A distributed Bragg reflector (DBR) is being designed to reflect yellow light with a wavelength of 560.0 nm. The DBR stack comprises a series of alternating pairs of aluminum arsenide (AlAs) and titanium dioxide (TiO2) layers. There are 16 pairs, that is, 32 layers. The refractive indices of AlAs and TiO2 are 3.199 and 2.638, respectively. The DBR will be deposited on a Si substrate with a refractive index of 4.054. Assume the speed of light to be 2.998 108 m s1. Assume the refractive index of air to be 1.0003.

i. Calculate the reflectivity of the DBR stack, as a percentage.

ii. Calculate the frequency bandwidth of the DBR stack.

iii. Describe how effectively the AlAs/TiO2 DBR stack increases the reflectivity compared to the Si substrate.