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

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

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

Optical Pattern Formation Input Nonlinear Medium c nl Cavity Output ( Plane Wave ) Pattern Nonlinear media in cavities Diffraction in the paraxial approximation: diffraction dissipation “Dissipative” NLSE: Kerr medium in cavity .Lugiato Lefever, PRL 58, 2209 (1987). Hexagons Honeycomb Rolls

Encoding a binary number in a 2D pattern?? 1 Problem: different peaks of the pattern are strongly correlated

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

Localised Structures Tlidi, Mandel, Lefever

CAVITY SOLITONS Holding beam Output field Writing pulses Nonlinear medium cnl Writing pulses Intensity profile In a semiconductor microcavity: Brambilla, Lugiato, Prati, Spinelli, Firth, Phys. Rev. Lett.79, 2042 (1997). Intensity 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 x y Possible applications: realisation of reconfigurable soliton matrices, serial/parallel converters, etc Phase profile

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

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

Long-Term Research Project PIANOS 1999-2001 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)

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

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

Th. Knoedl, M. Miller and R. Jaeger, University of Ulm The VCSEL Th. Knoedl, M. Miller and R. Jaeger, University of Ulm p-contact Bottom Emitter (150m) Bragg reflector Active layer (MQW) Bragg reflector GaAs Substrate E R E In n-contact 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)

Experimental results Above threshold, Below threshold, 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 Interaction disappears on the right side of the device due to cavity resonance gradient (400 GHz/150 mm, imposed by construction) Observation of different structures (symmetry and spatial wavelength) in different spatial regions In the homogeneous region: formation of a single spot of about 10 mm diameter

Control of two independent spots 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 Spots can be interpreted as CS

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

Theoretical interpretation x (m) 0 37.5 75 112.5 150 -2.25 -2.00 -1.75 -1.50 -1.25  Patterns (rolls, filaments) Cavity Solitons The vertical line corresponds to the MI boundary CS form close to the MI boundary, on the red side

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

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

Numerical simulations of CS dynamics in presence of gradients in the input fields or/and thermal effects CS in presence of a doughnut-shaped (TEM10 or 01) input beam: they experience a rotational motion due to the input phase profile e  i (x,y)  Input intensity profile Output intensity profile

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

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

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

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

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

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