Quasi-Babinet principle in dielectric resonators and Mie voids

TL;DR

This paper generalizes Babinet's principle to dielectric resonators and Mie voids, providing new insights and design rules for nanophotonic structures with complex functionalities.

Contribution

It introduces the quasi-Babinet principle for dielectric systems, extending the classical concept to non-ideal, finite-thickness structures, and demonstrates its application to Mie resonators.

Findings

Babinet's principle can be approximately applied to dielectric structures within certain limits.

Limitations are due to geometry, material dispersion, and losses.

The work offers new design guidelines for dielectric nanophotonics.

Abstract

Advancing resonant nanophotonics requires novel building blocks. Recently, cavities in high-index dielectrics have been shown to resonantly confine light inside a lower-index region. These so-called Mie voids represent a counterpart to solid high-index dielectric Mie resonators, offering novel functionality such as resonant behavior in the ultraviolet spectral region. However, the well-known and highly useful Babinet's principle, which relates the scattering of solid and inverse structures, is not strictly applicable for this dielectric case as it is only valid for infinitesimally thin perfect electric conductors. Here, we show that Babinet's principle can be generalized to dielectric systems within certain boundaries, which we refer to as the quasi-Babinet principle and demonstrate for spherical and more generically shaped Mie resonators. Limitations arise due to geometry-dependent terms as well as material frequency dispersion and losses. Thus, our work not only offers deeper physical insight into the working mechanism of these systems but also establishes simple design rules for constructing dielectric resonators with complex functionalities from their complementary counterparts.