Evanescent Waves in near field for aperture > lambda (diffraction)?

[PhDeezNutz]

Totally fine I'll enjoy reading it. Bethe's paper is of course a master piece. I have a similar paper by H. Levine and J. Schwinger that uses the variational approach. It appears in multiple publications. My copy is in "Theory of Electromagnetic Waves" a symposium circa 1951.

It truly is a master piece. I can't believe he devised a strategy almost 80 years ago to deal with diffraction by small holes. On one hand it can be shown the scattering cross section for large disks is $\sim k^2 a^4$ and the scattering cross section for small disks is $\sim k^4 a ^6$ so naturally we would expect small holes to diffract less power than large holes...that part is almost obvious. The thing that amazes me is that he knew how to approach the problem in a way that would reconcile this and because the paper is some 40 pages long, justifying the approach is not trivial. I used his approach and got pretty close to corroborating his claim that

$(Bethe) = (k^2 a^2) (Kirchhoff)$

How he knew his results would turn out so well 80 years ago is nothing short of amazing.

Also I just sent the write-up. I'm not going to lie, rather than using Bethe's paper directly I used this paper to guide my understanding of Bethe

https://www.tandfonline.com/doi/full/10.1080/02726343.2011.590960?scroll=top&needAccess=true&

Pretty clever way of deriving Hans Bethe's results from purely energy considerations instead of going into all sorts of math (that is beyond me at this point).