# Why are subwavelength structures not resolved by light?

I've been looking at the field of metamaterials for quite a while, now. Most of it is predicated on the assumption (which is empirically demonstrable) that electromagnetic waves, when they reach a structure significantly beneath the wavelength of the light, 'feel' the material as being a homogeneous medium, with an effective refractive index. However, I'm having some difficulty understanding this. I often see equations such as those for plane waves (see below). However, I don't see how these provide any hints towards my problem about resolution into a homogenous medium, or any upper bound on the structure size of said medium. $$\boldsymbol{E}(\boldsymbol{r},t)=\boldsymbol{E_0}cos(\omega t-\boldsymbol{k}\cdot \boldsymbol{r} + \phi _0)$$ $$\boldsymbol{B}(\boldsymbol{r},t)=\boldsymbol{B_0}cos(\omega t-\boldsymbol{k}\cdot \boldsymbol{r} + \phi _0)$$ I've also seen several other equations which simply appear to treat light waves as existing at a single point, and not actually taking up any space.

I've taken a look at the diffraction limit, but I can't seem to find any logical reasoning for how this could be applicable (as its derivation appears to be based around the distance between the feature and an objective - well, here there is no objective), as well as applying the Heisenberg uncertainty principle (which either leads me in rather cyclic logic, or which references the patterns observed on a screen - which I again, don't see how it helps).

In short, I understand how a the fields of a light-wave interact with a barrier, but I can't find a reason why these interactions should somehow be bounded, in terms of their range, by the wavelength enough resolve periodic subwavelength structures into an effective homogenised medium.