Planar Fourier optics for slab waveguides, surface plasmon polaritons, and 2D materials

Recent experimental work has demonstrated the potential of combining the merits of diffractive and on-chip photonic information processing devices in a single chip by making use of planar (or slab) waveguides. Here, arguments are developed to show that diffraction formulas familiar from 3D Fourier optics can be adapted to 2D under certain mild conditions on the operating speeds of the devices in question. In addition to serving those working in on-chip photonics, this Letter provides analytical tools for the study of surface plasmon polaritons, surface waves, and the optical, acoustic, and crystallographic properties of 2D materials.