Analysis of etched long-period fibre grating andits response to externalrefractive index

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