Complexity mapping of a photonic integrated circuit laser using a correlation-dimension-based approach

Christopher J. McMahon, Joshua P. Toomey, Apostolos Argyris, Deb M. Kane

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Quantifying complexity from experimental time series generated by nonlinear systems, including laser systems, remains a challenge. Methods that are based on entropy, such as permutation entropy (PE), have proven to be useful tools for the relative measure of time series complexity. However, the numerical value of PE is not readily linked to a specific type of dynamical output. Thus, the quest to calculate quantitatively meaningful fractal dimension values, such as the correlation dimension (CD), from experimental signals, is still important. A protocol for calculating minimum gradient values and their spread, an integral part of CD analysis, is used here. Minimum gradient values with small spread are presented as approximate CD values. Here-in we report mapping these values, derived from analyzing experimental time series, obtained from a 4-section photonic integrated circuit laser (PICL) across a large parameter space. The PICL is an integrated form of a semiconductor laser subject to controllable optical feedback system. The minimum gradient/approximate CD mapping shows it has some qualitatively different map regions in its dynamics as compared to a free-space-based equivalent system. We show that the minimum gradient values give insight into the dynamics even when approximate CD values cannot be determined. The agreement between the qualitative features of permutation entropy mapping and minimum gradient/approximate CD value mapping provides further support for this. Regions of time series with close to periodic and quasi-periodic dynamics are identifiable using minimum gradient value maps.

LanguageEnglish
Article number086202
Pages1-7
Number of pages7
JournalLaser Physics
Volume29
Issue number8
DOIs
Publication statusPublished - Jun 2019

Fingerprint

Photonics
integrated circuits
Integrated circuits
Time series
Entropy
photonics
Lasers
gradients
permutations
lasers
entropy
Optical feedback
Fractal dimension
Semiconductor lasers
Nonlinear systems
nonlinear systems
fractals
semiconductor lasers
output

Keywords

  • Chaos
  • Complex systems
  • Complexity
  • Integrated optoelectronic devices
  • Nonlinear dynamics
  • Semiconductor lasers

Cite this

McMahon, Christopher J. ; Toomey, Joshua P. ; Argyris, Apostolos ; Kane, Deb M. / Complexity mapping of a photonic integrated circuit laser using a correlation-dimension-based approach. In: Laser Physics. 2019 ; Vol. 29, No. 8. pp. 1-7.
@article{273348d57d034d0faf8ff1d8e9512c1f,
title = "Complexity mapping of a photonic integrated circuit laser using a correlation-dimension-based approach",
abstract = "Quantifying complexity from experimental time series generated by nonlinear systems, including laser systems, remains a challenge. Methods that are based on entropy, such as permutation entropy (PE), have proven to be useful tools for the relative measure of time series complexity. However, the numerical value of PE is not readily linked to a specific type of dynamical output. Thus, the quest to calculate quantitatively meaningful fractal dimension values, such as the correlation dimension (CD), from experimental signals, is still important. A protocol for calculating minimum gradient values and their spread, an integral part of CD analysis, is used here. Minimum gradient values with small spread are presented as approximate CD values. Here-in we report mapping these values, derived from analyzing experimental time series, obtained from a 4-section photonic integrated circuit laser (PICL) across a large parameter space. The PICL is an integrated form of a semiconductor laser subject to controllable optical feedback system. The minimum gradient/approximate CD mapping shows it has some qualitatively different map regions in its dynamics as compared to a free-space-based equivalent system. We show that the minimum gradient values give insight into the dynamics even when approximate CD values cannot be determined. The agreement between the qualitative features of permutation entropy mapping and minimum gradient/approximate CD value mapping provides further support for this. Regions of time series with close to periodic and quasi-periodic dynamics are identifiable using minimum gradient value maps.",
keywords = "Chaos, Complex systems, Complexity, Integrated optoelectronic devices, Nonlinear dynamics, Semiconductor lasers",
author = "McMahon, {Christopher J.} and Toomey, {Joshua P.} and Apostolos Argyris and Kane, {Deb M.}",
year = "2019",
month = "6",
doi = "10.1088/1555-6611/ab27bb",
language = "English",
volume = "29",
pages = "1--7",
journal = "Laser Physics",
issn = "1054-660X",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "8",

}

Complexity mapping of a photonic integrated circuit laser using a correlation-dimension-based approach. / McMahon, Christopher J.; Toomey, Joshua P.; Argyris, Apostolos; Kane, Deb M.

In: Laser Physics, Vol. 29, No. 8, 086202, 06.2019, p. 1-7.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Complexity mapping of a photonic integrated circuit laser using a correlation-dimension-based approach

AU - McMahon,Christopher J.

AU - Toomey,Joshua P.

AU - Argyris,Apostolos

AU - Kane,Deb M.

PY - 2019/6

Y1 - 2019/6

N2 - Quantifying complexity from experimental time series generated by nonlinear systems, including laser systems, remains a challenge. Methods that are based on entropy, such as permutation entropy (PE), have proven to be useful tools for the relative measure of time series complexity. However, the numerical value of PE is not readily linked to a specific type of dynamical output. Thus, the quest to calculate quantitatively meaningful fractal dimension values, such as the correlation dimension (CD), from experimental signals, is still important. A protocol for calculating minimum gradient values and their spread, an integral part of CD analysis, is used here. Minimum gradient values with small spread are presented as approximate CD values. Here-in we report mapping these values, derived from analyzing experimental time series, obtained from a 4-section photonic integrated circuit laser (PICL) across a large parameter space. The PICL is an integrated form of a semiconductor laser subject to controllable optical feedback system. The minimum gradient/approximate CD mapping shows it has some qualitatively different map regions in its dynamics as compared to a free-space-based equivalent system. We show that the minimum gradient values give insight into the dynamics even when approximate CD values cannot be determined. The agreement between the qualitative features of permutation entropy mapping and minimum gradient/approximate CD value mapping provides further support for this. Regions of time series with close to periodic and quasi-periodic dynamics are identifiable using minimum gradient value maps.

AB - Quantifying complexity from experimental time series generated by nonlinear systems, including laser systems, remains a challenge. Methods that are based on entropy, such as permutation entropy (PE), have proven to be useful tools for the relative measure of time series complexity. However, the numerical value of PE is not readily linked to a specific type of dynamical output. Thus, the quest to calculate quantitatively meaningful fractal dimension values, such as the correlation dimension (CD), from experimental signals, is still important. A protocol for calculating minimum gradient values and their spread, an integral part of CD analysis, is used here. Minimum gradient values with small spread are presented as approximate CD values. Here-in we report mapping these values, derived from analyzing experimental time series, obtained from a 4-section photonic integrated circuit laser (PICL) across a large parameter space. The PICL is an integrated form of a semiconductor laser subject to controllable optical feedback system. The minimum gradient/approximate CD mapping shows it has some qualitatively different map regions in its dynamics as compared to a free-space-based equivalent system. We show that the minimum gradient values give insight into the dynamics even when approximate CD values cannot be determined. The agreement between the qualitative features of permutation entropy mapping and minimum gradient/approximate CD value mapping provides further support for this. Regions of time series with close to periodic and quasi-periodic dynamics are identifiable using minimum gradient value maps.

KW - Chaos

KW - Complex systems

KW - Complexity

KW - Integrated optoelectronic devices

KW - Nonlinear dynamics

KW - Semiconductor lasers

UR - http://www.scopus.com/inward/record.url?scp=85070818815&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/LP100100312

U2 - 10.1088/1555-6611/ab27bb

DO - 10.1088/1555-6611/ab27bb

M3 - Article

VL - 29

SP - 1

EP - 7

JO - Laser Physics

T2 - Laser Physics

JF - Laser Physics

SN - 1054-660X

IS - 8

M1 - 086202

ER -