A long period grating (LPG) is a longitudinal periodic optical structure that drives couplings from the
fundamental core mode into phase-matched co-propagating cladding modes of an optical fiber and a series
of attenuation dips are formed in the transmission spectrum . LPGs have been applied as photonic
sensors to detect external perturbations including temperature, strain, bending and surrounding refractive
index, by monitoring the spectral shifts of the resonant dips . LPGs are conventionally fabricated by UV-light
exposure to induce periodic refractive-index variation of 10-5 ~ 10-4 in the fiber core. Such an LPG is
regarded as weak perturbation to the fiber and the mode coupling process has been described by the wellknown
coupled mode theory (CMT) .
In addition to the UV-inscription technique, stronger LPGs can also be formed by introducing refractive
index/geometry modulation by use of CO2-laser irradiation, arc discharge, and periodic tapering [4-6].
Photonic crystal fibers (PCFs), which contain a two-dimensional array of air holes in their claddings,
provide an extra-dimension for LPG-inscription through periodic deformation of the air-holes in the
cladding . However, the conventional CMT may not provide accurate description to these strong LPGs
because of the significant modification of the mode fields and refractive indexes over the modulated
regions. In this paper, the mode coupling process in a strong LPG inscribed in a PCF is quantitatively
analyzed based on the coupled local-mode theory. The analysis offers a physical insight and a better
understanding over the energy transfers in the LPGs. Based on the theory, a general phase-matching
condition for LPG is presented, which accurately determines the resonant wavelengths λres.