Effective medium theory for Kapitza stratified media

Abstract

Here, we consider that a novel regime of propagation occurs for Transverse Magnetic (TM) waves propagating, in the long wavelength regime, through rapidly modulated stratified media with a large dielectric modulation depth (Kapitza media). The considered electromagnetic situation is conceptually equivalent to that of the mechanical inverted pendulum whose pivot point is subjected to high-frequency vertical oscillations (Kapitza pendulum) [1], since these oscillations produce a rapidly varying contribution to the lagragian function with a large modulation depth. We consider a monochromatic TM electromagnetic field of complex amplitudes E = Ex(x, z)ex + Ez(x, z)ez, H = Hy(x, z) ey (assuming the time dependence e-iωt) in a dielectric medium modulated along the z-axis whose dielectric permittivity admits the Fourier series expansion e = em + Σn0 (an + bn/η) ein K/η z, where em and (an + bn/η) are the Fourier coefficients whereas 2pη/K is the spatial period.