All-dielectric filters with a butterworth line-shape composed of several resonant structures

Abstract

Resonant properties of composite structures consisting of several identical resonant structures (e.g. multilayer thin-film structures or guided-mode resonance gratings) separated by phase-shift layers are investigated. Using the scattering matrix formalism, we analytically demonstrate that, at properly chosen thicknesses of the phase-shift layers, composite structures comprising two or four resonant diffractive structures with a Lorentzian transmittance profile optically implement second- and third-order Butterworth filters, respectively, and enable achieving flat-top transmission spectra with steep slopes and low sidebands. We also show that composite structures consisting of three or four second-order Butterworth filters can accurately approximate fourth- or fifth-order Butterworth filters, respectively. The theoretical results are confirmed by rigorous simulations of composite structures consisting of simple three-layer resonant structures.