Beam propagation in cubic-quintic nonlinear optical system supported by modified parity-time symmetric Rosen-Morse complex potential

The present study explores the stability and persistence of nonlinear waves in self-focusing cubic-quintic media employing couplings of nonlinearity, spatial diffraction, and the parity-time symmetric Rosen-Morse complex field. Here, we discover that a system supported by Rosen-Morse potential can develop eigenmodes but does not accommodate stable soliton solutions for any potential parameters due to the non-vanishing terms in the imaginary component of potential. The study expands by modifying Rosen-Morse potential and discovers that the region of sustained PT-symmetry in the self-focusing material is enhanced and influenced by the order of the nonlinear function, spectral filtering, and gain/loss in the system. Stable soliton conditions for both broken PT-symmetric and PT-symmetric regions are established by the linear stability analysis using numerical simulations. Nonlinear propagation of the beam in the modified PT system is explored and identifies that stable beam propagation is possible only if the system is supported by the field, which is below the threshold imaginary potential.