Using the quasistatic approximation, we calculate the dispersion relations for plasmonic waves along a chain of
metallic nanoparticles when the host is a nematic or a cholesteric liquid crystal (NLC or CLC). If the director
of the NLC is perpendicular to the chain, the doubly degenerate transverse (T) branches split into two linearly
polarized branches. For a CLC with a twist axis parallel to the chain, the two T branches again split, but are
no longer linearly polarized. We illustrate these results numerically by calculating the dispersion relations for
Drude metal particles in either an NLC or a CLC.
The light transmission through metallic films with different types of nano-structures was studied both theoretically
and experimentally. It is shown, analytically, numerically and experimentally, that the positions of the
surface plasmon resonances depend on nano-structural details. This leads to a strong dependence of the amplitude
of the light transmission, as well as the polarization of the transmitted light and other optical properties, on
those details. Two complementary situations are considered: a metal film with dielectric holes and a dielectric
film with metallic islands. Two different possibilities for manipulating the light transmission are considered: One
is based upon application of a static magnetic field (actually, this is equivalent to changing the nano-structure
in a transformed configuration space), the other is based upon using liquid crystals as one of the constituents of
a nano-structured film.
We present a unified framework for a first-principles calculation of the electric force acting on dielectric or metallic nanospheres suspended in a dielectric host and subject to a uniform external electric field. This framework is based on the spectral representation of the local electric field in a composite medium. The quasi-static (or "surface-plasmon") eigenstates of a cluster of spheres are first calculated, numerically. Then those are used to calculate the force on any sphere as the gradient of the total electrostatic energy with respect to the position of that sphere. This approach is applicable even when the spheres are very closely spaced, and even when they are metallic: No infinities ever appear.
The forces are not limited to dipole-dipole forces. Moreover, the force acting on any sphere is not a simple sum of two-body forces: When the inter-sphere gaps are small, complicated many-body forces appear. This is due to the fact that, when a sphere center is displaced slightly, the electric polarization of all the other spheres is changed. Consequently, the total electrical energy is changed in a way that cannot be represented as a sum of two-body energy changes. Explicit calculations of these forces for a few selected sphere clusters are presented. The results are quite different from what is obtained in the dipole approximation.
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