Capabilities and Limitations of Slow Light Optical Buffers ... · Capabilities and. Limitations of Slow Light Optical Buffers: Searching for. the Killer Application. Rod Tucker. ARC

Capabilities andCapabilities and

Limitations of Limitations of Slow Light Optical Buffers:Slow Light Optical Buffers:

Searching forSearching for

the Killer Applicationthe Killer Application

Rod Tucker

ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN)Department of Electrical and Electronic Engineering

University of Melbourne, Australia

SummarySummary

•

Slow light and optical data-

Group velocity and data bit-size compression

•

Optical delay lines and buffers-

Signal bandwidth and information bandwidth-

FIFO buffers

•

Properties of an ideal slow light medium-

Delay-bandwidth product

•

Requirements of practical optical buffers-

Storage density-

Dispersion-

Attenuation

•

Busting some slow light myths

•

Data storage in high-Q resonators

Delay LineInput Output

Group VelocityGroup Velocity

x

gcv dnk n

d

ω

ωω

∂= =

∂ +Group velocity:

Optical frequency

Intrinsic attenuation:1 1

abs g abs

dnnv c d

α ωτ τ ω

⎛ ⎞= +⎜ ⎟⎝ ⎠

Waveguide loss (dB/cm) Absorption time (ns)

0.01 300.1 3

Time to attenuate by e-1

ω

Transfer Function

ωο

α(ω)

ω

n

Δω

Background

Kramers

Kronig

i.e. Hilbert transform

ωddn

becomes large

ElectromagneticallyElectromagnetically--Induced Transparency (EIT)Induced Transparency (EIT)

ω

n

FSR

avgn

Passband

pω

ωΔ

1−pω 2ω1ω

Micro-resonator Delay Line

Ideal SlowIdeal Slow--Light MaterialLight Material

Effective Index, n navg

ωωο

ω

Δω

0

nmin

ωmin ωmax

Bandwidth

0 dB

nmax

absτ →∞

ω

Signal Spectrum

Transfer Function

All-pass function

Signal Bandwidth and Data BandwidthSignal Bandwidth and Data BandwidthData “Bandwidth”

or Information Rate

(b/s)

Signal Bandwidth (Hz)

→ 0

t

t

t

t

~ 1/τ 1/Tbit

~ 1/τ

~ 1/

τ

~ 2/τ

τ

τ /2

τ

τ

Tbit

Tbit

1/Tbit

→ 0

1 1 11 1 11 1

1 0 01 1 11 1

Waveguide 1Input Output

Group Velocity Change at BoundaryGroup Velocity Change at Boundary

1

2

11

22

2

1(g

g

g

g

nn

ddnn

ddn

n

vv

S =+

+==)

ωω

ωω

ω

Waveguide 2

Slow-down factor:

1Index n= 2Index n=

Group indices

Group Velocity and Bit LengthGroup Velocity and Bit Length

x

Information Bandwidth

Bit Period

LinBit Length

= Period x Velocity x

x

Group Velocity

x

Regular Waveguide Slow Light Waveguide

Fieldx

inL bitL

Reduced Group Velocity Constant Bitrate

Car Analogy

Slow Light World

Lbit

Real World

100 km/h 20 km/h20100

x

vg

x

Fiel

dvg1

vg2

Region 1 Region 2Transition Region

Δvg

xA1 xA2

Lb (x)

Tapered Transition RegionTapered Transition Region

Circuit Switching and Packet SwitchingCircuit Switching and Packet Switching

Circuit-Switched Network Packet-Switched Network

Freeway Model

Car:

Packet

Lane:

Wavelength

Waveband Fiber

Interchange: Router

Freeway:

Statistical Multiplexing in BufferStatistical Multiplexing in Buffer

Buffer

Outgoing packets

Incoming packets

Nick McKeown http://tiny-tera.stanford.edu/~nickm/

Storage time, TSHold-off time, THO

Packet length, tpacket

Bit period, Tbit

Buffer

Control

Data outData in

Optical Buffer

1packet

bit

BT

=

Packet Bit rate

packetinfo packet

HO

tB B

T= ⋅

Information rateMinimum time between incoming

packets

Optical Packet SwitchOptical Packet Switch

First-In-First-Out (FIFO)Single Input Single Output

123 123

Demux

Wavelength-

Interchanging Cross Connect

MuxInput

FibersOutput Fibers

Incoming Packets

Outgoing PacketsOutput

BuffersInput

Buffers

Optical Packet SwitchOptical Packet Switch

First-In-First-Out (FIFO)

Multiple InputsSingle Output

Output Buffers

Input Buffers

Output buffering: -

optimum contention resolution

-

more complicated than input buffering

1

2

3

123

Demux

Wavelength-

Interchanging Cross Connect

MuxInput

FibersOutput Fibers

Incoming Packets

Outgoing Packets

SingleSingle--Input SingleInput Single--Output FIFOOutput FIFO

C1 C3C2CM

M cascaded delay lines with controllable delays

Control signals

Input Output

0 X1 X2 X3

For acceptable performance , M > 20

XM

Stage 1 Stage 3Stage 2 Stage M

0

vg1

vg2

Po

x

x

xM

FIFO Buffer Using Controllable Delay LinesFIFO Buffer Using Controllable Delay Lines

Packet 1

Group Velocity

0 xM

vg1

vg2

Po4 3 2

x

x

Call to Read Packet 1

Packet 1


Group Velocity

HO packetT t=Note: ; info packetB B=

xNx

vg1

vg2

0

Po

x

xM

4 3 2Packet 1


Group Velocity


Po4 3 25

x

vg1

vg2

0

x

xMxN

Packet 1


Group Velocity

HO packetT t=Note: HO packetT t=Note: ; info packetB B=

Po4 3 25

x

vg1

vg2

0

x

xMxN+1

Packet 1


Group Velocity


Po

x

vg1

vg2

0

x

xM

25 4 36

xN+1

Packet 1


Group Velocity


x

Po25 4 36

0

vg1

vg2 xxM

Packet 1


Group Velocity


x

Po36 5 47

0

vg1

vg2 xxM

2


Group Velocity


MultipleMultiple--Input SingleInput Single--Output FIFOOutput FIFO

Switch

All FIFO’s

provide full delay

FIFO

FIFO

FIFO

FIFO

Control signals

Key issues:

• Delay line utilization (i.e. “void”

filling)

• Complexity of control

10 –

100 Inputs

200 –

10,000 Delay lines

x

vg

Gro

up V

eloc

ity P

rofil

e

Field

vg1

vg2

Input Region

Slow Light Region

Optical Pulses in Slow Light Delay LineOptical Pulses in Slow Light Delay Line

L

2/ gvLT =Delay

inL2 /bit g packetL v B=

/ bitC L L=Capacity

Output Region

info packetT B T B⋅ = ⋅

Delay-Bandwidth Product0

(WG1) (WG3)(WG2)

2/packet gL B v= ⋅

C=x

Max. Delay-Bandwidth Product Minimum Bit Size

0

min )(λ

nnL avg −)( min

0nnavg −

λabs

bit

L τατ⋅

Fundamental Limitations of Ideal Slow LightFundamental Limitations of Ideal Slow Light

navg

ωο

2πBpacket

0

nmin

ωmin ωmax

nmax

2gcv dnn

dω

ω

=+

n

Information bandwidth

Two Classes of Slow Light Delay LineTwo Classes of Slow Light Delay Line

Class A

- Group velocity profile does not change while data stored

- Data enters and leaves slow-light regions across discontinuities

- All previous examples

Class B

- Bandwidth of medium changed adiabatically with time

- Group velocity changes while data is stored

n

navg

ω

nmin

ωmax

))(()( dttsjoeEdttE ++=+ δωω

minmax

minmax0

)()(ωωωωωωδω

−−

−=d

s

ωο

oωmin

ω

Signal Spectrum

Characteristics of Class B Slow LightCharacteristics of Class B Slow Light

x

Class A and Class B Slow LightClass A and Class B Slow Light

Bit Period

LinBit Length

= Period x Velocityx

x

Group Velocity

x

Lin

t

t

A: “Conventional”

-

Slow-down in Space B: Adiabatic -

Slow-down in Time

t , x

t , x

Tucker et al., JLT, 23, 2005

Information Bandwidth

Car Analogy Car Analogy ––

Class B Slow LightClass B Slow Light“Conventional”

Slow Light

Adiabatically-Slowed

Dangerous Adiabatic Driving

20 km/h Speed Limit100 km/h Speed Limit

slow togetherslow together

Solution: Toll Plaza

(Bitrate

Reduced)

(Bitrate Unchanged)

t

vg

x

vg1

vg2

bitL

Interval 1Interval 2

Bandwidth

t

Bg1

Bg2

t1 t2 t4t3

t1 t2 t3 t4

Interval 4

Interval 3

Interval 5Fi

eld

Inte

nsity

Operation of Class B FIFO Delay LineOperation of Class B FIFO Delay Line

HO packetT t>Note: ; info packetB B<

bitL

x

vg

vg1

vg2Class A Class B Class A

x1 x2

t

vg

vg2

vg3

Increased Slow-Down Factor

Mixed Delay LinesMixed Delay Lines

• Increased tuning range (product of tuning ranges)

• Smaller bandwidth constriction in Class B section


Class A and Class B BuffersClass A and Class B Buffers

1:p p:1

Class B

Stage pStage 2Stage 1

“Traditional” (Class A): FIFO

Adiabatically Compressed (Class B): FIFO

Delay


Class B

Class B

Scaling

SizeEnergy/bit

Cap

acity

Capacity 2

p

Capacity 2

Control

The MythThe Myth--BustersBusters

Myth #1:

Class B Slow Light breaks through the limitation of the Delay-Bandwidth Product.

Myth #2:

Attenuation in slow light waveguides can always be overcome using optical gain.

Input Region Slow Light Region

Myth #1 BustedMyth #1 Busted

2/ gvLT =Delay

/ bitC L L=Capacity

2

1

ginfo packet

g

BT B T B

B⋅ = ⋅

Delay-Bandwidth Product

(WG1) (WG2)

1/packet gL B v= ⋅

C=

Same as in WG1

vg

vg1

vg2

Interval 1Interval 2

Ban

dwid

th Bg1

Bg2

t1 t2 t3

t1 t2 t3

Interval 3

t

x

.

Requirements of Practical Optical BuffersRequirements of Practical Optical Buffers

Advanced 100 Tb/s electronic router 1000 ports @100 Gb/s

250 ms buffering per port

Optical packet switch with 1000 ports, 250 ms buffering per port

using optical fibre delay lines

Total buffer capacity of 2.5

TB

~ 103

RAM chips

< US$ 50k in cost

< 1 kW power dissipation

Total fibre length = 40 Gm

150 times distance from Earth to Moon!

Packet Switching with Reduced BufferingPacket Switching with Reduced BufferingEnachescu

et al., ACM/SIGCOMM July 2005: Buffer size can be reduced

Buffering with fiber delay lines is a challenge

2 μs

buffering per port (200 kb/port) ~20 packets @ 100 Gb/s

Total fibre length = 400 km (~ 400 m/port)

Is Slow Light a Viable Alternative?Is Slow Light a Viable Alternative?

.

100 -Tb/s Optical Router (1000 ports @ 100 Gb/s)(Input) buffer size: 20 packets (200 kb, or 2 μs) per port → 200 Mb total

Fiber

400 m/port, 400 km total

Storage Density: 1 bit / 2 mm

“Practical” Slow Light Waveguide

Slow-down factor = 100 4 m / port, 4 km total

Storage Density: 1 bit / 20 μm

Ideal Slow Light Waveguide

200 cm/port, 200 m total

Storage Density: ~1 bit / μm

~wavelength

λ

Size MattersSize Matters

Minimum bit area ~ 5λ2

(λ

= ~1 μm)

150 Gbit/m2

∼5λ

1 bit

Ideal Slow Light Waveguide CMOS (2018)

80 nm1 cell

eDRAM

cell area 80 nm x 80 nm

150 Tbit/m2

1.3 mm2

13 cm2

13 cm2 200 Mbit

1.3 m2 200 Gbit

Capacity

Area

Storage Density per wavelength

Size MattersSize Matters


(λ

= ~1 μm)

150 Gbit/m2

∼5λ

1 bit

Ideal Slow Light Waveguide CMOS (2018)

80 nm1 cell

eDRAM

cell area 80 nm x 80 nm

150 Tbit/m2

1.3 mm2

13 cm2

13 cm2 200 Mbit

1.3 m2 200 Gbit

Capacity

Area

Storage Density per wavelength


(λ

= ~1 μm)

15 Gbit/m2

10λ

“Practical” Slow Light Waveguide

130 cm2

13 m2

Loss HappensLoss Happens

Fibre: ~0.2 dB/km

In Out

15 km for 3-dB loss

“Low loss”

Planar WG: 0.01 dB/cm

InOut

3 cm for 3-dB loss

20 packets (2 μs) ~0.1 dB

e-1

absorption time ~ 100

μs

In

e-1

absorption time ~ 20

ns

20 packets (2 μs) 400 dB

0.0001 dB/cm (10 dB/km) 4 dB


Myth #1:


Myth #2:


Overcoming Attenuation with Optical GainOvercoming Attenuation with Optical Gain

Signal

Stage 1

g g

Stage m

β β

Slow light waveguide

Waveguide dispersion

compensation

Waveguide loss compensation

SignalPsat

Noise

Two key limitations:

• Output SNR

•

Amplifier Saturation Power (Psat)

Attenuation α α

L

NoiseC1 C1

Tucker, JLT, 24, 2006

Noise and PowerNoise and Power--Limited Buffer CapacityLimited Buffer Capacity

For 20 packets, require

Loss < 0.005 dB/cm


Amplifier saturation power, Psat

100 mW10 mW1 mW100 μW10 μW1 μW

Cap

acity

, (b)

1

100

10 k

1 M

100 M

Slow Light, Planar WG

Fiber + crosspoints

0.005 dB/cm

0.5 dB/cm

Buffer Size Requirements

20 Packets

40 Gb/s

100 (Gb/s)(dB/cm)bit

BN

α=

DispersionDispersion--Limited Buffer CapacityLimited Buffer Capacity


EIT

EIT

Nbit

= 10 k

Nbit

= 100

Slow-down factor = 1

Dispersion limits

Bit Rate (b/s)100 k 1 M 10 M 100 M 1 G 10 G 100 G 1 T

10-4

10-2

1

102

104

Buf

fer L

engt

h, L

(m)

Ideal

Ideal

CRW

CRW

Khurgin, J. Opt. Soc. Am. B, May 2005,

Amplitude limits

Length of Stored Bit Versus CapacityLength of Stored Bit Versus Capacity

Delay Line Capacity

(b)

Leng

th o

f Sto

red

bit

1 μm

1 10 100 1 k 10 k

10 μm

100 μm

1 mm

10 mm

Minimum (Ideal)

Maximum (Slow-down factor = 1) and fiber

Coupled Resonator dispersion limit

EIT dispersion limit

EIT amplitude limit

40 Gb/s

100 k

0.5 dB/cm

0.005 dB/cm

Psat

= 10 mW

20 Packets


τc

KInput Output

Ring Resonator Memory CellRing Resonator Memory Cell

Adjustable coupling coefficient

Crosspoint

• Asano and Noda, Topical Meeting on Slow and Fast Light, 2006.• Guo et al., LEOS Annual Meeting, 2004.• Savchenkov et al., LEOS Summer Topical Meeting, 2004.

Resonator RAMResonator RAM

bτ

bτ

bτbτ

bτ

bτ

Word Lines

Bit Lines

Row Decoder

Input

Output

Tucker, PTL, 2008

Cou

plin

g C

oeffi

cien

t K

0.0001

0.001

0.01

0.1

1.0

TimeStoreWrite Read

ER

storeK

writeK readK

Coupling CoefficientCoupling Coefficient

Input Pulse Output Pulse

τ

K

Retention TimeRetention Time

Nor

mal

ized

Am

plitu

de1.0

0.2

0

0.6

0.8

0.4

Time (ns)0 1.00.80.60.40.2

Input 5-ps pulse

Retention Time ~ 800 ps

Cavity Q = 2x106

Output Pulses

Simulation (VPI)

KstoreWaveguide power loss

Switch coupling coefficient

α

(dB/cm)Switch

Extinction(L = 100 μm)

Qstore Retention Time

0.01 > 40 dB 5x106 2 ns (0.02 packets)

0.0001 > 70 dB 5x109 2 μs (20 packets)

)/(2

LKn

Qstore

gstore +

=αλ

π

Resonator RAMResonator RAM

o

storef

Qπ2

= =+

=)/(

1LKv storeg α

Retention Time Absorption Time

Cavity length

α


Myth #1:


Myth #2:


Myth #3:

High Q resonators can break through the limitation of the Delay-Bandwidth Product.

Maximum delay = Retention time

Information rate (bandwidth) = 1/Retention time

Delay bandwidth product =1

Show stopper

Comparing Technologies for Packet BufferingComparing Technologies for Packet Buffering

Challenging

Technology Fiber Planar, Slow Light Resonator Holographic CMOS-

O/E/O

Access Time

Structure-

dependent

Structure-

dependent Small ~ 50 μs 200 ps

Retention Time > 500 μs < 5 μs 1-100 ns ∞ > 50 ms

Capacity (Packets) > 2,000 < 20 << 1 ∞ ∞Energy/bit ~ 1 fJ ~ 1 pJ ~ 1 pJ ~ 1 pJ ~ 1 fJ

Physical Size Very Large Medium Medium Small Very

Small

Chirp Sensitivity No Small Large Large No

• Limitations and capabilities of slow light buffers

- Dispersion and attenuation

- Delay bandwidth product (treat with care)

- Storage density

• Requirements of practical optical buffers

- Capacity limited to a few thousand bits, at best

- Very low loss waveguides required

ConclusionsConclusions

• There are no free lunches

Documents

Capabilities and Limitations of Slow Light Optical Buffers ... · Capabilities and. Limitations of Slow Light Optical Buffers: Searching for. the Killer Application. Rod Tucker. ARC