## Optical Coating Design : Introduction

Optical coatings design : Introduction
The basic building block of optical coatings is the quarterwave layer. A quarterwave layer is one where
 n.d = l / 4 n = refractive index of thin film d = thickness of thin film l = wavelength of light used
The important property of a quarterwave layer is that a stack of quarterwave layers of alternating refractive index high, low, high, low, ...., etc., has the reflection from every interface in phase. This gives constructive interference between every reflection, all the reflections add together and a quarterwave stack of enough layers (around 20) acts as a mirror at the wavelength l.
 Reflection of a quarterwave stack (each layer n.d = 525/4)
This mirror effect drops sharply a little way either side of the wavelength l (how far from l depends on the refractive indices of the layers used). So this quarterwave stack can also act as an edge filter simply by putting our wavelength l above or below where we want the edge. The pure quarterwave stack shown here has a lot of side ripple, this ripple can be reduced a variety of ways. The simplest is the addition of half a quarterwave layer at the top and bottom of the stack.

The quarterwave stack can then make high pass or low pass filters. We can also use it to make bandpass filters simply by putting two quarterwave stacks (each a stack of quarterwaves at different wavelengths, say one at 500nm, one at 1000nm) one on top of the other.

An other common optical coating is an anti-reflection coating. These are made by arranging destructive interference between the reflections from each interface of the thin films. The simplest anti-reflection (AR) coating is a single quarterwave where the refractive index is midway between that of the surface to be anti-reflected and the medium that surrounds it. So for glass (n=1.5) in air (n=1.0) the common single layer AR coat is MgF2 which has n=1.38.
 single layer MgF2 anti reflection of glass
Multi-layer AR coats give wider regions of anti-reflection and allow the use of harder materials, made at lower temperatures (MgF tends to need making at elevated temperatures).

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