【摘要】 任何一种理论都有它的适用范围，相位匹配条件亦不例外．因此我们可以问是否存在一个判据，它告诉我们什么时候可以“相位匹配地”讨论有效倍频现象以及什么时候必须“非相位匹配地”讨论．本文基于晶体的离散原子结构状态讨论了有效倍频行为中先前Ｆｒａｎｋｅｎ和Ｗａｒｄ所描述的相位匹配条件的适用范围，粗略地说，每当所有有关的光波波长都比晶格中原子间距大得多时，“相位匹配地”讨论就足够了，也即是足够精确了．更多还原

【Abstract】 Any theory has its limits of applicability including the phase-matching condition. Then we may ask whether a criterion exists which tells us when the effective frequency doubling may be discussed "phase-matchingly" and when it must be discussed " non-phase-matchingly". In this manuscript based on the actual discrete atomic structure of crystal, the limits of applicability of phase-matching condition described by Franken and Ward on the effective frequency doubling behavior are discussed. Roughly speaking a phase-matching treatment is adequate, i.e., sufficiently accurate, whenever all relevant optical wavelengths are large compared to the lattice constant of the crystal.更多还原