Full parameter study of multilayer coating for thermal applications
We present the formulation of the reversal engineering problem for designing coherent thermal radiators with a planar multilayer stacks coating.
In the context of this work, control of thermal coherence radiation means that we can design a surface finishes exhibiting a predefined spectral directional emittance (or emissivity) and reflectance (or reflectivity): `e(\lambda,\theta)` and `r(\lambda,\theta)` . The reverse engineering problem is defined by two main components: i) the objective function and ii) the optimisation solver.
The objective function provides a single numerical value by comparing the optical properties of a given planar multilayer structure with the desired optical properties. This number is an objective weight representing the quality of the solution. Mathematically such a function can be written as:
The Figure 1 contains a graphical representation of the target emittance together with the auxiliary parameters introduced above to describe it. In addition, the Figure contains a polar plot for three discrete values of `lambda`. The lobes results from the spatial coherence of the emittance while a small `\Delta\lambda` results from the temporal coherence. In summary, the target emittance/reflectance is defined by means of a set of nine parameters.
The optimisation problem is solved using a generic Genetic Algorithm consisting of only three genetic operators: reproduction, cross-over and mutation. Although many implementations of this problem are possible, we have adopted a pure integer one.
The thermal radiator is described by a given number of layers with each of the layers made of a given material and presenting a thickness. A straight way of implementing this problem consists in using an integer representation to define the materials of each layer and a real representation for the layer thickness. In this work, we describe also the layer thickness with integers. We define a minimum layer thickness unit and let the optimiser algorithm to determine the number of units building each layer. This approach requires to use a thin layer thickness units and consider a large number of layers. More details can be found in  and .
We are updating regularly the results obtained from the optimisation. Please visit the results web page and check what are the limits of this technology for controlling the coherent thermal radiation.