  In this paper we describe a methodology for tailoring the design of
metamaterial dielectric resonators, which represent a promising path toward
low-loss metamaterials at optical frequencies. We first describe a procedure to
decompose the far field scattered by subwavelength resonators in terms of
multipolar field components, providing explicit expressions for the multipolar
far fields. We apply this formulation to confirm that an isolated
high-permittivity cube resonator possesses frequency separated electric and
magnetic dipole resonances, as well as a magnetic quadrupole resonance in close
proximity to the electric dipole resonance. We then introduce multiple
dielectric gaps to the resonator geometry in a manner suggested by perturbation
theory, and demonstrate the ability to overlap the electric and magnetic dipole
resonances, thereby enabling directional scattering by satisfying the first
Kerker condition. We further demonstrate the ability to push the quadrupole
resonance away from the degenerate dipole resonances to achieve local behavior.
These properties are confirmed through the multipolar expansion and show that
the use of geometries suggested by perturbation theory is a viable route to
achieve purely dipole resonances for metamaterial applications such as
wave-front manipulation with Huygens' metasurfaces. Our results are fully
scalable across any frequency bands where high-permittivity dielectric
materials are available, including microwave, THz, and infrared frequencies.
