Compound laser modes of mutually delay-coupled lasers

Hartmut Erzgräber, Bernd Krauskopf, Daan Lenstra

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

42 Citaties (Scopus)

Uittreksel

We consider a model of two mutually delay-coupled semiconductor lasers (SLs) in a face to face configuration. The lasers are coherently coupled via their optical fields, where the time delay τ arises from the finite propagation time of the light from one laser to the other. This system is described well by single mode rate equations, which are a system of delay differential equations (DDEs) with one fixed delay. We study the compound laser modes (CLMs) of the system, where both lasers operate at an identical, time-independent frequency. By making use of numerical continuation applied to the full DDEs, we present a comprehensive geometrical picture of how CLMs depend on the two main physical parameters, namely, the coupling phase and the detuning between the two lasers. The different branches of CLMs are organized by unfoldings of pitchfork bifurcations that exist for zero detuning. As a function of the detuning, different branches of CLMs connect, split, or disappear in transitions through codimension-one singularities in the surface of CLMs.

Originele taal-2Engels
Pagina's (van-tot)30-65
Aantal pagina's36
TijdschriftSIAM Journal on Applied Dynamical Systems
Volume5
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - 20 mrt 2006

Vingerafdruk

Laser modes
Laser
Lasers
Differential equations
Delay Differential Equations
Branch
Semiconductor lasers
Time delay
Numerical Continuation
Pitchfork Bifurcation
Semiconductor Lasers
Rate Equations
Single Mode
Unfolding
Codimension
Time Delay
Singularity
Propagation
Configuration
Zero

Citeer dit

Erzgräber, Hartmut ; Krauskopf, Bernd ; Lenstra, Daan. / Compound laser modes of mutually delay-coupled lasers. In: SIAM Journal on Applied Dynamical Systems. 2006 ; Vol. 5, Nr. 1. blz. 30-65.
@article{4f715f4665754cc1bde85e18b63a7b5c,
title = "Compound laser modes of mutually delay-coupled lasers",
abstract = "We consider a model of two mutually delay-coupled semiconductor lasers (SLs) in a face to face configuration. The lasers are coherently coupled via their optical fields, where the time delay τ arises from the finite propagation time of the light from one laser to the other. This system is described well by single mode rate equations, which are a system of delay differential equations (DDEs) with one fixed delay. We study the compound laser modes (CLMs) of the system, where both lasers operate at an identical, time-independent frequency. By making use of numerical continuation applied to the full DDEs, we present a comprehensive geometrical picture of how CLMs depend on the two main physical parameters, namely, the coupling phase and the detuning between the two lasers. The different branches of CLMs are organized by unfoldings of pitchfork bifurcations that exist for zero detuning. As a function of the detuning, different branches of CLMs connect, split, or disappear in transitions through codimension-one singularities in the surface of CLMs.",
keywords = "Delay differential equations (DDEs), Mutually delay-coupled lasers, Numerical continuation, Singularity, Symmetry breaking",
author = "Hartmut Erzgr{\"a}ber and Bernd Krauskopf and Daan Lenstra",
year = "2006",
month = "3",
day = "20",
doi = "10.1137/040619958",
language = "English",
volume = "5",
pages = "30--65",
journal = "SIAM Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "1",

}

Compound laser modes of mutually delay-coupled lasers. / Erzgräber, Hartmut; Krauskopf, Bernd; Lenstra, Daan.

In: SIAM Journal on Applied Dynamical Systems, Vol. 5, Nr. 1, 20.03.2006, blz. 30-65.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

T1 - Compound laser modes of mutually delay-coupled lasers

AU - Erzgräber, Hartmut

AU - Krauskopf, Bernd

AU - Lenstra, Daan

PY - 2006/3/20

Y1 - 2006/3/20

N2 - We consider a model of two mutually delay-coupled semiconductor lasers (SLs) in a face to face configuration. The lasers are coherently coupled via their optical fields, where the time delay τ arises from the finite propagation time of the light from one laser to the other. This system is described well by single mode rate equations, which are a system of delay differential equations (DDEs) with one fixed delay. We study the compound laser modes (CLMs) of the system, where both lasers operate at an identical, time-independent frequency. By making use of numerical continuation applied to the full DDEs, we present a comprehensive geometrical picture of how CLMs depend on the two main physical parameters, namely, the coupling phase and the detuning between the two lasers. The different branches of CLMs are organized by unfoldings of pitchfork bifurcations that exist for zero detuning. As a function of the detuning, different branches of CLMs connect, split, or disappear in transitions through codimension-one singularities in the surface of CLMs.

AB - We consider a model of two mutually delay-coupled semiconductor lasers (SLs) in a face to face configuration. The lasers are coherently coupled via their optical fields, where the time delay τ arises from the finite propagation time of the light from one laser to the other. This system is described well by single mode rate equations, which are a system of delay differential equations (DDEs) with one fixed delay. We study the compound laser modes (CLMs) of the system, where both lasers operate at an identical, time-independent frequency. By making use of numerical continuation applied to the full DDEs, we present a comprehensive geometrical picture of how CLMs depend on the two main physical parameters, namely, the coupling phase and the detuning between the two lasers. The different branches of CLMs are organized by unfoldings of pitchfork bifurcations that exist for zero detuning. As a function of the detuning, different branches of CLMs connect, split, or disappear in transitions through codimension-one singularities in the surface of CLMs.

KW - Delay differential equations (DDEs)

KW - Mutually delay-coupled lasers

KW - Numerical continuation

KW - Singularity

KW - Symmetry breaking

UR - http://www.scopus.com/inward/record.url?scp=33644911803&partnerID=8YFLogxK

U2 - 10.1137/040619958

DO - 10.1137/040619958

M3 - Article

AN - SCOPUS:33644911803

VL - 5

SP - 30

EP - 65

JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

SN - 1536-0040

IS - 1

ER -