Electrostatic (Plasmon) Resonances in Metallic and Semiconductor
Nanoparticles

Isaak D. Mayergoyz
Dept. of Electrical & Computer Engineering, University of Maryland, College
Park, MD 20742


It is known that small objects can exhibit resonant behavior at certain
frequencies for which the object permittivity is negative and the
free-space wavelength is large in comparison with object dimensions. This
phenomenon usually occurs at nanoscale and at optical frequencies where
the above two conditions can be simultaneously realized. These resonances
are electrostatic in nature, and they result in powerful localized sources
of light, which have promising applications in nano-lithography,
nanophotonics, surface-enhanced Raman scattering, biosensors, and optical
data storage. These resonances in semiconductor nanoparticles are of
special interested because they can be controlled through optical
manipulation of carrier densities. This optical controllability can be
utilized for the development of nanoscale light switches and all-optical
transistors.


Currently these resonances in nanoparticles are found experimentally (or
numerically) by probing dielectric objects of complex shapes with
radiation of various frequencies, i.e. by using a trial-and-error?
method. There has not existed any technique for direct calculation of the
negative values of dielectric permittivities, and the corresponding
frequencies of electromagnetic radiation at which these resonances occur.
In the lecture, we present a new technique for direct calculation of
resonance frequencies and discuss unique physical features of these
resonances in nanoparticles. It is demonstrated that the resonance
values of permittivity, and hence the resonance frequencies, can be
directly (i.e. without laborious probing) found by computing the
eigenvalues of a specific boundary integral equation. Once the resonance
permittivity is known, the resonance frequency can be obtained by invoking
appropriate dispersion relations. This approach also reveals the unique
physical property of plasmon resonances: resonance frequencies depend on
dielectric object shapes, but they are scale invariant with respect to
object dimensions, provided that they remain appreciably smaller than the
free-space wavelength. It turns out that the integral operator in the
integral equation is compact, and hence the plasmon spectrum is discrete.
General properties of this spectrum have been studied along with the
excitation conditions for plasmon resonances. These results will be
outlined in the lecture.