Multi-Mode Coupling in Long-Period Fibre Gratings

We report multi-mode coupling in long-period fibre gratings (LPFGs). The analytical solution to three-mode coupling equations is presented for the first time. A 3×3 transmission matrix is attained and can be used to calculate the transmission spectra of nonuniform gratings in a way much faster than direct numerical integration. It is shown that when the resonant wavelengths of cladding modes are far from each other, two-mode coupling model can still be used. Otherwise we can only choose a multi-mode coupling model. Theoretically fitting of the result from the multi-mode coupling equations agrees well with the experimental one for mechanically-induced LPFGs.