Physics of CAVITY SOLITONS in Semiconductors

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Physics of CAVITY SOLITONS in Semiconductors

• L.A. Lugiato, G. Tissoni, M. Brambilla, T.
  Maggipinto INFM, Italy
• R. Kuscelewicz, S. Barbay LPN, CNRS
• X. Hachair, S. Barland, L. Furfaro, M. Giudici,
  J. Tredicce INLN, CNRS
• R. Jäegger ULM Photonics, Germany
• FUNFACS

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Spatially Extended System

• Property
• Correlation length
• much smaller than
• the size of the
• system

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Some Nonlinear Effects

• Strong non linearity
• Strong competing mechanisms
• Dispersion-non linearity
• Diffraction-non linearity
• Possible results
• a. pattern formation
• b. bistability between patterns
• c. Localized structures,
• (Rosanov, Opt. Spectrosc. 65, 449-450 (1988))

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Optical Cavity Soliton How to generate them?
(in theory)
Optical resonator
Holding beam
Output
Nonlinear medium
Writing pulses
Cavity Solitons
Mirror
Mirror
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Patterns versus Cavity Solitons

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

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S. Barland, et al. Nature, 2002
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Theoretical Model
Brambilla, M., et al. Phys. Rev. Lett. 79,
2042-2045 (1997). Spinelli, L. et al. Phys. Rev.
A 58, 2542-2559 (1998).
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Where can we find solitons?
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Patterns in VCSEL with Injection
Ackemann, T., et al. Opt. Lett. 25, 814-816
(2000).
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CS can also appear spontaneously ...........
Numerics
Experiment
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.
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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.
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     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.  
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They move ..............
In order to control CSs positions we inject an
holding beam in form of interference fringes.
The fringe pattern is moved in front of the VCSEL
allowing for repositioning of CSs. As the pattern
is moved the spatial frequency of the fringes 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)
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Analysis of the switching process/2
CS build-up time and delay time
Experiment
Theory
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.
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Analysis of the switching process/3
Delay time vs phase
Experiment
Theory
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)
X. Hachair at al. Submitted (2005)
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Analysis of the switching process/4
Delay time vs WB power
Theory
Experiment
Delay time decreases when WB power is increased,
both in experiment and theory
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Analysis of the switching process/5
Delay time vs pumping current
Theory
Experiment
In the experiment, delay time decreases when bias
is increased Experiment and theory disagree....
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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
0.75 obtained at I 2.
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• Numerical results obtained by including
• temperature variations induced by the excitation
  current
• the switch on time decreases as we increase the
  current

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

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VCSEL above threshold
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Cavity Solitons in a VCSEL above threshold
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Temporal oscillations
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Correlation measurements
Without holding beam
With holding beam
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Soliton Correlations
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They also may appear spontaneously and they can
be moved
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Correlated structure
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Fronts between a pattern and a homogeneous
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 D between the fronts.
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Stability of a front Y. Pommeau,
INTERACTION BETWEEN FRONTS Coullet, P., Riera,
C., Tresser, C. Stable Static Localized
Structures in One Dimension. Phys. Rev. Lett. 84,
3069-3072 (2000).
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Front InteractionM. Clerc, submitted (2005)
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• 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

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Robin Loznal / The Daily Inter
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I hope you enjoyed the presentation

• If not, please .do not kill me!!
• If Yes,
• Thank you

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• CAVITY SOLITON is a
• LOCALIZED STRUCTURE
• A pattern that can  live  independently in an
  spatially extended system

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CS in Semiconductors possible applications

• Reconfigurable buffer memory
• Serial-parallel converter
• Shift register
• All-optical processor

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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.
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Analysis of the switching process/1
To analyse the switching process in details, an
EOM (Electro-Optical Modulator) has been used to
replace the AOM (Acusto Optical Modulator).
WB is a Gaussian pulse injected into the cavity
for 100 ns. Time to reach the stationary value
is 700 ps WB width 10 - 20 ?m WB power 10 -160
?W (HB power 8.5 mW)
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1.      Ackemann, T. et al. J. Opt. B Quantum
Semiclass. Opt. 2, 406-412 (2000).
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Spatially resolved spectra
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Including q(x)q0-a x
Ei 1.8 Ei 2.0 q0 -1 a 5
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• Introduce the current crowding effect
• I I(r) Io-Xexp-r2/r02
• where rx2y2. Io 20 above threshold
• Intensity distribution when pumping above
  threshold

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  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