# Optical absorption in multilayer structure

Assume a hypothetical 3 media/ 1 layer structure with the following indices of refraction: $$n_1 = 2, n_2 = 2+i0.5, n_3 = 1$$ where the thickness of the layer is 100 nm and wavelength = 1000 nm.

Using Fresnel equations to derive the total transmittance and reflectance I get that about ~38% of incident power is absorbed in the layer.

If we now add another boundary, so that the structure now looks like: $$n_1 = 2, n_2 = 2+i0.5, n_3 = 1, n_4 = 3$$

The absorption in the first layer as a function of the second layer thickness now looks like:

My question is how is that the absorption now goes below the ~38%?

I understand that when deriving the transmission and reflectance I am summing up the electric field amplitude, some of which might cancel due to the reflections in the second layer but intuitively this still doesn't make sense.

• I'm just venturing a guess here, but because your films are quite thin, could this be a thin-film interference phenomenon? – Xcheckr Aug 11 '14 at 4:42
• @Xcheckr yes it is – user1830663 Aug 11 '14 at 4:44
• Looks like there's more reflection w/ the fourth layer, thus leading to a "second chance" for absorption. Perhaps you can trace the transmission and reflection at each interface to see what's actually happening? – Carl Witthoft Aug 11 '14 at 13:44
• @CarlWitthoft I get how there can be more absorption. Whats confusing is how can there be less than 38% – user1830663 Aug 11 '14 at 13:53
• Oops - maybe the reverse of my previous comment: less reflection, leading to less reflected light to be absorbed? – Carl Witthoft Aug 11 '14 at 14:25