Resonant mode conversion in partially parity-time-symmetric waveguides

Resonant mode conversions in partially parity-time ($\mathrm{PT}$)-symmetric multimode waveguides are investigated. First, the symmetry breaking and degeneracy splitting of linear eigenmodes are found numerically and analytically. Moreover, mode conversions in the nonconservative system are demonstrated using longitudinally periodic modulation of the complex refractive index. The results show that, under the resonance condition, conversions between the unbroken modes with the same topological charge can occur, with conversion frequency being presented analytically. Finally, the influence of nonlinear effects on the resonant mode conversions is also discussed. It is found that the mode conversions depend on the dynamic equilibrium of the modes in nonlinear media, resulting in the conversions between the quadrupole modes in self-focusing medium, and the basic modes with ring structure in defocusing medium can be achieved. These results are beneficial for our further understanding of mode conversions in complex waveguides and can be applied to manipulation of the optical beam.