Optical Self-Organization in Semiconductor Lasers Spatio-temporal Dynamics for All-Optical Processing

Optical Self-Organization in Semiconductor Lasers Spatio-temporal Dynamics for All-Optical Processing

Self-Organization for all-optical processing 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 interests. Strong intensity-dependent nonlinear optical properties near the band gap edge Integrability and ability to realize a large variety of optical devices with a complete crystal compatibility (compacity)

Self-Organization for all-optical processing A Universal Phenomenon Mascarets

Self-Organization for all-optical processing A Universal Phenomenon Morning Glory Clouds

Self-Organization for all-optical processing A Universal Phenomenon Patterned Vegetation

Self-Organization for all-optical processing A Universal Phenomenon Rayleigh-Bénard Rolls Conjugate actions : - liquid density - gravity - heat diffusion Side view Top view

Self-Organization for all-optical processing A Universal Phenomenon Localized particle structures Spherical particles on a vibrating plate

Self-Organization for all-optical processing Self-Organization in Physics - Introduction Mechanisms for Transverse Nonlinear Optics: Nonlinearity Competition mechanisms Transverse mechanisms Materials : Na-vapour LCLV III-V semiconductors Description of various systems : Amplifying injected systems Laser systems : injected or saturable absorber All-optical processing with Cavity Solitons Functions, Processing schemes Outline

Self-Organization for all-optical processing Physical Concepts and Theory The Potential Approach of Dynamical Systems Typical Nonlinear Dynamical Systems may be described by : A set of Internal Variables : X A Dynamical potential - 3rd order Nonlinearity X4 ¹X V (X) = X( + ) 4 - saturable nonlinearity X3 ¹X V (X) = X( + ) 4(1 + s ) ODE for the system Dynamics @t X = @X V + ºr? X : External control parameter ¹ : Depth of the potential 9

Self-Organization for all-optical processing Physical Concepts and Theory Switching on Spatial Effects X3 @t X = + ¹X + + ºr? X 1 + s Stability analysis : Small perturbations around steady homogenous states with ±X = X0 exp( t + i r) X = Xs + ±X Xs @t (±X) = 3 ±X + ¹±X + ºr? (±X) 1 + s Instability criterion : Xs + (3 ¹ º ) = 0 1 + s Xs (3 ¹ º ) < 0 1 + s Spatial instabilities may develop With a critical wavevector c c 1 3Xs = ( ¹) º 1 + s

Self-Organization for all-optical processing Physical Concepts and Theory Transverse Instabilities Steady-state

Self-Organization for all-optical processing Physical Concepts and Theory Temporal (Hopf) Instabilities Existence of imaginary solutions of λ yields Hopf instability: Periodic oscillation of the parameters of the state Example : Injected laser above threshold Competition between injected frequency and cavity resonant frequency yield Hopf instability frequency beating at Spectrum of an optically injected VCSEL under increasing injection current. (E. Caboche/INLN PhD thesis)

Self-Organization for all-optical processing What ingredients? Bistability, Self-localization, Stationarity Temporal competition : Bistability Subcritical bifurcation Spatial competition : High Fresnel number Independence from boundary conditions Concentration Spreading Focusing Kerr NL (F/C) Absorptive NL (F/C) Thermal NL (F/C) Diffraction (F) Diffusion (C)

Self-Organization for all-optical processing 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 Dielectric function

al systems Liquid Crystal Light Valve The pure Kerr Model

Material systems Liquid Crystal Light Valve LCLV in a Feedback Loop Patterns and localized states Non local interactions Residori et al., J. Opt. B: Quantum Semiclass. Opt. 6 (004) S169 S176

Material systems Na-vapor The two-level model Positive or negative nonlinear dispersion Inversion of properties above transparency

Material systems Na-vapor Feedback mirror systems Muenster Univ.(1996-001) Drift in a gradient Solitons in a patterned phase potential

Semiconductor systems Injected Amplifying VCSELs Coherent and Incoherent switching Cavity Soliton Lasers : Extended Cavity Saturable Absorber Lasers Integrated Cavity Saturable Absorber Lasers

Semiconductor systems Various Approches Bistable competition schemes Gain/Sat. Absorber Nonlinear Medium Write/Erase Write/Erase or Injection Output Output Output Pump Beam Pump Beam Amplifier Injected Below threshold Gain/Abs. Saturable Double Section Laser

Semiconductor systems Coherent and Incoherent control Control Competition Injected cavity Coherent @E = Ei (1 + iµ)e + (1 i )(N 1)E ir? E @t h i @N = N N N + (N 1) jej DN r? N @t Coherent Incoherent Gain/Saturable Absorber Incoherent @E = [1 + (1 i )(N 1) + (1 i )(n 1) + ir? ]E @t h i @N = N N N + (N 1) jej DN r? N @t h i @n = n n n + (n 1) jej Dn r? n @t M. Bache et al, Appl. Phys. B 81, 913(005) Incoherent

Semiconductor systems Electrical vs Optical pumping Pump I Advantages Disadvantages Pumping Electrical O ptical - High current densities - Integration - Joule heating - Technological steps - Spatial inhomogeneities at the borders - Few technological steps - No Joule heating - Choosing the pump spatial profile - External laser source - Coupling to the cavity - Therm al management due to the substrate (850 nm)

Semiconductor systems Injected Amplifying VCSELs Incoherent/Coherent local excitation reflected beam Holding beam Why optically pumping? Pump GaAs substrate ~10 µm Absence of heat source in the mirrors Fewer technological steps : lower defects density Pump uniformity no current crowding Control of the pump profile ~100 µm BUT... : special design of the samples

Semiconductor systems Optically-pumped Injected Amplifier Pattern formation Pump Pump @ ~800nm + injection 888.38nm 10 µm Increasing the pumping + Injection 890.98 nm 889.95 nm 888.3 nm Pump @ ~800nm + injection Decreasing the wavelength Y. Ménesguen et al, Phys. Rev. A 74, 03818 (006)74, 03818 (006)

Semiconductor systems Optically-pumped Injected Amplifier Writing/erasing with a local excitation Cavity solitons in semiconductors are composite objects : Control parameters Rpump : Carrier injection - Incoherent switching Ei : field Injection - Coherent switching Carriers Local reflected intensity Incoherent Field Coherent HB power PIERS 007 - Dissipative Solitons - March 8

Semiconductor systems Optically-pumped Injected Amplifier Incoherent writing/erasure interpretation Local carrier injection pulse Local temperature local detuning Fast : ~ ns Slow : ~ 100ns @E = Ei (1 + iµ)e + (1 i )(N 1)E ir? E @t h i @N = N N N + (N 1) jej DN r? N @t Additional equation for heat/detuning @µ = T (µ µ0 ) + f ( ) + Dn r? µ @t Thermally assisted incoherent switching S. Barbay, R. Kuszelewicz, Opt. Express 15, 1457 (007)

Semiconductor systems Cavity Soliton Lasers Saturable absorber systems Saturable absorber compact cavities VCSEL-SA Vertical Cavity Surface Emitting Laser with a saturable absorber Extended cavities VECSEL Vertical External Cavity Surface Emitting Laser ~µm 10 to 40 cm Lens(es) Mirror Absorber medium Mirror Gain medium Half-VCSEL = gain medium + mirror spherical, plane mirror or SESAM (Semiconductor Saturable Absorber Mirror) PIERS 007 - Dissipative Solitons - March 8

Semiconductor systems OP-VCSELSA cavity design Cavity with specific requirements Very good cavity finesse (use QW) Saturable absorber section : pump node (800nm) but laser (980nm) antinode Pump window (OP) Gain section : pump & laser nodes + optimized pumping Back mirror InAs QW Front mirror Laser field ~980 nm Pump fields 795-805 nm SA section 1 InAs/AlGaAs QW Gain section InAs/GaAs QW

Semiconductor systems VCSEL-SA in cw regime Bistable localized structure pump Profile

All-Optical processing with CS CS Manipulation CS drift in a field gradient (theory) Equation for normal incidence optical injection @t E = [1 + iµ (1 i ) (N 1)] E + EI + iar? E A tilted injected plane wave has a transverse wavevector component EI = EI0 eik? r? E = F eik? r? Equation for oblique incidence optical injection (@t + ak? r? ) F = 1 + i µ + ak? (1 i ) (N 1) F + EI0 + iar? F Yields an equivalent equation with convective derivative instead and velocity v = ak? More generally, for arbitrary phase (or amplitude) landscapes EI = EI0 eiá(r? ) E = F eiá(r? ) v = ar? Á Field gradients allow CS manipulations

All-Optical processing with CS CS Manipulation CS drift in a field gradient Linear gradient parabolic gradient Taranenko et al., Phys. Rev. E 56, 158 (1997)

All-Optical processing with CS CS Manipulation All-optical delay line phase gradient : drift amplitude gradient : channelling V C S E L n e a r fie ld. C y lin d ric a l le n s. IN P U T w ritin g p u ls e g ra d ie n ts d e la y e d O U TPU T CS drifts 36 µm in 7.5 ns average speed of 4.7 µm/ns = 4700 m/s Consistent with simulations S. Barland et al, submitted to Springer 3

All-Optical processing with CS CS Manipulation Modulated phase or amplitude landscape User controlled Structuration of information Reconfigurable array Cellular processor-type Optical Information processing Promote clock-cadenced interactions between neighbour CSs : operations Results are read at the fixed positions of the array The interaction is provided by third part beam arrays These are the ingredients of a cellular processor Precision-relaxed Information (IT) writing