Cavity Solitons : the semiconductor experimentalist's point of view

1. Cavity Solitons : the semiconductor experimentalist'spoint of view Robert Kuszelewicz Laboratoire de Photonique et de Nanostructures LPN-CNRS/UPR20, Marcoussis, France

2. What is at stake ? • Cavity solitons have a double concern : • Fundamental : • Phenomena, concepts and theoretical approaches of non linear pattern formation • Applied : Original Functions, all-optical signal processing. III-V Semiconductor materials are at the crossroad of two streams of interest. • Strong intensity-dependent nonlinear optical properties near the band gap edge • Integrability and ability to realise a large variety of optical devices with a complete crystal compatibility (compacity)

3. Purpose of the lecture • Show how theoretical concepts pertaining to TNO can be implemented into physical systems • Draw a short history of the most striking advances with various materials : • Na-vapor, LCLV, III-V semiconductors • Concentrate on semiconductor systems : • State of the art • Advantages, limitations, drawbacks • Capabilities and expectations

4. Outlines • Materials : • Na-vapour, LCLV and III-V semiconductors Mechanisms for Transverse Nonlinear Optics: • Nonlinearity • Competition mechanisms • Transverse mechanisms Phenomena : • From bistability to spatial pattern formation ... Transverse Nonlinear Optics Description of various systems : • Passively injected systems • Amplifying injected systems • Laser systems : injected or saturable absorber Limitations : • Uniformity : thickness, current, defects • Thermal effects : Production, dependance and dissipation What to do with ? • Functions, processing

5. Material systems and related optical models Liquid Crystal Light Valves Kerr-like dispersive medium Sodium Vapor : Two-level system : saturable dielectric function III-V semiconductors Electronic bands : Dynamical response Many-body interactions Dielectric function

6. LCLV : the Pure Kerr-model Residori et al., J. Opt. B: Quantum Semiclass. Opt. 6 (2004) S169–S176

7. The two level system : optical response • Positive or negative nonlinear dispersion • Inversion of properties above transparency

8. The bulk semiconductor model Direct gap semiconductors Parabolic model + Exciton Many-body effects + Band filling + Coulomb interactions Electron screening, Band gap renormalisation Exchange interaction

9. Recombination mechanisms Radiative Stimulated Spontaneous Auger phonon-assisted Non radiative Recombinations on defects Electron-phonon Direct Indirect

10. Dynamical regimes • Characteristic timescales Dephasing time Time after which phase relation is lost between the polarisation and the exciting field Populations lifetime Relaxation time of excited populations (probabilities) In general For III-V materials , Excitation duration • Dynamical regimes : ultra short pulses. Coherent transients : photons écho, superradiance, self-induced transparency.. Dynamical Stark Effect : : Dynamic nonlinearities. Polarization quasi-steady state vs Electric field. NL response ruled by the evolution of excited populations  : intraband relaxation : quasi-stationnary situation : adiabatic elimination of the carriers

11. Carrier dynamics Excitation of optically coupled states Intraband dynamics of carriers

12. The direct gap semiconductor dielectric function The Carrier density-dependant susceptibility with and without many-body effects (Koch model) Real and imaginary part are connected by the Kramers-Kronig transform : -factor derives as so that

13. QD susceptibility InAlAs/GaAlAs QD Density ~ 1011 cm-3 Inhomogeneous broadening Inhomogeneously broadened optical response Dynamic model of QD

14. Observations • The properties of the susceptibility in III-V semiconductor are multifactorial : • High background index n~3.5, • Strong NL in the vivinity of the band gap, • In the passive case, the NL dispersion is defocusing • Above transparency, focusing NL appear • III-V semiconductor are highly temperature-sensitive • via the shift of the band gap • Quantum dots seem quite a promising alternative for focusing NL

15. Mechanisms of TNO • Transverse Nonlinear Optical phenomenarequire : • Kerr-like or saturable intensity-dependent susceptibility • Positive feedback : Fabry-Perot resonance or feedback mirror enforces light-matter interaction duration yielding a “catastrophy”. Mechanism with threshold : NL + feedback PW bistability • Transverse effects : diffraction, diffusion Create the conditions of non locality. Mechanism with threshold : MI The conjunction of these three mechanisms generate the spatio-temporal dynamics.

16. Phenomena From bistability to spatial pattern formation ... Transverse Nonlinear Optics • PW bistability : thermal / electronic NL • Switching waves BISTABILITY + LARGE FRESNEL NUMBER • Pattern formation • Localised states

17. Devices • Description of various classes : • Passive injected systems : Na vapours and III-V semiconductors • Injected amplifying systems : optically- and electrically- pumped VCSEL • Laser systems : injected or saturable absorber systems

18. Passive injected systems

19. Na-vapor feedback mirror systems (Muenster univ.) • Drift in a gradient • Modulated landscape

20. LCLV in a feedback loop Patterns and localised states Non local interactions

21. Semiconductor systems Experimental system (LPN, PTB)

22. Switching waves Outward front Maxwell point Inward front

23. Patterns and dressed solitons

24. Injected semiconductor amplifiers

25. Injected semiconductor amplifiers • Arguments on the interest for over transparency operation • Positive : dispersive confinement • Amplification : cascadability • Two similar approaches : • Electrical pumping • INLN • Optical pumping • LPN • Discussion on the respective interest of each

26. Pump I Electrical vs Optical pumping

27. L = 1 Ûtransparency L = 1+1/2C Ûlaser threshold C largesmall excursion range in terms ofL smalla C small large excursion range in terms of L large a Theoretical model for field and carriers C : bistability parameter L : pump a : Henry factor [M. Brambilla, L. Lugiato, F. Prati, L. Spinelli, W. Firth, PRL 79, 2042 (1997)] Good compromise : C ≈ 0.5 high finesse cavity

28. Electrically injected VCSELs Bottom emitting laser (ULM)

29. Patterns and localised states (INLN)

30. The initial demonstration : independance of 2CS Writing Erasure sequence of 2 CS (Barland et al., Nature 419, 699(2002)

31. Interplay with non uniformity The thickness gradient scans the state space through the detuning parameter 80 mm Seven CS

32. Optical pump fewer technological steps, less heating Absorbing spacers Active layer Front mirror Aperiodic back mirror Pump window Cavity resonance Cavity design for optical pumping [Y. Ménesguen, R. Kuszelewicz, to appear IEEE-JQE 41,N°7 (2005)] [S. Barbay, Y. Ménesguen, I. Sagnes, R. Kuszelewicz, APL 86, 151119 (2005)]

33. Experimental setup Large-area semiconductor amplifier in AlGaAs/GaAs

34. Decreasing l 888.62 nm 890.98 nm 889.95 nm 889.27 nm 888.23 nm Results / pattern formation

35. Pump + injection 888.38nm 120 mm Increasing Pumping Spontaneous formation of CS Pump

36. Independance and multiplicity of CSs Independence of 2 CS W/E in the vicinity of 3 other CS Y. Ménesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes and R. Kuszelewicz, submitted PRA (2006)

37. Hysteresis Local reflected intensity HB power Field Carriers

38. CS on ~5 ns CS on ~2ns 60 ps writing pulse CS off CS off Fast incoherent writing/erasure : 60ps pulses Repeated writing and reset writing erasure

39. Semiconductor Laser devices

40. Laser systems Optically pumped monolithic active cavity with SA • Why going above threshold ? • Cascadability • Diversification of the bistable mechanisms • Injection or feedback lasers : mode competition • Saturable absorber (SA): gain loss competition • With SA, no holding beam is necessary • Incoherent switching

41. Injected lasers above Threshold (INLN)

42. Bistability of CS above threshold

43. Feedback Lasers (USTRAT)

44. Feedback laser Bistable localised states(Y. Tanguy, T. Ackemann, USTRAT) 80mm Laser (ULM) spatially filtered feedback,appear spontaneously at preferential locations Frequency tuning dependence With 200 mm, LS can be written without spatial filtering

45. QW gain medium(/QD?) Laser field Pump field QW or QD saturable absorber Saturable Absorber Semiconductor lasers (LPN) Optically pumped monolithic active cavity with SA OP-VCSELSA • Need a cavity with special requirements • Very good cavity finesse around lasing wavelength (use QW) • pump window (OP) + optimized pumping • Saturable absorber section • no pump field but laser field • Gain section • pump field & laser field

46. Front mirror Back mirror Laser field ~980 nm Pump fields 795-805 nm SA section Gain section 1 InGaAs/AlGaAs QW 2 InAs/GaAs QW OP-VCSELSA cavity design Experiment :Optically pumped monolithic active cavity with SA Theory :Laser with SA (coll. INFM/Como) QD model (coll. INFM/Bari) Simplex optimization procedure on layer thicknesses : front and back mirror R,T front and back mirror jR, jT overall cavity A

47. Laser L(P) curve

48. External cavity Laser with SA

49. Stability analysis vs Fresnel number

50. Transverse mode mapping