A dielectric resonator antenna (DRA) includes: a volume of a dielectric material configured to be responsive to a signal feed, the signal feed being productive of a main E-field component having a defined direction Ē in the DRA; wherein the volume of a dielectric material includes a volume of non-gaseous dielectric material having an inner region having a dielectric medium having a first dielectric constant, the volume of non-gaseous dielectric material that is other than the inner region having a second dielectric constant, the first dielectric constant being less than the second dielectric constant; wherein the volume of non-gaseous dielectric material has a cross sectional overall height Hv as observed in an elevation view of the DRA, and a cross sectional overall width Wv in a direction parallel to the defined direction Ē as observed in the plan view of the DRA; and wherein Hv is greater than Wv/2.