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

Group Velocity Group Velocity Input Output Delay Line x Optical frequency ∂ ω c = = v Group velocity: g dn ∂ k + ω ω n d ⎛ ⎞ 1 1 dn α = + ω � n ⎜ ⎟ Intrinsic attenuation: τ τ ω v c ⎝ d ⎠ abs g abs Time to attenuate by e -1 Waveguide loss (dB/cm) Absorption time (ns) 0.01 30 0.1 3

Electromagnetically- -Induced Transparency (EIT) Induced Transparency (EIT) Electromagnetically Background Transfer Function α(ω) ω i.e. Hilbert ω ο transform Kramers dn Kronig becomes large n ω d ω Δω

Micro-resonator Delay Line Passband Δ ω n n avg FSR ω ω ω ω ω − p 1 1 2 p

Ideal Slow- -Light Material Light Material Ideal Slow All-pass function Transfer τ → ∞ 0 dB Function abs ω n max n avg Effective Index , n n min ω 0 ω min ω max ω ο Signal Spectrum ω Δω Bandwidth

Signal Bandwidth and Data Bandwidth Signal Bandwidth and Data Bandwidth Signal Bandwidth Data “Bandwidth” (Hz) or Information Rate 1 1 1 1 1 1 1 1 (b/s) τ τ ~ 1/ → 0 t ~ 1/ τ → 0 τ t 1 0 1 1 1 1 1 0 ~ 1/ τ τ 1/ T bit t T bit ~ 2/ τ 1/ T bit τ/2 t T bit

Group Velocity Change at Boundary Group Velocity Change at Boundary = = Index n Index n 1 2 Waveguide 1 Waveguide 2 Input Output dn 2 + ω n v n 2 ω g 1 g 2 d ω ) = = = Group S ( Slow-down factor: dn indices v n 1 g 2 g 1 + ω n 1 ω d

Group Velocity and Bit Length Group Velocity and Bit Length Group Slow Light Waveguide Regular Waveguide Velocity x Information Bandwidth x Bit Period x L in Bit Length = Period x Velocity x Field x L L in bit

Car Analogy 100 20 100 km/h 20 km/h Real World Slow Light Reduced Group Velocity Constant Bitrate World L bit

Tapered Transition Region Tapered Transition Region Region 1 Transition Region 2 Region v g v g1 Δ v g v g2 x x A1 x A2 Field x L b (x)

Circuit Switching and Packet Switching Circuit Switching and Packet Switching Circuit-Switched Network Packet-Switched Network Freeway Model Car: Packet Lane: Wavelength Waveband Freeway: Fiber Interchange: Router

Statistical Multiplexing in Buffer Statistical Multiplexing in Buffer Incoming packets Outgoing packets Buffer Nick McKeown http://tiny-tera.stanford.edu/~nickm/

Optical Buffer Control Packet length, t packet Bit period, T bit Data out Data in Buffer Hold-off time, T HO Storage time, T S Minimum time Packet Bit rate Information rate between incoming t 1 packets = = ⋅ packet B B B packet info packet T T bit HO

Optical Packet Switch Optical Packet Switch Output Demux Input Fibers Fibers Mux Wavelength- Interchanging Cross Connect Outgoing Incoming Packets Packets Input Output Buffers Buffers 3 3 2 2 1 1 First-In-First-Out Single Output Single Input (FIFO)

Optical Packet Switch Optical Packet Switch Output Demux Input Fibers Fibers Mux Wavelength- Interchanging Cross Connect Outgoing Incoming Packets Packets Input Output Buffers Buffers 2 1 3 2 1 First-In-First-Out 3 Single Output (FIFO) Multiple Inputs Output buffering: - optimum contention resolution - more complicated than input buffering

Single- -Input Single Input Single- -Output FIFO Output FIFO Single Control signals C M C 2 C 1 C 3 Output Input Stage 1 Stage 2 Stage 3 Stage M 0 X M X 1 X 2 X 3 M cascaded delay lines with controllable delays For acceptable performance , M > 20

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines Group Velocity v g1 v g2 x 0 x M Packet 1 P o x

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines Call to Read Packet 1 Group Velocity v g1 v g2 x 0 x M Packet 1 4 3 2 P o x = = B B T t Note: ; HO packet info packet

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines Group Velocity v g1 v g2 x 0 x N x M Packet 1 4 3 2 P o x = = B B T t Note: ; HO packet info packet

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines Group Velocity v g1 v g2 x 0 x N x M Packet 1 5 4 3 2 P o x = = = B B T t T t Note: Note: ; HO packet info packet HO packet

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines Group Velocity v g1 v g2 x 0 x N+1 x M Packet 1 5 4 3 2 P o x = = B B T t Note: ; HO packet info packet

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines Group Velocity v g1 v g2 x 0 x N+1 x M Packet 1 6 5 4 3 2 P o x = = B B T t Note: ; HO packet info packet

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines Group Velocity v g1 v g2 x 0 x M Packet 1 6 5 4 3 2 P o x = = B B T t Note: ; HO packet info packet

FIFO Buffer Using Controllable Delay Lines FIFO Buffer Using Controllable Delay Lines Group Velocity v g1 v g2 x 0 x M 7 6 5 4 3 2 P o x = = B B T t Note: ; HO packet info packet

Multiple- -Input Single Input Single- -Output FIFO Output FIFO Multiple Control signals FIFO Switch FIFO 10 – 100 Inputs FIFO FIFO 200 – 10,000 All FIFO’s provide full delay Delay lines Key issues: • Delay line utilization (i.e. “void” filling) • Complexity of control

Optical Pulses in Slow Light Delay Line Optical Pulses in Slow Light Delay Line (WG1) (WG2) (WG3) Delay Group Velocity Profile Input Slow Light Output T = L / g v Region Region Region 2 v g v g1 Capacity = C L L / bit v g2 x 0 Delay-Bandwidth Product L ⋅ = ⋅ T B T B Field info packet = ⋅ L B / v packet g 2 = C x L = L v 2 / B in bit g packet

Fundamental Limitations of Ideal Slow Light Fundamental Limitations of Ideal Slow Light Max. Delay-Bandwidth Product Minimum Bit Size λ L τ avg − L ( n n min ) 0 α ⋅ abs n avg − ( n ) τ λ min 0 bit n n max c = v n avg g 2 dn + ω ω n d n min 0 ω min ω max ω ο 2π B packet 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

Characteristics of Class B Slow Light Characteristics of Class B Slow Light n ω + δω + j ( )( t dt ) + = s E ( t dt ) E o e n avg ω − ω d ( ) max min δω = ω − ω ( ) s 0 ω − ω max min n min ω o ω min ω ο ω max Signal Spectrum ω

Class A and Class B Slow Light Class A and Class B Slow Light A: “Conventional” - Slow-down in Space B: Adiabatic - Slow-down in Time Group Velocity x t Information Bandwidth x t Bit Period x t , x L in Bit Length L in = Period x Velocity t , x x Tucker et al., JLT , 23 , 2005

Car Analogy – – Class B Slow Light Car Analogy Class B Slow Light “Conventional” Slow Light 100 km/h Speed Limit 20 km/h Speed Limit (Bitrate Reduced) Adiabatically-Slowed slow together slow together Dangerous (Bitrate Unchanged) Adiabatic Driving Solution: Toll Plaza

Operation of Class B FIFO Delay Line Operation of Class B FIFO Delay Line v g Interval 1 Interval 5 Interval 4 Interval 2 v g1 Interval 3 v g2 t Field Intensity t 1 t 2 t 3 t 4 x L L bit bit B g1 Bandwidth B g2 t t 1 t 2 t 3 t 4 < > B B T t Note: ; info packet HO packet

Mixed Delay Lines Mixed Delay Lines Increased Slow-Down Factor v g v g2 v g v g3 t v g1 v g2 Class A Class B Class A x x 1 x 2 • 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 Scaling “Traditional” (Class A): FIFO Energy/bit Size Control Stage 1 Stage 2 Stage p Capacity 2 Adiabatically Compressed (Class B): FIFO Capacity Class B Class B Capacity 2 1:p p:1 p Class B Delay Tucker et al., JLT , 23 , 2005