Anti-reflection (AR) coatings

Anti-reflection coatings - how they work

AR coats are used in many applications to reduce glare, increase contrast and transmission, and generally improve performance. They can be made at any wavelength, provided that suitable coating materials are available, but how do AR coats work and what are the material requirements?

The simplest case is a single layer anti-reflection coating on a transparent substrate.
The anti-reflection is acheved by having a equal and oppposite reflections, one from each interface. These reflections cancel each other out by destructive interference. To acheive perfect anti-reflection we need :-

1. equal reflections
2. oppposite (out of phase) reflections

1. having the refractive index of the AR coat equal to the square root of the product of the refractive index of the subsrate and the surrounding medium.
2. making the AR coat thickness a quarterwave

n = refractive index
lambda = wavelength

So for example a single layer AR coat on glass (n=1.5) in air (n=1) would require a coating with a refractive index of square root(1.5 x 1) = 1.22. Suitable coating materials don't exist, the closest is MgF₂ where n=1.38 .

Our second condition requires a thickness such that
          n.d = 525 / 4
So the film thickness (to anti reflect at 525nm in the middle of the visible) is
          d = 525 / (1.38 . 4) = 95nm.

This gives the performance shown here :-

To acheive better performance more layers are usually required. A three layer AR coat can be thought of as a central layer with single layer anti-reflection each side.
The same conditions apply to each of these single layer AR coats (namely each has a refractive index equal to the square root of the product of the refractive indices on either side, and each is a quarterwave at the required wavelength).