We report an analysis of the transmission characteristics of long period gratings written in a linearly tapered optical fiber. Such gratings are best analyzed by a coupled mode theory that includes several cladding modes simultaneously. However, the numerical solution needs to be modified to take into account the changing propagation constants along the length of the fiber. The transmission spectra show certain distinctive features that depend on the grating period and choice of the phase-matched coupled cladding modes. For low-order modes, the resonances broaden and tend to vanish as the taper of the angle increases. For higher-order modes, the resonances remain well defined but shift toward higher or lower wavelengths and broaden. The transmission spectrum is also highly sensitive to a change in the ambient atmosphere.
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