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

TL;DR

This paper presents an analytical method using Herpin's equivalent layers to optimally design dielectric mirror coatings for gravitational wave detectors, achieving near-optimal performance with a simple, constructive solution.

Contribution

It introduces a turbo optimal analytical solution for dielectric coating design using Herpin's layers, surpassing periodic designs and rivaling brute-force numerical optimization.

Findings

Herpin-based design outperforms periodic coatings.

Analytical solutions match numerical optimization performance.

The method provides a simple, constructive approach to complex optimization.

Abstract

In this paper, an analytical solution to the problem of optimal dielectric coating design of mirrors for gravitational wave detectors is found. The technique used to solve this problem is based on Herpin's equivalent layers, which provide a simple, constructive, and analytical solution. The performance of the Herpin-type design exceeds that of the periodic design and is almost equal to the performance of the numerical, non-constructive optimized design obtained by brute force. Note that the existence of explicit analytic constructive solutions of a constrained optimization problem is not guaranteed in general, when such a solution is found, we speak of turbo optimal solutions.