3.1 Introduction

The purpose of AR coatings is twofold: improvement in transmitted energy and a simultaneous reduction of reflected light, typically for the widest possible spectral region. If there are many optical elements in a system, the energy lost through reflection can be substantial. Laser systems need to be loss free and generally at discrete wavelengths; I do not examine those systems. The main property of optical materials is the index of refraction. The production lenses have index values between 1.4 and 1.95; the designs shown are mostly for crown glass (BK7) with a nominal index of 1.52. In this chapter, I examine the visible (light) spectrum for most of the coatings. The eye is not very sensitive to light below 425 nm or above 625 nm, so AR coatings for people are designed to function well only within this range. If the coatings are to be used with cameras or CCDs, the effective range may need adjustment. To judge the surface treatment quality, the amount of light that is reflected or transmitted is calculated for the spectral area of interest, and then comparisons can be made.

3.2 Single-Layer Coatings

The simplest durable coating to reduce reflection consists of a single quarterwavethickness layer of material that has an index of refraction that approaches the square root of the index of the (glass or plastic) element. For common (BK7) glass, the index is 1.52 (in the middle of the spectrum), and the coating that removes reflection has an index of 1.23. This index is not possible for any durable material, so there will always be some reflection from this type of coating on lower-index elements. Porous coatings are not considered here. The thick line in Fig. 3.1 shows the performance of this quarterwave coating for the visible spectrum (for which AR coatings are typically designed). These reflectance curves are shown only for one coated side, and the quarterwave thickness for designs refer to the reference wavelength in the graph. The glass type BK7 reflects ~4.25%, as indicated by the thick line in Fig. 3.1. The lower line would be the ultimate coating that cannot be attained with a durable coating material. The material of choice from the point of view of durability is SiO₂. However, the reflection from this substance on glass is too high, about 2.5-3%, which is unacceptable.