Airy’s problem is the transmission of a monochromatic plane wave through a transparent film (ε , μ) of thickness d. The text solved this problem by summing an infinite number of single-interface Fresnel reflections and transmissions. Here, we specialize to normal incidence and use the matching conditions and a five-wave analysis (a forward-going wave in the z > d vacuum, a forward-going wave and a backward-going wave in the z

(a) If Z₀ and Z are the wave impedances in the vacuum and in the film, show that the fraction of the incident power transmitted into the vacuum through the z = d surface of the film is

(b) Show that the formula in part (a) agrees with Airy’s formula (derived in the text) for the same quantity.

Transcribed Image Text:

|T|² = 4ZZo (Z+Zo)²-(Z - Zo)² exp(2ikd) 12