In this thesis we have focused on the properties of surface plasmon resonance for core-shell particles by using an effective medium model (LSC model). According to this effective medium model we can treat the core-shell particle as an effective solid particle, thus, allowing us to generalize many theories form the solid particle version to the core-shell version.
This effective medium model has been verified to give the exact polarizability in electrostatic situation as demonstrated in chapter 2. This is a consequence of uniqueness property of the boundary value problem in electrostatic theory, which is based on the solution of Laplace equation.
When the particle is very small, typically smaller than 1% of the incident wavelength, we have used LSC model to obtain the exact electrostatic polarizability for spherical and spheroidal core-shell particles. Based on the Drude model for the metallic shell, the split surface plasmon resonance modes are obtained. These split resonance modes are determined by the materials, thickness and geometrical shapes of the core-shell particle.
The results obtained from the LSC model are identical to those results from the hybridization model.
After verified the static case, we have extended this model to the electrodynamic
case which is required for bigger particles. The wavelength dependence can be introduced by using long-wavelength approximation models such as MLWA and IMLWA.
Combining these long-wavelength approximation models with LSC model we have been able to generate the wavelength dependence for the polarizability of the core-shell particle. In comparison with Mie theory, we have verified that this core-shell result generated from LSC model is much better than the static model (i.e. closer to the results from Mie theory).
In the study of the near fields from the plasmonic excitation of the nanoshells, we have studied the FRET process between the two dipoles near a spheroidal nanoshell.
Large enhancements for the energy transfer due to surface plasmon resonance of the nanoshell have been observed. In agreement with the hybridization model, we have obtained the multipole resonance peaks which split into two groups corresponding to the two coupled bounding and anti-bounding interfacial plasmon modes. As the results have shown, the dominating modes depend on the positions and orientations of the two dipoles.
Finally, we have also considered the optical properties of metallic nanoshell composites. We have studied the fractal cluster systems with different fractal dimensions and cluster sizes. The results have shown three types of resonances: those from the whole system, those from the individual cluster, and those from the single shells. Among the
Summary and outlook 75
interesting results from our modeling, a large red-shift was observed with the decrease of the fractal dimension or increase of the cluster size.
Base on the results of this thesis one can propose some further studies. For nanoshell composites we discussed in chapter 5, it will be interest to generalize from spherical to spheroidal nanoshells. It has been thought in the literature that the anisotropic nature of the solid spheroidal particles can be used to enhance the nonlinear response of a composite of these shells [57-62]. It will be interest to study several effects from a composite of these nanoshells.
Another direction is to study the nonlocal effects. Since the local dielectric functions are usually based on the classical oscillator models, they only provide the classical responses. However, for the ultrasmall particles, typically smaller than 10 nm, the quantum effects will become more important and should not be neglected [63-67]. It will be easier to introduce the quantum effects via the nonlocal dielectric function than from solving the quantum mechanical many body Problem. According to the results we presented in this thesis, the LSC model may provide a simple approach to study the nonlocal effects for a system of multi-shell particle.
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