根据在非线性晶体中非共线谐波有效产生的相位匹配条件,导出了基波共线和非共线时可能产生的谐波环的解析表达式,给出了谐波环的大小与基波在晶体中传播方向的关系.对KDP和LiNbO3晶体中的谐波环的变化进行了观测,实验结果与理论计算相符.

According to the phase-matched condition of the non-collinear harmonic wave generated effectively in a non-linear crystal, the analytic expressions for the harmonic ring produced by collinear and non-collinear fundamental waves have been obtained. The relations between the size of harmonic ring and the direction of fundamental wave can be deduced from these analytic expressions. The harmonic rings of RDP and LiNbO3 crystals have been observed experimentally. Experimental results are in agreement with this theory.