Total internal reflection for illumination and displays

Abstract

Total internal reflection (TIR) can occur when a light ray traveling in a transparent material encounters an interface with another transparent, but less optically dense material. The phenomenon is interesting not only because the reflection can be close to perfect, but because the effect depends critically on the angle of incidence. Although TIR is used widely, in this article we discuss two less well known applications with which we have considerable experience. The first example is a device known as a prism light guide, a hollow dielectric structure that can transport a large luminous flux for illuminating engineering applications. The second example is a form of electronic paper. In both cases, it is the unique characteristics of TIR that make these practical devices possible. TIR is commonly said to occur when the angle of incidence exceeds the critical angle. Yet this notion is based on the inherent approximation of the ray model of light, an idea that is physically incorrect for any system of finite extent. Rather, the finite wavefront is equivalent to a superposition of a distribution of plane waves, which in turn have a range of propagation directions. Another fundamental shortcoming is that in any real system there is some degree of absorption loss in the materials. As a result, in reality, TIR is never truly total and the critical angle is never truly critical. Nevertheless, there is a profound quantitative difference between TIR and metallic reflection. In addition, in the case of TIR, the reflection can be modified by changing the external medium, which creates interesting possibilities. It is worth considering these ideas a bit more carefully and quantitatively. Light rays traveling from plastic (n1 = 1.5) to air (n2 = 1.0) will be transmitted through the interface for small angles of incidence, and the reflectance grows rapidly as a function of angle as the angle of incidence approaches the critical angle, (see Figure 1). It is important to note how tiny the angular range is in the plot in Figure 1. For all angles of incidence below the critical anFigure 1. The graph illustrates reflectance versus angle of incidence very close to the critical angle (indicated by the dotted vertical line).