Optical analogue of relativistic Dirac solitons in binary waveguide arrays

Abstract

We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr non-linearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. (C) 2013 Elsevier Inc. All rights reserved

Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity

“…An open issue is the study of collisions of NLD solitary waves with different κ values. Our results are relevant to understanding nonlinear phenomena in Bose-Einstein condensates in honeycomb lattices [1,2] and optical binary waveguides [3,4] as well as nonlinear dynamics [5] and diffraction in photonic graphene [6].…”

“…The exact spinor structure of the multicomponent condensate order parameter provides a bosonic analog to the relativisitic electrons in monolayer graphene. It has also found applications in binary optical waveguide arrays [3,4] and in understanding the nonlinear dynamics in honeycomb lattices [5] including nonlinear diffraction in photonic graphene [6]. The nonlinear Dirac equation has been studied [7,8] in detail in the past for the particular case that the nonlinearity parameter κ = 1 (massive Gross-Neveu [9] and massive Thirring models [10]).…”

Approximate analytic solutions to coupled nonlinear Dirac equations

“…In particular, we have given the first (approximate) analytic solitary wave solution to two coupled NLDEs for both scalar-scalar interactions and vector-vector interactions. These solutions are relevant in nonlinear optics [5] as well as for light solitons in waveguide arrays [6][7][8] among other applications in BECs and cosmology. Further,we have shown using the Moore's decoupling method that in the nonrelativisticlimit, NLDEs with both scalar-scalar and vector-vector interactions reduce tothe same coupled nonlinear Schrödinger equation (NLSE).…”

“…The nonlinear Dirac (NLD) equation in 1 + 1 dimensions [1] has a long history and has emerged as a useful model in many physical systems such as extended particles [2][3][4], the gap solitons in nonlinear optics [5], light solitons in waveguide arrays and experimental realization of an optical analog for relativistic quantum mechanics [6][7][8], BoseEinstein condensates in honeycomb optical lattices [9], phenomenological models of quantum chromodynamics [10], as well as matter influencing the evolution of the universe in cosmology [11]. Further, the multi-component BEC order parameter has an exact spinor structure and serves as the bosonic analog to the relativistic electrons in graphene.…”

Nonlinear Dirac equation solitary waves under a spinor force with different components

“…extended particles [2][3][4], nonlinear optics [5], waveguide arrays as well as experimental optical realization of relativistic quantum mechanics [6][7][8], and honeycomb optical lattices harboring Bose-Einstein condensates [9]. The NLD equation also arises in the context of phenomenological models of quantum chromodynamics [10] and the influence of matter on the evolution of the Universe in cosmology [11].…”