  Understanding bend-loss in single-ring hollow-core photonic crystal fibers is
becoming of increasing importance as the fibers enter practical applications.
While purely numerical approaches are useful, there is a need for a simpler
analytical formalism that provides physical insight and can be directly used in
the design of PCFs with low bend-loss. We show theoretically and experimentally
that a wavelength-dependent critical bend radius exists below which the
bend-loss reaches a maximum, and that this can be calculated from the
structural parameters of a fiber using a simple analytical formula. This allows
straightforward design of single-ring PCFs that are bend-insensitive for
specified ranges of bend radius and wavelength. It also can be used to derive
an expression for the bend radius that yields optimal higher-order mode
suppression for a given fiber structure.
