Applications of advanced artificial composite materials, in which photonic bands and band-gaps can be controlled though an external current, voltage bias or light source, require that implant sizes and lattice constants be comparable to at least a wavelength. For these cases, conventional effective medium approaches are inadequate. In this research, a double vector-integral equation (DOVIE) method for modeling of radiators and scatterers within advanced dielectric materials is proposed for first time development and implementation. The first integral equation formulation is to find the electromagnetic fields within the implants due to an array of sources. The second integral equation formulation is to find the currents or fields at the antennas or scatterers. The DOVIE methodology applies to general periodic structures with abnormalities, and will allow investigation of many interesting new phenomena of printed circuits and antennas involving advanced artificial materials. Expected applications include printed antennas with high directivity, high gain, multifunctionality and beam steering through controllable artificial material overlay; electromagnetic shielding provided by photonic band-gap material coatings on millimeter wave integrated circuits in which the conductor is too lossy for a desired frequency range (potentially very useful in integrated circuits); and DOVIE + CAD design of specialty integrated circuit components such as filters, directional couplers and interconnects.
