In this paper we study the scattering and transfer matrices for electric fields defined with respect to an angular spectrum of plane waves. For these matrices, we derive the constraints that are enforced by conservation of energy, reciprocity, and time reversal symmetry. Notably, we examine the general case of vector fields in three dimensions and allow for evanescent field components. Moreover, we consider fields described by both continuous and discrete angular spectra, the latter being more relevant to practical applications, such as optical scattering experiments. We compare our results to better-known constraints, such as the unitarity of the scattering matrix for far-field modes, and show that previous results follow from our framework as special cases. Finally, we demonstrate our results numerically with a simple example of wave propagation at a planar glass-air interface, including the effects of total internal reflection. Our formalism makes minimal assumptions about the nature of the scattering medium and is thus applicable to a wide range of scattering problems.

中文翻译：

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包含渐逝分量的矢量散射和传递矩阵的对称约束：节能，互易和时间反转

在本文中，我们研究了相对于平面波的角谱定义的电场的散射和传递矩阵。对于这些矩阵，我们导出了由能量守恒，互易性和时间反向对称性所强制执行的约束。值得注意的是，我们研究了三维矢量场的一般情况，并考虑了渐逝场分量。此外，我们考虑由连续和离散角度光谱描述的场，后者与实际应用（例如光学散射实验）更相关。我们将我们的结果与更广为人知的约束条件（例如，远场模式的散射矩阵的统一性）进行了比较，并表明先前的结果作为特殊情况从我们的框架中得出。最后，我们用一个简单的例子说明了在平面玻璃-空气界面处的波传播，包括全内反射的影响，以数值方式证明了我们的结果。我们的形式主义对散射介质的性质做出了最小的假设，因此适用于广泛的散射问题。