Scattering analysis of slanted fiber gratings

The diffraction efficiency of a tilted in-core fiber grating is analyzed with the scattering formalism and the first Born approximation. Without any prior physical assumptions about the shape or direction of the scattered wave, it is shown that diffraction occurs when the so-called Bragg conditions are nearly satisfied and the interaction process can be described by a pair of coupled first-order differential equations that are exactly the same as those obtained through the coupled-mode analysis.