Parity-time symmetric coupler in transverse periodic and aperiodic potentials

The dynamics of the parity-time (PT) symmetric coupler in the presence of transverse periodic and aperiodic potentials have been studied for linear and nonlinear regime. The propagation-invariant solutions of the system have been studied and found that the high-frequency and the low-frequency solitons reside in the minimum of the periodic and aperiodic potentials. The amplitude of the low-frequency mode is greater than that of the high-frequency mode. The high strength of the periodic potential causes the soliton to be more confined in the lattice whereas high depth of the parabolic potential leads to the confinement of the soliton at minimum of the potential. The linear coupler possesses real eigenvalues when the gain/loss coefficient is less than the coupling coefficient for both periodic and aperiodic potentials. The transverse periodic potential modulates the amplitude of the beam and causes the formation of bands in the unbroken regime. The intensity of the beam is trapped in the channel with gain in the case of periodic and aperiodic potentials for nonlinear coupler. When the center of the soliton is initially at minimum of transverse potentials, velocity of the soliton increases. If the center of the soliton is initially at maximum of the periodic potential, it moves with uniform velocity. The linear stability analysis reveals that the high-frequency soliton is stable for both periodic and aperiodic potentials whereas the low-frequency soliton is unstable.