Transcript CAVITY SOLITONS by J. R. Tredicce

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
Spatially Extended System
• Property:
Correlation length
much smaller than
the size of the
system
Some Nonlinear Effects
1. Strong non linearity
2. 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))
Optical Cavity Soliton:
How to generate them? (in theory)
Holding beam
Optical resonator
Output
Nonlinear medium
Writing
pulses
Cavity Solitons
Mirror
Mirror
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.
S. Barland, et al. Nature, 2002
Theoretical Model
E
2






  1  i  T E  i  N ,  E  E I  i   E
t
N
  N  I  Im  N ,   | E | 2 d 2 N
t


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?
Patterns in VCSEL with Injection
Ackemann, T., et al. Opt. Lett. 25, 814-816 (2000).
CS can also appear spontaneously ...........
Experiment
Numerics
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”.
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 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)
Analysis of the switching process/2
CS build-up time and delay time
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
0
2
4
6
8
10
12
14
16
18
20
t (ns)
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.
Analysis of the switching process/3
Delay time vs phase
4,0
|E|
=0
3,5
o
o
 = 57 (1 rad)
3,0
o
 = 70 (1.22 rad)
2,5
2,0
1,5
1,0
0,5
0,0
0,0
0,3
0,6
0,9
1,2
1,5
1,8
2,1
2,4
2,7
3,0
t (ns)
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)
Analysis of the switching process/4
Delay time vs WB power
Solid lines: intracavity field |E| at center
Dashed lines: total injected field E I at center
4,5
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
2,4
t (ns)
Experiment
Theory
Delay time decreases when WB power is increased, both in experiment and theory
Analysis of the switching process/5
Delay time vs pumping current
4,0
3,5
|E| 3,0
I = 1.97
I=2
I = 2.01
2,5
2,0
1,5
1,0
0,5
0,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
t (ns)
Experiment
Theory
In the experiment, delay time decreases when bias is increased
Experiment and theory disagree....
2,0
2,4
|ES|2,2
2,0
1,8
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
1,0
1,2
1,4
1,6
1,8
2,0
I
2,2
2,4
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.
• Numerical results
obtained by including
temperature variations
induced by the
excitation current:
the switch on time
decreases as we
increase the current
Quantitative Changes in
the switch on time
due to noise effects.
VCSEL above threshold
Cavity Solitons in a VCSEL above
threshold
Temporal oscillations
Correlation measurements
Without holding beam
With holding beam
Soliton Correlations
They also may appear
spontaneously and they can be
moved
Correlated structure
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.
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).
Front Interaction
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
presentation
• If not, please
….do not kill
me!!
• If Yes,
Thank you
• CAVITY SOLITON is a
LOCALIZED STRUCTURE
A pattern that can « live »
independently in an spatially
extended system
CS in Semiconductors: possible
applications
• Reconfigurable buffer memory
• Serial-parallel converter
• Shift register
• All-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
To analyse the switching process in details, an EOM (Electro-Optical Modulator)
has been used to replace the AOM (Acusto Optical Modulator).
WB peak intensity vs time
p
0
0
700 ps
100 ns
t
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)
1.
Ackemann, T. et al. J. Opt. B: Quantum Semiclass. Opt.
2, 406-412 (2000).
Spatially resolved spectra
Including (x)=0-a x
Ei = 1.8
0 = -1 a = 5
Ei= 2.0
• Introduce the current
crowding effect:
I = I(r)= Io-Xexp[-r2/r02]
where r=x2+y2. Io:
~20% above
threshold
• Intensity distribution
when pumping above
threshold
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
1,5
0,5
-0,5
-1,5
-2,5
0
7,5
15
22,5
30
37,5
45
52,5