Efficient analysis of periodic structures using a wide-band formulation of the Helmholtz Green's function

The generalized admittance matrix which characterizes the aperture plane of an infinite phased array is computed in the space domain using a wideband formulation of the periodic structure potential Green's functions. Each potential Green's function is expressed as a simple polynomial in frequency plus a correction consisting of a highly accelerated modal series. The polynomial coefficients consist of infinite series of spatial contributions which exhibit even more rapid exponential or Gaussian convergence characteristics. By grouping together the spatial contributions to the admittance matrix which correspond to specific powers of frequency, this portion of the matrix can be expressed as a rational function of frequency, the coefficients of which are computed only once and stored for reuse at new analysis frequencies. The modal correction series must be computed at each new analysis frequency, but it can be efficiently evaluated in tabular form using the fast Fourier transform. A simple, low-order interpolation scheme is then used to evaluate it rapidly at arbitrary locations within the unit cell.<>