In my optics course we have observed that in several applications, such as prism coupling of modes in an optical waveguide, coupling between two waveguides, attenuated total internal reflection (or frustrated internal reflection) in spectroscopy, part of the intensity of the incident wave goes from one medium to another one through a surface which has total internal reflection. This is because outside this surface we have an evanescent wave whose electric field goes to zero as an exponential function. In spite of that, in another part of the course we demonstrated (as was done, for instance, in Pedrotti et al., "Introduction to Optics") that this exponential electric field is perpendicular to the interface, therefore the Poynting vector is parallel to the surface. This means that there cannot be transferred energy from the first medium to the second one, because there is no flux of the Poynting vector in that direction.
Therefore, how can we have the coupling effects described before? I think there is something incorrect (or at least not always valid) in the deduction about the evanescent field, but I can not come up with what could it be.
EDIT (23-dec-2016):
Looking on the web, I found this page: https://en.m.wikipedia.org/wiki/Surface_plasmon, in which we have this application: https://en.m.wikipedia.org/wiki/Surface_plasmon_resonance. I don't think it is exactly my case, but since I haven't studied them yet in my course I can't fully comprehend them. Can this be a possible explanation to my problem? Why?
EDIT (26-dec-2016):
Trying to solve my question, I found a Wikipedia page about Near Field and Far Field in electromagnetic waves and in the "Near Field characteristics" section there is a description of some effects in the near field region. Are these effects the same as mine? Is there a way to investigate them more mathematically than as it is done there? Can somebody suggest some reference? Is there a way to explain them in Classical Physics or the only way to do that (as it seems on that page, if it is my case) is in term of virtual photons in Quantum Field Theory?
Best Answer
According to the book "Principles of Optics" by Born and Wolf, the electric field is not perpendicular to the interface in case of total internal reflection, and the component of the Poynting vector normal to the interface does not vanish. What vanishes is the averaged (over a period) normal component of the Poynting vector. In case of frustrated total internal reflection (that is, if the thickness of the layer with lower refraction coefficient is finite), the averaged normal component of the Poynting vector does not vanish, as per @fffred's comment.