I conjecture that the shadowing disrupts the evanescent wave that travels at the boundary of the surface. The surface of the material has a surface charge and a surface current that helps satisfies the boundary conditions on the surface. The evanescent wave on the surface penetrates below the surface, coupling to evanescent waves in deeper layers. Thus, the evanescent wave participates in interference phenomena in multiple reflection.

The evanescent wave can travel a large longitudinal distance if the surface were perfectly flat. However, roughness disrupts the travel of the evanescent wave. So surface roughness ends up reducing the interference phenomena from multiple reflection.

The effect of surface roughness can be characterized as a shadowing effect. The evanescent wave has an energy flux associated with it, similar to the energy flux of the bulk light waves. However, the surface roughness adds an extinction flux that is part of the shadowing.

The evanescent wave can also be considered a type of plasmon. Incident light perpendicular to the surface causes an evanescent wave like a surface plasmon. Incident light parallel to the surface causes a bulk plasmon. Shadowing causes a nonlinear optics effect similar to plasmon decay. Shadowing breaks a plasmon into smaller plasmons. Therefore, the plasmon can’t penetrate as deeply into the material. So there is less interference between the reflected light from different layers.

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http://www.physics.ucla.edu/~moonemp/diffuser/10_VesperinasGil1992.pdf

In a flat interface, the transition of the reflectivity about the critical angle is a steep one; then the transmitted field above this angle becomes evanescent, and its angular spectrum shows a peak in the nonradiative zone. On introducing roughness, we shall observe that this transition smooths and that the distri- bution of the evanescent components of the scattered transmitted field gradually broadens, the peak structure disappearing over the nonradiative region.

https://en.wikipedia.org/wiki/Total_internal_reflection#Derivation_of_evanescent_wave

‘An important side effect of total internal reflection is the appearance of an evanescent wave beyond the boundary surface. Essentially, even though the entire incident wave is reflected back into the originating medium, there is some penetration into the second medium at the boundary. The evanescent wave appears to travel along the boundary between the two materials, leading to the Goos-Hänchen shift.’

http://fulviofrisone.com/attachments/article/406/raether_2.pdf

‘Surface Plasmons on Smooth and Rough Surfaces and on Gratings

This review describes the basic physics of surface plasmons (SPs) propagat­ ing on smooth and corrugated surfaces. SPs represent electromagnetic surface waves that have their intensity maximum in the surface and exponentially de­ caying fields perpendicular to it. They can be produced not only by electrons, but also by light in an optical device called the attenuated total reflection (ATR). An important property of the SPs is their coupling with photons via corrugated surfaces and vice versa, so that the SPs become involved in a series of optical phenomena.’