7 Sep 2006 QEP17: Slow light using cavity solitons … 1

Slow light using cavity solitons in semiconductor resonators

willie@phys.strath.ac.uk

T. Ackemann, W J Firth, G L Oppo, A J Scroggie and A M Yao

SUPA and Department of Physics, University of Strathclyde, UK

acknowledgements: FunFACS partners : INLN (Nice) – FIRST EXPERIMENT!

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All-optical buffers and delay lines

buffers can enhance performance of

networks

future high-performance photonic

networks should be all-optical

need for all-optical buffers with

controllable delay

Boyd et al., OPN 17(4) 18 (2006)

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"Slow light"

Hau et al., Nature 397, 594 (1999)Boyd et al., OPN 17(4) 18 (2006)

OR –

Use small transverse component

of light velocity - this talk

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Writing solitons in a vertical cavity

writing cavity solitons (CS) stores pulses

indefinitely "stopped light"

an ideal homogeneous system has

translational symmetry

ability to choose position in plane at will

Saturable absorber model – Harkness et al., Strathclyde (1998)

in systems with translational symmetry translation is a neutral mode no energy is needed for translation any odd perturbation (gradient) couples easily to neutral mode

and causes lateral drift "slow light"

QuickTime™ and aAnimation decompressor

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All-optical CS delay line

inject train of solitons here

read out at other side

parameter gradient

time delayed version of input trainall-optical delay line

buffer register

for free: serial to parallel conversion and beam fanning

note: won‘t work for non-solitons/diffractive beams

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are needed to see this picture.

Saturable absorber model – Harkness et al., Strathclyde (1998)

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920 µm VCSEL (Ulm Photonics) 200

µm diam: pumped above

transparency but below threshold

amplifier

pump "stripes" for quasi-1D

gradient along the stripes

Spontaneous patterns and solitons

mostly aligned to stripes.

Home in on "soliton" in red ring.

First experiments in semiconductors

F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, 2006 (unpublished)

spatio-temporal

detection

system:

6 local

detectors

+ synchronized

digital

oscilloscopes

Bandwidth

about 300 MHz

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Optical addressing

F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished

gate addressing beam with an

electro-optical modulator

rise/fall times < 1 ns

100 ns

optically

addressed

drifting

structuredelay 12 ns

distance 25 µm

velocity 2.1 µm/ns

delay / width 2-4

superposition of

50 „CDE“ events:

reproducible,

solitonic

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Velocity in experiment (and theory)

experiment suggests speed of about 2 µm/ns = 2 km/s (slow-ish!)

in line with theoretical expectations for VCSEL amplifier model:

perturbative regime – linear in K

E field, N carriers. J current, P input.

response ratio, small, ~ 0.01

P constant amplitude, but constant

phase gradient K.

see also Kheramand et al., Opt. Exp. 11, 3612(2003)

( )

[ ]NDENJNt

N

EiENiiPEit

E

22

2

)1(

)1)((1

∇+−+−−=∂

∂

∇+−+Δ−++−=∂

∂

γ

σθ

spe

ed

phase gradient K

saturation: speed limit 1.5 µm/ns

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Comparison to other systems slow light in the vicinity of resonances: electro-magnetically induced transparency, linear cavities, photonic crystals interplay of useful bandwidth and achievable delay

system speed length delay bandwidth bandwidth times delay

EIT in cold vapor1 6 17 m/s 230 µm ~ 10 µs 300 kHz 2.1

EIT in SC QD1 4 (calc) 1250000 m/s 1 cm 8 ns 10 GHz 81

SC QW (PO, calc) 5 9600 m/s 0.2 µm 0.02 ns 2 GHz 0.04

SBS in fiber3 70500 km/s 2 m 18.6 ns 30-50 MHz > 1

Raman in fiber2 2 km 0.16 ns 10 GHz> THz

2 (demonstr.)

> 160 (pot.)

CS (demonstrated) 2000 m/s 25 µm 12 ns 300 MHz 3.6

CS (optimise delay) 2000 m/s 200 µm 100 ns 300 MHz 30

CS (optimise BW) 40000 m/s 200 µm 5 ns 6 GHz 30

1Tucker et al., Electron. Lett. 41, 208 (2005); 2Dahan, OptExp 13, 6234(2005); 3GonsalezHerraez, APL 87 081113 (2005); 4ChangHasnain Proc IEE 91 1884 (2003); 5Ku et al., Opt Lett 29, 2291(2004); 5Hau et al., Nature 397, 594 (1999)

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Bandwidth and bit rate observed velocity: 2 µm / ns; CS diameter typically 10 µm a local detector would see a signal of length

10 µm/(2 µm/ns) = 5 ns bit rate 100 Mbit/s

limit: time constant of medium (carriers) 1 ns 10 µm/ 3 ns = 3.3 µm /ns

K=0.0392

0 2 4-2log

log

(spe

ed

)

Analytic (perturbation theory)

and numerical dependences

of drift speed vs

(photon/carrier lifetimes)

~ 10-2

for carrier lifetime ~ 1 ns

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6 carrier lifetimes: solitons merge

How close can cavity solitons be packed?

Space-time plots of |E| for response ratio =0.01, phase gradient K=0.471with different time delays between address pulses

Simulation of VCSEL cavity soliton buffer with independent soliton "bits"

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

time

space

10 carrier lifetimes: solitons independent

time

space

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Soliton for K=0.471, =0.01 – large gradient, modest distortion – and some asymmetry

Soliton for K=0.0196, =0.01– small gradient, little distortion

Solitons are pretty robust against gradient

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Résumé: CS-based delay line

drifting CS are a novel approach to slow light with promising features potentially very large delays with good figure of merit lots of things to do

• theory: saturation behaviour

Auger etc.

patterning effects• fabrication: homogeneity, built-in gradients• experiment: control gradients,

improve ignition,

larger distances ... in a cavity soliton laser1 there are additional possibilities

• relaxation oscillations are faster than carrier decay time and modulation

frequency of modern SC lasers is certainly faster (at least 10 Gbit/s)

• possibility of fast spontaneous motion (Rosanov, 2002)

1 FunFACS project objective