  We propose a theoretical approach to some of the nanorod-based metamaterial
implementations that does not depend on macroscopic electrodynamics. The
approach is motivated by the fact that in actual experiments the incident
electromagnetic wave encounters a metamaterial structure which is planar in its
shape, contains a layer or two of artificially created building blocks, and
therefore cannot be regarded as a three-dimensional continuous medium. This
leads to a theoretical framework in which the phenomenological concept of
refractive index loses its principled meaning, and the deeper concept of
scattering is taking center stage. Our proposal and its mathematical
realization rely heavily on Feynman's explanation of the physical origin of the
index of refraction and on his formula for the field of a plane of oscillating
charges. We provide a complete proof of Feynman's formula, filling in some
steps that were missing in the original derivation, and then generalize it to
the case of a finite disk, which may be relevant to the actual experiments
involving laser beams. We then show how the formula can be applied to
metamaterial nanoplasmonics by considering some subtle interference effects in
narrow laser beams striking metamaterial plates. The first two effects use a
single layer of aligned plasmonic nanorods, while the third uses a single layer
of gyrotropic elements that may conveniently be described by the celebrated
Born-Kuhn oscillator model. The considered effects can potentially be used in
the development of quality standards for various metamaterial devices.
