1. 13/05/2006 Spring School ‚Solitons in Optical Cavities‘1 Applications of Cavity Solitons Email: thorsten.ackemann@strath.ac.uk T. Ackemann SUPA and Department of Physics, University of Strathclyde Glasgow, Scotland, UK

2. 2 Agenda  Paul: „This is a school, not a workshop“  everything known  now: not so well established, partially more like Science Fiction  but like every good piece of Science Fiction, it is based on facts What is special about CS?Some remarks:  parallelism optical interconnects  motion „plasticity“ novel ingredient  bistable all-optical processing all-optical network some early processing schemes: Rosanov 1990s

3. 3 Outline + input from: B. Schäpers, W. Lange (WWU Münster) F. Pedaci, S. Barland, M. Giudici, J. R. Tredicce + others (INLN, Nice) G. Tissoni, L. L. Lugiato, M. Brambilla + others (INFM, Como, Bari) A. Scroggie, W. J. Firth, G.-L. Oppo + others (U Strathclyde, Glasgow)  optical memory  all-optical delay line  buffering information in telecom  soliton forve microscope  characterization of structures  all-optical processing, routing  telecommunications + apologies to people working on LCLV (e.g. poster of Gütlich et al.)

4. 4 Writing information for optical memory an ideal homogeneous system has translational symmetry  ability to choose position in plane at will  all states are equally likely  code arbitrary information  memory Harkness et al., CNQO, U Strathclyde (1993) Can you really write arbitrary configurations?  interactions: minimum and discrete distances  not all configurations of clusters are stable

5. 5 Memories and arbitrary configurations Coullet et al., PRL 84, 3069 (2000); Chaos 14, 193 (2004) hom. state wins pattern wins fully decomposable  memory appearance of states with N peaks destruction of states with N peaks appearance of states with N holes Pomeau front destruction of states with N holes width of this region in general unknown and system dependent, but seems to be comfortable wide in worked out models  memory is feasible !(?) McSloy et al. PRE 66, 046606(2002) Gomila and Firth (2005) (questioned by Champneys and Firth)

6. 6 “Arbitrary” ensembles of spots !? Firth + McSloy saturable absorber model (private communication) Logvin et al. sodium vapor + feedback PRE 61, 4622 (2000) Taranenko et al. exp.: driven SC microresonator PRA 65, 013812 (2002) For a memory you should be able to create arbitrary arrangements of CS

7. 7 but rather unstable...  in systems with translational symmetry translation is a neutral mode  no energy is needed for translation  any perturbation couples easily to neutral mode and induces motion  neutral mode is derivate of soliton and odd  any odd perturbation (gradient) will cause drift  until you are in a local extremum (even) where CS at rest / trapped Maggipinto et al., Phys. Rev. E 62, 8726, 2000; McSloy et al. PRE 66, 046606(2002) plasticity

8. 8 Noise Spinelli et al., PRA 58, 2542 (1998) amplifier model, time between frames 7440/   90 ns in a homogeneous system: white noise  diffusive motion  CS will perform random walk but actually in reality this is not a problem...

9. 9 Inhomogeneities Hachair et al., INLN, Nice; similar to X. Hachair et al., PRA 69 (2004) 043817 semiconductor amplifier after addressing beam is switched off, CS moves to a position ‚slightly‘ away from ignition point interpretation: CS is moving and finally trapped in small-scale irregularities of wafer structure  good news: CS won‘t diffuse in real structure  bad news: CS can‘t be positioned arbitrarily and this is essentially uncontrolled

10. 10 (Radial) Gradients addressing beam on addressing beam on addressing beam on  CS/FS can exist at any locations equivalent by symmetry  in a system with a circular pump beam of Gaussian shape this is not translational symmetry but rotational symmetry  ring (or center) what happens typically in single-mirror feedback system Schäpers et al., WWU Münster; similar: PRL 85, 748 (2000); IEEE QE 39, 227(2003) B Na adressing beam holding beam AOM

11. 11 Application: Pixel array a) code arbitrary information  ability to choose position in plane at will system should be as homogeneous as possible b) robust against noise Solution: Pinning of positions of LS by intentional small-amplitude modulations Firth + Scroggie, PRL 76 1623 (1996); saturable absorber model; see also Rosanov 1990  defined positions  diffusive movement due to noise suppressed  accuracy requirements for aiming relaxed

12. 12 Simulations: Pixel array Spinelli et al., PRA 58, 2542 (1998) semiconductor amplifier model trap CS at lattice sites

13. 13 Experiment: Pixel array pinning of positions of LS by amplitude modulations  defined positions, diffusive movement due to noise suppressed  pixel array, however not all cells are bistable at the same time (residual inhomogeneities) input beam Schaepers et al., Proc. SPIE 4271, 130 (2001) experiment: single-mirror feedback system insert square aperture, slightly truncating input beam (diffractive ripples)

14. 14 CS-based optical memory ?  so it seems that a CS-based optical memory will work  but: CS are „large“ - some micrometers mediumGbit/inch 2 bit/  m 2 CD0.7 GB0.050.1 DVD4.7 GB0.350.5 blu-ray 25 GB1.92.9 blu-ray100 GB7.511.6 holografic storage515800 very best hard discs300470  simple memories won‘t compete with existing technology  need to exploit other, unique (!?) features

15. 15 Enhancing CS arrays  combine with processing  e.g. all-optical routing  remember that it is light  cavity soliton laser as self-luminescent optically-addressable display  exploit plasticity  all-optical delay line unique feature  best bang for the bug

16. 16 „Slow light“ this is cycling speed ! Hau et al., Nature 397, 594 (1999) Boyd et al., OPN 17(4) 18 (2006)

17. 17 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)

18. 18 All-optical 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 Harkness et al., CNQO, U Strathclyde (1998)  note: won‘t work for non-solitons / diffractive beams movie

19. 19 Experimental realization B Na adressing beam holding beam AOM sodium vapor driven in vicinity of D 1 -line with single feedback mirror t = 0  st = 80  st = 64  st = 48  st = 32  st = 16  s ignition of soliton by addressing beam proof of principle, quite slow, but in a semiconductor microresonator this is different ! Schäpers et. al., Proc. SPIE 4271, 130 (2001) tilt of mirror  soliton drifts

20. 20 First experiments in semiconductors F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished spatio-temporal detection system: 6 local detectors + synchronized digital oscilloscopes BW about 300 MHz VCSEL (UP) 200 µm diameter quite homogeneous cavity resonance pumped above transparency but below threshold  amplifier

21. 21 Preparation of holding beam with 6 detectors you cannot investigate two- dimensional spatio-temporal structures  create quasi-1D situation by introducing Mach-Zehnder interferometer  stripes with modulation depth of  1 there is also a gradient along the stripes F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished

22. 22 Results: Noise-driven events  anti-phase oscillation possible interpretation: structure oscillating back and forth in a potential well F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished  intentional (bang on table) or intrinsic perturbations trigger release of pulse

23. 23 An animation strong indication of a drifting structure F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished

24. 24 Reproducibility F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished noise triggered events appear at fairly random time intervals superposition of 50 events  deterministic propagation compatible with interpretation of a noise triggered drifting CS

25. 25 A theoretical analog !? J. McSloy, PhD thesis, 2002; cf. also Scroggie, PRE 66, 036607 (2002); Tissoni, Opt. Exp. 10_1009(2002). model: passive semiconductor microcavity + temperature dynamics  self-propelled CS  some oscillation  followed by ‚eruption‘ of CS  Caution: this is only to illustrate that similar things can happen in a model  it is not claimed that this is the explanation

26. 26 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 s this is an embryonic all – optical delay line ! optically addressed drifting structure delay  12 ns distance  25 µm velocity  2.1 µm/ns delay / width  2-4

27. 27 Velocity  experiment suggests velocity of about 2 µm / ns = 2000 m / s = 7200 km / h > supersonic jet !  theoretical expectation here amplifier model (‚standard‘ parameters)  perturbative regime  saturation speed limit  1.5 µm/ns  semi-quantitative agreement fortutious (at present stage) Tissoni et al., unpublished; see also Kheramand et al., Opt. Exp. 11, 3612(2003)

28. 28 Bandwidth and bit rate  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  not great, but certainly a start  limit: time constant of medium (carriers) typically assumed to be about 1 ns   -response some ns 10 µm / 3 ns = 3.3 µm /ns  origin of numerically observed saturation behaviour  even this makes sense with experiment

29. 29 „Slow media“: Non-instantaneous Kerr cavity A. Scroggie, Strathclyde, unpublished (1D, perturbation analysis)   0.01  semiconductor log (velocity / gradient) log (  ) slope 1  velocity determined by response time  saturation for instantaneous medium   faster medium will speed up response !  response time can be engineered by growers: low-temperature growth, ion implantation, QW close to surface, quantum dots  need to pay for it by increase of power

30. 30 „Conventional“ approaches to slow light  modification of group velocity in vicinity of a resonance  two-level atom  electro-magnetically induced transparency  cavity resonance .... Hau et al., Nature 397, 594 (1999)  bandwidth limited by absorption high-order dispersion  large effect needs steep slope, narrow resonance

31. 31 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 delay product EIT in cold vapor 1 6 17 m/s230 µm~ 10 µs300 kHz2.1 EIT in SC QD 1 4 (calc)125000 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 (optimize delay)2000 m/s200 µm100 ns300 MHz30 CS (optimize 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)

32. 32 Résumé: CS-based delay line  drifting CS are a quite different approach to slow light  pros and contras should be assessed  potentially very large delays  lot‘s of things to do theory: saturation behaviour patterning effects  t N = - A N – B N 2 – C N 3 +... fabrication:homogeneity experiment:control gradients, improve ignition, larger distances...  in a cavity soliton laser there are (at least) two other twists 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, since about 2002) other: wavelength-conversion by FOPA + dispersive fiber + back-conversion McSloy, Strathclyde

33. 33 Material parameters from nonlinear dynamics  nonlinear dynamics often depends sensitively on parameters  old idea: use this to determine material parameters  not many examples: e.g. ferro-fluids  apparently not much done in optics (remarks welcome) relaxation and diffusion constant from below threshold patterns (Agez et al., PhD thesis, 2005, Lille; Opt. Commun. ?) defect characterization by looking at symmetry breaking of SHG conical emission (Chen et al., PRL 96, 033905, 2006) characterize homogeneity of cavity resonance of a microcavity (INLN, Nice)

34. 34 Broad-area microcavity laser Barland et al., Nature 419, 699 (2002) 150 µm diameter VCSEL free-running with injection left-right asymmetry  gradient in detuning  gradient in cavity resonance this gradient was mapped out by other (tedious) experiments to be 400 GHz/150 µm Another clever way?

35. 35 Probing the gradient „fine“ structure „coarse“ structure wavenumber should scale as square root of detuning qualitative right but not suitable for quantitative analysis modulational instability threshold Barland et al, APB 83, 2303 (2003)

36. 36 Quantitative linear relation  351 GHz / 150 µm Barland et al, APB 83, 2303 (2003)

37. 37 Local probing Hachair et al., INLN, Nice; similar to X. Hachair et al., PRA 69 (2004) 043817  the patterns allow only for large-scale and „directed“ inhomogeneities  What about local probing?  the trapped CS indicate extrema of phase/amplitude  Can we find depth of potential well? Soliton force microscope W. J. Firth, Strathclyde map relative – possibly absolute – gradients in transverse plane by measuring the displacement between CS and a (small-amplitude) steering beam

38. 38 Idea of soliton force microscopy CS in a trap add focused steering beam (addressing beam) blow up CS moves to new equilibrium  measure displacement  infer relative local curvature (for fixed amplitude)  changing amplitude + calibrations  „absolute“ local curvature  „inverse“ problem: disentangle phase- and amplitude contributions identify origin of inhomogeneity

39. 39 All-optical processing  pulse trains with a high repetition rate are needed in optical communications time-division multiplexing (TDM) demultiplexing regeneration routing  self-pulsing CSL, ideally a mode-locked CSL array of self-pulsing laser sources  carrier pulse trains with high repetition rate in a large number of output channels all-optical control  „high-frequency carrier pulse train on demand“ e.g. Stubkjaer, IEEE Sel. Top. QE 6, 1428 (2000)

40. 40 Anticipated scheme de-multiplexing optical regeneration routing time scales  packet manipulation advanced schemes might use plasticity of CLB  processing, direct routing self-pulsing CSL control beams pulse train time

41. 41 Summary: Cavity solitons versus „pixels“ broad-area laser with CSarray of micro-fabricated bistable elements discrete bistable  memory  switch  optical processing continuous  utilize plasticity all-optical delay line (different access to slow light) soliton force microscope  continue to think hard about combination of parallelism, all-optical switching/processing/routing and plasticity

42. 42 Desirable Features and Systems  compact  integration  fast  robust (monolithic) semiconductor microcavity  moderate power requirements  cascadable active system amplifier or laser  robust (phase-insensitive) self-sustained laser incoherent switching of CS (or propagation in amplifier) cavity soliton laser

43. 43 Relevance of modulated backgrounds in general modulations of the pump or the refractive index can be used It is generally believed that cavity solitons get stuck at the maxima of the background modulation. a) advantageous improve accuracy and robustness of optical memories b) limiting provides pinning mechanism for drifting CS

44. 44 Pinning of drift motion A. Scroggie, unpublished (USTRAT) motion of CS might be affected – in extreme case pinned – by modulations or localized inhomogenities  study motion of CS on noisy backgrounds position along device  dashed line: perturbation solid line: speed of CS soliton averages over scales < CS width

45. 45 Transition between locking and drift example: single-mirror feedback system with Na as nonlinear medium locking of hexagonal patterns (not solitons !) at large-scale envelope produced by pump profile  transition discontinous  possibly we are close in semiconductors !? Seipenbusch et. al., PRA 56, R4401 (1997); AG Lange, WWU Münster