Fundamental Properties of Mie Resonances in Water Cylinders – TM and TE Case Studies

All-dielectric metamaterials have recently attracted great attention in the artificial material design. They consist of high permittivity inclusions which enable resonances in sub-wavelength structures. In contrast to optics, several high permittivity materials exist in the microwave range. Among these we find one of the most abundant materials on earth: water. In its liquid state, it offers great tunable dynamic properties that can be used in material design. To this end, we presently examine analytically the so-called Mie resonances in water cylinders. Particular attention is devoted to the ability of such cylinders to support electric and magnetic dipole modes, and how these behave with temperature and frequency. Subsequently, we demonstrate that directive forward and backward patterns can be achieved by specific water cylinders with balanced electric and magnetic dipole responses. The results of this work may be used directly in or as a guideline for metamaterial design as well as for simple, cheap and rather directive antennas.