Coated photonic bandgap fibres for low-index sensing applications: cutoff analysis

We investigate theoretically the performance of photonic crystal fibres with coated holes as refractive index sensors. We show that coating the holes with a high-index material allows to extend the extreme sensitivities analyte-waveguide based geometries offer to the case of low-index analytes, including water-based solutions. As the sensitivity of these sensors is intricately linked to the sensitivity of the cutoff of a single inclusion to the analyte refractive index, our approach relies on the derivation of cutoff equations for coated inclusions. This is performed analytically without approximations, in the fully vectorial case, for modes of all orders. Our analytic approach allows us to rapidly cover the parameter space, and to quickly identify promising geometries. The best results are obtained when considering fluorinated polymer fibres, for which the index of the background material is not too different to that of water, and with thin high-index coatings. Using these results, we propose a sensor based on a directional coupler geometry that would lead to a sensitivity of 2.2 x 10(4) nm/RIU for water based solutions with achievable smallest detectable refractive index changes below 10(-6).