  We analyze electromagnetic modes in multi-layered nano-composites and
demonstrate that the response of a majority of realistic layered structures is
strongly affected by the non-local effects originating from strong field
oscillations across the system, and is not described by conventional
effective-medium theories. We develop the analytical description of the
relevant phenomena and confirm our results with numerical solutions of Maxwell
equations. Finally, we use the developed formalism to demonstrate that
multi-layered plasmonic nanostructures support high-index volume modes,
confined to deep subwavelength areas, opening a wide class of applications in
nanoscale light management.
