PT-symmetric coupler with χ(2) nonlinearity

K. Li, D. A. Zezyulin, P. G. Kevrekidis, V. V. Konotop, and F. Kh. Abdullaev
Phys. Rev. A 88, 053820 – Published 15 November 2013

Abstract

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.

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  • Received 30 August 2013

DOI:https://doi.org/10.1103/PhysRevA.88.053820

©2013 American Physical Society

Authors & Affiliations

K. Li1, D. A. Zezyulin2, P. G. Kevrekidis1, V. V. Konotop2, and F. Kh. Abdullaev3,4

  • 1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
  • 2Centro de Física Teórica e Computacional, and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal
  • 3Instituto de Física Téorica, Universidade Estadual Paulista, 01140-070, São Paulo, São Paulo, Brazil
  • 4Department of Physics, Kulliyyah of Science, International Islamic University of Malaysia, Jalan Istana, Bandar Indera Mahkota 25200, Kuantan, Malaysia

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Vol. 88, Iss. 5 — November 2013

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