Exact solution of maximally flat antireflection coatings for coherent and incoherent light

TL;DR

This paper derives exact solutions for designing maximally flat antireflection coatings for both coherent and incoherent light, providing explicit formulas and a new approximation method for optimal layer refractive indices.

Contribution

It introduces two precise approaches for designing antireflection coatings in coherent and incoherent regimes, including explicit solutions for up to four layers and a novel approximation technique.

Findings

Explicit solutions for up to four-layer coatings in coherent light

Comparison of layer refractive indices for coherent and incoherent cases

A new method for approximating optimal refractive indices

Abstract

This paper presents two approaches to the precise design of maximally flat antireflection coatings reducing the reflectance of the substrate to near zero in a certain region around the central frequency. The first ideal case concerns coherent light interference, where it is required that for a chosen central frequency the maximum number of reflectance derivatives of the reflectance with respect to the frequency is zero. This approach makes it possible to determine the refractive indices of a system of homogeneous quarter-wave thin films by solving set of nonlinear equations that can be found in explicit form for a maximum of four layers; for higher numbers of layers, the result must be sought numerically. The second case is the incoherent superposition of light waves, which refers to the determination of the refractive indices of the layers independently of their thicknesses. For these two physically ideal cases, the obtained refractive indices of the layers and the dependence of their reflectivity on the light frequency are compared. A simple new method for approximating the refractive indices of a maximally flat system of antireflective layers is also proposed.