Multiscale Modeling &Simulation, Volume 19, Issue 1, Page 25-45, January 2021.
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its covariance operator is a pseudodifferential operator. The well-posedness of the direct source scattering problem is established, and the regularity of the electromagnetic field is given. For the inverse source scattering problem, the microcorrelation strength matrix of the covariance operator is shown to be uniquely determined by the high frequency limit of the expectation of the electric field measured in an open bounded domain disjoint with the support of the source. In particular, we show that the diagonal entries of the strength matrix can be uniquely determined by only using the amplitude of the electric field. Moreover, this result is extended to the almost surely sense by deducing an ergodic relation for the electric field over the frequencies.

中文翻译：

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麦克斯韦方程组的一个逆随机源问题

多尺度建模与仿真，第 19 卷，第 1 期，第 25-45 页，2021 年 1 月。
本文关注的是三维时谐麦克斯韦方程组的逆随机源问题。假设源是一个具有相关分量的中心复值高斯向量场，其协方差算子是一个伪微分算子。建立了直接源散射问题的适定性，并给出了电磁场的规律性。对于逆源散射问题，协方差算子的微相关强度矩阵显示为由在与源支持不相交的开放有界域中测量的电场期望的高频极限唯一确定。特别是，我们表明强度矩阵的对角线项可以仅通过使用电场的幅度来唯一确定。