Reflected wave extent into media

[johng23]

This question relates to second harmonic generation from a sub 100 nm nonlinear film.

When light impinges on an interface, some fraction is transmitted and reflected as described by the Fresnel equations. If I want to calculate the radiated second harmonic wave from a material, at first glance the reasonable thing to do is to consider only the amplitude of the transmitted fundamental wave. The reflected wave does not enter the second region so it does not generate any nonlinear polarization. This is the approach I have seen in at least one paper on the subject.

Classically we can imagine that the reflected fundamental wave is generated by radiating dipoles near the surface of the material. According to a qualitative argument in Hecht, this wave would be generated from a depth of about $\lambda$/2 in a transparent material. In any case, for a thin transparent film, the entire film feels the presence of the reflected field in addition to the transmitted component. In this case it seems to me that the entire incident field could contribute to second harmonic generation, including that fraction of the light which is reflected.

I don't know where my intuition fails, yet I don't think this is correct, as I don't know of any way that the equations of optics would distinguish between a near-surface region which polarizes in response to a field of amplitude E, and a bulk region which only feels a field of amplitude tE.

 

[johng23]

I've realized a simpler but related question:

The fresnel equations describe the reflectivity of a dielectric, but the thickness of the material does not appear in the equation. Does a correction need to be made for a nanoscale film? In a metal, the reflectivity is only partial when the thickness is comparable to the skin depth. There should be an analogous correction in this case.