Avinash Karamchandani with Rolfe Petschek

Adiabatic Products of Transfer Matrices: Chirped Random Dielectric Mirrors

We will study theoretically a class of dielectric mirrors. A simple dielectric mirror is a periodic stack of layers with different, alternating indices of refraction that reflects light whose wavelength is close to four times the thickness of each layer. A technology under development at Case allows inexpensive manufacture of such mirrors. This technique introduces significant randomness in the thickness of the layers but allows for a slow change (or “chirping”) in the average thickness, which can widen the reflection band. We will analyze the reflectivity of such chirped, random, dielectric mirrors, dependent on the indices of the layers, randomness in the layer thickness and the rate and way in which the average layer thickness changes. Prior work allows us to calculate the average reflectivity as a product of matrixes. The product for the proposed device involves a large number of matrices, but successive matrices in the product are very similar. We will analyze such products of slowly changing matrices and make predictions about performance of such devices.