Have you ever wondered why double rainbow colours are in different order? And why it is discussed here on optical coatings?
When our predecessors saw the light and rainbow, they tried to understand it. Even the first great physics authorities who formulated basic mechanical laws, tried as well. However, the first general theory was formulated not far from us – Dutch physicist Huygens. It explained light, an electromagnetic wave, reflection and refraction by terms of waves.
Huygens’ principle is:
All points on a wawefront serve as point sources of spherical secondary wavelets. After a time, t, the new position of the wawefront will be that of a surface tangent to these secondary wavelets.
From Huygens’ principle we can derive Snell’s law of refraction. A wave is partially reflected when it enters a different medium. Refraction in the case of water drops forms the different colors. In the spherical water drop, the reflected beam is scattered at 41-43° from the incident beam. This is the observation angle for the primary rainbow The red light after single reflection ends on top, so the red colour has the lower curvature in primary rainbow.
Then there is the case when second reflection occurs and we see fainter secondary rainbow. Its colours are reversed from the primary rainbow and the angle of observation is 52°. The difference in refractive index of water between blue and red wavelengths is only 0.0071 at 20 °C (0.5%), yet this produces the striking display of colour in the sky. If the raindrops had optical coating, the result would have been different!
For optics, the difference in refractive index is much larger, for example 1.0 of air and 1.5 of glass, and while rainbow is welcome sight in the sky, in optics it is not. As well as 4% loss due to reflected light part.
A fraction of the light or the electromagnetic waves in general, is reflected due to the mismatch of impedance caused by the sharp change of refractive index. An anti-reflection coating of a quarter-wave optical thickness is a well-known method for removing reflections of one specific wavelength, while more complex structures, such as multilayer coatings are used for broadband anti-reflection applications. The modern concept of light has shown that it has both wave and particle (now referred to as photon) properties and is the heart of duality theory.
Conventional anti-reflection technology relies on various refractive indices of thin coating layers to reduce the impedance mismatch and to get desired optical quality. This can decrease reflection to 0.1% or increase reflection to 99.9% according to your design. An optical coating is composed of a combination of thin layers of materials such as oxides, metals, or rare earth materials. The performance of an optical coating is dependent on the number of layers, their thickness, and the refractive index difference between them. Desired effect can be tuned to specific wavelength range according to design needs.
In the case of displays, there are not only top surface reflection but also reflection from all layers that are not index matched. None less, applying anti-reflection coating on outer surfaces will result in reduced reflection thus increasing overall open state transmittance.