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General context Physics and nonlinear dynamics of semiconductor lasers

Introduction. 2. General context Physics and nonlinear dynamics of semiconductor lasers. Goal To understand and identify the physical mechanisms governing the optical instabilities. Methodology Physical models with adequate level of description

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General context Physics and nonlinear dynamics of semiconductor lasers

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  1. Introduction 2 • General context Physics and nonlinear dynamics of semiconductor lasers • Goal • To understand and identify the physical mechanisms governing the optical instabilities • Methodology • Physical models with adequate level of description • Electromagnetic problem • Semiconductor response

  2. EEL Active layer ~1 mm VCSEL Motivation 3 • Longitudinal Structures • Evolution of compound-cavity modes Feedback Mutual coupling • Vertical Structures • Light polarization • Transverse modes Free-running

  3. Part I:Compound-cavity edge-emitting semiconductor lasers + Contents – Part I: Compound-cavity edge-emitting semiconductor lasers + Part II: Polarization and transverse mode dynamics in vertical-cavity surface-emitting lasers + Perspectives +

  4. Semiconductor lasers with optical feedback + Contents – Part I: Compound-cavity edge-emitting semiconductor lasers – Semiconductor lasers with optical feedback + Bidirectionally coupled semiconductor lasers + Part II: Polarization and transverse mode dynamics in vertical-cavity surface-emitting lasers + Perspectives +

  5. 100 80 60 40 20 0 Tn-1 Tn Tn+1 ··· Intensity [arb. units] T. Heil et al, PRA 58, R2674 (1998) 0 200 400 600 800 1000 Time [ns] Semiconductor lasers with optical feedback 6 Low Frequency Fluctuations • Low frequency fluctuations weak to moderate feedback, and injection current close-to-threshold • Power dropouts (slow dynamics) D. Lenstra et al., IEEE J. Quantum Electron. 21, 674 (1985) C. H. Henry et al., IEEE J. Quantum Electron. 22, 294 (1986) J. Mørk et al., IEEE J. Quantum Electron. 24, 123 (1986) J. Sacher et al., Phys. Rev. Lett. 63, 2224 (1989) T. Sano, Phys. Rev. A 50, 2719 (1994) M. Giudici et al., Phys. Rev. E 55, 6414 (1997) T. Heil et al, Phys. Rev. A 58, 2672 (1998) G. van Tartwijk and G. Agrawal, Prog. Quantum Electron. 22, 43 (1998)

  6.  Experiments • DFB lasers • Strongside-mode suppression •  Modeling • Lang-Kobayashi model • Single longitudinal mode approximation solitary feedback T. Heil, et al. Opt. Lett.18, 1275 (1999) Semiconductor lasers with optical feedback 7 Distributed Feedback Lasers (DFB) • Contribution: Statistical characterization of the time T between consecutive power dropouts Comparison between experiments and simulations

  7. Semiconductor lasers with optical feedback 8 Lang-Kobayashi Model (LK) Weak feedback conditions SVA electric field: Carriers: Gain: R. Lang and K. Kobayashi, IEEE JQE 16, 347 (1980) Monochromatic solutions: External-cavity modes G.H.M van Tartwijk et al., IEEE JSTQE 1, 446 (1995)  Extensive numerical simulation of the LK model  Long time intervals (~ms) ~106 external roundtrips ~104 power dropouts

  8. Experiment LK model I=0.98 Ith T. Heil, et al. Opt. Lett.18, 1275 (1999) t=2.3 ns, Rm=5.4%,Rk=16% Semiconductor lasers with optical feedback 9 Results: Probability Density Functions • Control parameter • Injection current I/Ith • Transitions among regimes • Stable operation • LFFs • CC

  9. ExperimentNumerics I=0.98 Ith I=1.04 Ith I=1.08 Ith Semiconductor lasers with optical feedback 10 Results: Probability Density Functions • Control parameter • Injection current I/Ith • Transitions among regimes • Stable operation • LFFs • CC • Distribution of power dropouts • Dead time: refractory time • One side exponential decay t=2.3 ns, Rm=5.4%,Rk=16%

  10. Normalization LFF onset Power law g –1.0 J. Mulet et al., Phys. Rev. E 59, 5400 (1999) T. Heil et al., Opt. Lett. 18, 1275 (1999) t=2.3 ns, Rm=5.4%,Rk=16% Semiconductor lasers with optical feedback 11 Results: Scaling Laws • Transition from Stable LFF regime Tscales with the injection current • Power dropouts ~ Intermittent process

  11. Bidirectionally coupled semiconductor lasers +

  12. I2 r’ r E2 L+l Modeling: Electromagnetic problem Tasks J. Mulet et al., PRA 65, 063815 (2002) Synchronization of distant oscillators T. Heil et al., PRL 86, 795 (2001) J. Mulet et al., Proc. SPIE 4283, 293 (2001) Bidirectionally coupled semiconductor lasers 13 Motivation I1 r r’ E1 z • Natural generalization of the feedback system Passive mirror  Active semiconductor section • Nonlinear feedbackeffect –L–l –l 0 l Generalize unidirectional or lateral coupling

  13. Mutual injection with delay • Monochromatic solutions compound-cavity modes • Symmetric: In-phase, anti-phase locking • Experiments • Twin Fabry-Perot lasers c Bidirectionally coupled semiconductor lasers 14 Dynamical Properties • Phenomenological modelweak coupling, no detuning J. Mulet et al., PRA 65, 063815 (2002) A. Hohl et al., PRL 78, 4745 (1997)

  14. Twofold threshold behavior upon coupling increases 1. Onset of coupling-induced instabilities  Irregular pulsations with small correlation 2. Transition to correlated dynamics Normalized cross-correlation 1 2 J. Mulet et al., Proc. SPIE 4283, 293 (2001) Bidirectionally coupled semiconductor lasers 15 Results:Synchronization Scenario D=0and I1=I2 long coupling times: tc ~ 4 ns Symmetric conditions

  15. Synchronized subnanosecond pulsations with a time shift I1=I2 < 2Ithsol Experiment Numerics tc Intensity Intensity 0 2 4 6 8 10 0 2 4 6 8 10 Time / ns Time / ns Bidirectionally coupled semiconductor lasers 16 Results:Dynamics in regime 2 tc Experiment tc Numerics LASER 1 • I1=I2IthsolCorrelated power dropouts with a time shift Intensity Intensity LASER 2 400 450 500 550 600 400 450 500 550 600 Time / ns Time / ns T. Heil et al. PRL 86, 795 (2001)

  16. Phase h1 (t)=j2(t-tc)-j1(t) h2 (t)=j1(t-tc)-j2(t) • Within phase locking regime although do not occur dynamically Bidirectionally coupled semiconductor lasers 17 Results:Achronal Synchronization • Isochronal state + small perturbation  Achronal state Intensity Deterministic simulation

  17. Conclusion to Part I 18 • Feedback-induced instabilities appear in singlemode lasers • Power law <T>~(I/ILFF-1)–1 associated with the transition from stable operation to LFFs. Deterministic mechanisms • Phase-locked compound-cavity modes of two mutually coupled semiconductor lasers • Twofold threshold behavior: i) coupling-induced instabilities ii) transition to synchronization • Achronal synchronization persists in symmetrically coupled lasers

  18. Part II: Polarization and transverse mode dynamics in vertical-cavity surface-emitting lasers + Contents – Part I: Compound-cavity edge-emitting semiconductor lasers + Part II: Polarization and transverse mode dynamics in vertical-cavity surface-emitting lasers + Perspectives +

  19. Polarization resolved intensity noise in VCSELs + Contents – Part I: Compound-cavity edge-emitting semiconductor lasers + Part II: Polarization and transverse mode dynamics in vertical-cavity surface-emitting lasers – Polarization resolved intensity noise in VCSELs + Spatiotemporal optical model for VCSELs + Perspectives +

  20. Fundamental mode Ex Ey z No preferential direction imposed by the geometry Top contact Oxide layer Active region x y Bottom contact Two different contributions Polarization resolved intensity noise in VCSELs 21 What does Determine the Light Polarization State? M. San Miguel, In semiconductor quantum optoelectronics, 339 (1999) • Active material (QWs) • Light – matter • Nonlinear effect • Linear effect • Cavity anisotropiesgp, ga • Preferential directions x (HF),y (LF) •  Passive material

  21. Spin-Flip Model M. San Miguel, Q. Feng, J.V. Moloney, PRA 54, 1728 (1995) spontaneous recombination rate injection rate spin-flip rate stimulated recombination noise Polarization resolved intensity noise in VCSELs 22 Spin Dynamics and Light Polarization State Spin-flip reverse electron’s spin gj +1/2 –1/2 Ne– Electrons CB Holes HHB Ne+ E+ ge ge Four-level system: magnetic sublevels E– Nh+ Nh– Jz=+3/2 Jz= –3/2 Population inversion per spin channel: NNe – Nh

  22. Spin-Flip Model M. San Miguel, Q. Feng, J.V. Moloney, PRA 54, 1728 (1995) spontaneous recombination rate injection rate spin-flip rate stimulated recombination noise Polarizationresolved intensity noise in VCSELs 23 Spin Dynamics and Light Polarization State Nonthermal polarization switching and optical bistability –J. Martín-Regalado et al., APL 70, 3550 (1997)–M. B. Willemsen, et al. PRL 82, 4815 (1999) Nonlinear anisotropies in the spectra of the polarization components – M.P. van Exter, et al. PRL 80, 4875 (1998) Anticorrelated polarization fluctuations –E. Goodbar et al., APL 67,3697 (1995)– C. Degen et al., Electron Lett.34, 1585 (1998) • VCSELs in magnetic fields (Larmor oscillations) – S. Hallstein et al. PRB 56, R7076 (1997)– A. Gahl et al. IEEE JQE 35, 342 (1999)

  23. Spin-flip rate gj E+ E– Birefringence Polarization resolved intensity noise in VCSELs 24 Anticorrelated Polarization Fluctuations Effective birefringence ROs ROs a=3, gp=1 ns–1,gs=100 ns–1, I/Ith=1.04 J. Mulet et al., PRA 64, 023817 (2001)

  24. Spatiotemporal optical model for VCSELs +

  25. Motivation • Joint interplay of transverse and polarizationinstabilities 90º 0º current C. Degen et al. J. Opt. B2, 517 (2000) T. Ackemann et al, J. Opt. B 2, 406 (2000) H. Li et al., Chaos 4, 1619 (1994) Spatiotemporal optical model for VCSELs 26 Transverse Effects in VCSELs • Polarization in the fundamental transverse mode •  Spin-flip model M. San Miguel et al, PRA 54, 1728 (1995) •  Dressed spin-flip model S. Balle et al, Opt. Lett. 24, 1121 (1999) • Spatiotemporal model •  Large signal dynamics •  Mechanisms that affect the selection of • Transverse modes and Polarization modes

  26. Passive waveguiding • Material polarization diffraction thermal lensing Instantaneous frequency Spatiotemporal optical model for VCSELs 27 Spatiotemporal Optical Model • Transverse dependence of SVA electric fields cavity losses QW Material Polarization linear anisotropies spontaneous emission J. Mulet and S. Balle. IEEE J. Quantum Electron. 38, 291 (2002)

  27. Carrierdynamics (Spin-Flip) spontaneous recombination current profile spin flip for e- stimulated recombination (Spatial Hole Burning) carrier diffusion Spatiotemporal optical model for VCSELs 28 Material Model • Optical susceptibility to circular light Normalized frequency: Detuning: S. Balle. Phys. Rev. A 57, 1304 (1998) J. Mulet and S. Balle. IEEE J. Quantum Electron. 38, 291 (2002)

  28. Structures Bottom-emitter Top-emitter Dntl=5·10–3 Dntl=5·10–4 Dntl=10–3 Dntl=10–2 Parameters: fc=15mm, fg=18mm Spatiotemporal optical model for VCSELs 29 Results:Transverse Mode Selection at Threshold • Analytical theory: Stability analysis “off” solution J. Mulet and S. Balle. IEEE JQE38, 291 (2002) • Relevant factors when ( I Ith) • - Material gain: Detuning • - Modal gain : Confinement  thermal lensing & current profile • - However SHB neglected

  29. Spatiotemporal optical model for VCSELs 30 Results:Transverse Mode Selection at Threshold Numerical simulations LP10 Disc LP12 sin - cos Ring Parameters: fc=15 mm, fg=18 mm, D=0.25

  30. mon mon=1 mth 9 mth mb=0.85 mth current mth 8290 8288 8286 8284 mb 1ms 1ns 1ns wavelength () time 0 400 800 1200 1600 time (ps) Spatiotemporal optical model for VCSELs 31 Subnanosecond Electrical Excitation Excitation current pulses  Experimental findings Delayed onset of higher order modes O. Buccafusca, et al., IEEE JQE35, 608 (1999) M. Giudici, et al., Opt. Comm. 158, 313 (1998) O. Buccafusca, et al., APL68, 590 (1996)

  31. mon mon=1 mth 9 mth mb=0.85 mth current mth 8290 8288 8286 8284 mb 1ms 1ns 1ns wavelength () time 0 400 800 1200 1600 time (ps) Spatiotemporal optical model for VCSELs 32 Subnanosecond Electrical Excitation Excitation current pulses  Experimental findings Delayed onset of higher order modes O. Buccafusca, et al., IEEE JQE35, 608 (1999) M. Giudici, et al., Opt. Comm. 158, 313 (1998) O. Buccafusca, et al., APL68, 590 (1996) Results:Bottom-Emitter mon = 4 mth Evolution of the near fields (Both LP) 22 mm 12 mm 0º 0º 90º 90º J. Mulet et al., Proc SPIE 4283, 293 (2001)

  32. fc=22 mm 400 300 200 100 0 Turn-on delay (ps) 0 2 4 6 8 10 Ip/Ith t • Physical mechanisms defining the onset D Spatial hole burning g N y x progressive enhance of the gain of higher-order modes Blue-shift gain peak (band filling) w Spatiotemporal optical model for VCSELs 33 Turn-on Delay - Fundamental mode fc=12 mm fc=22 mm O. Buccafusca et al., IEEE JQE35, 608 (1999) J. Mulet et al., Proc.SPIE4283, 139 (2001)

  33. Near Fields Optical spectra 0º Strong TL Dntl=10–2 90º 0º Weak TL Dntl=5·10–4 90º Time [ns] fc=15 mm,m=4mth, gp=30 ns– 1, ga=0.5 ns–1, gJ=25 ns–1, D=0.5 Spatiotemporal optical model for VCSELs 34 Turn-on Delay versus Thermal Lensing Turn-on delay  when thermal lensing (TL)  Single mode operation: i) Moderate thermal lensing ii) Detuning at the blue side of the gain peak

  34. single mode favored by weak thermal lensing • passive guiding carrier-induced refractive index • Dynamical modes spatiotemporal model Modal expansion ? Thermal lensing Spatiotemporal model Spatiotemporal optical model for VCSELs 35 Carrier-Induced Index of Refraction Gain-guided VCSELs passive guiding = thermal lensing

  35. turn-off transients Secondary Pulsations A. Valle et al, JOSAB 12, 1741 (1995) Results Intense thermal lensing Spatiotemporal Modal expansion hole filling Good agreement Dn=10–2Disc: mb= mth, mon= 4mth, D=1.0 Optical modal expansion 36 Large-signal Current Modulation I Small devices (6mm single mode) Large-signal modulation 4mth current mth time J. Mulet and S. Balle. PRA 66, 053802 (2002)

  36. turn-off transients Secondary Pulsations A. Valle et al, JOSAB 12, 1741 (1995) hole filling Worse agreement Optical modal expansion 37 Large-signal Current Modulation II Small devices (6mm single mode) Large-signal modulation 4mth current mth time Results weak thermal lensing J. Mulet and S. Balle. PRA 66, 053802 (2002) Spatiotemporal Modal expansion Dn=3·10–3Disc: mb= mth, mon= 4mth, D=1.0

  37. Optical Susceptibility Evolution  Profile shrinkage  Carrier antiguiding (Extra waveguide!) Initial Final  Spatial hole burning Optical modal expansion 38 Origin of the discrepancies between the models? (weak TL, Dn=9·10–4) • Optical profiles fromthe spatiotemporal model during turn-on turn-on intensity J. Mulet and S. Balle. PRA 66, 053802 (2002)

  38. Selection of transverse modes • Close-to-threshold:Onset in a higher-order mode in top-emitters • material gain & optical confinement •  Large-signal excitation • Well defined onset of transverse modes • Secondary pulsations spatial-hole burning carrier diffusion band filling Conclusions to Part II 39 • Relevance of spin determining light polarization •  Anticorrelated polarization fluctuations •  Selection of polarization modes • Optical modal expansion •  Strong TL: Validity of the modal expansion Dntl3·10–3 •  Weak TL : Distortion of the optical profiles • Spatial redistribution of carrier-induced refractive index

  39. Perspectives + Contents – Part I: Compound-cavity edge-emitting semiconductor lasers + Part II: Polarization and transverse mode dynamics in vertical-cavity surface-emitting lasers + Perspectives +

  40. Novel applications of semiconductor lasers  Encoded communication systems using chaotic carriers • Nonlinear Optical Feedback • CSK – On-off Phase Shift Keying C. Mirasso et al, IEEE PTL 14, 456 (2002) – T. Heil et al, IEEE JQE 38, 1162 (2002) • VCSEL with Saturable Absorber – Vectorial Chaos A. Scirè et al, Opt. Lett. 27, 391 (2002) • Polarization Encoding • Device design • Spatiotemporal model for VCSELs • - Range of single mode operation • - Realistic large-signal modulation conditions • • Self-consistent solutions • • VCSEL arrays • • VCSEL with optical injection / feedback • • Mode locking in VCSELs Extension Perspectives 41

  41. Acknowledgments + • C. Mirasso and M. San Miguel • Technical University of Darmstadt (Germany) •  T. Heil and I. Fischer • Universidad de la República Uruguay •  C. Masoller • Institut Mediterrani d’Estudis Avançats •  S. Balle and A. Scirè • Instituto de Física de Cantabria •  A. Valle and L. Pesquera • Vrije University of Brussels  J. Danckaert

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