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Quantum Dot Shell Clusters as Optical Metamaterials
Jared Maxson and Slava V. Rotkin
Department of Physics, Lehigh University
Motivation and Model
Computational Methods
• Coupling between Q.D.’s in shell clusters
changes the optical response
• The response function of the system:
• Coupled dipole systems are promising optical
metamaterials for plasmonic applications
• We model system as point-dipole lattices with
lattice constant much less than the wavelength
of light.
where is the set of all quantum numbers of the system, V is the
volume per dipole, is the direction of the incident external field,
and e is the effective charge per dipole.
• Eigenfrequency:
Where
are the eigenvalues of the interaction potential matrix,
and
is a characteristic frequency of a single dipole.
where
is the dipole dipole interaction potential,
is
the polarizability of a single dipole (which is a function of
excitation frequency), and , are polarization indices.
• We consider low dimensional lattices: a linear
chain, a ring, a planar lattice, and a cylindrical
lattice.
• We apply a two step diagonalization of
:
(1) a Fourier transformation block diagonalizes
the matrix in i and j
(2) Direct diagonalization over polarization
indices.
1
i
Ring
Lattice
Plane
Lattice
2
3
4
5
6
7
1
8
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
F.T.
2
3
V(m)
Upper Curve: Numerical
dispersion
m
Lower Curve: Continuum
approximation dispersion
kx
ky
4
5
j
Polarization Decomposition
(ky held constant)

6
7
8
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
2
3
4
5
6
7
k
8
8
k
• Developed numerical and
analytical techniques of
modeling quantum dot shell
metamaterials.
• Simulated resonant light
absorption for a number of
lattice geometries.
• Performed polarization
analysis and identified
resonances of the response
function with eigenmodes of
certain frequencies.

kx
We require both frequency
and space synchronism
between the incident photon
and the eigenmode.
5
Conclusions
Plane Response Function (Total)

7
4
• We verify numerical results with analytic
dispersion. For small k, we use the continuum
approximation.
Response Function Analysis
||
6
3
1
1
1
2
Acknowledgement
This requirement implies
conservation of energy and
momentum.
This work was supported in part by
the PA Infrastructure Technology
Fund (grant PIT-735-07)