Page 262 - Modern Optical Engineering The Design of Optical Systems

242 Chapter Eleven

From Eq. 11.3 it is apparent that the reflectivity of a coated surface
will vary with wavelength. Obviously a quarter-wave coating for one
wavelength will be either more or less than a quarter-wave thick for
other wavelengths, and the interference effects will be modified
accordingly. Thus a low-reflection coating designed for use in the visible
region of the spectrum will have a minimum reflectance for yellow
light, and the reflectance for red and blue light will be appreciably
higher. This is the cause of the characteristic purple color of single-
layer low-reflection coatings. Figure 11.4a indicates this variation.
With more than one layer, more effective antireflection coatings can
be constructed. Theoretically, two layers allow the reduction of the
reflection to zero, provided that materials of suitable index are avail-
able; frequently, three layers are used for this purpose. Such a coating
achieves a zero reflectivity at a single wavelength at the expense of a
much higher reflectivity on either side. Because of the shape of the
reflectivity curve, this is called a V-coating. It is widely used for mono-
chromatic systems, such as those utilizing lasers as light sources.
With three or more layers, a broad-band, higher-efficiency, low-
reflection coating may be achieved as shown in Fig. 11.4b. Such a
coating may have two, or three minima, depending on the complexity
of the coating design. A typical reflection over the visual spectrum is to
the order of 0.25 percent, sometimes with another 0.25 percent lost to
scattering and absorption.

5%

4%
REFLECTANCE 3%

2%

1% INDEX = 1.52
INDEX = 1.72

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
RELATIVE WAVELENGTH
Figure 11.4a The reflectivity of a quarter-wave MgF (n = 1.38)
2
coating on high (n = 1.72) and low (n = 1.52) index substrates.
The wavelength scale is normalized to the wavelength at which
the coating has an optical thickness of one quarter-wave. Note
that as the wavelength approaches infinity, the reflectivity will
approach the value of the uncoated substrate (4.26 percent for the
1.52 index, and 7.01 percent for the 1.72 index), as it will also at
the normalized wavelength of 0.5.