Effective medium theory for Kapitza stratified media

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 = E
_x
(x, z)ê
_x
+ E
_z
(x, z)ê
_z
, H = H
_y
(x, z) ê
_y
(assuming the time dependence e
^-iωt
) in a dielectric medium modulated along the z-axis whose dielectric permittivity admits the Fourier series expansion ε = ε
_m
+ Σ
_n0
(a
_n
+ b
_n
/η) e
^{in K/η z}
, where e
_m
and (a
_n
+ b
_n
/η) are the Fourier coefficients whereas 2pη/K is the spatial period.