Diffraction through a slit in a non-optically opaque material?
I have been studying some optical physics on the side of my usual work (I am not a physicist) and I recently have been studying the mathematical expression of the Huygens-Fresnel Principle for modeling plane and spherical waves. I'm aware that in this model, all points p on a wavefront surface S at a given time t act as point sources and can be integrated to find the contribution at a further point q in space. So diffraction in this model is a natural consequence of these point sources extending when a plane wave reachs the far edge of a slit in a material.
However, it seems that typically the material in which the slit is made is assumed to allow no transmission of incident waves. (In fact, it seems like reflection isn't considered either.) What happens when diffraction occurs through a material that does allow transmission? I guess the transmitted waves will probably be out of phase with the diffracted waves in most configurations, but what does the E-field actually look like?
With multiple slits, how would an interference pattern change? I assume it would be somewhat blurred just from physical intuition, but I'm not competent enough with the mathematics yet to figure it out for myself.
Posted Mar 7, 2023, 1:23 AM UTC
I can’t give you a great answer, but I figure it’s better than nothing.
Getting an analytic solution for diffraction through slits already has a lot of approximations.
I suspect that adding in transmission and reflection would complicate the situation to the point where no analytic solution exists, and the best we can do is simulate it.
It’s entirely possible I’m wrong cause I haven’t tried calculating that (if you’re interested in trying for transmission at least, it would be just like single slit diffraction, except when you integrate the points that pass through the substance, you would have to scale back the initial intensity and add a phase factor).
Sorry I couldn’t be more help!
That’s what I figured. Thanks for the response. It was at least a little helpful. What’s really bothering me is that there doesn’t seem to be any literature even considering it. I’m just very curious about what the wavefront would look like due to the phase delay. Probably would be a good idea to check something like the optical path difference to get a vague estimate of the behavior.