neuronas ópticas y pulsos extremos en láseres de semiconductor
TRANSCRIPT
Neuronas ópticas y pulsos extremos
en láseres de semiconductor
Cristina Masoller [email protected]
www.fisica.edu.uy/~cris
Centro de Investigaciones en Óptica
Leon, Mexico, July 2015
Donde estamos?
Quienes somos?
12 senior researchers,
2 posdoctoral researchers
10 phd students
Fenómenos nolineales en sistemas complejos
• Fotónica (láseres de semiconductor, pulsos
ultracortos, cristales fotonicos, etc.)
• Sistemas biológicos, neurociencia
• Análisis de series temporales, datos climáticos
Que estudiamos?
En nuestro lab: dinámica de
láseres de semiconductor
¿Son similares los spikes opticos y los neuronales?
Laser Espejo
Pulsos extremos:
• ¿se pueden predecir?
• ¿se pueden controlar?
Neuronas:
Usan spikes para transmitir información
‒ Posibilidad de construir sistemas ópticos de procesamiento ultra-
rápido de información “biológicamente inspirados” (ms vs ns-s).
‒ Posibilidad de realizar experimentos simples para comprender el
comportamiento neuronal (codificación de información).
Pulsos extremos (eventos raros):
Ocurren en muchos sistemas complejos
‒ La posibilidad de capturar muchos datos permite desarrollar
algoritmos de predicción y métodos de control.
‒ La comparación experimentos-modelos permite verificar modelos,
desarrollar modelos mas avanzados, estimar parámetros, etc.
Porque nos interesa?
Entrada (proyectos): ~ 1.000.000 €
• Unión Europea: 2 FP7 Marie Curie Initial Training Networks
(LINC-clima and NETT-neurons),
• Regional (Catalán ICREA Academia),
• Nacional (España),
• Gobierno americano (EOARD-AFRL).
Salida (resultados)
• Publicaciones: 38 articulos (Scientific Reports, PRL, Opt.
Express, Opt. Letts., New J. of Phys. etc.)
• 5 tesis doctorales dirigidas (Zamora, Perrone, Aragoneses, Deza
& Tirabassi)
Números: mi investigación en
los últimos 5 años
Outline
Introducción
• a la dinámica de los láseres de semiconductor
• al método simbólico de análisis de datos
Parte 1: neuronas ópticas
Parte 2: pulsos extremos
Widely used in:
Communications
Data storage (CDs, DVDs …)
Barcode scanners, laser printers, computer mice
Life sciences (imaging, sensing …)
Etc.
Optical Feedback induces nonlinear dynamics:
Multi-stability
Irregular power dropouts
Chaos, intermittency …
Semiconductor lasers
9
Laser Mirror
C. Masoller 10
sp
i
p
etEEGidt
dE
0)( )1)(1(2
1
feedback 2
1EGN
dt
dN
N
Governing equations
noise
mirror
)1/(2
ENG
R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980)
|E|2 photon number (output intensity)
N number of carriers (electron-holes)
31/10/2015
= feedback strength
= feedback delay time
= pump current
(control parameter)
Gain:
Model predictions
In deterministic simulations: the
spikes are transient.
A. Torcini et al, Phys. Rev. A 74, 063801 (2006)
J. Zamora-Munt et al, Phys Rev A 81, 033820 (2010)
Laser intensity
But in stochastic simulations:
bursts of spikes.
11
In the experiments:
Can we infer signatures of determinism?
Is there any information in the spike sequence?
which spikes are noise-induced
and which ones are deterministic?
In the spike rate? in the spike timing? In the order in
which neurons fire?
The temporal structure of the spikes produced by a
population of neurons matters:
• In many situations processing is too fast to be
compatible with a rate-based code.
• Temporal codes can transmit more information
How neurons encode
information?
How to extract information
from optical spikes?
13
Solution: event-level
description. We analyze
the sequence of inter-
spike-intervals (ISIs):
Problem: we can measure only one variable (the laser
output intensity).
Also a problem: the
detection system
(photodiode, oscilloscope)
has a finite bandwidth that
gives very limited
temporal resolution.
Ti = ti+1 - ti
Examples:
─ Neurons: spikes
─ Cardiac tissue: beats
─ Earth, climate: earthquakes, extreme events (tornados,
rainfalls) etc.
Analysis: times when the events occur
─ Relative timing: intervals between events (waiting times)
Example: a population of neurons might encode information
in the relative timing of the spikes, or in the order in which
neurons fire.
Method of analysis: symbolic ordinal analysis
Event level description of
complex systems
14
Ordinal Patterns (OPs)
─ Advantage: the OP probabilities uncover 4-spike correlations.
X= {…Ti, Ti+1, Ti+2, …}
Example: (5, 1, 7) gives “102” because 1 < 5 < 7
Brandt & Pompe, PRL 88, 174102 (2002)
( inter-spike-intervals)
012 210
Random spikes
all patterns
are equally
probable
─ Drawback: we lose information (5,1,100) also gives “102”.
1 2 3 4 5 6
Example
1 2 3 4 5 60
50
100
150
200
0 0.2 0.4 0.6 0.8 10
10
20
30
40
50
0 100 200 300 400 500 6000
0.2
0.4
0.6
0.8
1
550 555 560 565 570 575 580 585 590 595 6000
0.2
0.4
0.6
0.8
1
Time series Detail
Histogram Patterns Histogram x(t)
210 is
forbidden
Take home message: the analysis of OP probabilities can yield
information about more frequent (and/or missing) patterns in the data.
Number of possible
ordinal patterns: D!
D=4
17
D=5
How to select optimal D?
depends on:
─ The length of the data.
─ The length of correlations in the data.
With D=3 we study correlations among 4
consecutive spikes.
Spike correlations can encode information
210
Widely used to analyze the observed output signals of complex systems
- Financial
- Biological
- Geosciences, climate
The identification of patterns in the sequence of events allows for:
─ Model validation, parameter estimation
─ Classification of dynamical behaviors (pathological, healthy)
─ Predictability - forecasting
Ordinal analysis has been able to:
- Distinguish stochasticity and determinism
- Quantify complexity
- Identify couplings and directionality
Ordinal Analysis
31/10/2015 18 C. Masoller
Example 1
19
Classifying cardiac biosignals using ordinal pattern statistics
Congestive heart failure (CHF) vs healthy subjects.
Entropy: early warning indicator of an abrupt transition
(polarization switching)
Example 2
C. Masoller et al, New J. Phys. 17 (2015) 023068
Transition laminar-- turbulence in a fiber laser
Example 3
A. Aragoneses et al, submitted (2015)
22
Laser Diode 50/50 Beamsplitter
External
reflector
Detector to Oscilloscope
(1 GHz)
Temperature
and pump
current
controller
to Optical
Spectrum Analizer
External cavity - 45 cm
Hitachi Laser Diode (HL6724MG)
nm
5mW
~ 7% threshold reduction 31/10/2015
23
Spiking dynamics
0 0.5 1 1.5 2-3
-2
-1
0
1
2
Time (microseconds
Lase
r in
tensit
y (a
rb.
unit
s)
Probabilities of 01 and 10 reveal 3-spike correlations
Null Hypothesis: random spikes P(01) = P(10)
Low pump current Higher pump current
ISI
Histograms
Are the spikes random?
A. Aragoneses et al, Scientific Reports 3, 1778 (2013)
26 26.5 27 27.5 28-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
012
021
102
120
201
210
26 26.5 27 27.5 28-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
01
10
012 210
45000 - 220000 spikes
Pump current (mA)
P-
1/2 P-
1/6
Pump current (mA)
31/10/2015 24
D=2 D=3
Recorded data Surrogated data
31/10/2015 25
Are the results significant?
Error bars computed with a binomial test, gray region is consistent with N.H.
A. Aragoneses et al, Scientific Reports 3, 1778 (2013)
Which spikes are triggered by noise?
31/10/2015 26 C. Masoller
We use a threshold to
classify the intervals as
short or long
Inter-dropout-intervals (ns)
0 500 1000 1500 2000 2500 30000
1000
2000
3000
4000
5000
Exponential decay
SIs LIs ISI Histogram
At high currents:
─ Long intervals: random
─ Short intervals: not consistent with random.
But at low currents: the spikes can not be distinguished.
Pump current (mA)
31/10/2015 27
A. Aragoneses et al, Scientific Reports 3, 1778 (2013)
Pump current (mA)
Long intervals Short intervals
26 26.5 27 27.5 28-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
012
021
102
120
201
210
T=18 C T=20 C
Ordinal analysis unveils
new information
There is a hierarchical and clustered
organization of the pattern probabilities
Pump current (mA)
31/10/2015 28
Pump current (mA)
P-
1/6
26 26.5 27 27.5 28-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
012
021
102
120
201
210
In another experiment: the same
transition, hierarchy and clusters
75,000 – 880,000 spikes
(different laser, new oscilloscope)
A. Aragoneses et al, Sci. Rep. 4, 4696 (2014)
LK model in good agreement
with observations
31/10/2015 30
Low feedback Stronger feedback
A. Aragoneses et al, Sci. Rep. 4, 4696 (2014)
1 1.2 1.4 1.6 1.8 2-0.2
-0.1
0
0.1
0.2
0.3
Map parameter
P-1
/6
3.5 3.6 3.7 3.8 3.9 4-0.2
-0.1
0
0.1
0.2
0.3
Map parameter
P-1
/6
012
021
102
120
201
210
Logistic map Tent map
Can we find a minimal model that
displays these features?
3.5 3.55 3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.950
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
31/10/2015 31
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
P-1
/6
012
021
102
120
201
210
Modified circle map
)4sin()2sin(2
1 iiii
K
=0.23
K=0.04
26 26.5 27 27.5 28-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
012
021
102
120
201
210
Pump current (mA)
iiiX 1
Minimal phenomenological model
The circle map describes many excitable
systems (neurons)
The modified circle map has been used to
describe correlations in the spikes of biological
neurons.
Neiman and Russell, Models of stochastic biperiodic
oscillations and extended serial correlations in
electroreceptors of paddlefish, PRE 71, 061915 (2005)
Connection with neurons
How similar the spikes of
lasers and neurons are?
A. Longtin et al, PRL 67 (1991) 656.
Laser ISI histogram Neuron Interspike interval (ISI)
histogram
With direct current modulation, data
recorded in our lab
Response to periodic modulation
31/10/2015 35 Time (ns)
Laser intensity:
Increasing
modulation
amplitude
=660 nm
=1550 nm
Two experiments:
Relevant for understanding neuronal encoding of external stimuli
Tendency
to lock
Similar observations @ 1550 nm
Interpretation: locking to external forcing
0 2 4 6 8 10-0.06
-0.04
-0.02
0
0.02
0.04
Modulation amplitude (arb. units)
P-1
/6
Experiments - minimal model
comparison
Experiments @ 660 nm
(68,000 - 200,000 dropouts)
012
210
DK
iiii )4sin()2sin(2
1
Circle map
New method proposed to identify signatures of determinism
in the apparently random sequence of optical spikes.
The method allows to classify the spikes in two categories.
New symbolic states found, with a clear hierarchical and
clustered organization.
Good agreement with LK model.
Minimal model identified. Robust under external forcing.
Present work: can the laser be an “optical neuron”? Detailed
comparison with neuronal models & real data.
Part 1: Conclusions
Stochastic time-delayed systems are complex and high-dimensional.
Event-level description + ordinal analysis: powerful method to analyze the observed output signals.
─ useful for understanding data, uncovering patterns,
─ for model comparison, parameter estimation,
─ for classifying events,
─ for forecasting events.
Take home message
31/10/2015 38
Press attention
Papers @ www.fisica.edu.uy/~cris ─ A. Aragoneses et al, Scientific Reports 3, 1778 (2013).
─ A. Aragoneses et al, Scientific Reports 4, 4696 (2014).
Outline
Introducción
• a la dinámica de los láseres de semiconductor
• al método simbólico de análisis de datos
Parte 1: neuronas ópticas
Parte 2: pulsos extremos
What is a Rogue Wave?
A “monster wave”, a “freak wave”, an ultra-high wave.
Adapted from F. Dias (Dublin, Ireland)
Can develop suddenly even in calm and apparently safe seas.
Source: National Geographic
RWs appear suddenly and
vanish without a trace
A challenge for boats and also, for the oil and gas
industry, for the design of safe off-shore platforms.
Adapted from F. Dias (Dublin)
Examples
• Since 2003 wave
profiles were measured
with 4 lasers mounted
on a bridge at the oil
production site Ekofisk
in the North Sea.
• A RW was detected
9/11/2007 during a
storm.
Optical RWs: first observation
D. R. Solli et al, Nature 450, 1054, 2007
Semiconductor lasers with continuous-wave optical injection
provide a controllable setup for the study of RWs
C. Bonatto et al, PRL 107, 053901 (2011)
• Parameters:
o Injection ratio
o Frequency detuning
A RW: extreme pulse above a threshold (<H> + 4-8 )
RW definition
Time series
RWs can be deterministic, generated by a crisis-like process.
RWs can be predicted with a certain anticipation time.
RWs can be controlled via noise and/or modulation.
47
What we have learned
• C. Bonatto et al, Deterministic optical rogue waves, PRL 107, 053901 (2011).
• J. Zamora-Munt et al, Rogue waves in optically injected lasers: origin,
predictability and suppression, PRA 87, 035802 (2013).
• S. Perrone et al, Controlling the likelihood of RWs in an optically injected
semiconductor laser via direct current modulation, PRA 89, 033804 (2014).
• J. Ahuja et al, Rogue waves in injected semiconductor lasers with current
modulation: role of the modulation phase, Optics Express 22, 28377 (2014).
C. Masoller 48
o Complex field, E
o Carrier density, N
)(/2 )1)(1(2
1inj tPiENi
dt
dENsp
p
2
1Eμ-N-N
dt
dN
N
Solitary laser
parameters: p N
optical injection
: injection strength
= s-m: detuning
spontaneous
emission
noise
: normalized pump current parameter
Typical parameter values:
= 3, p = 1 ps, N = 1 ns
Governing equations
Threshold: <H> + 8
o Injection locking (cw output)
o Periodic oscillations
o Chaos
= s-m
Dynamical regimes
C. Masoller 50
A simulated RW
51 Chaos without RWs Chaos with RWs
Lyapunov diagram
(detuning, pump current)
Deterministic simulations (sp=0)
Deterministic RWs (sp=0) Weak noise (sp=0.0001)
Strong noise (sp=0.01)
Weak noise reduces the number
of RWs, but strong noise can
induce RWs
White = No RWs
Number of RWs vs (pump
current, detuning)
Pump current modulation:
RW control in Point A (deterministic RWs)
Current modulation with appropriated amplitude and
frequency can completely suppress the RWs.
White =
No RWs
S. Perrone, J. Zamora Munt, R. Vilaseca and C. Masoller, PRA 89, 033804 (2014)
) 2sin( modmod0 tf
No noise (sp=0) Stochastic simulations (sp=0.01)
RW control in Point A: influence of noise
“safe parameter region” is robust to the presence of noise.
White = No RWs
S. Perrone, J. Zamora Munt, R. Vilaseca and C. Masoller, PRA 89, 033804 (2014)
) 2sin( modmod0 tf
White = No RWs
sp=0 sp=0.01
in Point B (no deterministic RWs)
White = No RWs
“safe” parameter region also in point B, also robust to noise
Modulation suppressed RWs:
We can think of triggering controlled small avalanches
to avoid a large and dangerous avalanche.
Analogy: avalanche risk
When RWs are not suppressed:
role of the modulation phase
RWs occur during the
first ¾ of the
modulation cycle.
The highest RWs occur
just before the “safe”
phase window.
fmod= 3.5 GHz
J. Ahuja, D. Bhiku Nalawade, J. Zamora-Munt, R. Vilaseca and C. Masoller,
Optics Express 22, 28377 (2014)
RW Control: noise and modulation strongly affect the likelihood of RWs.
RW Predictability: when the modulation does not fully suppress RWs, it
enables certain predictability because RWs occur only in well-defined
windows of the modulation cycle.
Ongoing work: how to improve RW predictability from observed data,
relation between RW amplitude and waiting time.
58
Summary part II
Papers @ www.fisica.edu.uy/~cris
• C. Bonatto et al, PRL 107, 053901 (2011).
• S. Perrone et al, Phys. Rev. A 89, 033804 (2014).
• J. Ahuja et al, Optics Express 22, 28377 (2014).
Taciano Sorrentino
Collaborators
59 Carme Torrent
Carlos Quintero
Andres Aragoneses (now
at Duke University, USA)
Sandro Perrone (now at
Leicester University, UK)
Ramon Vilaseca
Jordi Zamora
Jatin Ahuja D. Bhiku
Indian Institute of
Technology,
Guwahati, Assam,
India
THANK YOU FOR YOUR ATTENTION !
http://www.fisica.edu.uy/~cris/
Advertising:
1. We are looking for PhD students to join our group in a new
European project on biomedical imaging
2. We welcome undergrad students (summer internships) and
postdocs.