Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects

A rigorous formulation for the scattering of surface plasmon polaritons (SPP’s) from a one-dimensional surface defect of any shape that yields the electromagnetic field in the vacuum half-space above the vacuum-metal interface is developed by the use of an impedance boundary condition. The electric and magnetic near fields, the angular distribution of the far-field radiation into vacuum due to SPP-photon coupling, and the SPP reflection and transmission coefficients are calculated by numerically solving the k-space integral equation upon which the formulation is based. In particular, we consider Gaussian-shaped defects (either protuberances or indentations) and study the dependence of the above-mentioned physical quantities on their $1/e$ half-width a and height h. SPP reflection is significant for narrow defects $(a\lesssim \lambda /5,$ for either protuberances or indentations, where $\lambda$ is the wavelength of the SPP); maximum reflection (plasmon mirrors) is achieved for $a\approx \lambda /10.\mathrm{}$ For increasing defect widths, protuberances and indentations behave differently. The former give rise to a monotonic increase of radiation at the expense of SPP transmission for increasing defect half-width. However, indentations exhibit a significant increase of radiation (decrease of SPP transmission) for half-widths of the order of or smaller than the wavelength, but tend to total SPP transmission in an oscillatory manner upon further increasing the half-width. Both the position of the maximum radiation and the oscillation period depend on the defect height, which in all other cases only affects the process quantitatively. Light emitters might thus be associated with either wide indentations or protuberances with widths that are of the order of or smaller than the wavelength.