Bright Solitons in aPT-Symmetric Chain of Dimers

We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT-) symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.

Elastic Modes of an Anisotropic Ridge Waveguide

A semi-analytical method for finding the elastic modes propagating along the edge of an anisotropic semi-infinite plate is presented. Solutions are constructed as linear combinations of a finite number of the corresponding infinite plate modes with the constraint that they decay in the direction perpendicular to the edge and collectively satisfy the free boundary condition over the edge surface. Such modes that are confined to the edge can be used to approximate solutions of acoustic ridge waveguides whose supporting structures are sufficiently far away from the free edge. The semi-infinite plate or ridge is allowed to be oriented arbitrarily in the anisotropic crystal. Modifications to the theory to find symmetric and antisymmetric solutions for special crystal orientations are also presented. Accuracy of the solutions can be improved by including more plate modes in the series. Numerical techniques to find modal dispersion relations and orientation dependent modal behavior, are discussed. Results for ridges etched in single crystal Silicon are found to be in good agreement with Finite Element simulations. It is found that variations in modal phase velocity with respect to crystal orientation are not significant, suggesting that anisotropy may not be a critical issue while designing ridge waveguides in Silicon.