Comparison of Methods for Calculating the Field Excited by a Dipole Near a 2-D Periodic Material

A comparison of methods for calculating the field from a single dipole source in the proximity of an infinite periodic artificial material (PAM) is given. A direct plane-wave expansion method (PWM) is compared with the ldquoarray scanning methodrdquo (ASM). The ASM is shown to be the most efficient method for sources that are close to the PAM, since it only requires integration in the wavenumber plane over the Brillouin zone rather than over the entire wavenumber plane. It is also shown how the ASM may be used to efficiently calculate the Fourier transform of the field at any aperture plane, which is useful for asymptotic analysis. The ASM is shown to be more efficient than the PWM or the reciprocity method for calculating the transform of the aperture field. A discussion of the nature of the singularities in the complex wavenumber plane is given, and numerical issues associated with the implementation of the ASM are discussed.