We thoroughly compare the out-of-plane bandgaps generated by three realistic two-dimensional lattices: a triangular and a square arrangement of holes and a triangular arrangement of rods. We demonstrate that, for any given hole-diameter-to-pitch ratio , the triangular arrangement of interconnected resonators generates the widest possible bandgap along the air line, and we propose a physical interpretation explaining these results. The design of a hollow core photonic bandgap fiber based on such a lattice and able to transmit light with sub-decibel-per-meter losses over an octave of frequencies is presented for the first time, to the best of our knowledge.
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