Evolution of the near-field patterns into the far-field in surface plasmonic band gap nano-structures

We study emission patterns in periodic nano-hole arrays perforated in a metal film. In the near-field region, higher order multiple components of diffraction interfere with each other to generate complicated spatial patterns. These patterns simplify to a sinusoidal one in the intermediate region and become either homogeneous or sinusoidal in the far-field region, depending on whether the excitation wavelength is larger or smaller than the lattice constant. For an incident wavelength much smaller than the lattice constant, complicated patterns can survive into the far-field. Detailed analytic and numerical studies are presented, which show good qualitative agreement with experiment.