arXiv subjects

O. B. Kirikchi

Publications and source records attributed to O. B. Kirikchi.

3 recordsLinked to original sources

arXiv2020

Discrete solitons dynamics in $\cal{PT}$-symmetric oligomers with complex-valued couplings

We consider an array of double oligomers in an optical waveguide device. A mathematical model for the system is the coupled discrete nonlinear Schrödinger (NLS) equations, where the gain-and-loss parameter contributes to the complex-valued linear coupling. The array caters to an optical simulation of the parity-time ($\cal{PT}$)-symmetry property between the coupled arms. The system admits fundamental bright discrete soliton solutions. We investigate their existence and spectral stability using perturbation theory analysis. These analytical findings are verified further numerically using the Newton-Raphson method and a standard eigenvalue-problem solver. Our study focuses on two natural discrete modes of the solitons: single- and double-excited-sites, also known as onsite and intersite modes, respectively. Each of these modes acquires three distinct configurations between the dimer arms, i.e., symmetric, asymmetric, and antisymmetric. Although both intersite and onsite discrete solitons are generally unstable, the latter can be stable, depending on the combined values of the propagation constant, horizontal linear coupling coefficient, and gain-loss parameter.

nlin.PS↗

arXiv2019

Solitons in a chain of charge-parity-symmetric dimers

We consider an array of dual-core waveguides, which represent an optical realization of a chain of dimers, with an active (gain-loss) coupling between the cores, opposite signs of discrete diffraction in the parallel arrays, and a phase-velocity mismatch between them (which is necessary for the stability of the system). The array provides an optical emulation of the charge-parity ($\mathcal{CP}$) symmetry. The addition of the intracore cubic nonlinearity gives rise to several species of fundamental discrete solitons, which exist in continuous families, although the system is non-Hermitian. The existence and stability of the soliton families are explored by means of analytical and numerical methods. An asymptotic analysis is presented for the case of weak intersite coupling (i.e., near the anticontinuum limit), as well as weak coupling between cores in each dimer. Several families of fundamental discrete solitons are found in the semi-infinite gap of the system's spectrum, that have no counterparts in the continuum limit, as well as a branch which belongs to the finite band gap and carries over into a family of stable gap solitons in that limit. One branch develops an oscillatory instability above a critical strength of the intersite coupling, others being stable in their entire existence regions. Unlike solitons in conservative lattices, which are controlled solely by the strength of the intersite coupling, here fundamental-soliton families have several control parameters, one of which, viz., the coefficient of the intercore coupling in the active host medium, may be readily adjusted in the experiment by varying the gain applied to the medium.

nlin.PS↗

arXiv2018

Snakes and ghosts in a parity-time-symmetric chain of dimers

We consider linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms and with a cubic-quintic nonlinearity. The system models a parity-time ($\cal{PT}$)-symmetric coupler composed by a chain of dimers. Particularly we study site-centered and bond-centered spatially-localized solutions and present that each solution has a symmetric and antisymmetric configuration between the arms. When a parameter is varied, the resulting bifurcation diagrams for the existence of standing localized solutions have a snaking behaviour. The critical gain/loss coefficient above which the $\cal{PT}-$symmetry is broken corresponds to the condition when bifurcation diagrams of symmetric and antisymmetric states merge. Past the symmetry breaking, the system no longer has time-independent states. Nevertheless, equilibrium solutions can be analytically continued by defining a dual equation that leads to so-called ghost states associated with growth or decay, that are also identified and examined here. We show that ghost localized states also exhibit snaking bifurcation diagrams. We analyse the width of the snaking region and provide asymptotic approximations in the limit of strong and weak coupling where good agreement is obtained.

nlin.PS↗