Full-vectorial coupled mode theory for the evaluation of macro-bending loss in multimode fibers. application to the hollow-core photonic bandgap fibers.

In the hollow core photonic bandgap fibers, modal losses are strongly differentiated, potentially enabling effectively single mode guidance. However, in the presence of macro-bending, due to mode coupling, power in the low-loss mode launched into a bend is partially transferred into the modes with higher losses, thus resulting in increased propagation loss, and degradation of the beam quality. We show that coupled mode theory formulated in the curvilinear coordinates associated with a bend can describe correctly both the bending induced loss and beam degradation. Suggested approach works both in absorption dominated regime in which fiber modes are square integrable over the fiber crossection, as well as in radiation dominated regime in which leaky modes are not square integrable. It is important to stress that for multimode fibers, full-vectorial coupled mode theory developed in this work is not a simple approximation, but it is on par with such "exact" numerical approaches as finite element and finite difference methods for prediction of macro-bending induced losses.