Theoretical formulation for an electrically small microstrip patch antenna loaded with negative index materials

Composite metamaterials that possess simultaneously negative permeability and permittivity, causing them to exhibit a negative index of refraction known, are known as a negative index materials (NIM). An application of NIMs is to increase the power radiated from electrically small antennas. NIMs can also be used to design thin sub-wavelength cavity resonators. We expand on this principle by introducing a method to miniaturize a circular microstrip patch antenna that uses NIM loading. This is accomplished by including two distinct regions inside the cavity of the microstrip patch antenna, one consisting of a NIM and one consisting of a conventional positive index material (PIM). By applying the boundary conditions commonly associated with the cavity model of a patch antenna, a "resonance condition" is found that is dependent only on the permittivities of the two embedded substrate materials.