2D PT-symmetric nonlinear couplers: Stability and power dynamics in sinusoidal system

This work investigates the stability and power dynamics of a beam in a two-dimensional parity-time (PT)-symmetric cubic nonlinear sinusoidal coupled system under varying imaginary potentials. By analyzing eigenvalues, the phase angle indicating the mode synchronization, eigenfunctions, phase evolution, Poynting vector, and power exchange between coupled channels, we identify stability thresholds and characterize the soliton behavior in both PT-symmetric and broken PT-symmetric phases. Below the threshold potential, solitons remain stable, exhibiting periodic power oscillations and symmetric waveforms. Above the threshold, instabilities emerge, leading to asymmetric eigenfunctions, irregular amplitude fluctuations, and distorted power transfer. The transition is marked by a shift from smooth Gaussian-like waveforms to asymmetric, irregular profiles. The oscillation frequency, which dictates the energy transfer between channels, reflects the influence of the gain/loss balance on soliton dynamics. Our findings highlight the crucial role of nonlinearity, coupling strength, and imaginary potential in dictating soliton stability, providing insights into optical beam propagation and nonlinear wave control in PT-symmetric systems.