Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

Abstract

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external P T-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogenous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the selffocusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Stability through asymmetry: Modulationally stable nonlinear supermodes of asymmetric non-Hermitian optical couplers

“…Recent attempts, along this direction, have utilized a rather special complex potential, in which the spatial forms of the real and the imaginary part are functionally related. Under this condition, constant-intensity waves with non-trivial spatially inhomogeneous phase are shown to exist [28,29]. However, this condition restricts the generality of the structure and its potential application in realistic configurations.…”

Modulation instability in a microresonator with graphene saturable absorber, frequency selective feedback and external potential

“…The effect of δ potential on MI has also been studied via using linear stability analysis [42]. Linear stability analysis has also been studied for MI in nonlinear complex parity-time symmetric periodic potential [43] ,even, for different regimes of threshold [44]. It has also been observed that MI is independent of PT symmetric potential term [45].…”