Automated Algorithms for Multilayer Thin Film Filter Design Using Metamaterials

Currently, infrared filters for astronomical telescopes and satellite radiometers are based on multilayer thin film stacks of alternating high and low refractive index materials. However, the choice of suitable layer materials is limited and this places limitations on the filter performance that can be achieved. With the introduction of metamaterials into the design of multilayer thin film filters, it is now possible to include layers with arbitrary refractive indices to ensure an optimal transmission profile. However, the introduction of more variables into the design process has made many traditional iterative design methods near obsolete. Evolutionary algorithms are extremely effective in solving problems with large solution spaces such as the design of multilayer thin film filters. By using an altered differential evolutionary algorithm (Pantoja et al., Design of thin film filters using differential evolution optimization technique. In: 2009 SBMO/IEEE MTT-S international microwave and optoelectronics conference (IMOC), pp 447–452, 2009), multilayer thin-film filters which have the desired transmission profile can be designed with minimal human input. The algorithm was adapted to design layers which have arbitrary refractive indices, as opposed to being designed using only traditional materials. Once the design of a multilayer thin film filter is completed by a evolutionary algorithm, each layer can be designed as a metamaterial with the required refractive index – in this case a bulk material of known refractive index with sub-wavelength structures (Wada et al., Appl Phys Express 3(10):102503, 2010). The period and size of the sub-wavelength structures for each layer were designed using Bruggeman’s effective material approximation to give the required refractive index and depth for that layer.