A transfer-matrix method based on the coupled-mode theory is developed for the analysis of an all-fiber coupler consisting of two parallel long-period fiber gratings (LPFGs), which can be dissimilar and nonuniform. Using this method, the effects of various forms of nonuniformity introduced along the gratings on the transmission characteristics of the coupler are studied. The nonuniformities considered include pitch detuning, chirping, phase shifts, and index apodization. Numerical examples are given to highlight the conditions of achieving high coupling efficiency and the possibility of suppressing ripples and side lobes in the transmission spectrum. The obtained results are useful for the understanding and the design of various kinds of long-period grating-based devices, such as filters, broadband couplers, signal taps, and add/drop multiplexers.
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