Modeling Plasmonic Effects in the Nanoscale Brendan McNamara, Andrei Nemilentsau and Slava V. Rotkin Department of Physics, Lehigh University Problem Statement •We seek to examine the plasmonic properties of metallic nanostructures. •To do this, we consider plane electromagnetic wave scattering by a gold nanosphere placed in the air and examine the scattered near-field. We expect to see field enhancement of the scattered field when the frequency of the incident field is in resonance with surface plasmon frequencies in the nanostructure. Surface Plasmons •Surface Plasmons are collective excitations of the electron gas at the metal/dielectric interface. Dispersion Relation for Surface Plasmons: Imaginary and real parts of the electric ﬁeld enhancement evaluated at the poles of the gold rod (L = 110 nm, R = 5 nm) Surface Plasmon Resonance Condition: Novotny, Lukas. "Effective Wavelength Scaling for Optical Antennas." Physical Review Letters 98.26 (2007). Print. The Models Methodology •We utilize COMSOL Multiphysics software to simulate scattering in the nanoscale. •COMSOL utilizes finite element methods to solve the Maxwell equations over the defined geometries. •The domain to be discretized is infinite in our case. Thus it must be truncated. For a new limited domain we chose a plasmonic nanoparticle placed inside a large sphere of air. In order for the solution to be meaningful the appropriate boundary conditions had to be imposed on the outer boundary of the air sphere. Boundary Conditions We use the following built-in boundary conditions: 1. Scattering Boundary Condition The scattering boundary condition sets the boundary to be transparent for an incoming plane wave. The boundary is also assumed to be transparent for However, the electric near-field scattered by the sphere has a more complex structure, and thus the back reflections from the outer boundary take place. 2. Perfectly Matched Layers Perfectly Matched Layer conditions are used to absorb the scattered waves and prevent their back reflection from the outer boundary in the modeling domain. The following models have been built: 1. Metallic Nanosphere in Air • The geometry for this problem is a small, metallic nanosphere inside a larger sphere of air, excited by a plane electromagnetic wave. Convergence was not attained for this problem, although in principle for increasing size of the outer sphere it should converge to a single solution. Unfortunately, computational limitations forced us to keep the sphere small, and back-scattering reflections prevented convergence. 2. Perfectly Matched Layers with Incident Field • The geometry remained that of a sphere in an air sphere, but an additional, larger sphere was added beyond the air sphere for the PMLs. No solution was obtained with this model as the PMLs absorbed the incident plane wave. 3. Perfectly Matched Layers with Field Input inside PMLs • The geometry in this case is identical to that of the previous case. The difference is in the incidence of the electric field; rather than simply applying a general field across the entire model, the innermost layer of the PMLs was designated as an input port to allow the incident field to access the model without being absorbed on the way in. This method is still in testing.