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This paper proposes a novel generalized total-field/scattered-field (G-TF/SF) formulation for finite-difference time-domain (FDTD) to efficiently model an infinite material scatterer illuminated by an arbitrarily oriented plane wave within a compact FDTD grid. This requires the sourcing of numerical plane waves traveling into, or originating from, the perfectly matched layer (PML) absorber bounding the grid. In this formulation, the G-TF/SF wave source boundary is located in part within the PML. We apply this technique to efficiently model two-dimensional (2D) transverse-magnetic diffraction of an infinite right-angle dielectric wedge and an infinite 45°-angle perfect-electrical-conductor wedge. This approach improves the computational efficiency of FDTD calculations of diffraction coefficients by one to two orders of magnitude (16:1 demonstrated in 2D; 64:1 or more projected for three-dimensions).