Alkhoori Hamad M, Lakhtakia Akhlesh, Breakall James K, Bohren Craig F
J Opt Soc Am A Opt Image Sci Vis. 2018 Dec 1;35(12):2026-2034. doi: 10.1364/JOSAA.35.002026.
The simplest Lorentz-nonreciprocal medium has the constitutive relations (=-× and =+×). Scattering by a three-dimensional object composed of this medium was investigated using the extended boundary condition method. Scattering by this object in free space must be attributed to nonzero =||. The differential scattering efficiency is immune to the transformation of the incident toroidal electric field phasor into a poloidal electric field phasor, or vice versa, and a consequence of this source invariance is the polarization-state invariance of the differential scattering efficiency when the irradiating field is a plane wave. Both the total scattering and forward-scattering efficiencies of an ellipsoid composed of the simplest Lorentz-nonreciprocal medium are maximum when the plane wave is incident in a direction coparallel (but not antiparallel) to , and the backscattering efficiency is minimum when is parallel to the incidence direction. The total scattering and forward-scattering efficiencies are maximum when the incidence direction is parallel to the largest semi-axis of the ellipsoid if the incidence direction is coparallel (but not antiparallel) to . Lorentz nonreciprocity in an object is thus intimately connected to the shape of that object in affecting the scattered field.
最简单的洛伦兹非互易介质具有本构关系（(\mathbf{D}=-\xi\mathbf{H}\times\mathbf{k}) 和 (\mathbf{B}=\mu\mathbf{H}+\xi\mathbf{E}\times\mathbf{k})）。使用扩展边界条件方法研究了由这种介质组成的三维物体的散射。在自由空间中该物体的散射必定归因于非零的 (\xi = \xi_{\parallel})。微分散射效率不受入射环形电场相量到极向电场相量的变换影响，反之亦然，当辐照场为平面波时，这种源不变性的一个结果是微分散射效率的偏振态不变性。当平面波沿与 (\mathbf{k}) 共线（但非反平行）的方向入射时，由最简单的洛伦兹非互易介质组成的椭球体的总散射效率和前向散射效率均达到最大值，而当 (\mathbf{k}) 与入射方向平行时，后向散射效率达到最小值。如果入射方向与 (\mathbf{k}) 共线（但非反平行），则当入射方向与椭球体的最大半轴平行时，总散射效率和前向散射效率达到最大值。因此，物体中的洛伦兹非互易性在影响散射场方面与该物体的形状密切相关。
