# [EM] Diffusion by a rod

[EM] Scattering by a rod

Hello everyone :)

I'm interrested by the diffusion of an electromagnetic field by a rod with rectangular section i.e. a parallelepiped with one infinite dimension.
Does anyone know if that's already been done ? If it is even possible analytically ?

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A rod of what material?
What do you mean by diffusion? That's a term that normally applies to molecular movement - I've never seen it used in relation to EM.

You might know the Fresnel reflexion coefficients. Well, they describe the diffusion of an EM field by a planar interface.
You might also know the Mie coefficients. Well, they describe the diffusion of an EM field by a sphere of a certain size (for other sizes of the sphere, that will be the Rayleigh coefficients).
I use diffusion here in the sense that you shine a plane wave onto the object and look at what is reflected and transmitted.

I was wondering if the diffusion of an EM field by a rectangular rod has been done. I know that the diffusion of an EM field by an infinite cylinder has been done…

As for the material, any material. It will be described by its dielectric function epsilon(omega) :)

Edit : I understand now: I should use the word scattering instead of diffusion. Sorry :)

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Fresnel's equations deal with reflection and transmission of light at an interface with a transparent medium. It's an extension of simple wave theory.

Mie scattering is similar to Rayleigh scattering but in relation to slightly larger atmospheric particles.

Both of these are theoretical analyses that seek to explain an observed, natural effect in terms of Physical theory.

I don't know of any observed effects involving infinitely long rods of material.

The best I found so far is this paper: Petrov D, Shkuratov Y and Videen G, JQSRT(2010), doi:10.1016/j.jqsrt.2010.01.024
Seems rather involved I don't think there is an analytical solution to this problem… Maybe I'm wrong…

As the OP stated in post #3, he/she meant to use the word 'scattering' instead of diffusion. Since it's been brought up though, I thought I would just shed some light on electromagnetic diffusion.

If you take the Maxwell equations as quasi-static, i.e. you use both Faraday's law and Ampere's law but neglect the existence of the displacement current, then it is possible to derive diffusion equations for the magnetic field, electric field, and conduction current. These equations are in the exact form of what is commonly called "the diffusion equation;" although, I think there may be some other assumptions you have to make (e.g. spatially homogeneous material parameters) and the quasi-static approximation implies that the wavelengths are much larger than the characteristic system dimensions. In fact, the occurrence of the skin effect, among other things, in AC circuits can be attributed to EM diffusion.

Such discussions are given in Jackson and Smythe, among other places.