Dirac gratings.

We propose the concept of a Dirac grating, where periodic permittivity perturbations approach a train of Dirac functions. We show that Dirac gratings can yield identical spectral characteristics for higher-order gratings compared to first-order gratings of the same length. Using an inverse Fourier transform technique, we design different types of Dirac gratings, including structures operating at the exceptional point where parity-time symmetry breaks down, producing unidirectional reflectance. We employ analytical and numerical techniques to validate our theory by modelling practical examples of Dirac gratings implemented in dielectric stacks and silicon nanophotonic waveguides.