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In this paper, an analytical solution to the problem of optimal dielectriccoating design of mirrors for gravitational wave detectors is found. Thetechnique used to solve this problem is based on Herpin's equivalent layers,which provide a simple, constructive, and analytical solution. The performanceof the Herpin-type design exceeds that of the periodic design and is almostequal to the performance of the numerical, non-constructive optimized designobtained by brute force. Note that the existence of explicit analyticconstructive solutions of a constrained optimization problem is not guaranteedin general, when such a solution is found, we speak of turbo optimal solutions.

Optimal Design of Coatings for Mirrors of Gravitational Wave Detectors: Analytic Turbo Solution via Herpin Equivalent Layers