Influence of angular deviation on sum-frequency mode under type-I critical phase matching

This study addresses the mode distortion of the sum-frequency optical field induced by angular deviation under type-I critical phase matching. A nonlinear numerical model based on the three-wave coupling equations and angular spectrum decomposition is established. This model accurately resolves angular deviations and complex nonlinear coupling processes. By simultaneously considering the refractive index distribution and phase mismatch of each angular spectral component along different incident directions, the model enables the simulation of harmonic conversion processes and the far-field beam profile within the crystal. Numerical simulations of the near-field and far-field evolution of the sum-frequency optical field under different θ-angle and φ-angle deviations in the LBO crystal demonstrate that when the incident angle deviates from the ideal phase-matching direction, the refractive index distribution becomes asymmetric. This asymmetry leads to mode splitting, rotation, and fringe-like patterns in the sum-frequency optical field. A deviation in the φ angle (along the walk-off direction) causes beam pointing shifts and an increase in fringe number, while a deviation in the θ angle introduces walk-off of the incident beams, resulting in rotation of the sum-frequency field. Using a fundamental beam at 1547 nm (15 W, 1 MHz, 2.8 ns), the influence of angular deviation on the 310 nm laser is experimentally verified under both circular and elliptical focusing conditions. Under elliptical focusing, the sum-frequency optical field is more prone to mode splitting. The experimental results are in good agreement with the simulation trends, revealing how refractive index variations and phase mismatch induced by angular deviation alter the mode of the sum-frequency optical field. This study provides both theoretical guidance and experimental reference for mode control of sum-frequency light under type-I critical phase matching.