Lecture 14 Dispersion engineering part 1 - Introduction. EECS Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.Ku

Transcription

1 Lecture 14 Dispersion engineering part 1 - Introduction EEC Winter 26 Nanophotonics and Nano-scale Fabrication P.C.Ku

2 chedule for the rest of the semester Introduction to light-matter interaction (1/26): How to determine ε(r)? The relationship to basic excitations. Basic excitations and measurement of ε(r). (1/31) tructure dependence of ε(r) overview (2/2) urface effects (2/7): urface EM wave urface polaritons ize dependence Case studies (2/9 2/21): Quantum wells, wires, and dots Nanophotonics in microscopy Nanophotonics in plasmonics Dispersion engineering (2/23 3/7): Material dispersion Waveguide dispersion (photonic crystals) 2

3 Optical signal i( z t ) Re[ Ee β ω + φ ]

4 Phase, group, and signal velocities Phase velocity = velocity of the oscillation v p = 1 µ ε Group velocity = velocity of the envelope v g ω( k) k = = slope of the dispersion curve ignal velocity v s = v If the signal reaches the receiving end. g 4

5 Group velocity dispersion If v g depends on ω, the signal will experience distortion. 2 3 dβ d β 2 d β 3 β ( ω) = β + ( ω) + 2 ( ω) + 3 ( ω) + dω dω dω β + β ω + β ω + β ω + ( ) ( ) ( ) If β3 = β4 = = : Input = gaussian pulse = 2 1 t A(, t) = A exp 2 T Pulse width = TFWHM = 2 ln 2T 1.665T Output pulse width = T T β z = T 2 5

6 τ = L c low and fast light v g ω ωn( ω, k) = k = k c n ω n n k k = = c c ω k ω ω v g Dispersion engineering to vary group velocity Control of signal velocity: c = = v g n n + ω ω ω n 1 c k Material dispersion patial variation of n n(ω,k) * Constant slope * Variability Control by changing n or ω n k signal bandwidth ω or k 6

7 Waveguide dispersion Photonic crystals nz ( ) = n+ ncos(2 π z/ Λ) for L/ 2 < z< L/ 2 nk ( ) = kl πl kl πl 2/ π Λ n 2π cos sin kλsin cos 2 Λ 2 Λ π k Λ = 1 n ω n c k n Λ nk ( ) k L z k 7

8 Material dispersion and its control α ω Kramers-Kronig n ω c = = v ω g n n + ω ω ω n 1 c k Electromagnetically induced transparency (EIT) Population oscillation (coherence dip) 8

9 EIT and slow light slow light region 1 3 ω p = ω 31 α ω s = ω 21 n 2 9

10 Population oscillation (PO) Coherent interaction between intense pump and signal in a two-level system population grating E 2 (Exciton) population inversion ω P ω E 1 (Ground) time Population grating coherently scatters energy b/w pump and signal population inversion due to pump time time time Increasing pump-signal detuning 1

11 PO in semiconductor QWs First demonstration of light slowing down in semiconductor materials. 2 GHz = 23 Ref: P. C. Ku et al, Opt. Lett., 29 (24)

12 Applications of slow/fast light Computer simulation of 4 Gbs pseudorandom digitally modulated optical signal transmission through a uniform quantum dot waveguide low light Optical signal Brake Vehicle distance GaAs InAs QD GaAs γ H =1meV, γ 31 =1µeV, uniform sample Ku and Chang-Hasnain, UC Berkeley Press Release (24) 12

13 cope of applications optical switch contention resolution phased array antenna communication beam steering imaging information storage optical RAM τ τ τ signal processing τ τ τ τ τ τ convolution f(τ)f 1 2(t - τ)dτ =F(ω)F 1 2(ω) 13

14 Trade-off that matters in applications Many applications demand bandwidth D = T B / L = B / v const eff g 14

15 low-light buffer Control Packet length, τ p Bit period, τ b Data in Data out Buffer λ Hold-off time, T HO torage time, Τ Figure of merit : storage density D and efficiency E ( τ / ) T B T D = L E = DT / L packet p HO ~ bandwidth-delay product / L ~ storage density x storage time 15

16 Buffer classification and hold-off time c = = v g n n + ω ω ω n 1 c k Material dispersion patial variation of n Class 1 Class 2 Class 3 A B v g v g v g v g x,t x x t Fiber delay line EIT and PO Photonic crystal based Photonic crystal based with index tuning T HO = Loop time T HO = T R T HO = T R T HO = Loop time T R = Loop time if v g needs to be changed 16

17 caling and fundamental limit Class ingle wavelength operation WDM 1 D = B n/ c n / λ packet avg packet ( / ) 2 E = B n c D = B n/ c fiber fiber ( / ) 2 E = B n c 2 D = α() n / λ avg E = α 2 / B DL B = B τ / T DL packet p HO D = N α() ( α ) 2 / E = N B DL 3 D = n / λ avg ( λ ) 2 E = n / / B avg DL D = Nn avg ( λ ) 2 / λ E = Nn / / B avg DL R.. Tucker, P. C. Ku, C. Chang-Hasnain, OFC 25. Fundamental limit of storage density is inversely proportional to the optical wavelength in the device 1/5 nm for 1.55 µm signal torage efficiency rolls off for high bit rate signal. low-light buffer favors medium bit-rate WDM system. 17

18 Can we overcome the trade-off? Adding gain to the system may overcome the bandwidthdelay product tradeoff. But distortion needs to be characterized and compensated. g Kramers-Kronig n ω ω ω 18