Approximate equivalence between guided modes in a low-contrast photonic bandgap fiber and Maxwell TM modes of a high-contrast two-dimensional photonic structure

We present a formal analogy between the eigenvalue problem for guided scalar modes in a low-contrast photonic bandgap fiber and quasi-stationary TM modes of a two-dimensional (2D) photonic structure. Using this analogy, we numerically study the confinement losses of disordered microstructured fibers through the leakage rate of an open 2D system with high refractive index inclusions. Our results show that for large values of the disorder, the confinement losses increase. However, they also suggest that losses might be improved in strongly disordered fibers by exploring ranges of physical parameters where Anderson localization sets in.