两组份复合材料光学非线性性质的临界行为

Critical Behavior of Optical Nonlinear Properties in Two-Component Composites

对两组份非线性复合材料的光学非线性性质的临界行为进行了研究。考虑第一组份为非线性材料 ,其电流、电压间服从I=g1V +χ1Vβ 关系 ;而第二组份为线性材料 ,电流、电压间满足I=g2 V ,其中g1,χ1是第一组份的线性电导和光学非线性极化率 ,g2 是第二组份的线性电导 ,β是第一组份材料的光学非线性指数。分别采用了有效介质近似和相对电阻涨落的标度理论两种方法计算了系统有效响应的临界指数随光学非线性指数及维数的变化规律。用不同的方法得到系统的有效线性电导ge 和有效光学非线性极化率 χe(β)的临界指数M(β)和N(β)的结论也不同。有效介质近似得到M(β) =1和N(β) =(β+1) / 2 ,即M(β)与 β和d都无关 ,而N(β)只与有 β关而与d无关 ;而相对电阻涨落标度理论方法得到的M(β)和N(β)与 β和d都有关。

The critical behavior of nonlinear properties in the component composites is studied. The first component is assumed to be nonlinear and obeys the nonlinear current (Ⅰ)-voltage (Ⅴ) characteristic of form formula I=g 1V+χ 1Vβ, while the second component is linear with I=g 2V, where g 1 and g 2 are linear conductance of constituents and χ 1 is the nonlinear susceptibility and β is nonlinear exponent. The volume fractions of two components are p and 1-p respectively. The critical exponents of effective response is calculated by means of effective medium approximation and the relative resistance fluctuation method, respectively. The conclusions are the critical exponents of linear conductance M(β)=1 and nonlinear susceptibility N(β)=(β+1)/2 for all spatial dimensions d can be obtained within the effective medium approximation; while based on the scaling theory of the relative resistance fluctuation, the critical exponents depends on arbitrary nonlinear β and spatial dimensions d.