Starting from the Fresnel Principle, we can calculate the electromagnetic response of a nanoparticle, at any point in space, using internal and scattered principal modes; the properties of these modes are intrinsic to the particle and do not depend on the incident field. The principal modes are coupled pairwise (internal with scattered) at the surface of the particle, and the pairs are indexed (inversely*) according to their sensitivity to excitation, for any given wavelength. We can visualise the response spectrum for a particular nanoparticle as a “landscape” by plotting the sensitivity of the mode pairs as a function of the mode index and wavelength. Peaks of these landscapes indicate intrinsic resonances of the modes — and potentially, therefore, of the electromagnetic response of the particle to excitation.

In the figure, we use colourmaps overlayed onto the mode landscape of a rounded gold nanorod, with an aspect ratio of 12, to examine the response to a plane wave excitation. In (a) and (d) the colour** (green) overlay corresponds to the capability of the scattering and internal modes of each principal mode pair, respectively, to carry energy away from the particle surface. The amplitudes of the scattering and internal modes are then shown, in blue, in (b) and (e) respectively, for an axial plane wave excitation. The transport of power for both the scattering and internal modes of each pair is then overlayed (red) for the same excitation in (c) and (f).

*Lower index = higher sensitivity

**The colour encoded data has been normalised to be between the values of 0 and 1 at each wavelength in (a), (c), (d) and (f).

F. Papoff and B. Hourahine, “Geometrical Mie theory for resonances in nanoparticles of any shape,” Opt. Express 19, 21432-21444 (2011).

B. Hourahine, D. McArthur, F. Papoff, “Principal Modes of Maxwell’s Equations.” In: Wriedt T., Eremin Y. (eds) “The Generalized Multipole Technique for Light Scattering.” Springer Series on Atomic, Optical, and Plasma Physics, vol 99. Springer, Cham (2018).