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.