弱非线性复合体中的高阶非线性响应

Higher-order nonlinear responses in weakly nonlinear composite materials within the effective medium approximation

利用谱表示理论和微扰展开法 ,从理论上给出了适合于一般微结构复合体系的有效非线性响应的一般表示式 ,并结合有效媒质近似 (EMA) ,在弱非线性条件下研究了由三阶非线性组分 (体积分数为p)和线性组分构成的非线性复合体系的有效非线性响应 ,讨论了复合体系的有效介电常数ε～e =εe+χe｜E0 ｜2 +ηe｜E0 ｜4 中的有效三次非线性响应 χe 和有效高次非线性响应 ηe 与体积分数p和退极化因子L之间的关系 ,分析了非线性组分的介电常数为复数情形时体系的有效高阶非线性响应 ,从理论上说明了组分的高次非线性响应对整个复合体系的有效介电常数的影响 .

Based on the spectral representation theory and the perturbative expansion method, the general expressions for effective nonlinear responses (chi(e) and eta(e)) are derived for any complicated micro structures. The higher-order nonlinear response of two-component composite is studied by using the effective medium approximation. The effective dielectric constant of the composite is given by epsilon<overbar>(e) = epsilon(e) + chi(e) \E-0\(2) + eta(e) \E-0\(4). The effective cubic order nonlinear response chi(e) and the higher-order response le for the whole volume fraction p of the nonlinear component are investigated and the general expressions of X and V, are given in this paper. We also perform numerical simulations for chi(e) and eta(e), in the case of complex dielectric constant of the nonlinear component, The effect of the higher order nonlinear responses on the effective dielectric constant of the composite is theoretically studied.