Analytical formulation for the bend-loss in single-ring hollow-core photonic crystal fibers

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.