  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.
