We formulate the problem of designing gradient-index optical coatings as the task of solving a system of operator equations. We use iterative numerical procedures known from the theory of inverse problems to solve it with respect to the coating refractive index profile and thickness. The mathematical derivations necessary for the application of the procedures are presented, and different numerical methods (Landweber, Newton, and Gauss–Newton methods, Tikhonov minimization with surrogate functionals) are implemented. Procedures for the transformation of the gradient coating designs into quasi-gradient ones (i.e., multilayer stacks of homogeneous layers with different refractive indices) are also developed. The design algorithms work with physically available coating materials that could be produced with the modern coating technologies.
© 2012 Optical Society of America
Original Manuscript: August 7, 2012
Revised Manuscript: September 28, 2012
Manuscript Accepted: October 12, 2012
Published: November 30, 2012
Stephan W. Anzengruber, Esther Klann, Ronny Ramlau, and Diana Tonova, "Numerical methods for the design of gradient-index optical coatings," Appl. Opt. 51, 8277-8295 (2012)