Coupled wave theory has historically been successfully used to provide various analytic theories of optical diffraction in volume phase gratings. Here we develop a different approach based on a decomposition of the permittivity profile of the grating into an infinite array of infinitesimal discontinuities or step functions. By considering the corresponding ele- mentary Fresnel solutions from each discontinuity, a first-order set of coupled partial differential equations can be derived and then solved in a rotated frame of reference to give analytical expres- sions for the diffraction efficiency of the general slanted grating at arbitrary angle of incidence. The underlying differential equations derived from the approach are a rigorous representation of Maxwell’s equations for the case of the unslanted grating and few assumptions are required to provide highly accurate solutions for harmonic or quasi-harmonic permittivity distributions, even at large grating slant.