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Synchronization and clustering in a quantum dot laser

Outline. Self-assembled quantum dot lasers: some properties of a different laserMultimode lasing: clusteringCorrelation measurements: antiphase dynamics- from disordered to

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Synchronization and clustering in a quantum dot laser

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    1. Synchronization and clustering in a quantum dot laser Evgeny Viktorov Paul Mandel Universit Libre de Bruxelles Yann Tanguy John Houlihan Guillaume Huyet National University of Ireland, Cork, Ireland Andrei Vladimirov Weierstrass Institute, Berlin, Germany

    2. Outline Self-assembled quantum dot lasers: some properties of a different laser Multimode lasing: clustering Correlation measurements: antiphase dynamics- from disordered to regular switching Modeling: physical background Modeling: (non)degenerate Hopf, normal forms

    3. Quantum dots: nanocrystalline gain medium

    4. A summary of laser performance: Low threshold current < 30 A/cm2 (Huang 2000; Park 2000) Modulation characteristics: 10 Gb/s (Hatori 2004, Kuntz 2005) CW operation up to 80C Small a-factor < 1 or as low as 0.7 (Martinez, 2005) ?? Prospects: Lowest threshold current High temperature operation Tunability High quality beam Low sensitivity to feedback Reliable lasing without filamentation and parasitic instabilities for ultrahigh-speed applications dream laser

    5. Seminal picture

    6. Multimode lasing

    7. We measure with:

    8. Control parameter (pumping current) leads to increasing : number of lasing modes asymmetry in the gain profile a-factor - a global measure of the phase-amplitude coupling.

    9. Experimental timetraces Antiphase fluctuations : strongly chaotic 40 % of the amplitude low frequency range : up to 50 MHz 50 MHz << 5GHz (relaxation oscillation frequency timescale of field-matter interaction): Mode-to-Mode coupling???

    10. Experimental timetraces Observations: total output remains nearly constant antiphase fluctuations : perfect antisynchronization, correlation??? "Chaos must shimmer through the veil of order, Novalis

    11. Experimental power spectra:

    13. Detection noise influence two detectors, the same mode, phase difference.

    14. Equally separated clusters?

    15. Correlation dimension vs clustering

    16. Cross-correlation measurements:

    17. Cross-correlation measurements: from disorder to regularity

    18. Main Results clustering in averaged frequencies the spread of frequencies narrows oscillations can be equally phase-shifted Switching from blue to red MODE-TO-MODE COUPLING

    19. Quantum Well Laser: experiment

    20. Quantum Well Laser: more advanced modeling

    21. Two types of semiconductor lasers Quantum Well Laser a-factor 4-5 homogemeous material strong carrier diffusion Quantum Dot Laser a-factor <1, increasing with the current inhomogemeous material small carrier diffusion total output remains nearly constant antiphase fluctuations low frequency range periodic, 100 % of the amplitude the same frequency of oscillations for all modes total output remains nearly constant antiphase fluctuations low frequency range chaotic, 40 % of the amplitude different frequences of oscillations, clustering

    22. Physical model Equations: The modal gains and the cross-coupling coefficient typically depend on four-wave-mixing processes and inhomogeneous broadening, but physical mechanisms are complex and not fully understood yet

    23. Challenge Quantum dot laser is an ensemble of independent nanolasers ??? carrier capture and recombination in individual quantum dots are random processes so each quantum dot couples to its own excited carrier Conclusion: UNCORRELATED OUTPUT FROM THE DIFFERNET QUANTUM DOTS We assume: Modes are globally coupled Hopf bifurcation Inhomogeneous broadening (different shapes/sizes) results in different frequencies of oscillations Two main effects to describe: -frequency clustering -antiphase state

    24. Degenerate Hopf Equations: First good approximation: frequency dependent parameters are equal Degenerate Hopf, normal form equations:

    25. Hopf: nondegeneracy - the modes have different average oscillation frequencies. - we relate this non-degeneracy to the high degree of inhomogeneous broadening. weak perturbation of the linear part Phase approximation: Kuramoto, Hansel Global linear coupling do not exhibit phase clustering behavior right after Hopf bifurcation (Okuda,1993) Nonlinear coupling: frequency clustering? antiphase state?

    26. Normal forms, N=5

    27. Normal forms, N=5: clustering

    28. conclusion Modal oscillations in quantum dot laser result from the global coupling and exhibit clustering and antiphase state.

    29. Thank you!

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