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This paper reports on the modeling of arrayed-waveguide gratings (AWGs) by means of Fourier optics where the coupling between the grating waveguides and defocus of the star couplers is taken into account as well. Special interest is drawn to the geometrical modeling of AWGs. The paraxial approximation for the free-space propagation within the star couplers, the exact calculation of the coupling coefficients for the star couplers by an orthonormal basis (ONB) expansion, and the drawbacks due to the nonunitary transfer matrix provided by the Green's functions approach for the coupling between the grating waveguides, as well as possible improvements thereof, are identified as crucial points. An efficient orthonormalization procedure by means of an eigenvector decomposition is presented. A unitary approximation of the transfer matrix, which is in itself approximate but in general not unitary, introduced within the impulse response method, is obtained. The presented simulation technique allows for ab initio simulations, which do not fall back on any experimental input, for the spectral response of AWGs, which are found in good agreement with experimental results.