二维随机介质中柱面波传播及其局域性的随机泛函分析

分析了二维各向同性均匀随机介质中柱面波的传播特性及局域化现象.用随机泛函理论,在频域内将随机介电起伏展开成柱坐标系下的Wiener积分式,将波场表示为内外行柱面波的线性和,求解二维Helmholtz波动方程,得到随机介电起伏对柱面波幅度与相位调制的解析表达.由柱面波能量的空间分布验证了波的局域化现象,并求解局域化长度.二维随机介质中平面波按柱面波展开的波转换方程与非随机介质中的情形有相似的表达,但具有随机介电起伏对幅度和相位的调制,并给出数值模拟结果.

Stochastic functional analysis of propagation and localization of cylindrical wave in a two-dimensional random medium

Propagation and localization of cylindrical wave in a two-dimensional isotropic and homogeneous random medium is studied. By expanding the random permittivity fluctuation in the form of a Wiener integral equation in the frequency domain, and representing the wave fields by a linear combination of outgoing and incoming waves, the scalar Helmholtz equation is solved by means of stochastic functional approach to obtain the analytical expression of cylindrical wave. The spatial wave energy distribution is derived to demonstrate the localization phenomenon, and the localization length is also calculated. Compared with the waves in non-random medium, the wave transfer equation between plane wave and cylindrical wave in random medium shows an additional exponential factor to indicate the modulation effects due to the medium randomness in both the amplitude and the phase. Numerical simulations are presented to illustrate the functional dependence of the localization phenomenon.