## 1 Introduction  
Electromagnetism occupies the crowning role in physics, science, and modern technology. As in the cases of the Second and the Third Industrial Revolutions, research into electromagnetism is driving the ongoing Fourth Industrial Revolution [1] related to the transition to renewable energy, telecommunications in the 5G and 6G standards [2], advanced micro-/nanofabrication for novel electronic devices [3], bioelectromagnetics [4], information and electronic warfare [5], machine learning, material training [6, 7], and in other realms. The slide towards scientific and technological unification of the physical, chemical, biological, and digital worlds brought by the Fourth Industrial Revolution is due to the inalienable electromagnetic nature of these phenomena, based on the rule of the underlying laws of [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] [8, 9, 10]. We, the researchers of modern electromagnetism, are devoted to the development of the new electromagnetic materials collectively called composite artificial materials or metamaterials [11, 12, 13, 14, 15, 16, 17]. Metamaterials are made of arrays of subwavelength scatterers designed to exhibit the desired electromagnetic properties. In many important cases, metamaterials can be described as bianisotropic media [13, 14, 15, 16, 17]. In bianisotropic media, both the electric and magnetic responses depend on both the electric and magnetic fields of the external radiation [18, 19]. The studies of bianisotropic materials are almost as old as electromagnetism itself, persisting through the 19 th and 20 th centuries in the work of scientists such as [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] [18, 19, 20, 21, 22, 23, 24]. In the 21 st century the field of bianisotropic optical materials has received the name of bianisotropics [25, 26, 27] and is closely related to the research on electromagnetic metamaterials, since, typically, the desired properties of metamaterials depend on them being anisotropic and bianisotropic media [13, 14, 15, 16, 17, 18, 19]. Despite all these efforts and the rich history of research into bianisotropics until recently, very few general properties of bianisotropic media were established due to the complexity of these media [14; 18; 28; 29; 30; 31; 32; 33; 34; 35]. The bianisotropic media are the most general case of local linear media [18; 19; 25; 36; 37], with the effective material parameters combined into a 6 \(\times\) 6 matrix of material parameters \(\hat{M}\), which characterizes the electric displacement field \(\mathbf{D}\) and magnetic field \(\mathbf{B}\) in terms of the fields \(\mathbf{E}\) and \(\mathbf{H}\):  
\[ \begin{pmatrix}\mathbf{D}\\ \mathbf{B}\end{pmatrix} =\hat{M} \begin{pmatrix}\mathbf{E}\\ \mathbf{H}\end{pmatrix} = \begin{pmatrix}\hat{e}&\hat{X}\\ \hat{Y}&\hat{\eta}\end{pmatrix}\begin{pmatrix}\mathbf{E}\\ \mathbf{H}\end{pmatrix}  \tag{1}\]  
The 3 \(\times\) 3 matrices \(\hat{e},~{}\hat{\mu},~{}\hat{X},~{}\hat{Y}\) are dielectric permittivity, magnetic permeability, and two magnetoelectric coupling matrices respectively. The inverse relationship can also be formulated:  
\[ \begin{pmatrix}\mathbf{E}\\ \mathbf{H}\end{pmatrix} = \begin{bmatrix}\hat{e}&\hat{X}\\ \hat{Y}&\hat{\mu}\end{bmatrix} ^{-1} \begin{pmatrix}\mathbf{D}\\ \mathbf{B}\end{pmatrix} = \begin{bmatrix}\hat{\alpha}_{ED}&\hat{\alpha}_{EB}\\ \hat{\alpha}_{HB}&\hat{\alpha}_{HD}\end{bmatrix}\begin{pmatrix}\mathbf{D}\\ \mathbf{B}\end{pmatrix}  \tag{2}\]  
The relationships in Equations (1) and (2) mean that, unlike in many naturally occurring isotropic media, the electrical polarization and magnetization vectors in bianisotropic media are not directed in the same direction as the electric and magnetic fields. Such differences in the isotropic media can be achieved in engineered metamaterial structures [13; 14; 15; 16; 17]. One of the jewels in the crown of electromagnetism is [PERSON]'s theory of scattering by spheres.