Thickness of a partially reflective copper mirror

[Ngineer]

Hello everyone,

We are trying to fabricate a copper layer that is 41% reflective to a beam of 1521nm wavelength.

The formula I have used to calculate the thickness is:

R = 1 - e^-αt

Where
R: desired reflectance of mirror
t: thickness of mirror that would produce said reflectance
α: material- and wavelength-specific absorption coefficient. (for copper at 1521nm: α = 8.4327e+5 cm^-1, from http://refractiveindex.info/?shelf=main&book=Cu&page=Rakic)

For these values, I get t=6.25nm. When they fabricated it at the lab, there was almost no reflection at all.

Is the formula wrong? I based it on the transmission of a mirror being approximately T=e^-αt and R being 1-T for a mirror. Is there a siginificant amount of energy absorbed by the copper itself?

Your help is highly appreciated.

 

[nasu]

That exponential formula represents how much of the radiation entering the sample is absorbed. The rest goes through.
Reflection is another story. It may depend on the substrate too.
Maybe this will be useful
http://www.filmetrics.com/reflectance-calculator

 

[Ngineer]

Hi Nasu,

Reflection is what we are interested in. Unfortunately, the link you provided does not offer an insight into the theory involved. Where do I start reading?

I have assumed it would be rather simple as only normal incidence is involved.

 

[Ngineer]

Also, if a portion of the energy is transmitted, and the rest is absorbed (as described by this formula), wouldn't that mean that no reflection at all takes place?

Moreover, the fabricated mirror was almost completely transmissive, and not 59% transmissive as it should according to the formula (regardless of whether remaining energy is reflected or absorbed).

 

[nasu]

At the interface part of the beam is reflected, part enters the second medium. Your formula describes how this second part behaves as it propagates through the medium.

And your observed behaviour makes sense. If the medium is very transparent, the reflectivity is very low.

You can use that online calculator to calculate the reflection coefficient for layers of copper of various thicknesses on a substrate. I suppose your copper layer is on some substrate, isn't it?