Photonic bandgap fibers based on a composite honeycomb lattice

We propose a new type of photonic bandgap fiber that is composed of an internal honeycomb lattice of air holes within each unit cell of the original honeycomb lattice. The bandgaps of such fibers are investigated, and a critical value of the air-hole position is found below which the gaps are reduced by the internal lattice. We have also identified some cases where the secondary gap can be suppressed while the primary gap is not.