Analytical formulation of bend-loss sensitivity in single-ring hollow-core photonic crystal fibres

Hollow-core fibres with a single ring of glass capillaries surrounding the core are receiving increased attention due to their relative simplicity, low loss, and broad transmission windows [1, 2]. Recently it was reported that such fibres are effectively single-mode at all guided wavelengths if the inner diameter d of the cladding capillaries and the core diameter D satisfy the relationship d/D = 0.682 [3]. Endlessly single-mode behaviour is highly desirable in applications such as beam delivery and fibre gyroscopes. Here we address another important issue: the dependence of the bend-sensitivity on fibre structure and wavelength. We present a simple analytical expression for the minimum radius to which the fibre can be bent before the losses increase dramatically. The analysis can also be used to calculate the optimum bend-radius for suppression of a given higher-order mode.