Proca Metamaterials, Massive Electromagnetism, and Nonlocality

We investigate a new type of electromagnetic meta-materials (MTMs),
which we dub Proca MTMs, constituting an interesting medium behaving
like a “relativistic material” for potential use in electromagnetic
applications. It is rigorously proved using a field-theoretic approach
that Maxwell theory inside certain classes of nonlocal metamaterials is
equivalent to Maxwell-Proca theory in vacuum, where in the latter
photons acquire a nonzero mass (massive electromagnetism.) It turns out
that the key to the operation of Proca MTM is nonlocality (here spatial
dispersion since the Proca MTM is homogeneous), and hence Proca MTMs
represent an important example of the more general family of nonlocal
MTMs. Our 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 MTMs. Proca waves carry an additional
polarization degree of freedom and each wave appears to behave like a
single mode with two transverse components and one longitudinal. This
opens the door for applications in wireless communications and other
fields where information could be encoded in polarization. As a concrete
application, we develop the main ingredients of Proca antennas as an
example of the emerging technology of nonlocal antennas, where we
establish that a single Proca dipole possesses a perfect isotropic
radiation pattern, a radical departure from conventional local antennas
(radiators in vacuum and temporally dispersive media) where such
radiation characteristics is impossible. Moreover, the new connection
between electromagnetic theory in some nonlocal MTMs and Maxwell-Proca
theory allows the use of relativistic techniques developed in the latter
in order to efficiently perform calculations like field quantization in
nonlocal domains which would be very difficult to perform otherwise.