Much, if not most, interesting optics happens at interfaces, the transition from one material to another. The phenomena of reflection and refraction are both interface effects, and since these are the basis for the functional behavior of almost all optical components, we must address the question of what happens when an electromagnetic wave impinges on the boundary between two materials.

We begin this chapter with a discussion of refraction, which occurs when a beam of light strikes an interface and is deflected in its propagation direction. Based on consideration of the electromagnetic fields and their polarization across the material transition, we will then derive relationships between the reflected and transmitted parts of the optical field: both of these considerations, we will see, are to first order a function of the refractive indices of the materials on either side of the interface. After looking at the reflection and transmission of power, we will look at the important difference between external and internal incidence, and for the latter consider total internal reflection and the evanescent field.

Reflection and refraction

When a light beam is incident from a material with refractive index ni onto an interface formed with a material of refractive index nt, as shown in Figure 4.1, part of the light is reflected back into ni and a portion is transmitted into nt.