Transmission of nonlinear localized modes through waveguide bends

Maria Agrotis; Panayotis G. Kevrekidis; Boris A. Malomed

doi:10.1016/j.matcom.2005.01.001

Transmission of nonlinear localized modes through waveguide bends

Maria Agrotis, Panayotis G. Kevrekidis, Boris A. Malomed^*

^*Corresponding author for this work

School of Electrical Engineering

University of Massachusetts

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

In a recent work, a model for a bend of a nonlinear waveguide in planar geometry was introduced [Yu.S. Kivshar, P.G. Kevrekidis, S. Takeno, Phys. Lett. 307 (2003) 287]. Motivated by photonic-crystal waveguides, we examine transmission of localized pulses through the bend, and identify outcomes of the interaction of a moving pulse with the bend, as a function of the bend's strength and the initial velocity of the pulse. Comparisons with the linear counterpart of the model are also discussed. Some features, such as transition from capture to reflection, may be explained by an analytical perturbation theory based on the quasi-continuum approximation.

Original language	English
Pages (from-to)	223-234
Number of pages	12
Journal	Mathematics and Computers in Simulation
Volume	69
Issue number	3-4
DOIs	https://doi.org/10.1016/j.matcom.2005.01.001
State	Published - 24 Jun 2005
Event	Nonlinear Waves: Computation and Theory III - Duration: 7 Apr 2003 → 10 Apr 2003

Funding

Funders	Funder number
National Science Foundation	DMS-0204585
University of Massachusetts
Eppley Foundation for Research

Keywords

Discrete nonlinear Schroedinger equation
Dynamical lattice
Photonic crystal
Soliton

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10.1016/j.matcom.2005.01.001

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@article{28603001cd444ce7847adc5768a91dee,

title = "Transmission of nonlinear localized modes through waveguide bends",

abstract = "In a recent work, a model for a bend of a nonlinear waveguide in planar geometry was introduced [Yu.S. Kivshar, P.G. Kevrekidis, S. Takeno, Phys. Lett. 307 (2003) 287]. Motivated by photonic-crystal waveguides, we examine transmission of localized pulses through the bend, and identify outcomes of the interaction of a moving pulse with the bend, as a function of the bend's strength and the initial velocity of the pulse. Comparisons with the linear counterpart of the model are also discussed. Some features, such as transition from capture to reflection, may be explained by an analytical perturbation theory based on the quasi-continuum approximation.",

keywords = "Discrete nonlinear Schroedinger equation, Dynamical lattice, Photonic crystal, Soliton",

author = "Maria Agrotis and Kevrekidis, {Panayotis G.} and Malomed, {Boris A.}",

note = "Funding Information: PGK gratefully acknowledges partial support from the University of Massachusetts through a Faculty Research Grant, from the Eppley Foundation, and from NSF through DMS-0204585 and a CAREER award. PGK is also thankful to Yu.S. Kivshar for valuable discussions at the initial stages of this project.; Nonlinear Waves: Computation and Theory III ; Conference date: 07-04-2003 Through 10-04-2003",

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doi = "10.1016/j.matcom.2005.01.001",

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T1 - Transmission of nonlinear localized modes through waveguide bends

AU - Agrotis, Maria

AU - Kevrekidis, Panayotis G.

AU - Malomed, Boris A.

N1 - Funding Information: PGK gratefully acknowledges partial support from the University of Massachusetts through a Faculty Research Grant, from the Eppley Foundation, and from NSF through DMS-0204585 and a CAREER award. PGK is also thankful to Yu.S. Kivshar for valuable discussions at the initial stages of this project.

PY - 2005/6/24

Y1 - 2005/6/24

N2 - In a recent work, a model for a bend of a nonlinear waveguide in planar geometry was introduced [Yu.S. Kivshar, P.G. Kevrekidis, S. Takeno, Phys. Lett. 307 (2003) 287]. Motivated by photonic-crystal waveguides, we examine transmission of localized pulses through the bend, and identify outcomes of the interaction of a moving pulse with the bend, as a function of the bend's strength and the initial velocity of the pulse. Comparisons with the linear counterpart of the model are also discussed. Some features, such as transition from capture to reflection, may be explained by an analytical perturbation theory based on the quasi-continuum approximation.

AB - In a recent work, a model for a bend of a nonlinear waveguide in planar geometry was introduced [Yu.S. Kivshar, P.G. Kevrekidis, S. Takeno, Phys. Lett. 307 (2003) 287]. Motivated by photonic-crystal waveguides, we examine transmission of localized pulses through the bend, and identify outcomes of the interaction of a moving pulse with the bend, as a function of the bend's strength and the initial velocity of the pulse. Comparisons with the linear counterpart of the model are also discussed. Some features, such as transition from capture to reflection, may be explained by an analytical perturbation theory based on the quasi-continuum approximation.

KW - Discrete nonlinear Schroedinger equation

KW - Dynamical lattice

KW - Photonic crystal

KW - Soliton

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IS - 3-4

T2 - Nonlinear Waves: Computation and Theory III

Y2 - 7 April 2003 through 10 April 2003

ER -

Transmission of nonlinear localized modes through waveguide bends

Abstract

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Keywords

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