Cavity solitons in semiconductor microcavities

1. 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

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

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

5. 1 1 0 0 0 1 1 1 0 Encoding a binary number in a 2D pattern?? Problem: different peaks of the pattern are strongly correlated

6. 1D case 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

7. Localised Structures Tlidi, Mandel, Lefever

8. Writing pulses Possible applications: realisation of reconfigurable soliton matrices, serial/parallel converters, etc Phase profile CAVITY SOLITONS Holding beam Output field Nonlinear medium cnl 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

9. Dissipation Non-propagative problem: CS profiles Intensity y x y x Cavity Solitons 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 Mean field limit: field is assumed uniform along the cavity (along z)

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

11. Long-Term Research ProjectPIANOS 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)

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

13. 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

14. E In E R 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 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)

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

16. 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 Control of two independent spots Spots can be interpreted as CS

17. The Model 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.

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

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

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

21. 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

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

23. 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

24. 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

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

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