Phase properties of multilayers

The phase shift upon transmission of a nonabsorbing multilayer is shown to be a monotonically decreasing function of the wave number, with an average slope proportional to the optical thickness of the coating. Two limiting situations of the phase shift upon reflection are examined: In one the phase monotonically increases with wavelength, and in the other the phase oscillates. The phase shift upon reflection is derivable from Kramers-Kronig-type relationships, provided the radiant reflectance and the Blaschke factors are known. Characteristic features of the refractive-index profile related to these factors are discussed.