A class of electromagnetic metamaterials (MTMs) is investigated, which the author dubs Proca MTMs, constituting a medium behaving like a “relativistic material” for potential use in electromagnetic applications. This work is motivated by numerous previous results on particular structures such as plasma, waveguides, photonic crystals, magnetic materials, where it has been observed that photons may acquire mass in some dispersive domains. In this approach, it is rigorously proved using a field-theoretic approach that Maxwell theory inside certain classes of nonlocal (spatially-dispersive) metamaterials is equivalent to Proca theory in vacuum, where in the latter photons acquire a nonzero mass (massive electromagnetism.) An explicit closed-form general expression for the Proca MTM dielectric function is given. It turns out that the key to the operation of Proca MTM is spatial dispersion, and hence Proca MTMs represent an important example of the more general family of nonlocal MTMs. The author's analysis involves multiphysics aspects, utilizing concepts and methods taken from classical electromagnetism, special relativity, quantum theory, electromagnetic materials, and antenna theory. Extensive discussion of the physics, computational methods, and design parameters of Proca MTMs is provided to further understand the nature of massive electromagnetism in nonlocal (spatially-dispersive) MTMs. As a concrete application, the main ingredients of Proca antennas are developed as an example of the emerging technology of nonlocal antennas, where the author establishes that a single Proca dipole possesses a perfect isotropic radiation pattern, a noteworthy departure from conventional local antennas (radiators in vacuum and temporally dispersive media) where such radiation characteristics is impossible.

中文翻译：

---

Proca 超材料、大电磁学和空间色散

研究了一类电磁超材料 (MTM)，作者将其称为 Proca MTM，它构成一种介质，其行为类似于“相对论材料”，可用于电磁应用。这项工作的动机是先前在特定结构（例如等离子体、波导、光子晶体、磁性材料）上的许多结果，其中已经观察到光子可能在某些色散域中获得质量。在这种方法中，使用场论方法严格证明，某些类别的非局域（空间色散）超材料中的麦克斯韦理论等效于真空中的普罗卡理论，在后者中，光子获得非零质量（大电磁力）。给出了 Proca MTM 介电函数的显式闭式一般表达式。事实证明，Proca MTM 操作的关键是空间分散，因此 Proca MTM 代表了更一般的非局部 MTM 家族的一个重要例子。作者的分析涉及多物理场方面，利用了经典电磁学、狭义相对论、量子理论、电磁材料和天线理论中的概念和方法。提供了对 Proca MTM 的物理、计算方法和设计参数的广泛讨论，以进一步了解非局部（空间色散）MTM 中大量电磁的性质。作为一个具体的应用，Proca 天线的主要成分是作为非本地天线新兴技术的一个例子而开发的，作者在其中建立了单个 Proca 偶极子具有完美的各向同性辐射图，