Higher eigenmodes of nonlocal gap solitons in parity-time symmetric complex potential with a defocusing nonlinearity

Abstract

This work analyzes the existence and the stability of the double-hump gap solitons in an inhomogeneous medium having the parity-time (PT) symmetric complex potential with defocusing nonlocal nonlinearity. The stationary eigenvalues and the dynamical states have been investigated in the nonlinear regime. For stationary states, it is found that double-hump nonlocal gap solitons exist above a threshold value of energy and spread through two neighboring channels in the PT symmetric region. The power carried by the imaginary component of the double-hump soliton increases with the imaginary part of the complex potential. The total power is invariant with respect to the strength of the imaginary part of the potential and the range of the nonlocality. The power of the soliton increases with the propagation constant or energy.The dynamical states have been investigated. The double-hump soliton exists in the PT symmetric domain whereas dies out in the broken PT symmetric region. Linear stability of the double-hump solitons are studied using Bogoliobov-De-Genes equations. The double-hump solitons are unstable and the perturbation modes vary exponentially.