A method is disclosed for fabricating a two- or three-dimensional photonic bandgap structure (also termed a photonic crystal, photonic lattice, or photonic dielectric structure). The method uses microelectronic integrated circuit (IC) processes to fabricate the photonic bandgap structure directly upon a silicon substrate. One or more layers of arrayed elements used to form the structure are deposited and patterned, with chemical-mechanical polishing being used to planarize each layer for uniformity and a precise vertical tolerancing of the layer. The use of chemical-mechanical planarization allows the photonic bandgap structure to be formed over a large area with a layer uniformity of about two-percent. Air-gap photonic bandgap structures can also be formed by removing a spacer material separating the arrayed elements by selective etching. The method is useful for fabricating photonic bandgap structures including Fabry-Perot resonators and optical filters for use at wavelengths in the range of about 0.2-20 .mu.m.