peacock dogbane beetle opal Thin Film Interference

k1k1 k2k2 y Maxima at: if then

Reflection from a dielectric slab: n IoIo Reflectance: IRIR (near normal incidence) R = 0.04 for glass To consider interference between the front and back reflection, assume they have the same amplitude: 0.04 I o ( n = relative index)

Dielectric Films n Assume near normal incidence: What is  ? Physical path difference: 2 t t Optical path difference:

Wait!! Reflections can cause phase shifts! First reflection:  phase shift Second reflection: no phase shift “Reflection” path difference: Total phase difference: ConstructiveDestructive How does this lead to color?

white n t o (nm) R t = 400 nm, n = 1.515,  = 0

For varying angle of incidence: normal and 45 degrees 045

4% per interface adds up!

Goal: R = 0, T = 1 (Impedance Matching) E k n g n o Can only adjust n

nfnf nono E k ngng Antireflection coating

Antireflection coating: two requirements n f = x t n s = 1.5 n o = Destructive interference:

1. Equal amplitudes:

Reflections from the front and back surfaces of a dielectric slab result in two plane waves with an optical path difference and therefore exhibit interference. The interference effects can be engineered to minimize reflectance or produce pretty colors.