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Controlling the dynamics time scale of a diode laser using filtered optical feedback.

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,

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Controlling the dynamics time scale of a diode laser using filtered optical feedback.

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  1. 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

  2. Motivation C.O.F  F.O.F Conventional Optical Feedback  Filtered Optical Feedback • 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. WORKSHOP Les Houches - September 25, 26, 27st, 2001

  3. Schematic Filter : 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 Description of the system WORKSHOP Les Houches - September 25, 26, 27st, 2001

  4. 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, 2001

  5. Filter features • 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 WORKSHOP Les Houches - September 25, 26, 27st, 2001

  6. 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, 2001

  7. 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 P0=(J-Jthr)/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 Semiconductor Diode Laser WORKSHOP Les Houches - September 25, 26, 27st, 2001

  8. Experiment EXTERNAL CAVITY : RING EXTERNALTY CAVITY Optical Feedback • 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 / P0=(J-Jthr)/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, 2001

  9. Analytical steady state solutions • Frequency shift sinduced 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, 2001

  10. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) • Ceff=0 No feedback WORKSHOP Les Houches - September 25, 26, 27st, 2001

  11. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) • No filter COF WORKSHOP Les Houches - September 25, 26, 27st, 2001

  12. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) • No filter COF WORKSHOP Les Houches - September 25, 26, 27st, 2001

  13. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  14. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  15. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  16. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  17. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  18. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  19. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  20. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  21. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  22. Graphical solutions - Steady state • 0 (free running solution ) ----> = 0 + D (new frequency due to FOF) Lorentzian filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  23. Hysteresis • Principle of hysteresis in frequency WORKSHOP Les Houches - September 25, 26, 27st, 2001

  24. Hysteresis in case of multiple filters • Sketch • Experiment WORKSHOP Les Houches - September 25, 26, 27st, 2001

  25. Temporal aspects of the steady state Power transmitted through the filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  26. Temporal aspects of the steady state Power transmitted through the filter WORKSHOP Les Houches - September 25, 26, 27st, 2001

  27. Dynamical aspects WORKSHOP Les Houches - September 25, 26, 27st, 2001

  28. Dynamical aspects - “complexity” WORKSHOP Les Houches - September 25, 26, 27st, 2001

  29. Dynamical aspects - Experiment • Fabry-Pérot filter d=0.027m, f=6,FWHM=926MHz WORKSHOP Les Houches - September 25, 26, 27st, 2001

  30. 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, 2001

  31. Dynamics of the periodic frequency variations • How to explain a self frequency modulation in a diode laser ? WORKSHOP Les Houches - September 25, 26, 27st, 2001

  32. 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, 2001

  33. Narrow filter (30MHz) Large filter 3,5 GHz Relaxation oscillations filtering ? • 230MHz • COF • inifinite • 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) WORKSHOP Les Houches - September 25, 26, 27st, 2001

  34. Fabry-Pérot filter FWHM= 230MHz Fabry-Pérot filter FWHM=520 MHz Influence of the strengh of the non-linearity • How does the filter width influences the dynamical behaviour ? WORKSHOP Les Houches - September 25, 26, 27st, 2001

  35. Comparison of the spectra WORKSHOP Les Houches - September 25, 26, 27st, 2001

  36. Comparison of the different spectra • Controlled dynamics and chaos- Trade-off WORKSHOP Les Houches - September 25, 26, 27st, 2001

  37. Diode lasers basicsRelaxation 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 WORKSHOP Les Houches - September 25, 26, 27st, 2001

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