Site-controlled gain-loss managed solitons in the nonlinear Schrӧdinger equation with complex potential wells

This paper investigates the propagation of localized solutions, i.e. solitons, iterated from the real parts of complex potentials in the cubic nonlinear Schrӧdinger equation (NLSE). We identify single state, dipole, and multipole solutions, all exhibiting stable yet varied propagation within these complex potential wells. Our results demonstrate that the beams formed by these solutions can be sustained in the NLSE, maintaining their localized structure and propagating stably. However, by adjusting the position of the real part, the intensity of the beam can be controlled to decrease, remain constant, or increase, accompanied by a varied evolution of the power during propagation. This behavior results from a local imbalance between gain and loss. More interestingly, by designing the range of imaginary parts, the beams can transform between different states and achieve stationary propagation with variable parameters. Furthermore, the control of beam patterns and power can also be accomplished by manipulating beam's propagation path. Our findings not only enhance the understanding of beam dynamics in non-Hermitian systems but also provide new methods for the localization and control of optical beams.