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General contextGeneral context Physics and nonlinear dynamics of semiconductor lasers Introduction 2 2 Goal Goal To understand and identify the physical.

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Presentation on theme: "General contextGeneral context Physics and nonlinear dynamics of semiconductor lasers Introduction 2 2 Goal Goal To understand and identify the physical."— Presentation transcript:

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

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

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

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

6 Low frequency fluctuations weak to moderate feedback, and injection current close-to-threshold Low Frequency Fluctuations 6 6 Semiconductor lasers with optical feedback 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) Power dropouts (slow dynamics) T n-1 T n T n+1 ··· 0 200 400 600 800 1000 100 80 60 40 20 0 Time [ns] Intensity [arb. units] T. Heil et al, PRA 58, R2674 (1998)

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

8 Lang-Kobayashi Model (LK) 8 8 Semiconductor lasers with optical feedback Weak feedback conditions 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) ~ 10 6 external roundtrips ~ 10 4 power dropouts SVA electric field: Carriers: Gain: R. Lang and K. Kobayashi, IEEE JQE 16, 347 (1980)

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

10 Results: Probability Density Functions 10 Semiconductor lasers with optical feedback Experiment Numerics I =0.98 I th I=1.04 I th I=1.08 I th = 2.3 ns, R = 5.4%, R 16 Distribution of power dropouts – Dead time: refractory time – One side exponential decay Control parameter Injection current I/I th Transitions among regimes – Stable operation – LFFs – CC

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

12 + + Bidirectionally coupled semiconductor lasers

13 Natural generalization of the feedback system Passive mirror Active semiconductor section Nonlinear feedback effect Motivation 13 Bidirectionally coupled semiconductor lasers –L– l–L– l – l– l l z I1I1 r 0 L+ l I2I2 E 2 rr r E 1 Synchronization of distant oscillators Modeling: Electromagnetic problem Tasks J. Mulet et al., PRA 65, 063815 (2002) T. Heil et al., PRL 86, 795 (2001) J. Mulet et al., Proc. SPIE 4283, 293 (2001) Generalize unidirectional or lateral coupling

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

15 Results: Synchronization Scenario 15 Bidirectionally coupled semiconductor lasers =0 and I long coupling times: c ~ 4 ns Symmetric conditions 1. Onset of coupling-induced instabilities Irregular pulsations with small correlation 2. Transition to correlated dynamics Twofold threshold behavior upon coupling increases Normalized cross-correlation 12 J. Mulet et al., Proc. SPIE 4283, 293 (2001)

16 th sol Correlated power dropouts with a time shift Results: Dynamics in regime 2 16 Bidirectionally coupled semiconductor lasers T. Heil et al. PRL 86, 795 (2001) Experiment Numerics Intensity 400 450 500 550 600 Time / ns LASER 1 LASER 2 c c Synchronized subnanosecond pulsations with a time shift th sol Intensity Time / ns Experiment Numerics 0 2 4 6 8 10 Time / ns c

17 Isochronal state + small perturbation Achronal state Results: Achronal Synchronization 17 Bidirectionally coupled semiconductor lasers Intensity Within phase locking regime although do not occur dynamically t t c t Phase Deterministic simulation

18 18 Conclusion to Part I Power law ~(I/I LFF -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 Feedback-induced instabilities appear in singlemode lasers

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

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

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

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

23 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 Polarization resolved intensity noise in VCSELs Spin Dynamics and Light Polarization State noise spontaneous recombination rate injection ratespin-flip rate M. San Miguel, Q. Feng, J.V. Moloney, PRA 54, 1728 (1995) Spin-Flip Model stimulated recombination

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

25 + + Spatiotemporal optical model for VCSELs

26 Spatiotemporal model Large signal dynamics Mechanisms that affect the selection of Transverse modes and Polarization modes Transverse modes and Polarization modes Transverse Effects in VCSELs 26 Spatiotemporal optical model for VCSELs Motivation transverse and polarization instabilities Joint interplay of transverse and polarization instabilities C. Degen et al. J. Opt. B 2, 517 (2000) T. Ackemann et al, J. Opt. B 2, 406 (2000) H. Li et al., Chaos 4, 1619 (1994) 0º 90º current 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)

27 Spatiotemporal Optical Model 27 Spatiotemporal optical model for VCSELs 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) Material polarization Instantaneous frequency Passive waveguiding thermal lensing diffraction

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

29 Results: Transverse Mode Selection at Threshold 29 Spatiotemporal optical model for VCSELs Analytical theory: Stability analysis off solution Relevant factors when ( I I th ) - Material gain: Detuning - Modal gain : Confinement thermal lensing & current profile - However SHB neglected J. Mulet and S. Balle. IEEE JQE 38, 291 (2002) Structures Parameters: c =15 m, g =18 m n tl =5·10 –3 n tl =5·10 –4 n tl =10 –3 n tl =10 –2

30 30 Spatiotemporal optical model for VCSELs Parameters: c =15 m, g =18 m, =0.25 Numerical simulations LP 12 sin - cos LP 10 Results: Transverse Mode Selection at Threshold

31 Subnanosecond Electrical Excitation 31 Spatiotemporal optical model for VCSELs Excitation current pulses Experimental findings O. Buccafusca, et al., IEEE JQE 35, 608 (1999) M. Giudici, et al., Opt. Comm. 158, 313 (1998) O. Buccafusca, et al., APL 68, 590 (1996) Delayed onset of higher order modes 8290 8288 8286 8284 0 400 800 1200 1600 time (ps) wavelength ( ) on 1ns th b current on = 1 th 9 th b = 0.85 th 1 s 1ns time

32 Subnanosecond Electrical Excitation 32 Spatiotemporal optical model for VCSELs Evolution of the near fields (Both LP) Results: Bottom-Emitter on = 4 th 12 m 12 m 22 m 22 m 0º90º0º 90º Excitation current pulses Experimental findings O. Buccafusca, et al., IEEE JQE 35, 608 (1999) M. Giudici, et al., Opt. Comm. 158, 313 (1998) O. Buccafusca, et al., APL 68, 590 (1996) Delayed onset of higher order modes 8290 8288 8286 8284 0 400 800 1200 1600 time (ps) wavelength ( ) on 1ns th b current on = 1 th 9 th b = 0.85 th 1 s 1ns time J. Mulet et al., Proc SPIE 4283, 293 (2001)

33 Turn-on Delay 33 Spatiotemporal optical model for VCSELs - Fundamental mode c =12 m c =22 m O. Buccafusca et al., IEEE JQE 35, 608 (1999) 400 300 200 100 0 0 2 4 6 8 10 I p /I th Turn-on delay (ps) c =22 m J. Mulet et al., Proc. SPIE 4283, 139 (2001) Physical mechanisms defining the onset Spatial hole burning Blue-shift gain peak (band filling) N g progressive enhance of the gain of higher-order modes D x y t

34 Turn-on Delay versus Thermal Lensing 34 Spatiotemporal optical model for VCSELs Single mode operation: i) Moderate thermal lensing ii) Detuning at the blue side of the gain peak Turn-on delay when thermal lensing (TL) Strong TL Weak TL c m =4 th, p =30 ns – 1, a =0.5 ns –1, J =25 ns –1, Near Fields n tl =10 –2 n tl =5·10 –4 Time [ns] 0º 90º 0º 90º Optical spectra

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

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

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

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

39 39 Conclusions to Part II 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 Relevance of spin determining light polarization Anticorrelated polarization fluctuations Selection of polarization modes Optical modal expansion Strong TL: Validity of the modal expansion n tl 3·10 –3 Weak TL : Distortion of the optical profiles Spatial redistribution of carrier-induced refractive index

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

41 41 Perspectives Novel applications of semiconductor lasers 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 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

42 + + Acknowledgments Technical University of Darmstadt (Germany) T. Heil and I. Fischer Institut Mediterrani dEstudis Avançats S. Balle and A. Scirè Instituto de Física de Cantabria A. Valle and L. Pesquera Universidad de la República Uruguay C. Masoller C. Mirasso and M. San Miguel Vrije University of Brussels J. Danckaert


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