Regarding the fresnel term on (Rough)Conductive material

[munechika-koyo]

Hello.

I have a question regarding the fresnel term, which is coded in the conductor.pyx: file:https://github.com/raysect/source/blob/0973260f115212aa954ad103080f465ffed78a11/raysect/optical/material/conductor.pyx#L136

I can understand the one which is coded in the dielectric.pyx, but I am wondering why the conductive's fresnel term is such a simple form. I would appreciate it if you could tell me how to derive this term or which reference you referred to.

Sorry for my basic question, and thank you in advance. Best regards,

Koyo

[CnlPepper]

Hi Koyo,

it's one of the standard undergraduate derivations of electromagnetic waves incident on a conducting boundary. I believe I rederived it myself based on the derivation in Electricity And Magnetism by W. Duffin. It is only a basic model, but was sufficient to be able to use data from refractiveindex.info for the different metals.

Best regards, Alex

[munechika-koyo]

Sorry for my late reply. I also tried to derive the Fresnel reflectivity which is coded in raysect using the standard fresnel reflectance coefficient:

This is the s-polarized light's reflectance coefficient. And, assuming that light waves travel through a vacuum and hit the conductive material, the complex refractive index of which is n_hat, r_s is represented by as follows:

So, I tried to take the absolute value of this equation (|r_s|^2 = (r_s) x (r_s)*) and derive the raysect's s-paralyzed reflectivity form, but I don't have any idea how to transform it.

And the raysect's form seems to be more simple form than the original one. Did you apply any approximation to that?

I would appreciate it if you could give me a little hint on that.

[CnlPepper]

I can't find my derivation unfortunately. If I remember correctly, when you substitute the complex refractive index into the full unpolarised light (parallel + perpendicular polarisation) reflectance equation, many of the terms end up cancelling.

[CnlPepper]

I've had a dig into this a bit more, there is in fact an approximation in the Raysect equation. It's a common, and very robust one for dielectric-conductor interfaces. See the following for a good write up. The approximation is described:

https://seblagarde.wordpress.com/2013/04/29/memo-on-fresnel-equations/

I'm tempted to also include the full equation now you've brought this to my attention, though it probably wouldn't be required for the metal library included with Raysect.

[munechika-koyo]

thank you @CnlPepper the approximation which you told me was very useful for me to understand how the fresnel term is calculated. And I am sorry not to replying sooner.

[CnlPepper]

No worries, happy it was helpful. :)