High-frequency dark envelope electromagnetic waves and nonlinear Faraday rotation in magnetized plasmas

Nonlinear high-frequency electromagnetic waves in magnetized electron-ion plasmas are investigated, with an emphasis on dark envelope nonlinear waves, polarization rotation, both left-handed and right-handed mode splitting, which are relevant to polarization-based diagnostics and wave control. Analytical theory based on a nonlinear Schrödinger equation framework and fully electromagnetic PIC simulations jointly confirm that dark envelope solitons are stable under weak magnetization, whereas stronger magnetic fields induce clear amplitude modulation. The simulations further reveal polarization rotation and a frequency splitting between left-handed and right-handed circularly polarized waves, in agreement with theory and representing a nonlinear extension of Faraday rotation. We also quantify the dependence of the rotation frequency on the wave amplitude. These results provide new insights into wave dynamics, polarization, and plasma diagnostics in magnetized environments. The research offers significant advances in plasma diagnostics, space plasma modeling, and magneto-optical control technologies for strong field environments.