Perturbation theory for plasmonic eigenvalues

We develop a perturbative approach for calculating, within the quasistatic approximation, the shift of surface resonances in response to a deformation of a dielectric volume. Our strategy is based on the conversion of the homogeneous system for the potential which determines the plasmonic eigenvalues into an inhomogeneous system for the potential’s derivative with respect to the deformation strength and on the exploitation of the corresponding compatibility condition. The resulting general expression for the first-order shift is verified for two explicitly solvable cases and for a realistic example of a deformed nanosphere. It can be used for scanning the huge parameter space of possible shape fluctuations with only quite small computational effort.

Figure 1

(Color online) Sketch of the particular perturbed nanosphere (54) employed as example for demonstrating the accuracy of the perturbative approach. The deviation of the scaled surface radii $r\left(\vartheta ,\phi \right)/R$ from their ideal value 1 is visualized here for $h=0.2$.

Figure 2

Numerically computed plasmonic eigenvalues for the dipole modes of the deformed nanosphere depicted in Fig. 1 (crosses), in comparison with the results of first-order perturbation theory (full lines).