I was reading that for an incident angle greater than the critical angle, there will be a total internal reflection. The cosine of the refraction angle is therefore an imaginary number. If we make a straight forward derivation we get an exponential attenuation factor for the refracted wave. And this wave (named Evanescent wave) only propagates along the boundary. When we replace the cosine of the refraction angle on the Fresnel's formula, the amplitude of the reflected wave is the same of the incident wave, i.e the real part of Fresnel's reflection coefficient is equal to the unity. More calculations gives that there is no flow energy across the boundary and I guess this is why the total amplitude is reflected backward, i.e without losing energy. My questions are here: What is the physical meaning of the evanescent wave? If there are no flow energy why is there a propagation factor (along the boundary) for this wave? If this wave is not propagating how we can understand the existence of this wave? If there is no flow energy across the boundary but there is energy, why is the amplitude of reflected wave the same of the incident wave? is there no loss of energy?
thanks a lot.