  We develop a modal method that solves Maxwell's equations in the presence of
the linearized hydrodynamic correction. Using this approach, it is now possible
to calculate the full diffraction for structures with period of the order of
the plasma wavelength, including not only the transverse but also the
longitudinal modes appearing above the plasma frequency. As an example for
using this method we solve the diffraction of a plane wave near the plasma
frequency from a bi-metallic layer, modeled as a continuous variation of the
plasma frequency. We observe absorption oscillations around the plasma
frequency. The lower frequency absorption peaks and dips correspond to lowest
longitudinal modes concentrated in the lower plasma frequency region. As the
frequency is increased, higher order longitudinal modes are excited and extent
to the region of higher plasma frequency. Moreover, examination of the
propagation constants of these modes reveals that the absorption peaks and dips
are directly related to the direction of phase propagation of the longitudinal
modes. Furthermore, we formulate a variant of the Plane Wave Expansion method,
and used it to calculate the dispersion diagram of such longitudinal modes in a
periodically modulated plasma frequency layer.
