Forskningsseminarium i fysik: Optimal plasmonic multipole resonances of a sphere in lossy media

The figure shows the predicted normalized dipole absorption cross section for a small 10 nm aluminum nanosphere (blue dashed) in comparison to the corresponding optimal bound (blue solid) and the optimal total extinction for various bandwidths (black solid, dashed and dash-dotted).

Föreläsare: professor Sven Nordebo, Linnéuniversitetet
Titel: Optimal plasmonic multipole resonances of a sphere in lossy media

Plats: Kalmar – sal N304, Norrgård.
Växjö – via länk, rum D0073, hus D.
Live – via Adobe Connect, https://connect.sunet.se/cmp-kalmar.

Kaffe och bullar kl 13.45 på Västergård, sal N1002.

Abstract

Fundamental upper bounds are given for the optimal plasmonic multipole resonances of a rotationally invariant sphere embedded in a lossy surrounding medium. An asymptotic analysis is then carried out to characterize the corresponding resonances of the small homogeneous sphere. A specialized Mie theory is developed for this purpose and when combined with Bohrens optical theorem for a spherical particle in an absorbing medium, an optimization problem is obtained which is readily solved by straightforward analysis. In particular, the absorption is a concave quadratic form in the related Mie parameters and the convex scattering function can be maximized by using a Lagrange multiplier constraining the absorption to be non-negative. The Weierstrass preparation theorem is used to establish the existence and the uniqueness of the plasmonic singularities of the homogeneous sphere and explicit asymptotic expressions are given for the dipole and the quadrupole.

It is shown that the optimal passive material for multipole absorption and scattering of a small homogeneous sphere in a dispersive medium is given approximately as the complex conjugate and the real part of the corresponding pole-singularities, respectively.

Numerical examples are included to illustrate the theory, and in particular a comparison with the plasmonic dipole and quadrupole resonances obtained in metal nanospheres based on a specific Brendel-Bormann (BB) model for the dielectric functions of gold, silver and aluminum. Based on these BB-models, it is interesting to note that a small aluminum sphere would have a near-optimal plasmonic dipole absorption resonance in the UVC spectrum around 150 nm.

Finally, it is emphasized that the presented optimal bounds are valid only on the basis of single frequency excitation. Hence, for the case with a lossless background medium it is also illustrated how the efficiency of the predicted near-optimal multipole resonances can be evaluated using a fundamental sum rule constraining the total extinction cross section for the sphere over any given bandwidth.