Analytical calculation of SPP generation with structured substrates

Unusual optical properties of structured metal surfaces arise from plasmon resonances and interactions through surface plasmon-polariton waves (SPPs). Predicting these properties is generally challenging. However, simplifying the problem using harmonic Fourier components allows one to decompose the initial problem down to the problem of SPP generation by the finite-length sinusoidal grating. In this work, we propose an analytical method for the description of SPP generation with such gratings by utilising methods from the waveguide theory based on the Lorentz reciprocity theorem.