1. 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!

2. 2 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)

3. 3 "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

4. 4 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"

5. 5 All-optical CS delay line inject train of solitons here read out at other side parameter gradient  time delayed version of input train all-optical delay line buffer register  for free: serial to parallel conversion and beam fanning  note: won‘t work for non-solitons/diffractive beams Saturable absorber model – Harkness et al., Strathclyde (1998)

6. 6 920 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 First experiments in semiconductors F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, 2006 (unpublished) spatio-temporal detection system: 6 local detectors + synchronized digital oscilloscopes Bandwidth about 300 MHz

7. 7 Optical addressing F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished gate addressing beam with an electro-optical modulator rise/fall times 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 structure delay  12 ns distance  25 µm velocity  2.1 µm/ns delay / width  2-4 superposition of 50 „CDE“ events: reproducible, solitonic

8. 8 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) speed phase gradient K  saturation: speed limit  1.5 µm/ns

9. 9 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 systemspeedlengthdelaybandwidthbandwidth times delay EIT in cold vapor 1 6 17 m/s230 µm~ 10 µs300 kHz2.1 EIT in SC QD 1 4 (calc)1250000 m/s1 cm8 ns10 GHz81 SC QW (PO, calc) 5 9600 m/s0.2 µm0.02 ns2 GHz0.04 SBS in fiber 3 70500 km/s2 m18.6 ns30-50 MHz> 1 Raman in fiber 2 2 km0.16 ns10 GHz > THz 2 (demonstr.) > 160 (pot.) CS (demonstrated)2000 m/s25 µm12 ns300 MHz3.6 CS (optimise delay)2000 m/s200 µm100 ns300 MHz30 CS (optimise BW)40000 m/s200 µm5 ns6 GHz30 1 Tucker et al., Electron. Lett. 41, 208 (2005); 2 Dahan, OptExp 13, 6234(2005); 3 GonsalezHerraez, APL 87 081113 (2005); 4 ChangHasnain Proc IEE 91 1884 (2003); 5 Ku et al., Opt Lett 29, 2291(2004); 5 Hau et al., Nature 397, 594 (1999)

10. 10 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 02 4-2 log    log(speed) Analytic (perturbation theory) and numerical dependences of drift speed vs  (photon/carrier lifetimes)  ~ 10 -2 for carrier lifetime ~ 1 ns

11. 11 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=0.471 with different time delays between address pulses Simulation of VCSEL cavity soliton buffer with independent soliton "bits" time  space  10 carrier lifetimes: solitons independent time  space 

12. 12 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

13. 13 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 laser 1 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