.5

SiO2 Si

0.2, 2

,

Ti:LiNbO3

0.5

LiNbO3

0.1

Si

1.5 0.1 Polymer

Polymer Si

• C. Doerr
• C. Doerr

Common phase shifters

Mechanism

Chrome

• Temp. dependence of

refractive index

Silica (SiO2)

Thermooptic Forward bias: Carrier density change Reverse bias: Carrier density change & Pockels

n n p i

Polyimide Gold

Indium phosphide (InP)

Electrooptic

,

Gold

Lithium niobate (LiNbO3)

Pockels Electrooptic

Silicon (Si)

Current Injection

• C. Doerr
• C. Doerr

Chromatic Dispersion Tolerance

100 km 1700 ps/nm 50 km 850 ps/nm 0 km 0 ps/nm 10Gb/s NRZ Eye Diagram

inter-symbol interference (ISI)

tolerance scales as 1/(bitrate)^2

Example: ~1dB system penalty 10 Gb/s D=±800 ps/nm 40 Gb/s D=±50 ps/nm! 160 Gb/s D=±3 ps/nm!!!

⇒ Tunable dispersion

compensation

Fiber +17 ps/nm/km

Test Drive … Tunable Dispersion Compensators

Periodic Delay Constant Dispersion Across Passband

80GHz 100GHz

key for λ-agile networks! (per channel, any channel)

Multi-Stage Group Delay

In Out

φ1

κ 1

φΝ

κ N

...

Phase Shifter

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

In κr Out φr

Basic Design

Phase Shifter

R

Symmetric MZI Asymmetric MZI

Phase Shifter

Tunable Design

φ m φ m φ r φ r r

κ ρ − = 1

ρ φ ρ

ϕ m j

e

b g =

ρ φ λ ρ λ

ϕ λ m j

e ,

b g a f

a f

=

Tunable Ring Dispersion Compensators

Tunable Allpass Designs

Phase Shifter

Dispersion Slope

κ κ

φr φm κ

κ

φr φm

Constant Dispersion

Tunable constant dispersion or dispersion slope compensators Tunable constant dispersion or dispersion slope compensators Fabrication tolerances greatly reduced (insensitive to coupling ratios) Fabrication tolerances greatly reduced (insensitive to coupling ratios)

Madsen, et al, IPR’99

40Gb/s Compensator* with 280 ps/nm Tuning

Madsen, et al, OFC’02 PD

Fiber=+100 TDC=0 Fiber=+100 TDC=-115 NRZ back-to-back

Passband=60 GHz FSR=75 GHz N=4, BWU=80%

Back-to-back TDC=0 ps/nm TDC=+100 ps/nm TDC=-100 ps/nm

CSRZ *with 50 GHz bandlimiting filter

A more difficult test drive … Polarization Mode Dispersion (PMD)

Fibers & components are birefringent & randomly oriented

...

∆τ1 ∆τ2

Coupled, frequency-dependent time-varying phase & amplitude responses!

( ) ( ) ( ) ( )

              − =        

in y in x

• ut

y

• ut

x

E E u v v u E E ω ω ω ω

* *

Electronic or Optical PMD Compensation? Electronic – update at bitrate! Optical – update at channel fluctuation rate! – “best” compensation (pre-||2 detection)

Integrated Polarization Control & Filter Architecture

Polarization Beam Splitter Polarization Control and 2x2 filtering

Xout Yout

PBS

90°

PBS Φ0

Xin

PBS

Yin

PBS filtering

Polarization beam combiner Polarization rotator

PC & 2x2

Mode Router 1 pol-mode 2 paths coherent interference 2 pol-modes 1 path

⇒ ⇒

Basic Architecture: Ozeki, OFC’91

Planar Lightwave Circuit Polarization Control

( )

1 cos sin 1 sin 1 cos 2 j j j j α α α α α − −   =   − +   QWP

QWP-HWP-QWP

Φ θ π ≈ 4 ϕ s / 2 ϕ s / 2 90°

PBS

PBS

Poincare Sphere

Heisman, JLT’94 Madsen et al, April JLT’04

All-order Compensation with APFs

APF1x APF1y

κ

APF2x APF2y

κ

N1 stages N2 stages “Worst Cases” from N=1000 cases with PMD=18 ps (mean) FSR=100 GHz Passband=50 GHz #APFs=[4 2 4] channel estimation: [-25:5:25] GHz

Equivalent to 40 taps x 40 GHz 1600 MACs! (per channel)

Madsen & Oswald, Optics Letters ‘03

Optical Filter Toolbox

Ring resonator/Fabry-Perot Infinite impulse response Mach-Zehnder Finite impulse response

R=L/2π

( )

1 D z

( ) ( )

N z D z

∆L

( )

N z

Allpass Filter (APF) Phase response design MZI+Allpass Filter APF Decomposition

κ=0.5 κ=0.5

κ1 κ2 κ3

κ1

κ2 κ3

( ) ( )

1 2

A z A z ±

( )

polynomial in z N z =

φ

κ

( ) ( )

*

D z D z

Multi-Stage/Port ⇒ Amplitude, Phase & Polarization!

Integrated Circuits

“People were able to visualize and design systems that if realized with the prevailing technology would be too big, too heavy, consume too much power and simply get too hot to work … unrealiable and unaffordable.” Jack Kilby (Nobel Laureate 2000)

λ-selective switch 2003

Integrated and Tunable!

3-rings 1996

Bandwidth Processing Engines

complex alg Baseband Digital Low to Hi-speed Decades! Optical difficult Octave(s) RF & Microwave Tunable or Adaptive Bandwidth Technology 10-100’s THz Sub- to 10’s GHz

Lots of potential!