Controlling the dynamics time scale of a diode laser using filtered optical feedback. A.P.A. FISCHER, Laboratoire de Physique des Lasers, Universite Paris XIII, UMR CNRS 7538, FRANCE  G.VEMURI, Indiana University, Indianapolis, IN, USA  M. YOUSEFI, D. LENSTRA, Vrije Universiteit Amsterdam, THE NETHERLANDS

WORKSHOP Les Houches - September 25, 26, 27st, Motivation Defining and Designing optical systems for all optical signal processing. (Fast all optical device (ns time scale) for optical telecommunication) (DWDM). Investigating stability of DL locked on a selective element Ability of locked laser to switch from one locked frequency to another one (switching time) Dynamics and chaos for diode laser with filtered optical feedback Frequency selective element introduce a non linearity in frequency that leads to new dynamics in frequency. Is FOF a way of controlling the chaos “complexity”, in restricting the “freedom” of the system ? Only combination of experimental and theoretical results (simulations) can distinguish noise from chaos. C.O.F  F.O.F Conventional Optical Feedback  Filtered Optical Feedback

WORKSHOP Les Houches - September 25, 26, 27st, Description of the system SchematicFilter : frequency to power conversion –Gain –Phase Diode laser : tunable frequency generator –Current I –optical injection Optical Feedback loop : –An external cavity loop –A ring cavity

WORKSHOP Les Houches - September 25, 26, 27st, Filter Fabry-Perot interferometer Transmitivity in power is an Airy function Equation of the filter for the simulation Lorentzian filter : 2  : FWHM  m : resonance frequency Amplitude &Phase Michelson interferometer birefringent slab in between polarizers

WORKSHOP Les Houches - September 25, 26, 27st, On the flank of the filter a “linear” frequency- power conversion is operated. It is a frequency selective element It can be seen as a non linear element Filter features

WORKSHOP Les Houches - September 25, 26, 27st, Filter properties for a Fabry-Pérot interferometer The inverse of the resolution (  =c/2ef) of the Fabry- Perot filter define a delay  =1/ . Dynamics faster than  are smoothed and averaged The Fabry-Perot acts as a RC=  filter. The cavity (M1,M2) need to be “fulfilled” with multiple reflections.

WORKSHOP Les Houches - September 25, 26, 27st, Semiconductor Diode Laser Simulation parameters –FIELD –INVERSION –Frequency tunability –Slowly varying envelope approach –  : external cavity round trip time –n : normalized carrier inversion to threshold –P=|E| 2 : photon number –P 0 =(J-J thr )/  0 photon number under solitqry laser operation –  : linewidth enhancement factor –  : differential gain coefficient –T1 : carrier lifetime,  =(1+T1  P0)/T1 –  0 : photon decay rate –J and J thr : pump current and threshold value Experimental characteristics –Fabry-Pérot type DL –Single mode 5mW output – =780nm –solitary laser spectrum –Tunabitlity : –1 mA ---> 0,750 GHz

WORKSHOP Les Houches - September 25, 26, 27st, Optical Feedback Experiment –EXTERNAL CAVITY : –RING EXTERNALTY CAVITY Simulation parameters –FIELD –INVERSION –Frequency tunability –FILTER –Slowly varying envelope approach /  : external cavity round trip time / n : normalized carrier inversion to threshold / P=|E| 2 : photon number / P 0 =(J-J thr )/  0 photon number under solitqry laser operation /  : linewidth enhancement factor /  : differential gain coefficient / T1 : carrier lifetime,  =(1+T1  P0)/T1 /  0 : photon decay rate / J and J thr : pump current and threshold value /  : feedback rate

WORKSHOP Les Houches - September 25, 26, 27st, Analytical steady state solutions Frequency shift  s induced by the FOF : It is a transcendental equation with related to the filter profile is the extra phase added by the filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) C eff =0 No feedback

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) No filter COF

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) No filter COF

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Graphical solutions - Steady state  0 (free running solution ) ---->  =  0 +  (new frequency due to FOF) Lorentzian filter

WORKSHOP Les Houches - September 25, 26, 27st, Hysteresis Principle of hysteresis in frequency

WORKSHOP Les Houches - September 25, 26, 27st, Hysteresis in case of multiple filters Experiment Sketch

WORKSHOP Les Houches - September 25, 26, 27st, Temporal aspects of the steady state Power transmitted through the filter

WORKSHOP Les Houches - September 25, 26, 27st, Temporal aspects of the steady state Power transmitted through the filter

WORKSHOP Les Houches - September 25, 26, 27st, Dynamical aspects

WORKSHOP Les Houches - September 25, 26, 27st, Dynamical aspects - “complexity”

WORKSHOP Les Houches - September 25, 26, 27st, Dynamical aspects - Experiment Fabry-Pérot filter d=0.027m, f=6,FWHM=926MHz

WORKSHOP Les Houches - September 25, 26, 27st, Dynamical aspects - Experiment Time series show periodic frequency variations Period is related to the external cavity length  Large filter (FWHM  =1,47GHz) (e=1,7cm, finesse=6) –External cavity oscillations. (52 MHz - 19ns - L1=2,85m) Period of the frequency variations is proportional to the external cavity length.

WORKSHOP Les Houches - September 25, 26, 27st, Dynamics of the periodic frequency variations How to explain a self frequency modulation in a diode laser ?

WORKSHOP Les Houches - September 25, 26, 27st, Dynamics FOF creates “islands” of different behaviours Some ‘island” with periodical Frequency variations “Islands” with undamping of the relaxation oscillations (RO) Is that possible to suppress completely the RO ? (with a narrow filter)

WORKSHOP Les Houches - September 25, 26, 27st, Relaxation oscillations filtering ? Narrow filter (30MHz) Large filter 3,5 GHz 230MHz Free running (~50MHz) (No feedback) Line width narrowing ~10MH (Feedback ~-40dB) Periodical Frequency Variations (~ -35dB) (FM with low modulation index) Undamping of the RO (~ -30dB) Coherence collapse (-20dB) COF inifinite

WORKSHOP Les Houches - September 25, 26, 27st, Influence of the strengh of the non-linearity Fabry-Pérot filter FWHM= 230MHz Fabry-Pérot filter FWHM=520 MHz How does the filter width influences the dynamical behaviour ?

WORKSHOP Les Houches - September 25, 26, 27st, Comparison of the spectra

WORKSHOP Les Houches - September 25, 26, 27st, Comparison of the different spectra Controlled dynamics and chaos- Trade-off

WORKSHOP Les Houches - September 25, 26, 27st, Diode lasers basics Relaxation Oscillations Energy exchange between the inversion and the field in the laser. Frequencies are typical a few GHz - related to the carrier lifetime ~0,2ns Photon lifetime ~5 ps Damping rates : 10 9 s -1