PT-symmetric coupler with χ(2) nonlinearity

We introduce the notion of a PT -symmetric dimer with a χ(2) nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that b...

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Main Authors:	Li, K., Zezyulin, D. A., Kevrekidis, P. G., Konotop, V. V., Abdullaev, Fatkhulla
Format:	Article
Language:	English
Published:	American Physical Society 2013
Subjects:	QC Physics
Online Access:	http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/1/PhysRevA.88.053820.pdf

id	iium-33038
recordtype	eprints
spelling	iium-330382013-12-04T02:28:43Z http://irep.iium.edu.my/33038/ PT-symmetric coupler with χ(2) nonlinearity Li, K. Zezyulin, D. A. Kevrekidis, P. G. Konotop, V. V. Abdullaev, Fatkhulla QC Physics We introduce the notion of a PT -symmetric dimer with a χ(2) nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain and loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first- or the second-harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur, including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable. American Physical Society 2013-11-13 Article PeerReviewed application/pdf en http://irep.iium.edu.my/33038/1/PhysRevA.88.053820.pdf Li, K. and Zezyulin, D. A. and Kevrekidis, P. G. and Konotop, V. V. and Abdullaev, Fatkhulla (2013) PT-symmetric coupler with χ(2) nonlinearity. Physical Review A - Atomic, Molecular, and Optical Physics, 88. 053820(1)-053820(11). ISSN 1050-2947 http://pra.aps.org/abstract/PRA/v88/i5/e053820 10.1103/PhysRevA.88.053820
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QC Physics
spellingShingle	QC Physics Li, K. Zezyulin, D. A. Kevrekidis, P. G. Konotop, V. V. Abdullaev, Fatkhulla PT-symmetric coupler with χ(2) nonlinearity
description	We introduce the notion of a PT -symmetric dimer with a χ(2) nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain and loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first- or the second-harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur, including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.
format	Article
author	Li, K. Zezyulin, D. A. Kevrekidis, P. G. Konotop, V. V. Abdullaev, Fatkhulla
author_facet	Li, K. Zezyulin, D. A. Kevrekidis, P. G. Konotop, V. V. Abdullaev, Fatkhulla
author_sort	Li, K.
title	PT-symmetric coupler with χ(2) nonlinearity
title_short	PT-symmetric coupler with χ(2) nonlinearity
title_full	PT-symmetric coupler with χ(2) nonlinearity
title_fullStr	PT-symmetric coupler with χ(2) nonlinearity
title_full_unstemmed	PT-symmetric coupler with χ(2) nonlinearity
title_sort	pt-symmetric coupler with χ(2) nonlinearity
publisher	American Physical Society
publishDate	2013
url	http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/ http://irep.iium.edu.my/33038/1/PhysRevA.88.053820.pdf
first_indexed	2023-09-18T20:47:43Z
last_indexed	2023-09-18T20:47:43Z
_version_	1777409786614120448

PT-symmetric coupler with χ(2) nonlinearity

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