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