In our prior blog post we discussed the properties and major uses of Antireflective Coatings. We also talked about how how anti-reflection is not a property of materials. Rather, it is a consequence of light’s wavelike behavior when passing through a specific geometric setup, and is therefore somewhat independent of which material we are using. Today we will dive into that concept further and learn about the inner working of antireflective coatings.

Similarly, transparency and reflection are also opposites, since more photons reflected entails less photons passing through. However, increasing transparency at the cost of reflection is not straightforward. The amount of light reflected by a transparent material does not depend on the wavelength. Common glass, for instance, reflects around 8% of light, no matter which kind of light is incident. In fact, increasing some materials’ transparency actually improves their reflection.

Light exhibits many wave-like phenomena. Anti-reflection is a process involving three of these processes: interference, refraction and reflection.

Interference is one of the most beautiful but complex aspects of waves. And it is also the key ingredient of anti-reflection. So let us tackle it first.

Unlike particles, two waves can exist at the same point in space at the same time. When waves meet, unlike particles, they don’t ‘bump’ into each other, they don’t collide. Instead they merge into a single wave (see figure below). The merged wave is simply the sum of the amplitudes of its two constituent waves. Therefore if a crest meets a crest, the crests add up. This is a common sight on the beach: reflected waves from the shore meet the incoming waves.

Antireflective coatings are simply a transparent layer of a different material from the original transparent object. Both materials have different refractive index. Light passing through both mediums ends up being reflected twice. First when it hits the surface of the AR coat, second when it hits the surface of the object. Thus we have two distinct rays R1 and R2 traveling in the same direction away from the object.

Interference from two similar waves traveling in the same direction is a regular wave – that depends solely on the phase difference of the two waves (see figure below). The phase difference is caused by the fact that ray R1 travels a distance shorter by 2w than ray R2 (w – being the width of the coating layer). Different phase differences produce different merged waves. The most interesting case is when the two waves are separated by half the wavelength. The resultant wave has zero amplitude. At every point, the two waves cancel each other.

This is exactly how antireflective coatings work. But for this to happen, we need to guarantee that the two reflected waves are completely out of phase.

This is a wonderful but strange phenomenon. Adding a transparent layer actually doubles the reflected light. But by doubling the reflected rays, we have effectively managed to eliminate them!

Reflection occurs when light travels from one medium to another. The portion of reflected light depends on the difference of the refractive index of the two mediums. So when light travels from air into the Antireflective coating, and then from the Antireflective Coating into the object, the refractive index of the coat should be roughly in between that of the air and the object.

This produces reflected rays of equal strength from the Antireflective Coating and the object, so their interference is a perfect cancellation. When the primary transparent object is glass, MgF2 is used because its refractive index is the closest to the mean value.

If the refractive index of the antireflective layer is higher than the object, a wave inversion occurs for reflected waves, which must be also taken into account. In this case, anti-reflection works for all wavelengths at least 10 times greater than the width of the aR coat. You can read more about that here.

Light’s speed is slower when traveling through a medium. The refractive index is proportional to the speed drop. The wavelength also shortens. This fact also needs to be taken into account when calculating the phase difference between the two rays. The extra distance travelled by the second reflected ray must be equal to half of the shortened wavelength of light, and not the wavelength of light in air.

To sum up, the surface of the antireflective coatings and the object surface on which it is applied reflect incident light rays. Light’s ability to break up into multiple rays and interfere with itself to cancel out produces one of the most unexpected but useful effect. The thinner the layer, the shorter the wavelength of light it can cancel.