Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index

We present a graphic method of analyzing the spectral displacements of a long-period fiber grating as a function of ambient index. Mode dependence of the maximum displacement, disappearance of a particular resonance peak, and spectral behavior when the ambient index is larger than that of the cladding material are investigated and compared with experimental results.