混合微扰展开：级联模型的有效性
Mixed perturbative expansion: the validity of a model for the cascading
摘要：
建立了一种新的微扰展开式，对一些常用的模型方程进行了严格的推导，并阐明了它们的适用范围。该模型描述了两个短的和本地化的脉冲，基波和二次谐波，在具有非零二阶极化率$χ^(2)$的体单轴晶体中一起传播，并通过非线性光学中称为“双折射”的非线性效应相互作用的调制的演变。微扰方法将磁化率的多尺度展开与幂级数展开混合，并且必须仔细地适应物理情况。它允许确定模型有效的物理条件：离散、相位失配和各向异性的数量级必须具有确定的值。
英文摘要：
A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized pulses, fundamental and second harmonic, propagating together in a bulk uniaxial crystal with non-vanishing second order susceptibility $χ^(2)$ and interacting through the nonlinear effect known as ``cascading'' in nonlinear optics. The perturbative method mixes a multi-scale expansion with a power series expansion of the susceptibility, and must be carefully adapted to the physical situation. It allows the determination of the physical conditions under which the model is valid: the order of magnitude of the walk-off, phase-mismatch,and anisotropy must have determined values.
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