Efficient optimization of multilayer coatings for ultrafast optics using analytic gradients of dispersion

A fully analytic method for computing gradients of dispersion (to any order) for a dielectric multilayer coating is developed, and it is demonstrated how group delay gradients can be used to optimize the dispersion of such a filter. The algorithm complexity is linear with the number of layers and quadratic in dispersion order. To our knowledge, this is the first published algorithm for computing exact analytic gradients of dispersion. We show an approximation that speeds up the computation significantly, making it linear in dispersion order. MATLAB and C code implementing the algorithms are made available.