Abstract
A new electromagnetic cavity structure, a lattice of 3D cavities consisting of an array of posts and gaps is presented. The individual cavity elements are based on the cylindrical re-entrant (or Klystron) cavity. We show that these cavities can also be thought of as 3D split-ring resonators, which is confirmed by applying symmetry transformations, each of which is an electromagnetic resonator with spatially separated magnetic and electric field. The characteristics of the cavity is used to mimic phonon behaviour of a one-dimensional (1D) chain of atoms. It is demonstrated how magnetic field coupling can lead to phonon-like dispersion curves with acoustical and optical branches. The system is able to reproduce a number of effects typical to 1D lattices exhibiting acoustic vibration, such as band gaps, phonon trapping, and effects of impurities. In addition, quasicrystal emulations predict the results expected from this class of ordered structures. The system is easily scalable to simulate two-dimensional and 3D lattices and shows a new way to engineer arrays of coupled microwave resonators with a variety of possible applications to hybrid quantum systems proposed.
Highlights
Metamaterials are structures made of artificial building blocks with a scale smaller than the working wavelength[1]
The classical example of such an application is metamaterials with negative refractive index[2]. Such metamaterials are definitely in need in both science and engineering. There could be another potential application of metamaterials: They can be used to emulate the behaviour of systems from one physical realm by making experiments in another one, potentially with some boosted parameters
Can the behaviour of a mechanical solid be emulated in an electromagnetic cavity with the speed of sound approaching the speed of light? Such systems can be used to study properties of solids that cannot be found in nature, for example quasicrystals or phonon trapping lattices
Summary
Metamaterials are structures made of artificial building blocks with a scale smaller than the working wavelength[1]. Such materials are typically designed to possess properties that cannot be found in natural materials. In this work we take this approach and undertake 3D finite-element electromagnetic modelling of a multiple post 3D cavities and compare the results to the phonon behaviour in a one dimensional chain of atoms. These similarities enable the emulation of defects in crystals, as well as the emulation of some properties of quasicrystals
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