When the long period fiber grating (LPG) is surrounded with dielectric material whose refractive index is higher than that of cladding, core mode to radiation mode coupling occurs. In this paper, a theoretical method to analyze the radiation-mode resonance in LPG is presented. The coupled-mode equations of LPG are derived based on Amnon Yariv’s coupled-mode theory. Here, the radiation-mode theory is used. The electric field of individual radiation mode is given based on the weakly guiding approximation of three-layer optical waveguide. The expansion of the total radiation modes, which is a Fourier-Bessel integral, is presented. It’s noted that the weight of the integral is not one. The normalization of the individual radiation mode is discussed in detail. It’s found that the normalization integral is
unbounded but changed to a Dirac function. Thus, it’s calculated only through theoretical derivation. The approximate numerical method to deal with the coupled-mode equations is presented. The transmission spectra of LPG, which are surrounded with several surrounding refractive indices, are numerically calculated.
Long period fiber gratings couple the fundamental guided mode to forward propagating cladding modes. A Characteristic of LPGs in SMF is that their spectral properties (resonant wavelength and coupling strength) are sensitive to the refractive index of the surface surrounding the cladding region. Because of this, LPGs are typically packaged unrecoated to obtain insensitive spectral properties. In this paper the effective index model combined with the coupling-mode theory are used to study the characteristics of LPGs based on photonic crystal fiber (PCF). After plenty of numerical simulation, the results demonstrate that PCF-based LPGs will be more insensitive to the surrounding medium than those written in SMF.