Reflectance of Titanium as Function of Thin Film Thickness

Question

As far as I know, transmittance equals $e^{-\alpha x}$, where $\alpha$ is absorption coefficient and $x$ is thin film thickness($100-300\,nm$). My team and I have engineered a way to find absorption. Transmittance, T= (Output intensity)/(initial intensity). And, absorption A=(initial intensity-output intensity)/(initial intensity). After simplifying the equation, one should get $$A= 1-T$$

The problem I am facing is I do not know any equation, which will give me reflectance of Ti as a function of thin film thickness at $808\,nm$ wavelength. If someone gives me an equation of transmittance, please include the effects of absorption so that I can calculate the reflectance afterwards.

Answer 1

Grab a copy of Optical Properties of Thin Solid Films by O. S Heavens. This discusses the transmission and reflection in great detail. There is more info on Google Books here, but it hasn't been scanned so you'll need to find a paper copy.

However, the overall transmission and reflection are calculated by calculating the transmission and reflection at each interface and summing them to one. So for films thin enough that you don't get interference the end result is just that R = 1 - T. There is no equation for reflection that is separate to the equation for transmittance.

Answer 2

You can calculate the reflectance in a very similar way to how I calculate the transmittance in this answer. Simply take $E_{out}$ to be the coherent sum of the light reflected back from the 0-1 interface, after any number of round trips through the metal film.

This allows you to calculate $T$ and $R$ independently, and so then you will simply be able to express the absorption as

$$ A = 1 - T - R $$