Electromagnetic near and far fields from the interaction between surface plasmons and a surface defect in a thin metallic film

The near- and far-field intensities produced by the interaction between surface plasmons and a surface nanodefect at the surface of a thin metallic film are studied theoretically. Both intensities are computed using a perturbative solution of the reduced Rayleigh equation, up to second order in the surface defect profile. The near-field isointensities and isoheight intensities are calculated using a Gaussian-shaped defect. The isointensity curve, as well as the near-field isoheight intensity, show oscillations associated with two different origins. The first is related to the interaction of the surface plasmons excited at the glass/metal and metal/air interfaces. For this case an analytical equation is obtained to express the period of oscillation in terms of the wave vector of the surface plasmons. The second case occurs when the width of the defect is in the nanometer range, and its origin is related to the interference between the excited surface plasmon and reflected back by the defect. The angular position of the maximum of the computed differential transmission coefficient changes from positive to negative angles as the width of the defect is diminished. The total integrated scattering in transmission has a maximum for the width of the defect approximately equal to 15% of the wavelength used for the calculation.