Analytical formulas are presented for the first time to describe the shift
in the resonance wavelength of a long-period fibre grating (LPFG) in respon
se to etching of the fibre cladding or a change in the external refractive
index. The accuracy of the formulas is confirmed by comparison with numeric
al simulations and experimental results. It is shown that the resonance wav
elengths of an etched LPFG are more sensitive to the external refractive in
dex than those of an unetched grating.