On the Huygens principle for bianisotropic mediums with symmetric permittivity and permeability dyadics

Mathematical statements of the Huygens principle relate the electric and magnetic field phasors at an arbitrary location in a source-free region enclosed by a surface to the tangential components of the electric and magnetic field phasors over that surface, via the dyadic Green functions applicable to the linear homogeneous medium occupying that region. We have mathematically formulated the Huygens principle for the electric and magnetic field phasors when the permittivity and permeability dyadics of the medium are symmetric, the symmetric parts of the two magnetoelectric dyadics of the medium are negative of each other, and both magnetoelectric dyadics also contain anti-symmetric terms. We have also formulated the Huygens principle for the electric (resp. magnetic) field phasor in a medium whose permittivity (resp. permeability) is scalar, the permeability (resp. permittivity) is symmetric, the symmetric parts of the two magnetoelectric dyadics reduce to dissimilar scalars, and anti-symmetric parts of the two magnetoelectric dyadics are identical.

惠更斯原理的数学表述通过适用于占据某区域的线性均匀介质的并矢格林函数，将无场源区域内被一个表面所包围的任意位置处的电场和磁场相量与该表面上电场和磁场相量的切向分量联系起来。当介质的介电常数和磁导率并矢是对称的，介质的两个磁电并矢的对称部分彼此互为相反数，并且两个磁电并矢也都包含反对称项时，我们对电场和磁场相量在数学上阐述了惠更斯原理。我们还针对介电常数（相应地，磁导率）为标量、磁导率（相应地，介电常数）是对称的、两个磁电并矢的对称部分简化为不同的标量且两个磁电并矢的反对称部分相同的介质中的电场（相应地，磁场）相量阐述了惠更斯原理。