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Capabilities and Capabilities and Limitations of Limitations of Slow Light Optical Buffers: Slow Light Optical Buffers: Searching for Searching for the Killer Application the Killer Application

Rod Tucker

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

Summary Summary

• 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 Line Input Output

Group Velocity Group Velocity

x

g

c v dn k n d ω ω ω ∂ = = ∂ +

Group velocity:

Optical frequency

Intrinsic attenuation:

1 1

abs g abs

dn n v c d α ω τ τ ω ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠

• Waveguide loss (dB/cm)

Absorption time (ns) 0.01 30 0.1 3

Time to attenuate by e-1

ω Transfer Function ωο α(ω) ω

n

Δω Background

Kramers Kronig i.e. Hilbert transform

ω d dn

becomes large

Electromagnetically Electromagnetically-

• Induced Transparency (EIT)

Induced Transparency (EIT)

ω

n

FSR

avg

n

Passband

p

ω

ω Δ

1 − p

ω

2

ω

1

ω

Micro-resonator Delay Line

Ideal Slow Ideal Slow-

• Light Material

Light Material

Effective Index, n navg ω ωο ω Δω nmin ωmin ωmax Bandwidth 0 dB nmax

abs

τ → ∞

ω Signal Spectrum Transfer Function All-pass function

Signal Bandwidth and Data Bandwidth Signal Bandwidth and Data Bandwidth

Data “Bandwidth”

• r 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 1 1 1 1 1 1 1 1 1 1 1 1

Waveguide 1 Input Output

Group Velocity Change at Boundary Group Velocity Change at Boundary

1 2 1 1 2 2 2 1

(

g g g g

n n d dn n d dn n v v S = + + = = ) ω ω ω ω ω

Waveguide 2 Slow-down factor:

1

Index n =

2

Index n =

Group indices

Group Velocity and Bit Length Group Velocity and Bit Length

x Information Bandwidth Bit Period Lin Bit Length = Period x Velocity x x Group Velocity x

Regular Waveguide Slow Light Waveguide

Field x

in

L

bit

L

Reduced Group Velocity Constant Bitrate

Car Analogy

Slow Light World

Lbit

Real World 100 km/h 20 km/h

20 100

x vg x

Field

vg1 vg2 Region 1 Region 2 Transition Region Δvg xA1 xA2 Lb (x)

Tapered Transition Region Tapered Transition Region

Circuit Switching and Packet Switching Circuit Switching and Packet Switching

Circuit-Switched Network Packet-Switched Network Freeway Model

Car: Packet Lane: Wavelength Waveband Fiber Interchange: Router Freeway:

Statistical Multiplexing in Buffer Statistical Multiplexing in Buffer

Buffer Outgoing packets Incoming packets

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

Storage time, TS Hold-off time, THO Packet length, tpacket Bit period, Tbit Buffer Control Data out Data in

Optical Buffer

1

packet bit

B T =

Packet Bit rate

packet info packet HO

t B B T = ⋅

Information rate

Minimum time between incoming packets

Optical Packet Switch Optical Packet Switch

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

1 2 3 1 2 3

Demux Wavelength- Interchanging Cross Connect Mux Input Fibers Output Fibers Incoming Packets Outgoing Packets Output Buffers Input Buffers

Optical Packet Switch Optical Packet Switch

First-In-First-Out (FIFO) Multiple Inputs Single Output Output Buffers Input Buffers

Output buffering: -

• ptimum contention resolution
• more complicated than input buffering

1 2 3 1 2 3

Demux Wavelength- Interchanging Cross Connect Mux Input Fibers Output Fibers Incoming Packets Outgoing Packets

Single Single-

• Input Single

Input Single-

• Output FIFO

Output FIFO

C1 C3 C2 CM

M cascaded delay lines with controllable delays Control signals Input Output

X1 X2 X3

For acceptable performance , M > 20

XM

Stage 1 Stage 3 Stage 2 Stage M

vg1 vg2 Po x x xM

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines

Packet 1

Group Velocity

xM vg1 vg2 Po 4 3 2 x x

Call to Read Packet 1

Packet 1

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines

Group Velocity

HO packet

T t =

Note: ;

info packet

B B =

xN x vg1 vg2 Po x xM 4 3 2 Packet 1

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines

Group Velocity

HO packet

T t =

Note: ;

info packet

B B =

Po 4 3 2 5 x vg1 vg2 x xM xN Packet 1

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines

Group Velocity

HO packet

T t =

Note:

HO packet

T t =

Note: ;

info packet

B B =

Po 4 3 2 5 x vg1 vg2 x xM xN+1 Packet 1

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines

Group Velocity

HO packet

T t =

Note: ;

info packet

B B =

Po x vg1 vg2 x xM 2 5 4 3 6 xN+1 Packet 1

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines

Group Velocity

HO packet

T t =

Note: ;

info packet

B B =

x Po 2 5 4 3 6 vg1 vg2 x xM Packet 1

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines

Group Velocity

HO packet

T t =

Note: ;

info packet

B B =

x Po 3 6 5 4 7 vg1 vg2 x xM 2

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines

Group Velocity

HO packet

T t =

Note: ;

info packet

B B =

Multiple Multiple-

• Input Single

Input Single-

• Output FIFO

Output 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 Group Velocity Profile Field vg1 vg2 Input Region Slow Light Region

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

L

2

/ g v L T =

Delay

in

L

2 / bit g packet

L v B =

/

bit

C L L =

Capacity Output Region

info packet

T B T B ⋅ = ⋅

Delay-Bandwidth Product

(WG1) (WG3) (WG2)

2

/

packet g

L B v = ⋅ C =

x

• Max. Delay-Bandwidth Product

Minimum Bit Size min )

( λ n n L

avg −

) (

min

n navg − λ

abs bit

L τ α τ ⋅

Fundamental Limitations of Ideal Slow Light Fundamental Limitations of Ideal Slow Light

navg ωο 2πBpacket nmin ωmin ωmax nmax

2 g

c v dn n d ω ω = +

n

Information bandwidth

Two Classes of Slow Light Delay Line Two 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

) )( (

) (

dt t s j

• e

E dt t E

+ +

= +

δω ω

min max min max

) ( ) ( ω ω ω ω ω ω δω − − − = d

s

ωο

• ωmin

ω Signal Spectrum

Characteristics of Class B Slow Light Characteristics of Class B Slow Light

x

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

Bit Period Lin Bit Length = Period x Velocity x 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 Light Class B Slow Light

“Conventional” Slow Light Adiabatically-Slowed Dangerous Adiabatic Driving

20 km/h Speed Limit 100 km/h Speed Limit

slow together slow together Solution: Toll Plaza (Bitrate Reduced) (Bitrate Unchanged)

t vg x vg1 vg2

bit

L Interval 1 Interval 2

Bandwidth t Bg1 Bg2 t1 t2 t4 t3 t1 t2 t3 t4

Interval 4 Interval 3 Interval 5

Field Intensity

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

HO packet

T t >

Note: ;

info packet

B B <

bit

L

x vg vg1 vg2 Class A Class B Class A x1 x2 t vg vg2 vg3

Increased Slow-Down Factor

Mixed Delay Lines Mixed Delay Lines

• Increased tuning range (product of tuning ranges)
• Smaller bandwidth constriction in Class B section

Tucker et al., JLT, 23, 2005

Class A and Class B Buffers Class A and Class B Buffers

1:p p:1

Class B Stage p Stage 2 Stage 1

“Traditional” (Class A): FIFO Adiabatically Compressed (Class B): FIFO Delay

Tucker et al., JLT, 23, 2005

Class B Class B

Scaling Size Energy/bit Capacity Capacity 2 p Capacity 2

Control

The Myth The Myth-

• Busters

Busters

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

• vercome using optical gain.

Input Region Slow Light Region

Myth #1 Busted Myth #1 Busted

2

/ g v L T =

Delay

/

bit

C L L =

Capacity

2 1 g info packet g

B T B T B B ⋅ = ⋅

Delay-Bandwidth Product

(WG1) (WG2)

1

/

packet g

L B v = ⋅ C =

Same as in WG1 vg vg1 vg2

Interval 1 Interval 2

Bandwidth Bg1 Bg2 t1 t2 t3 t1 t2 t3

Interval 3

t x

.

Requirements of Practical Optical Buffers Requirements 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 Buffering Packet Switching with Reduced Buffering

Enachescu 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 Matters Size Matters

Minimum bit area ~ 5λ2 (λ

= ~1 μm)

150 Gbit/m2

∼5λ

1 bit

Ideal Slow Light Waveguide CMOS (2018)

80 nm

1 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 Matters Size Matters

Minimum bit area ~ 5λ2 (λ

= ~1 μm)

150 Gbit/m2

∼5λ

1 bit

Ideal Slow Light Waveguide CMOS (2018)

80 nm

1 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 Minimum bit area ~ 50λ2 (λ

= ~1 μm)

15 Gbit/m2 10λ “Practical” Slow Light Waveguide 130 cm2 13 m2

Loss Happens Loss Happens

Fibre: ~0.2 dB/km In Out 15 km for 3-dB loss “Low loss” Planar WG: 0.01 dB/cm In Out 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

The Myth The Myth-

• Busters

Busters

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

• vercome using optical gain.

Overcoming Attenuation with Optical Gain Overcoming Attenuation with Optical Gain

Signal Stage 1 g g Stage m β β Slow light waveguide Waveguide dispersion compensation Waveguide loss compensation Signal

Psat

Noise

Two key limitations:

• Output SNR
• Amplifier

Saturation Power (Psat) Attenuation α α

L

Noise C1 C1

Tucker, JLT, 24, 2006

Noise and Power Noise and Power-

• Limited Buffer Capacity

Limited Buffer Capacity

For 20 packets, require Loss < 0.005 dB/cm

Tucker, JLT, 24, 2006

Amplifier saturation power, Psat

100 mW 10 mW 1 mW 100 μW 10 μW 1 μW

Capacity, (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

B N α =

Dispersion Dispersion-

• Limited Buffer Capacity

Limited Buffer Capacity

Tucker, JLT, 24, 2006

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

Buffer Length, L (m)

Ideal Ideal CRW CRW

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

Amplitude limits

Length of Stored Bit Versus Capacity Length of Stored Bit Versus Capacity

Delay Line Capacity (b) Length of Stored 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

Tucker, JLT, 24, 2006

τc

K

Input Output

Ring Resonator Memory Cell Ring 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 RAM Resonator RAM

b

τ

b

τ

b

τ

b

τ

b

τ

b

τ

Word Lines Bit Lines Row Decoder Input Output

Tucker, PTL, 2008

Coupling Coefficient K

0.0001 0.001 0.01 0.1 1.0

Time

Store Write Read

ER

store

K

write

K

read

K

Coupling Coefficient Coupling Coefficient

Input Pulse Output Pulse

τ

K

Retention Time Retention Time

Normalized Amplitude

1.0 0.2 0.6 0.8 0.4

Time (ns)

1.0 0.8 0.6 0.4 0.2

Input 5-ps pulse Retention Time ~ 800 ps Cavity Q = 2x106 Output Pulses Simulation (VPI)

Kstore

Waveguide 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 L K n Q

store g store

+ = α λ π

Resonator RAM Resonator RAM

• store

f Q π 2 =

= + = ) / ( 1 L K v

store g α

Retention Time Absorption Time

Cavity length

α

The Myth The Myth-

• Busters

Busters

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

• vercome using optical gain.

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 Buffering Comparing 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

Conclusions Conclusions

• There are no free lunches