Photonic crystal fiber long-period gratings (PCF-LPGs) operating near the phase-matching turning point to achieve high sensitivity to the refractive index of gas and liquid analytes infiltrated into cladding air holes are designed by numerical optimization. The vectorial finite element method is employed for the modal analysis of an index-guiding PCF and the calculation of the phase matching curves. The geometrical parameters of PCF (pitch and diameter of air holes arranged in a periodic triangular array) are optimized by using the down-hill simplex technique to engineer the dispersion of modes coupled by a LPG to obtain the turning point in the phase-matching curve at a desired wavelength for a given analyte refractive index. The resonant wavelength is subsequently extremely sensitive to the analyte refractive index, however, its large shifts can be detected with a substantially reduced resolution because the resonance dip in the LPG transmission spectrum is very broad. On the other hand, the broad resonance provides a broadband operation of a PCF-LPG sensor and its high sensitivity to the refractive index can still be achieved by relying on changes in the coupling strength (and consequently in the transmission loss) rather than in the resonant wavelength of LPG. We consider coupling between the fundamental core mode and the first-order symmetric cladding mode. We also explore an alternative approach based on coupling between the fundamental core mode and the fundamental space-filling mode instead of the individual cladding mode. The PCF-LPG structure optimized for refractive-index sensing is also assessed for label-free biosensing.
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