Ultimate Absorption in Light Scattering by a Finite Obstacle

Based on fundamental properties of the light scattering by a particle under a plane, linearly polarized wave illumination, we rigorously prove the existence of the ultimate upper limit for the light absorption by any partial mode and calculate this limit explicitly. The limit is a certain simple universal function of the incident light wave number, and the multipolarity of the corresponding partial mode solely. It does not depend on the optical constants of the scatterer, its size, or even its shape. First, we obtain this result for the scattering by a spherical particle. Then, we generalize it to an arbitrary finite obstacle. The results are valid for any polarization of the incident wave, any angle of its incidence, and any type of the scatterer (homogeneous, stratified, or with smoothly variable refractive index). We also prove that the maximal partial absorption cross section for any finite scatterer cannot exceed the corresponding value for a homogeneous sphere in 3D and circular cylinder in 2D. As an example, the results are applied to maximize the absorption cross section of a spherical core-shell structure.

Figure 1

The exact Mie solution. Partial scattering (brown) and absorption (blue, green, yellow) electric quadrupolar efficiencies $Q_{\mathrm{sca},\mathrm{abs}}^{\mathrm{sph}(a,2)}\equiv {\sigma }_{\mathrm{sca},\mathrm{abs}}^{\mathrm{sph}(a,2)}/(\pi R^2)$ at light scattering by a sphere with $q=2$ as functions of its complex permittivity ($\mu =1$). Grey plane corresponds to ${\epsilon }^{\prime \prime }=1.218$. See the text for details.

Figure 2

Cross section of the plots shown in Fig. 1 by the plane ${\epsilon }^{\prime \prime }=1.218$ (the grey plane in Fig. 1), passing through the UA point $\epsilon \approx 19.470+i1.218$. Brown solid and blue dashed lines correspond to $Q_{\mathrm{sca}}^{\mathrm{sph}(a,2)}$ and $Q_{\mathrm{abs}}^{\mathrm{sph}(a,2)}$, respectively. Note that the intersection of the two lines occurs exactly at the point of the local maximum of $Q_{\mathrm{abs}}^{\mathrm{sph}(a,2)}$.