27 - Some quirks of total internal reflection

Summary

Readers are undoubtedly familiar with the phenomenon of total internal reflection (TIR), which occurs when a beam of light within a high-index medium arrives with a sufficiently great angle of incidence at an interface with a lower-index medium. What is generally not appreciated is the complexity of phenomena that accompany TIR. For instance, consider the simple optical setup shown in Figure 27.1, where a uniform beam of light is brought to focus by a positive lens, being reflected, somewhere along the way, at the rear facet of a glass prism. Assuming a refractive index n = 1.65 for the prism material, the critical angle of incidence is readily found to be θ_crit = sin⁻¹(1/n) = 37.3°. Let the lens have numerical aperture NA = 0.2 (i.e., f-number = 2.5). Then the range of angles of incidence on the prism's rear facet will be (33.5°, 56.5°). The majority of the rays thus suffer total internal reflection and converge, as depicted in Figure 27.1, towards a common focus in the observation plane.

Figure 27.2 shows computed plots of intensity and phase at the observation plane, indicating that the focused spot essentially has the Airy pattern, albeit with minor deviations from the ideal. The diameter of the first dark ring, for example, is approximately 6λ, which is close to the theoretical value of 1.22λ /NA for the Airy disk.