Abstract

In the literature, several multilayer coating configurations have been proposed which have a reflectance stop band at the tuned wavelength and for which various orders of harmonic stopbands have been suppressed. Baumeister ^1,2 has outlined a procedure for designing a symmetric multilayer in which any number of higher order harmonic stopbands are suppressed. He makes the statement that, "As more and more contiguous stopbands are suppressed, the stepped-index profile approximates a sinusoid." However, the algebraic complexities of his approach make it difficult to determine the index profile as it approaches the continuous limit. Prior to this, Thelen³ published plots of the equivalent index for an inhomogeneous system where the index varies with the Jacobian elliptic function⁴ dn. Recently, Carniglia⁵ showed that stepped-index designs in which the natural log of the index follows a sinusoid will have good harmonic suppression out to a certain order. (This log index sinusoid dependence we call an exponential sinusoid in this paper, since that is how the index itself varies.)

© 1988 Optical Society of America