Layered superconductors like High-Tc cuprates display out-of-plane plasma
oscillations between layers sustained by the weak Josephson coupling among the
superconducting sheets, the so-called Josephson plasmons. Bilayer cuprates
hosts two of such modes, but due to the anisotropy of the electronic response
their description at generic wavevector cannot be separated from that of the
in-plane oscillations. In this paper we provide an analytical theoretical
framework able to describe the dispersions and the polarizations of the
generalized plasma modes of such systems, that has been only partly addressed
by previous work in the literature. We then employ it to explain the peculiar
characteristics of their linear optical response, by providing a fully
microscopic explanation for the appearance of a finite-frequency peak in the
real part of the optical conductivity. On a wider perspective, the complete
characterization of the Josephson plasma modes provided by our approach
represents a groundwork to address open issues raised by recent experiments
with strong THz pulses, able to drive them beyond the linear-response regime.Comment: 21 pages, 8 figure