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.