Beating solitons in parity-time symmetric potential well with unmatched imaginary part

The soliton solutions in ring-shaped parity-time symmetric potential wells are obtained through the accelerated imaginary time method. Subsequently, the split-step Fourier method is employed to simulate the dynamics of these solutions in the parity-time symmetric system with an unmatched imaginary component, which differs from the imaginary part utilized in the iterative solution process. The results indicate that the beam maintains a localized state with a fixed width in the ring potential well, while displaying a periodically varying intensity pattern accompanied by oscillating power. Beams exhibiting this distinctive propagation behavior are referred to as beating solitons in this work. More interestingly, the period and degree of oscillation of these beating solitons can be modulated by adjusting the parameters associated with the imaginary part of the parity-time symmetric system. Furthermore, the conversion between different beam states can also be realized. Our findings not only enhance the understanding of beam dynamics in PT-symmetric systems but also provide new possibilities for achieving stable beam control.