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Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy

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Presentation on theme: "Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy"— Presentation transcript:

1 Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy Collaborators: Giovanna Tissoni, Reza Kheradmand INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy Jorge Tredicce, Massimo Giudici, Stephane Barland Institut Non Lineaire de Nice, France Massimo Brambilla, Tommaso Maggipinto INFM, Dipartimento di Fisica Interateneo, Università e Politecnico di Bari, Italy

2 MENU What are cavity solitons and why are they interesting? The experiment at INLN (Nice): First experimental demonstration of CS in semiconductors microcavities Tailored numerical simulations steering the experiment Thermally induced and guided motion of CS in presence of phase/amplitude gradients: numerical simulations

3 Solitons in propagation problems Temporal Solitons: no dispersion broadening z Temporal NLSE: dispersion propagation Solitons are localized waves that propagate (in nonlinear media) without change of form Spatial Solitons: no diffraction broadening Spatial NLSE: 1D 2D x y z diffraction

4 Input Nonlinear Medium nl Cavity Output (Plane Wave ) ( Pattern ) Nonlinear Medium nl Nonlinear media in cavities HexagonsHoneycombRolls Optical Pattern Formation Diffraction in the paraxial approximation: diffractiondissipation Dissipative NLSE: Kerr medium in cavity. Lugiato Lefever, PRL 58, 2209 (1987).

5 Encoding a binary number in a 2D pattern?? Problem: different peaks of the pattern are strongly correlated

6 Spatial structures concentrated in a relatively small region of an extended system, created by stable fronts connecting two spatial structures coexisting in the system Solution: Localised Structures 1D case

7 Localised Structures Tlidi, Mandel, Lefever

8 Intensity xy CAVITY SOLITONS Cavity solitons persist after the passage of the pulse, and their position can be controlled by appropriate phase and amplitude gradients in the holding field Phase profile Intensity profile In a semiconductor microcavity: Brambilla, Lugiato, Prati, Spinelli, Firth, Phys. Rev. Lett.79, 2042 (1997). Nonlinear medium nl Holding beamOutput field Writing pulses Possible applications: realisation of reconfigurable soliton matrices, serial/parallel converters, etc

9 Cavity Solitons Cavity Mean field limit: field is assumed uniform along the cavity (along z) CS height, width, number and interaction properties do not depend directly on the total energy of the system Dissipation Non-propagative problem: CS profiles Intensity xy x y Cavity Solitons are individual entities, independent from one another

10 What are the mechanisms responsible for CS formation? Absorption CS as Optical Bullet Holes (OBH): the pulse locally creates a bleached area where the material is transparent Interplay between cavity detuning and diffraction At the soliton peak the system is closer to resonance with the cavity Refractive effects Self-focusing action of the material: the nonlinearity counteracts diffraction broadening

11 Long-Term Research Project PIANOS Processing of Information with Arrays of Nonlinear Optical Solitons France Telecom, Bagneux (Kuszelewicz, now LPN, Marcoussis ) PTB, Braunschweig (Weiss, Taranenko) INLN, Nice (Tredicce) University of Ulm (Knoedl) Strathclyde University, Glasgow (Firth) INFM, Como + Bari, (Lugiato, Brambilla)

12 Nature 419, 699 (2002) The experiment at INLN (Nice) and its theoretical interpretation was published in

13 Tunable Laser CCD Holding beam Writing beam Detector linear array VCSEL BS aom C L C MM Experimental Set-up S. Barland, M. Giudici and J. Tredicce, Institut Non-lineaire de Nice (INLN) BS: beam splitter, C: collimator, L: lens, aom: acousto-optic modulator

14 Active layer (MQW) E R Bottom Emitter (150 m) Features 1) Current crowding at borders (not critical for CS) 2) Cavity resonance detuning (x,y) 3) Cavity resonance roughness (layer jumps) See R.Kuszelewicz et al. "Optical self- organisation in bulk and MQW GaAlAs Microresonators", Phys.Rev.Lett. 84, 6006 (2000) n-contact The VCSEL Th. Knoedl, M. Miller and R. Jaeger, University of Ulm Bragg reflector GaAs Substrate E In p-contact

15 Experimental results In the homogeneous region: formation of a single spot of about 10 m diameter Observation of different structures (symmetry and spatial wavelength) in different spatial regions Interaction disappears on the right side of the device due to cavity resonance gradient (400 GHz/150 m, imposed by construction) Intensity (a.u.) x ( m) Frequency (GHz) x Above threshold, no injection (FRL) Intensity (a.u.) x ( m) Frequency (GHz) x Below threshold, injected field

16 Control of two independent spots Spots can be interpreted as CS 50 W writing beam (WB) in b,d. WB-phase changed by in h,k All the circled states coexist when only the broad beam is present

17 E = normalized S.V.E. of the intracavity field E I = normalized S.V.E. of the input field N = carrier density scaled to transp. value = cavity detuning parameter = bistability parameter Where Choice of a simple model: it describes the basic physics and more refined models showed no qualitatively different behaviours. (x,y) = ( C - in ) / + (x,y) Broad Gaussian (twice the VCSEL) The Model L.Spinelli, G.Tissoni, M. Brambilla, F. Prati and L. A. Lugiato, Phys.Rev.A 58, 2542 (1998)

18 Theoretical interpretation x ( m) Patterns (rolls, filaments) Cavity Solitons The vertical line corresponds to the MI boundary CS form close to the MI boundary, on the red side

19 Pinning by inhomogeneities Broad beam only Experiment Add local perturbation Broad beam only Cavity Solitons appear close to the MI boundary, Final Position is imposed by roughness of the cavity resonance frequency Numerics (x,y)

20 7 Solitons: a more recent achievement Courtesy of Luca Furfaro e Xavier Hacier

21 CS in presence of a doughnut-shaped (TEM 10 or 01 ) input beam: they experience a rotational motion due to the input phase profile e i (x,y) Numerical simulations of CS dynamics in presence of gradients in the input fields or/and thermal effects Output intensity profileInput intensity profile

22 Intensity profileTemperature profile Thermal effects induce on CS a spontaneous translational motion, originated by a Hopf instability with k 0

23 The thermal motion of CS can be guided on tracks, created by means of a 1D phase modulation in the input field Output intensity profile Input phase modulation

24 The thermal motion of CS can be guided on a ring, created by means of an input amplitude modulation Output intensity profileInput amplitude modulation

25 CS in guided VCSEL above threshold: they are sitting on an unstable background Output intensity profile By reducing the input intensity, the system passes from the pattern branch (filaments) to CS

26 Next step: Conclusions Cavity solitons look like very interesting objects To achieve control of CS position and of CS motion by means of phase-amplitude modulations in the holding beam There is by now a solid experimental demonstration of CS in semiconductor microresonators

27 Thermal effects induce on CS a spontaneous translational motion, that can be guided by means of appropriate phase/amplitude modulations in the holding beam. Preliminary numerical simulations demonstrate that CS persist also above the laser threshold

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