Dispersion synthesis with multi-ordered metatronic filters

We propose the synthesis of frequency dispersion of layered structures based on the design of multi-ordered optical filters using nanocircuit concepts. Following the well-known insertion loss method commonly employed in the design of electronic and microwave filters, here we theoretically show how we can tailor optical dispersion as we carry out the design of several low-pass, high-pass, band-pass and band-stop filters of different order with a (maximally flat) Butterworth response. We numerically demonstrate that these filters can be designed by combining metasurfaces made of one or two materials acting as optical lumped elements, and, hence, leading to simple, easy to apply, design rules. The theoretical results based on this circuital approach are validated with full-wave numerical simulations. The results presented here can be extended to virtually any frequency dispersion synthesis, filter design procedure and/or functionality, thus opening up exciting possibilities in the design of composite materials with on-demand dispersion and high-performance and compact optical filters using one or two materials.