Interference Filters and Mirrors

The transmission maximum of an interference filter is shifted towards shorter wavelengths if it is used at an inclined angle. The new transmission wavelength is related to the nominal wavelength Ag by 

Here B is the angle of incidence and n is the refractive index of the spacer layer. As an example, for Q = 10 , n = 1.45 and a filter wavelength of 600 nm we obtain AA = Aq -A 4 nm. This means, that if a filter is used 

Mirrors are also made using multiple dielectric layers of thickness A/4. The more layers that are added, the better the reflectivity that can be achieved in a certain wavelength region. In Fig.6.40 the effect of an increase in the number of layers is demonstrated. A reflectivity better than 0.999 can be obtained using 30 layers. Clearly, thin-film techniques of this kind are of great importance for the construction of laser cavities and for interferometers with sharp frequency discrimination characteristics. 

We will also briefly discuss anti-reflection layers. A surface without any special preparation between an external medium (frequently air), with refractive index ng, and an optical component with refractive index n, has a reflectivity R given by 

For a quai tz-air boundary we have R = [(1.5 — 1)/(1.5 + 1)] 4%. It can be shown that if a layer of refractive index ni and thickness A/4 is evaporated onto the optical component the reflectivity will be zero provided that ni = y/n. MgF2 with n = 1.35 is frequently a suitable material. In order to achieve anti-reflection properties in a larger wavelength region, e.g. in the whole visible region, multiple-layer tecimiques are used. 

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