Cavity solitons in semiconductor VISTA meeting Santander, May 23-24, 2003 Cavity solitons in semiconductor microresonators: theory and experiment Giovanna Tissoni INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy giovanna.tissoni@mi.infn.it Jorge Tredicce, Massimo Giudici, Stephane Barland, X. Hachair, L. Furfaro INLN Nice, France Salvador Balle IMEDEA (CSIC-UIB), Palma de Mallorca, Spain Luigi A. Lugiato, Reza Kheradmand INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy Massimo Brambilla, Tommaso Maggipinto, Ida Perrini INFM, Dipartimento di Fisica Interateneo, Università e Politecnico di Bari, Italy

Cavity solitons in semiconductor microcavities: MENU What are cavity solitons and why are they interesting? Cavity solitons in semiconductor microcavities: the experiment at INLN THERMAL EFFECTS: spontaneous motion of patterns and cavity solitons Guiding thermally induced motion of CS by means of phase/amplitude gradients: numerical simulations CS above laser threshold: preliminary results

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

Solution: Localised Structures Spatial structures concentrated in a relatively small region of an extended system, created by stable fronts connecting two spatial structures coexisting in the system 1D case Tlidi, Mandel, Lefever 2D case

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

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

S. Barland, M. Giudici and J. Tredicce (INLN), S. Balle (IMEDEA) Experimental Set-up S. Barland, M. Giudici and J. Tredicce (INLN), S. Balle (IMEDEA) 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

R. Jaeger, T. Knoedl and M. Miller, University of Ulm The VCSEL R. Jaeger, T. Knoedl and M. Miller, 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: spontaneous 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. Furthermore, we included the more realistic features, like the gradient of the cavity resonance, the spatial profile of the injected current and the spatial inhomogeneities related to the growth process of the device.

Reproducing the experimental results Time averaged transverse intensity profile of a VCSEL driven by a coherent holding beam: A patterned region appears on the left, a homogeneous domain on the right. Experiment Numerical simulation  (x,y)

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 a ring, created by means of an input amplitude modulation Input amplitude modulation Output intensity profile

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

The phase modulation is not strong enough to stop thermal motion. CS PINBALL During thermal drift the CS is momentarily captured by the phase maxima. The phase modulation is not strong enough to stop thermal motion. 2D input phase modulation Output intensity profile

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

CS in guided VCSEL above threshold: experimental results Reducing the intensity of the injected field the pattern contracts, and two CS remain.

Conclusions Cavity solitons look like very interesting objects There is by now a solid experimental demonstration of CS in semiconductor microresonators Theoretical and numerical studies show that thermal effects induce on CS a spontaneous translational motion, that can be guided by means of appropriate phase/amplitude modulations in the holding beam. The experimental results and preliminary numerical simulations demonstrate that CS persist also above the laser threshold