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

Absorption and eigenmode calculation for one-dimensional periodic metallic structures using the hydrodynamic approximation