Two dimensional spatial solitons in parity-time symmetric potential

This work analyzes the propagation of (2 + 1) dimensional spatial solitons in parity-time (PTPT) symmetric potential. The stationary solution of the system has been studied. The beam dynamics has been analyzed using variational and numerical methods. The soliton beam propagation is stable when the coefficient of imaginary potential is less than a threshold, which is called the phase transition point. Above the transition point, the imaginary component of the solution starts to evolve and the solution becomes unstable. When the coefficient of imaginary potential exceeds this critical value, the power of the beam increases and results in the unstable beam propagation. The stability of the stationary solution against small perturbation has been studied using linear stability analysis. The imaginary eigen value is zero when the coefficient of the imaginary potential is low. Above the phase transition point, the imaginary eigen value becomes comparable with the real eigen value and hence the solution becomes linearly unstable.