An embodiment of a microwave heating apparatus includes a solid state microwave energy source, a chamber, a dielectric resonator antenna with an exciter dielectric resonator and a feed structure, and one or more additional dielectric resonators each positioned within a distance of the exciter resonator to form a dielectric resonator antenna array. The distance is selected so that each additional resonator is closely capacitively coupled with the exciter resonator. The feed structure receives an excitation signal from the microwave energy source. The exciter resonator is configured to produce a first electric field in response to the excitation signal, and the first electric field may directly impinge on the additional resonator(s). Impingement of the first electric field may cause each of the additional resonators to produce a second electric field. The electric fields are directed into the chamber to increase the thermal energy of a load within the chamber.