When an EM Wave comes to a boundary of two different media (i.e different electrical permitivity and magnetic permeability media), the things below could be seen:
I want to learn the criteria for the above events. For example, when do reflections occur? When does transmittance occur? Do they depend on the characteristic impedance or electrical permittivity differences of the media?
Yea dependence is there.
At the interface between two mediums : 1 and 2, the amount of reflection of EM waves for perpendicular incidence, can be described by its reflection coefficient. $$\rho = \left(\frac{\eta_1 -\eta_2}{\eta_1 +\eta_2}\right)$$ where, $$\eta_1 = \sqrt{\mu_1/\epsilon_1}$$ $$\eta_2 = \sqrt{\mu_2/\epsilon_2}$$ similarly the amount of transmission can be described corresponding transmission coefficient $$\tau = 1+\rho $$
EDIT:
The coefficients are defined in terms of amplitudes of the incident, transmitted and reflected waves.
- Reflections
- Refractions (Transmitted wave)
- Absorption
- scattering (I am not sure)
Generally, all four will happen at each interface between media.
Reflection occurs when the index of refraction is not perfectly matched between the two media.
Refraction will occur when the index of refraction is not perfectly matched and the angle of incidence is not exactly \$0^\circ\$ from normal. (And when there is not 100% reflection)
Scattering will occur when the interface between the media is not a perfectly flat plane.
Absorption mainly comes from propagation through any medium that is not perfectly lossless. It can also happen at an interface between media if there is some loss mechanism localized at the interface, such as a surface charge that isn't perfectly conductive.
There is a set of equations exactly describing what you are asking for: they are called the Fresnel equations.
Reflection and transmission are covered by the Fresnel equations.
Scattering is, however, not covered as it would depend on the roughness of the surface. So there can't be a generic formula for the scattering without quantifying the roughness (it also would be very dependent on the wavelength). The Fresnel equations assume a smooth surface (i.e. roughness much smaller than wavelength).
Absorption doesn't matter, as it doesn't happen at the surface but requires a non-zero length of medium to be passed.
The Fresnel equations give coefficients of reflectance \$R\$ (i.e. ratio of reflected power to incident power) for EM radiation that is either polarized in the plane of incidence (p-polarized) or polarized perpendicular to the plane of incidence (s-polarized).
\$R_s = \lvert\frac{Z_2\cos\theta_i - Z_1\cos\theta_i}{Z_2\cos\theta_i + Z_1\cos\theta_i}\rvert^2\$
\$R_p = \lvert\frac{Z_2\cos\theta_t - Z_1\cos\theta_i}{Z_2\cos\theta_t + Z_1\cos\theta_i}\rvert^2\$
where
\$\theta_i =\$angle of incidence
\$\theta_t =\$angle of transmission
\$Z_k=\frac{\mu_k}{\epsilon_k}\$ and \$k\$ is an index 1 or 2 for the medium.
There are other versions of the formulars. E.g. under the assumption that \$\mu_1= \mu_2 = \mu_0\$ (permeability of vacuum) they can be rewritten as expressions of indices of refraction of both media.
(Note: since there are no non-linear effects involved you can compose any polarization into a linear combination of p- and s- polarized components).
From what I've recently read, in trying to understand Efield shielding myself from the first principles, reflections occur when the material has polarizable atoms. The incoming energy gets (partially) stored by warping the electron orbits; warped orbits cause exciting behaviors in the material.
Look for the "wave coefficient" or "propagation coefficient" in the literature; this variable in its most general form will show various resonances (spectral lines) and show a general dependency with frequency, hence dispersion of pulses will occur.
