All solid photonic bandgap optical fiber comprising a core region and a cladding region is disclosed. The cladding region surrounding the core region includes a background optical material having a first refractive index and elements arranged in a two-dimensional periodic structure. In one embodiment, each of the elements comprises a center part and peripheral part having a higher refractive than the central part. In other embodiments, each element comprises a plurality of rods having a higher refractive index higher than the fist, the rods of each element arranged in a circle or polygon. Light transmission apparatus and methods of using the fiber are also disclosed.