Tunable wave propagation in nonlinear PT−symmetric systems: Stability and power switching of coupled symmetric and asymmetric modes

This study investigates beam dynamics, mode bifurcation, and power switching in one-dimensional PT-symmetric nonlinear directional coupler with spatially varying cubic–quintic nonlinearities and a complex hyperbolic potential. We compute symmetric and asymmetric eigenmodes in Kerr nonlinear system and analyze their stability using both eigenvalue analysis and Bogoliubov–de Gennes (BdG) spectra. Unlike conventional symmetry breaking, we observe power-induced coexistence of symmetric and asymmetric states without bifurcation of the base mode. The instability threshold W_th increases with coupling strength, real component of the complex potential, and inter peak separation, but it is suppressed by field localization width, and narrower nonlinear profiles. Propagation simulations reveal how input power and system parameters affect the beam width, localization, and stability. Notably, asymmetric modes exhibit more robust and faster power switching between waveguides, though nonlinear saturation limits this behavior at high powers. The inclusion of a quintic term offers further control over symmetry and coupling. These results highlight tunable non-Hermitian nonlinear effects with potential applications in optical switching, signal routing, and nonreciprocal light transport.