Independence of plasmonic near-field enhancements to illumination beam profile

Near-field enhancements of the electric field at the center of spheroidal multilayer metallic nanoparticles (NPs) are investigated when illuminated by focused beams of arbitrary field structure (i.e., amplitude, phase, and polarization distributions). Employing a Mie-type representation, the enhancement at the center of such NPs (such as a core-shell geometry) is analytically shown to be independent of the field structure of the illumination beam for both on- and off-axis NPs. Furthermore, it is shown that, to leading order, the average field enhancement in the near field of these NPs is also approximately illumination independent.

Figure 1

Schematic illustration of the focusing of a structured beam (e.g., a Gaussian beam with spiral phase) onto a nanoparticle.

Figure 2

Schematic illustration of a multilayer nanoparticle, with distinct layers indexed as $I,II,...N-1$, of respective radius $r_I,r_{II},...r_{N-1}$, immersed in a medium indexed as $N$.

Figure 3

Theoretical enhancement factors at the center of a two-layer NP with a SiO${}_2$ core and Au shell immersed in water, for different core radii $r_I$ as a function of illumination wavelength. For small NPs good agreement with quasistatic predictions are found, however, this quickly breaks down as the NP dimensions are increased.

Figure 4

Maps of the near-field enhancement $\Gamma \left(\mathbf{r}\right)$ for scattering from a 2-nm radius homogenous Au NP illuminated by a focused $x$-polarized LG${}_{00}$ (a) and LG${}_{01}$ beams (b). White dashed lines in (a) represent the fixed radii at which the effective enhancement is calculated in Fig. 5 as defined by $r=\beta r_I$ for $\beta =1,1.1$ and $1.5$.

Figure 5

Colored lines with data points show the variation of the calculated effective enhancements $\tilde{\Gamma }\left(r\right)$ at fixed radii above the surface of an Au NP, as its radius is varied. White dashed lines in Fig. 4a represent the fixed radii at which the effective enhancement is calculated as defined by $r=\beta r_I$ for $\beta =1,1.1$ and $1.5$. Different colored lines represent different illumination beams as follows: (blue) LG${}_{00}$, (green) LG${}_{01}$, (red) radial polarization, and (purple) azimuthal polarization (shown in a separate panel for clarity). Black solids lines represent the effective enhancement as predicted by Eq. (23) for electric dipole terms only (top panel) and magnetic dipole terms only (bottom panel).

Figure 6

Variation of effective enhancement factor $\tilde{\Gamma }$ as a function of NA of the illumination lens. $\tilde{\Gamma }$ has been evaluated at the surface of differently sized homogeneous Au NPs for differing focused beam profiles (see text) and NP dimensions. Illumination wavelength was fixed at 533 nm.