Consider two parallel wire "comb" filters oriented at 45 degrees relative "tooth" angle.
The comb tooth spacing spacing is much less than one wavelength, and the comb tooth length is much more than one wavelength.
They are filtering a perpendicular beam of long wavelength monochromatic unpolarized radiation.
(Think microwaves.)
If the two filters are far apart, ie spaced by more than three wavelengths, 50 % of the radiation passes through the first filter and 50% of that, or 25%, passes through both filters. (Basic polarization theory.)
However, if the filters are actually touching, they form an intersecting grid with holes much less than one wavelength in every direction and essentially no radiation passes through the combined filters.
I assume this no-transmission condition still applies if the two filters are close together, ie almost touching, or separated by much less than one wavelength.
My assumption is that as the separation between the filters increases from zero to three wavelengths, the transmission increases smoothly, but not linearly, from 0 to 25%.
My question is "What is the formula describing this increase in transmission percentage as a function of distance?"
For extra credit, include also the dependence, if any, on the relative angle of the two polarizing filters.
If a reference is available, I would appreciate receiving it.
Does the answer change in any way if the wires are absorbing, rather than reflecting?
(This is very similar to a previous question I asked, Formula for polarized "light" transmission through close filters? but I did not get a good answer, so I have simplified the question.)
