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