Neuronas ópticas y pulsos extremos en láseres de semiconductor

Transcription

1 Neuronas ópticas y pulsos extremos en láseres de semiconductor Cristina Masoller Cristina.masoller@upc.edu Centro de Investigaciones en Óptica Leon, Mexico, July 2015

2 Donde estamos?

3 Quienes somos? 12 senior researchers, 2 posdoctoral researchers 10 phd students

4 Que estudiamos? Fenómenos nolineales en sistemas complejos Fotónica (láseres de semiconductor, pulsos ultracortos, cristales fotonicos, etc.) Sistemas biológicos, neurociencia Análisis de series temporales, datos climáticos

5 En nuestro lab: dinámica de láseres de semiconductor Laser Espejo Son similares los spikes opticos y los neuronales? Pulsos extremos: se pueden predecir? se pueden controlar?

6 Porque nos interesa? Neuronas: Usan spikes para transmitir información Posibilidad de construir sistemas ópticos de procesamiento ultrarápido 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.

7 Entrada (proyectos): ~ Unión Europea: 2 FP7 Marie Curie Initial Training Networks (LINC-clima and NETT-neurons), Regional (Catalán ICREA Academia), Nacional (España), Gobierno americano (EOARD-AFRL). Números: mi investigación en los últimos 5 años 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)

8 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

9 Semiconductor lasers 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 Laser Irregular power dropouts Chaos, intermittency Mirror 9

10 Governing equations R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980) mirror E 2 photon number (output intensity) N number of carriers (electron-holes) de dt dn dt Gain: 1 2 p (1 i )( G 1 N N G G E N /(1 E 2 1) E ) 2 E( t ) e feedback 0 i sp noise = feedback strength = feedback delay time = pump current (control parameter) 31/10/2015 C. Masoller 10

11 Model predictions In deterministic simulations: the spikes are transient. But in stochastic simulations: bursts of spikes. Laser intensity In the experiments: which spikes are noise-induced and which ones are deterministic? Can we infer signatures of determinism? Is there any information in the spike sequence? A. Torcini et al, Phys. Rev. A 74, (2006) J. Zamora-Munt et al, Phys Rev A 81, (2010) 11

12 How neurons encode information? 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

13 How to extract information from optical spikes? 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. Solution: event-level description. We analyze the sequence of interspike-intervals (ISIs): T i = t i+1 - t i 13

14 Examples: Neurons: spikes Cardiac tissue: beats Event level description of complex systems 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 14

15 Ordinal Patterns (OPs) Brandt & Pompe, PRL 88, (2002) X= { T i, T i+1, T i+2, } ( inter-spike-intervals) Example: (5, 1, 7) gives 102 because 1 < 5 < Random spikes all patterns are equally probable Advantage: the OP probabilities uncover 4-spike correlations. Drawback: we lose information (5,1,100) also gives 102.

16 Example 1 Time series 1 Detail Histogram Patterns Histogram x(t) is forbidden Take home message: the analysis of OP probabilities can yield information about more frequent (and/or missing) patterns in the data.

17 Number of possible ordinal patterns: D! D=4 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

18 Ordinal Analysis 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 31/10/2015 C. Masoller 18

19 Example 1 Classifying cardiac biosignals using ordinal pattern statistics Congestive heart failure (CHF) vs healthy subjects. 19

20 Example 2 Entropy: early warning indicator of an abrupt transition (polarization switching) C. Masoller et al, New J. Phys. 17 (2015)

21 Example 3 Transition laminar-- turbulence in a fiber laser A. Aragoneses et al, submitted (2015)

22 Laser Diode External cavity - 45 cm 50/50 Beamsplitter External reflector to Optical Spectrum Analizer Temperature and pump current controller Detector 31/10/2015 to Oscilloscope (1 GHz) Hitachi Laser Diode (HL6724MG) nm 5mW ~ 7% threshold reduction 22

23 Laser intensity (arb. units) Spiking dynamics Low pump current Higher pump current Time (microseconds ISI Histograms Probabilities of 01 and 10 reveal 3-spike correlations Null Hypothesis: random spikes P(01) = P(10) 23

24 Are the spikes random? P / P D= D= / Pump current (ma) Pump current (ma) spikes A. Aragoneses et al, Scientific Reports 3, 1778 (2013) 31/10/

25 Are the results significant? Recorded data Surrogated data Error bars computed with a binomial test, gray region is consistent with N.H. 31/10/ A. Aragoneses et al, Scientific Reports 3, 1778 (2013)

26 Which spikes are triggered by noise? SIs LIs ISI Histogram Exponential decay We use a threshold to classify the intervals as short or long Inter-dropout-intervals (ns) 31/10/2015 C. Masoller 26

27 Long intervals Short intervals Pump current (ma) Pump current (ma) At high currents: Long intervals: random Short intervals: not consistent with random. But at low currents: the spikes can not be distinguished. 31/10/ A. Aragoneses et al, Scientific Reports 3, 1778 (2013)

28 Ordinal analysis unveils new information P- 1/ T=18 C T=20 C Pump current (ma) Pump current (ma) There is a hierarchical and clustered organization of the pattern probabilities 31/10/

29 In another experiment: the same transition, hierarchy and clusters 75, ,000 spikes (different laser, new oscilloscope) A. Aragoneses et al, Sci. Rep. 4, 4696 (2014)

30 LK model in good agreement with observations Low feedback Stronger feedback 31/10/ A. Aragoneses et al, Sci. Rep. 4, 4696 (2014)

31 P-1/6 P-1/ Logistic map Can we find a minimal model that displays these features? Tent map Map parameter Map parameter /10/

32 P-1/6 Modified circle map K sin(2 i ) sin(4 ) 2 i 1 i i =0.23 K= Xi i 1 i Pump current (ma) Minimal phenomenological model

33 Connection with neurons 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, (2005)

34 How similar the spikes of lasers and neurons are? Neuron Interspike interval (ISI) histogram Laser ISI histogram With direct current modulation, data recorded in our lab A. Longtin et al, PRL 67 (1991) 656.

35 Response to periodic modulation Relevant for understanding neuronal encoding of external stimuli Increasing modulation amplitude Laser intensity: Two experiments: =660 nm Tendency to lock =1550 nm 31/10/2015 Time (ns) 35

36 P-1/6 Experiments - minimal model comparison 660 nm (68, ,000 dropouts) 0.04 Circle map Modulation amplitude (arb. units) Similar 1550 nm Interpretation: locking to external forcing K i 1 i i i) 2 sin(2 ) sin(4 D

37 Part 1: Conclusions 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.

38 Take home message Stochastic time-delayed systems are complex and highdimensional. 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. 31/10/

39 Press attention A. Aragoneses et al, Scientific Reports 3, 1778 (2013). A. Aragoneses et al, Scientific Reports 4, 4696 (2014).

40 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

41 What is a Rogue Wave? A monster wave, a freak wave, an ultra-high wave. Can develop suddenly even in calm and apparently safe seas. Adapted from F. Dias (Dublin, Ireland)

42 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. Source: National Geographic

43 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. Adapted from F. Dias (Dublin)

44 D. R. Solli et al, Nature 450, 1054, 2007 Optical RWs: first observation

45 Semiconductor lasers with continuous-wave optical injection provide a controllable setup for the study of RWs Parameters: o Injection ratio o Frequency detuning C. Bonatto et al, PRL 107, (2011)

46 RW definition A RW: extreme pulse above a threshold (<H> ) Time series PDF

47 What we have learned 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. C. Bonatto et al, Deterministic optical rogue waves, PRL 107, (2011). J. Zamora-Munt et al, Rogue waves in optically injected lasers: origin, predictability and suppression, PRA 87, (2013). S. Perrone et al, Controlling the likelihood of RWs in an optically injected semiconductor laser via direct current modulation, PRA 89, (2014). J. Ahuja et al, Rogue waves in injected semiconductor lasers with current modulation: role of the modulation phase, Optics Express 22, (2014). 47

48 Governing equations o Complex field, E o Carrier density, N de dt dn dt 1 2 p (1 i )( N 1) E 1 N μ-n-n E 2 i optical injection : injection strength = s - m : detuning P inj 2 / ( t) sp N spontaneous emission noise Solitary laser parameters: p N Typical parameter values: = 3, p = 1 ps, N = 1 ns : normalized pump current parameter C. Masoller 48

49 Dynamical regimes o Injection locking (cw output) o Periodic oscillations o Chaos Threshold: <H> + 8 = s - m

50 A simulated RW C. Masoller 50

51 Deterministic simulations ( sp =0) Lyapunov diagram (detuning, pump current) Chaos without RWs Chaos with RWs 51

52 Number of RWs vs (pump current, detuning) Deterministic RWs ( sp =0) Weak noise ( sp =0.0001) Strong noise ( sp =0.01) White = No RWs Weak noise reduces the number of RWs, but strong noise can induce RWs

53 Pump current modulation: RW control in Point A (deterministic RWs) 0 mod sin( 2 fmod t) White = No RWs Current modulation with appropriated amplitude and frequency can completely suppress the RWs. S. Perrone, J. Zamora Munt, R. Vilaseca and C. Masoller, PRA 89, (2014)

54 RW control in Point A: influence of noise 0 mod sin( 2 fmod t) No noise ( sp =0) Stochastic simulations ( sp =0.01) White = No RWs White = No RWs safe parameter region is robust to the presence of noise. S. Perrone, J. Zamora Munt, R. Vilaseca and C. Masoller, PRA 89, (2014)

55 in Point B (no deterministic RWs) sp =0 sp =0.01 White = No RWs safe parameter region also in point B, also robust to noise

56 Analogy: avalanche risk Modulation suppressed RWs: We can think of triggering controlled small avalanches to avoid a large and dangerous avalanche.

57 When RWs are not suppressed: role of the modulation phase f mod = 3.5 GHz RWs occur during the first ¾ of the modulation cycle. The highest RWs occur just before the safe phase window. J. Ahuja, D. Bhiku Nalawade, J. Zamora-Munt, R. Vilaseca and C. Masoller, Optics Express 22, (2014)

58 Summary part II 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. C. Bonatto et al, PRL 107, (2011). S. Perrone et al, Phys. Rev. A 89, (2014). J. Ahuja et al, Optics Express 22, (2014). 58

59 Collaborators Taciano Sorrentino Carlos Quintero Jatin Ahuja D. Bhiku Indian Institute of Technology, Guwahati, Assam, India Andres Aragoneses (now at Duke University, USA) Sandro Perrone (now at Leicester University, UK) Jordi Zamora Ramon Vilaseca Carme Torrent 59

60 THANK YOU FOR YOUR ATTENTION! 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.