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A new measurement technique for characterizing the magnitude of power coupling from the fundamental mode to higher order core- and cladding-bounded modes occurring in a fiber Bragg grating (FBG) inscribed in a large-mode-area (LMA) fiber is demonstrated and studied. The method is based on inducing mode selective fiber bending losses on the modes propagating in the core and monitoring the power guided by the cladding of the LMA fiber. Besides transmitted, also reflected distributions of modes can be resolved in terms of the relative powers carried by them and thus the fraction of higher order modes (HOMs) can be quantified. Additionally, the method can distinguish the mode content spectrally with high resolution. Sample FBGs having a chirped index profile are characterized using the method. The effect of direction reversal of light propagation on mode coupling in these gratings is also studied. Distinct wavelength regions corresponding to the fundamental mode coupling to the reflected fundamental mode, core HOM and cladding modes can be identified. The measurement method also reveals a wavelength dependent fine structure of the modal coupling, i.e., at certain wavelengths there can be coupling to all of the above mentioned modes simultaneously with varying amounts. These effects can be partly attributed to the phase matching between different modes being dependent on the spatial location in chirped gratings. It is shown that the method can yield information that is useful for better design and optimization of fiber optic devices utilizing FBGs in LMA fibers, such as fiber lasers.