For light incident on metallic nanoparticles, resonant interactions with the electronic charge density near the surface, called surface plasmon polaritons, play an important role. Here we determine, for a silver nanowire with diameter 50 nm, the surface plasmon polariton resonance and calculate the scattering, extinction and absorption cross sections as a function of wavelength near this resonance.

## Problem definition: More details

The scattering cross-section is defined as

,

where Pscat is the total scattered power [W] and Iinc is the incident source intensity [W/m2]. In 2D, source intensity is described per unit length [W/m], and thus the scattering cross-section has dimensions of length. The total scattered power can be calculated by summing the power flowing outward through the four power monitors located in the scattered field region of the Simulation Area.

The absorption cross-section is similarly defined as

,

where Pabs is the total power absorbed by the particle. The power absorbed by the particle can be calculated using the net power flowing inward through the four monitors located in the total field region of the Simulation Area.

The extinction cross-section is the sum of the absorption and scattering cross-sections

.