Antireflection coatings with Chebyshev or Butterworth response: design.

There are several methods of designing an antireflection (AR) coating for a dielectric substrate of refractive index n by depositing one or more nonabsorbing films on it. For example, one approach' is to use only two materials in a coating but to vary the thicknesses of the layers to achieve a filter in which the radiant transmittance vs wavenumber simulates a Chebyshev function. Another approach2 3 was developed by the designers of microwave filters in the 1950s. Young3 explains how optical AR coatings are designed using an algorithm of Riblet.4 In this method, at a given wavelength X the phase thicknesses A,