a) Consider three dielectric media with flat and parallel boundaries with refractive indices n1, n2, and n3. Show that for normal incidence the reflection coefficient between layers 1 and 2 is the same as that between layers 2 and 3 if
\(n_2=[n_1n_3]^.5\)
What is the significance of this result?
b) Consider a Si phtodiode that is designed for operation at 900 nm. GIven a choice of two possible AR coatings, SiO2 with a refractive ndex of 1.4 and TiO2 with a refractive index of 2.3, which would you use and what would be the thickness of the AR coating? The refractive index of Si is 3.5. Explain your decision.
c) COnsider a Ge photodiode that is designed for operation around 1200 nm. What are the best AR coating refractive index and thickness if the refractive index of Ge is about 4.0?