Page 453 - Engineering Electromagnetics, 8th Edition

CHAPTER 12 Plane Wave Reflection and Dispersion 435

Figure 12.8 Beam-steering prism for
Example 12.8.

as beam-steering prisms, where light within the glass structure totally reflects from
glass-air interfaces.

EXAMPLE 12.8
A prism is to be used to turn a beam of light by 90 ,as shown in Figure 12.8.
◦
Light enters and exits the prism through two antireflective (AR-coated) surfaces.
Total reflection is to occur at the back surface, where the incident angle is 45 to the
◦
normal. Determine the minimum required refractive index of the prism material if the
surrounding region is air.
Solution. Considering the back surface, the medium beyond the interface is air, with
n 2 = 1.00. Because θ 1 = 45 , (76) is used to obtain
◦
n 2 √
n 1 ≥ = 2 = 1.41
sin 45
Because fused silica glass has refractive index n g = 1.45, it is a suitable material for
this application and is in fact widely used.

Another important application of total reflection is in optical waveguides. These,
in their simplest form, are constructed of three layers of glass, in which the middle
layer has a slightly higher refractive index than the outer two. Figure 12.9 shows
the basic structure. Light, propagating from left to right, is confined to the middle
layer by total reflection at the two interfaces, as shown. Optical fiber waveguides are
constructed on this principle, in which a cylindrical glass core region of small radius
is surrounded coaxially by a lower-index cladding glass material of larger radius.
Basic waveguiding principles as applied to metallic and dielectric structures will be
presented in Chapter 13.