On the limits of quasi-static theory in plasmonic nanostructures

The approximated analytical approach of quasi-static theory (QST) is widely used in modelling the optical response of plasmonic nanoparticles. It is well known that its accuracy is remarkable provided that the particle is much smaller than the wavelength of the interacting radiation and that the field induced inside the structure is approximately uniform. Here, we investigate the limits of QST range of validity for gold nanostructures freestanding in air. First, we compare QST predictions of scattering spectra of nanospheres and cylindrical nanowires of various sizes with the exact results provided by Mie scattering theory. We observe a non-monotonic behaviour of the error of QST as a function of the characteristic length of the nanostructures, revealing a non-trivial scaling of its accuracy with the scatterer size. Second, we study nanowires with elliptical section upon different excitation conditions by performing finite element numerical analysis. Comparing simulation results with QST estimates of the extinction cross-section, we find that QST accuracy is strongly dependent on the excitation conditions, yielding good results even if the field is highly inhomogeneous inside the structure.