Proca Metamaterials, Massive Electromagnetism, and Spatial Dispersion

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.