# Can the intensity distribution behind edges and slits be explaint by the interaction with the surface electrons of the edges?

Reading about diffraction of EM radiation on edges, slits and multi slits as well as about electron diffraction behind a wire I came to the conclusion that the intensity distributions on an observers screen is the result of the interaction between radiation (electron beam) and a quantized field of surface electrons of the edges.

Going pregnant with such an idea, I started to read Physics.StackExchange. In this forum doesn't play a role that intensity pattern occurs behind every edge (in the contour of the geometrical shadow) and not only behind slits. Is it a possible point of view that behind a slit with a large enough distance between the edges of this slit occurs the same patterns like behind a single left edge and a single right edge - if we cut out the images of their intensity patterns and stick them together? I'm searching for arguments that this is not possible. This argumentation I need to contradict my idea about quantized field between photons and the surface electrons from one edge or the edges of single, double or multi slits.

That exists a well accepted and established theory about interference of EM radiation I know by myself, there is no need to talk about this fact. But I don't see a mistake in my explanation and need an argument to step away from my theory.

Beside the traditional point of view about interference of EM waves in the slits region even for single photons or electrons I found in the forum some evidence for the distribution pattern as a result of the quantized field of the interacting electrons from the edge(s): "... the electric field component perpendicular to the surface will be discontinuous, because there is electric field normal to the surface from bound surface charges...". This is an answer from @rob. Is this statement adoptable to my point of view?

I see no way to put this in different questions and hope it will be accepted as one question.

• How then do you explain the fact that you get the same diffraction pattern whether the slits are made from a conductor or an insulator, even though light interacts with these different types of materials in different ways? – John Rennie Jan 7 '15 at 16:21
• @John Rennie Thanks for replay at all. It's not known to me that there are experiments with different materials where the fringes distances where measured under equal circumstances for the distances from the source to the edges and to the screen. Moellenstedt experimented with different electrical potential and get not surprising different patterns. ... – HolgerFiedler Jan 7 '15 at 17:07
• ... What I know is that there is a difference between the position of the first fringe from photons and from electrons. The first intensity fringe for photons lay half inside and half outside the geometrical shadow. And for electrons there is a repulsive potential and the fringe starts wider the geometrical shadow. – HolgerFiedler Jan 7 '15 at 17:08
• @JánLalinský Edges are geometric designations for a border area made from valence electrons and due to the sharpness of such edges in double slit experiments with a high electrostatic potential. – HolgerFiedler May 15 '15 at 5:15
• Of course there is "an effect" in a absolutest sense, but the thing that optics people know that makes this a non-question is that it doesn't matter unless either the slit width or the wavelength is comparable to the depth of the boundary region. In other cases the final solution is dominated by the portion of wave passing far from the slit boundary. Certainly in the case of a plane wave passing an isolated edge the contribution from the half-plane completely overwhelm the edge effects. This follows from Huygens' principle. – dmckee --- ex-moderator kitten Nov 3 '15 at 19:18

@Holger Fiedler Hi,

Thanks for your comment on my answer here. Here I would like to say that I am an experimental physicist and working on the ultrashort coherent XUV radiation. I have first hand experience with the interference of XUV radiation using double slits.

Your question is very genuine. Long ago I have thought over this question for quite a some time. The first comment made by @John Rennie is very pertinent. He is absolutely right in his saying that the slit material plays no role in the diffraction. If you can make double slit of same width, same separation, same thickness (this is just a practical consideration because with thicker slits alignment of the slit become tedious), same edge roughness you will get same diffraction pattern with any material (be it paper, copper, aluminum, steel or wood). Note that last two requirements of roughness and thickness are not that stringent.

To test this assumption I would like to suggest you to make a simulation. I presume that you must be familiar with some high level programming language like matlab or python.

Take a plane wave of wave vector $k$ (since you are dealing with time stationary diffraction you do not need $\omega t$ term) write the wave equation $exp\left(i kr\right)$, now construct two slits of width w and separation d and finally a screen at distance D. Take several points on the screen and on slits. Now trace the rays and calculate path from above equation and construct the intensity distribution on the plate by overlapping all the rays from double slit on a single point of screen.

The simulated interference pattern will be an exact replica of the observed diffraction pattern (If you can do such experiment). I have tested this myself, the matching between these two spectra is quantitative. Once you have made such program you can change your incident pulse to anything you like and so on or you can easily convert it into the simulation of knife edge.

The idea behind suggestion for making this simulation (where we did not consider any interaction between light and the electrons present in slit) is to illustrate that the wave nature of the light is responsible for the diffraction and not the interaction of the electrons at the edge of the slit. The interaction of the electrons in material is responsible for blocking of light.

I would like to mention that you can deduce all the above things (at least qualitatively) via very basic equations for plane wave but in my opinion by making such program you can see the effect of changing the parameters on the actual diffraction pattern and seeing is believing.

PS: If you like I can upload python code of my simulation.

• The question is could one do a simulation of what I await about the electrons electric field on sharp edges. And this I think is it impossible. Since I'm an engineer I'm not in the position to do so. BTW has you read about the the distribution of magnetic dipole moments inside atoms? – HolgerFiedler Jul 21 '16 at 19:41
• Thanks for your replay. Instead of a simulation I would prefer an experiment. Any idea an possibility? – HolgerFiedler Jul 21 '16 at 19:45
• Hsinghal There is a historical overview of mine about electron diffraction. Unfortunately until now only in German ru.wikipedia.org/wiki/Участник:HolgerFiedler/… . It is interesting that to the biprisma could be applied an electric potential and this changes the deflection and diffraction of the electrons path. More than this in the potentialfree case as well as with potential the intensity distribution on the observers screen is equally distributed. upload.wikimedia.org/wikipedia/commons/b/b6/… – HolgerFiedler Jul 22 '16 at 4:36
• Perhaps this is applicable to your work, XUV is used to mask microelectronic devices? – HolgerFiedler Jul 22 '16 at 4:37
• The first link in my reply seems not to work ru.wikipedia.org/wiki/Участник:HolgerFiedler/…. After ..org/wiki has to be a slash "/" – HolgerFiedler Jul 22 '16 at 4:43