1-D Periodic Green’s Function for Leaky and Complex Waves Using the Ewald Method

摘要

The Ewald method for evaluating the free-space 1-D periodic Green's function is extended to leaky waves by allowing for complex wavenumbers. It is shown that care must be taken when choosing the path of integration in the complex plane in the derivation of the Ewald method in order to obtain solutions that correspond to physical leaky-wave solutions. The use of different paths results in an evaluation of the Ewald method using an analytical continuation of the exponential integral function previously used when the wavenumber is real. The extension of the Ewald method to complex wavenumbers allows for the treatment of practical periodic leaky-wave antennas and periodic guiding structures with losses, as well as metamaterials, including 1-D chains of plasmonic nanoparticles.