Theoretical analysis of radiation-mode resonance in long-period fiber gratings

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.