Light-induced hot carriers in nanostructures and their corresponding optical nonlinearity have been extensively examined during the last decades. However, nonlinear optical effects dictated by the spatio-temporal evolution of out-of-equilibrium electrons at the nanoscale represent a much more recent research focus. Here we theoretically discuss the role of spatial inhomogeneities that energetic electrons feature across individual nanoantennas in metasurface configuration upon illumination with femtosecond laser pulses. As exemplary cases, we consider two-dimensional geometries of gold meta-atoms having either a high aspect ratio or a tapered cross-section and model their ultrafast optical response. A comparison with numerical results obtained either neglecting or accounting for spatial effects indicates that deep sub-wavelength spatio-temporal transients of carriers may have a significant impact on the dynamics of the all- optically modulated signal, with major quantitative corrections up to predicted changes in sign. Our results present hot-electron local inhomogeneities as an emerging subject with potentially relevant applications in various ultrafast nanophotonic configurations.
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.
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