  In this work we develop a theory of surface electromagnetic waves localized
at the interface of periodic metal-dielectric structures. We have shown that
the anisotropy of plasma frequency in metal layers lifts the degeneracy of
plasma oscillations and opens a series of photonic band gaps. This results in
appearance of surface waves with singular density of states - we refer to them
as Tamm-Langmuir waves. Such naming is natural since we have found that their
properties are very similar to the properties of both bulk Langmuir and surface
Tamm waves. Depending on the anisotropy parameters, Tamm-Langmuir waves can be
either forward or backward waves. Singular density of states and high
sensitivity of the dispersion to the anisotropy of the structure makes
Tamm-Langmuir waves very promising for potential applications in nanophotonics
and biosensing.
