Physics of CAVITY SOLITONS in Physics of CAVITY SOLITONS in SemiconductorsSemiconductors

• L.A. Lugiato, G. Tissoni, M. L.A. Lugiato, G. Tissoni, M. Brambilla, T. Maggipinto Brambilla, T. Maggipinto INFM, ItalyINFM, Italy

• R. Kuscelewicz, S. Barbay R. Kuscelewicz, S. Barbay LPN, CNRSLPN, CNRS

• X. Hachair, S. Barland, L. Furfaro, M. X. Hachair, S. Barland, L. Furfaro, M. Giudici, J. Tredicce Giudici, J. Tredicce INLN, CNRSINLN, CNRS

• R. Jäegger R. Jäegger ULM Photonics, GermanyULM Photonics, Germany

FUNFACS FUNFACS

Spatially Extended SystemSpatially Extended System

• Property:Property:Correlation length Correlation length much smaller much smaller

than than the size of the the size of the systemsystem

Some Nonlinear EffectsSome Nonlinear Effects

1.1. Strong non linearityStrong non linearity2.2. Strong competing Strong competing

mechanisms: mechanisms: Dispersion-non linearity Dispersion-non linearity Diffraction-non linearityDiffraction-non linearity

Possible results: Possible results: a. a. pattern formationpattern formationb. b. bistability between bistability between

patternspatternsc.c. Localized structures, Localized structures, (Rosanov, (Rosanov, Opt. Spectrosc.Opt. Spectrosc. 6565, ,

449-450 (1988))449-450 (1988))

Nonlinear medium

Holding beam

Writingpulses

Output

Mirror Mirror

Optical resonator

Cavity Solitons

Optical Cavity Soliton:

How to generate them? (in theory)

Patterns versus Cavity Patterns versus Cavity SolitonsSolitons• Optical patterns may Optical patterns may

display an array of display an array of light spots, but the light spots, but the intensity peaks are intensity peaks are strongly correlated strongly correlated with one another, so with one another, so that they cannot be that they cannot be manipulated as manipulated as independent objects.independent objects.

S. Barland, et al. Nature, 2002

Theoretical ModelTheoretical Model

NdENINt

N

EiEENiETit

EI

22

2

||,Im

,1

Brambilla, M., et al. Phys. Rev. Lett. 79, 2042-2045 (1997). Spinelli, L. et al. Phys. Rev. A 58, 2542-2559 (1998).

Where can we find solitons?Where can we find solitons?

Patterns in VCSEL with Patterns in VCSEL with InjectionInjection

Ackemann, T., et al. Opt. Lett. 25, 814-816 (2000).

CS can also appear spontaneously ...........

In this animation we reduce the injection level of the holding beam starting from values where patterns are stable and ending to homogeneous solutions which is the only stable solution for low holding beam levels. During this excursion we cross the region where CSs exist. It is interesting to see how pattern evolves into CS decreasing the parameters. Qualitatively this animation confirms the interpretation of CS as “elements or remains of bifurcating patterns”.

Experiment Numerics

The holding beam HB has been tilted in order to vectorially compensate the force exerted on CS by the cavity length gradient across the cavity.

  

 Properties of Cavity Solitons and Localized Structures. 

1.- Spatially localized (of course). 2.- Single addressable objects. A single peak structure can be switch on and off independently of the others if the parameter values are « well » choosen. 3.- Intensity or phase gradients can control their position and/or speed of motion. 

They move ..............

In order to control CSs positions we inject an holding beam in In order to control CSs positions we inject an holding beam in form of interferenceform of interference

fringes. The fringe pattern is moved in front of the VCSEL fringes. The fringe pattern is moved in front of the VCSEL allowing for repositioning ofallowing for repositioning of

CSs. As the pattern is moved the spatial frequency of the CSs. As the pattern is moved the spatial frequency of the fringes is gradually decreasedfringes is gradually decreased

• As the fringes are moved CSs follow the peak of HB intensity for a wide distance.

• CSs “feel” the fringes as their width are comparable to the CSs width

• They disappear for exiting from the spatial region where they are stable or for collision against pattern or against other CSs.

• Impurities make the path rather random

X. Hachair, et al. PRA (2004)

Analysis of the switching process/2

The switch-on time of CS after application of the WB is composed by the CS buildup time and a delay time between the WB application and the start of the CS rising front.

CS buildup time results around 600 ps, both in experiment and theory.

Delay time is a function of parameters, such as WB phase (relative to the HB), WB power and current injection level.

CS build-up time and delay time

0 2 4 6 8 10 12 14 16 18 200,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

t (ns)

Experiment Theory

0,0 0,3 0,6 0,9 1,2 1,5 1,8 2,1 2,4 2,7 3,00,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

|E|

t (ns)

= 0o

= 57o (1 rad)

= 70o (1.22 rad)

Analysis of the switching process/3

WB phase (relative to the the holding beam) is a critical parameter: delay time is minimum when = 0 both in experiment and theory

(Optimal phase is 0)

Delay time vs phase

ExperimentTheory

X. Hachair at al. Submitted (2005)

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,40,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5 Solid lines: intracavity field |E| at centerDashed lines: total injected field EI at center

t (ns)

Analysis of the switching process/4

Delay time vs WB power

Delay time decreases when WB power is increased, both in experiment and theory

Experiment Theory

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,00,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

t (ns)

|E| I = 1.97 I = 2 I = 2.01

Analysis of the switching process/5

In the experiment, delay time decreases when bias is increased Experiment and theory disagree....

Delay time vs pumping current

Experiment Theory

1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,40,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

|ES|

I

Homogeneous steady state curve (black stable, red unstable) and CS branch as a function of the injected current. I = 1 is transparency, I = 2.11 is the lasing threshold. CS branch extends from I = 1.97 to I = 2.01.The injected field is EI = 0.75obtained at I = 2.

• Numerical results Numerical results obtained by obtained by including including

temperature temperature variations induced variations induced by the excitation by the excitation current:current:

the switch on time the switch on time decreases as we decreases as we increase the increase the currentcurrent

Quantitative Quantitative Changes in the Changes in the switch on time due switch on time due to noise effects. to noise effects.

VCSEL above thresholdVCSEL above threshold

Cavity Solitons in a VCSEL Cavity Solitons in a VCSEL above thresholdabove threshold

Temporal oscillationsTemporal oscillations

Correlation measurementsCorrelation measurements

Without holding beam With holding beam

Soliton CorrelationsSoliton Correlations

They also may appear They also may appear spontaneously and they can be spontaneously and they can be movedmoved

Correlated structureCorrelated structure

Fronts between a pattern and a Fronts between a pattern and a homogeneous solutionhomogeneous solution

If the fronts are stable, it is possible to create a localized state. The number of high intensity peaks inside the localized structure depends on the distance between the fronts.

Stability of a front Stability of a front Y. Pommeau, Y. Pommeau,

INTERACTION BETWEEN FRONTSCoullet, P., Riera, C., Tresser, C. Stable Static Localized Structures in One Dimension. Phys. Rev. Lett. 84, 3069-3072 (2000).

Front InteractionFront InteractionM. Clerc, submitted (2005)M. Clerc, submitted (2005)

Conclusions

We have proven experimentally and theoretically that Cavity Solitons in VCSELS below and above laser threshold are robust structures that can be switched on and off by all optical control, and move under the influence of intensity gradients.

The CS switching process has been analyzed in details:CS build-up time is on the order of half nanosecond,

while the delay time after WB excitation depends critically on parameters, such as the relative phase between HB and WB, the current injection level, the WB energy

• We are able to generate single and multiple peak localized structures structures and to control their generation

Robin Loznal / The Daily Inter

I hope you enjoyed the I hope you enjoyed the presentationpresentation

• If not, please If not, please ….do not kill ….do not kill me!!me!!

• If Yes, If Yes,

Thank you Thank you

• CAVITY SOLITON is aCAVITY SOLITON is a

LOCALIZED STRUCTURELOCALIZED STRUCTURE

A pattern that can « live » A pattern that can « live » independently in an spatially independently in an spatially extended systemextended system

CS in Semiconductors: possible CS in Semiconductors: possible applicationsapplications

• Reconfigurable buffer memoryReconfigurable buffer memory

• Serial-parallel converterSerial-parallel converter

• Shift registerShift register

• All-optical processorAll-optical processor

Numerical simulation showing the intracavity field amplitude. The initial condition are filaments obtained at EI = 0.9, the evolution (1 ns) is with EI = 0.75.

Analysis of the switching process/1

WB is a Gaussian pulse injected into the cavity for 100 ns. Time to reach the stationary value is 700 psWB width: 10 - 20 m WB power: 10 -160 W (HB power: 8.5 mW)

t

WB peak intensity vs time

0

p

0

700 ps 100 ns

To analyse the switching process in details, an EOM (Electro-Optical Modulator) has been used to replace the AOM (Acusto Optical Modulator).

1.      Ackemann, T. et al. J. Opt. B: Quantum Semiclass. Opt. 2, 406-412 (2000).

Spatially resolved spectra

Including Including (x)=(x)=00-- x x

Ei = 1.8 Ei= 2.00 = -1 = 5

• Introduce the current Introduce the current crowding effect:crowding effect:

I = I(r)= I = I(r)= IIoo-Xexp[-r-Xexp[-r22/r/r0022]]

where r=xwhere r=x22+y+y22. . Io: Io: ~20% above~20% above thresholdthreshold

• Intensity distribution Intensity distribution when pumping above when pumping above thresholdthreshold

 

LOCALIZED STRUCTURES 

 Coullet, P., Riera, C., Tresser, C. Stable Static Localized Structures in One Dimension. Phys. Rev. Lett. 84, 3069-3072 (2000). SPATIAL STRUCTURES (CONCENTRATED IN RELATIVELY SMALL REGION OF AN EXTENDED SYSTEM) CREATED BY STABLE FRONTS CONNECTING TWO SPATIAL STRUCTURES

 

-2,5

-1,5

-0,5

0,5

1,5

0 7,5 15 22,5 30 37,5 45 52,5