General context physics and nonlinear dynamics of semiconductor lasers
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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

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


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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

+


General context physics and nonlinear dynamics of semiconductor lasers

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

+


General context physics and nonlinear dynamics of semiconductor lasers

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)


General context physics and nonlinear dynamics of semiconductor lasers

  •  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


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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%


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

Bidirectionally coupled semiconductor lasers

+


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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)


General context physics and nonlinear dynamics of semiconductor lasers

  • 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


General context physics and nonlinear dynamics of semiconductor lasers

  • 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)


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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

+


General context physics and nonlinear dynamics of semiconductor lasers

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

+


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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)


General context physics and nonlinear dynamics of semiconductor lasers

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)


General context physics and nonlinear dynamics of semiconductor lasers

Spatiotemporal optical model for VCSELs

+


General context physics and nonlinear dynamics of semiconductor lasers

  • Motivation

    • Joint interplay of transverse and polarizationinstabilities

90º

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


General context physics and nonlinear dynamics of semiconductor lasers

  • 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)


General context physics and nonlinear dynamics of semiconductor lasers

  • 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)


General context physics and nonlinear dynamics of semiconductor lasers

  • 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


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

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)


General context physics and nonlinear dynamics of semiconductor lasers

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

90º

90º

J. Mulet et al., Proc SPIE 4283, 293 (2001)


General context physics and nonlinear dynamics of semiconductor lasers

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)


General context physics and nonlinear dynamics of semiconductor lasers

Near Fields

Optical spectra

Strong

TL

Dntl=10–2

90º

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


General context physics and nonlinear dynamics of semiconductor lasers

  • 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


General context physics and nonlinear dynamics of semiconductor lasers

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)


General context physics and nonlinear dynamics of semiconductor lasers

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


General context physics and nonlinear dynamics of semiconductor lasers

  • 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)


General context physics and nonlinear dynamics of semiconductor lasers

  • 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


General context physics and nonlinear dynamics of semiconductor lasers

Perspectives

+

Contents

Part I: Compound-cavity edge-emitting semiconductor lasers

+

Part II: Polarization and transverse mode dynamics in

vertical-cavity surface-emitting lasers

+

Perspectives

+


General context physics and nonlinear dynamics 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

    • 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


General context physics and nonlinear dynamics of semiconductor lasers

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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