根据KBBF(KBe2BO3F2)晶体的色散方程、非共线相位匹配时各个光束应该满足的能量和动量守恒条件,用牛顿拉夫逊迭代法求解非线性方程组,以YAG激光器1064 nm波长入射为例,数值计算了KBBF晶体的Ⅰ类非共线倍频相位匹配角、有效非线性系数和允许角。结果以关系曲线形式给出。第一束基频波角度在20°-85°的范围内,都可以实现非共线相位匹配,相应的第二基频波和倍频波的匹配角度在29.1°-52.7°,24.6°-68.8°范围内;随着第一束基频波角度的增大,第二基频波和倍频波的相位匹配角以及倍频光相位匹配允许角也相应增大,而有效非线性系数随之减小;当第一束基频波的角度在26.1°-26.8°的范围内时它们的取值都出现了振荡现象。

Based on the Sellmeier equations of Kbe2BO3F2 (KBBF),non-collinear phase matching conditions and Newton-Raphson iterative approach,the type-Ⅰsecond harmonic phase-matching angle,effective nonlinear coefficient and the acceptance angle of KBBF crystal whose fundamental-wave wavelength is 1064 nm are respectively calculated with numerical method,under the non-collinear phase matching. The results show that the non-collinear phase matching can be realized when the angle of the first fundamental-wave angle is 20°-85°. Accordingly the angle of the second fundamental-wave the double-frequency wave is 29.1°-52.7°and 24.6°-68.83° respectively. The effective nonlinear coefficient decreases and the acceptance angle increases as the first fundamental-wave angle grows. When the first fundamental-wave angle is 26.1°-26.8°,both of them have an oscillation phenomenon.