Self-trapping of light and nonlinear localized modes in two-dimensional photonic crystals

S. F. Mingaleev; Y. S. Kivshar

doi:10.1117/12.424682

Self-trapping of light and nonlinear localized modes in two-dimensional photonic crystals

S. F. Mingaleev^*, Y. S. Kivshar

^*Corresponding author for this work

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

Abstract

We develop a theory of nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we demonstrate that it provides an accurate method for investigating the existence and properties of localized defect modes. Using this technique, we describe the existence of nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.

Original language	English
Pages (from-to)	97-107
Number of pages	11
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	4271
DOIs	https://doi.org/10.1117/12.424682
Publication status	Published - 2001
Event	Optical Pulse and Beam Propagation III - San Jose, CA, United States Duration: 24 Jan 2001 → 25 Jan 2001

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10.1117/12.424682

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title = "Self-trapping of light and nonlinear localized modes in two-dimensional photonic crystals",

abstract = "We develop a theory of nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we demonstrate that it provides an accurate method for investigating the existence and properties of localized defect modes. Using this technique, we describe the existence of nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.",

keywords = "Linear stability, Nonlinear localized modes, Nonlinear waveguides, Photonic crystals, The Green function",

author = "Mingaleev, {S. F.} and Kivshar, {Y. S.}",

year = "2001",

doi = "10.1117/12.424682",

language = "English",

volume = "4271",

pages = "97--107",

journal = "Proceedings of SPIE - The International Society for Optical Engineering",

issn = "0277-786X",

publisher = "SPIE",

note = "Optical Pulse and Beam Propagation III ; Conference date: 24-01-2001 Through 25-01-2001",

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TY - JOUR

T1 - Self-trapping of light and nonlinear localized modes in two-dimensional photonic crystals

AU - Mingaleev, S. F.

AU - Kivshar, Y. S.

PY - 2001

Y1 - 2001

N2 - We develop a theory of nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we demonstrate that it provides an accurate method for investigating the existence and properties of localized defect modes. Using this technique, we describe the existence of nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.

AB - We develop a theory of nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we demonstrate that it provides an accurate method for investigating the existence and properties of localized defect modes. Using this technique, we describe the existence of nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.

KW - Linear stability

KW - Nonlinear localized modes

KW - Nonlinear waveguides

KW - Photonic crystals

KW - The Green function

UR - http://www.scopus.com/inward/record.url?scp=0034946990&partnerID=8YFLogxK

U2 - 10.1117/12.424682

DO - 10.1117/12.424682

M3 - Conference article

SN - 0277-786X

VL - 4271

SP - 97

EP - 107

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

T2 - Optical Pulse and Beam Propagation III

Y2 - 24 January 2001 through 25 January 2001

ER -

Self-trapping of light and nonlinear localized modes in two-dimensional photonic crystals

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