Prevention of polarization frequency splitting in isotropic medium with high-order transverse modes

This paper investigates experimental and numerical simulation methods for achieving frequency degeneracy in high-order modes with orthogonal polarization of a CW diode-pumped Nd: YAG laser. In isotropic crystals, weak phase anisotropy from factors like inhomogeneous dopant distribution can cause polarization eigenmode frequency splitting. While frequency degeneracy can be achieved in the fundamental transverse mode through spot detection and frequency analysis, higher-order modes exhibit more complex frequency characteristics, and their interaction with this mechanism remains unclear. This study explores the polarization eigenmode frequency degeneracy in higher-order modes (TEM₅,₀). By introducing two quarter-wave plates into the resonator, we achieve effective frequency control, leading to polarization frequency degeneracy. Experimentally, we focus on the high-order mode generated by an off-axis laser. The polarization state is successfully controlled by rotating the angles of two quarter-wave plates in the resonator. Consequently, a linearly polarized TEM_5,0 mode laser is produced, reaching a maximum polarization extinction ratio (PER) of 24.77 dB. To further understand this phenomenon, numerical simulations are conducted to analyze the mechanism of polarization frequency degeneracy. The results indicate that the initial phase difference between two polarization eigenmodes, caused by weak birefringence, can be effectively adjusted by fine-tuning orientations of the two quarter-wave plates in the cavity, thereby achieving polarization frequency degeneracy. This study presents a novel approach to polarization control for high-order mode laser.