neuronas ópticas y pulsos extremos en láseres de semiconductor

Neuronas ópticas y pulsos extremos

en láseres de semiconductor

Cristina Masoller Cristina.masoller@upc.edu

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

PDF

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 !

<cristina.masoller@upc.edu>

http://www.fisica.edu.uy/~cris/

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