Nonlinear multicore waveguiding structures with balanced gain and loss

Alejandro J. Martínez, Mario I. Molina, Sergei K. Turitsyn, Yuri S. Kivshar

Research output: Contribution to journalArticle

Abstract

We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective PT-symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the PT-symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.

Original languageEnglish
Article number023822
JournalPhysical Review A
Volume91
Issue number2
DOIs
Publication statusPublished - 17 Feb 2015

Fingerprint

propagation
broken symmetry
stabilization
nonlinearity
dimers
waveguides
modulation
rings

Cite this

Martínez, Alejandro J. ; Molina, Mario I. ; Turitsyn, Sergei K. ; Kivshar, Yuri S. / Nonlinear multicore waveguiding structures with balanced gain and loss. In: Physical Review A. 2015 ; Vol. 91, No. 2.
@article{b055a5792d5b4cf9a6c10d64681f432f,
title = "Nonlinear multicore waveguiding structures with balanced gain and loss",
abstract = "We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective PT-symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the PT-symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.",
author = "Mart{\'i}nez, {Alejandro J.} and Molina, {Mario I.} and Turitsyn, {Sergei K.} and Kivshar, {Yuri S.}",
year = "2015",
month = "2",
day = "17",
doi = "10.1103/PhysRevA.91.023822",
language = "English",
volume = "91",
journal = "Physical Review A",
issn = "1050-2947",
publisher = "American Physical Society",
number = "2",

}

Nonlinear multicore waveguiding structures with balanced gain and loss. / Martínez, Alejandro J.; Molina, Mario I.; Turitsyn, Sergei K.; Kivshar, Yuri S.

In: Physical Review A, Vol. 91, No. 2, 023822, 17.02.2015.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Nonlinear multicore waveguiding structures with balanced gain and loss

AU - Martínez, Alejandro J.

AU - Molina, Mario I.

AU - Turitsyn, Sergei K.

AU - Kivshar, Yuri S.

PY - 2015/2/17

Y1 - 2015/2/17

N2 - We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective PT-symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the PT-symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.

AB - We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective PT-symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the PT-symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.

UR - http://www.scopus.com/inward/record.url?scp=84923233533&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.91.023822

DO - 10.1103/PhysRevA.91.023822

M3 - Article

AN - SCOPUS:84923233533

VL - 91

JO - Physical Review A

JF - Physical Review A

SN - 1050-2947

IS - 2

M1 - 023822

ER -