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excitations determine carrier and thermal transport, and surface photo-chemistry
including photocatalysis, with distinct characteristics for planar and nanostructured
metal surfaces. Collective excitations in the form of surface plasmon polaritons
(SPPs) at the boundaries of metallic media permit the tailoring of optical fields
for surface-enhanced spectroscopy and sub-wavelength resolution microscopy, and
have attracted wide attention for their potential for the design of new micro- and
nano-scale photonic devices. The near-field and optical antenna properties of surface plasmon polaritons, in particular, may even open the door for qualitatively new
optical physics in the near-field. This includes new ways to control the light-matter
interaction in quantum systems, negative-index and related meta-materials, or new
nonlinear optical phenomena.
The possibilities and fundamental limitations associated with several of these proposed ideas are linked to the fundamental properties of surface plasmon polaritons.
Excellent books have been devoted to their linear optical properties [1–3]. Here we
will discuss in particular the ultrafast and nonlinear optical properties of surface plasmon polaritons, and how they relate to the elementary electronic properties of metals
that ultimately determine the radiative and non-radiative evolution of the plasmon
excitation.
We start with a brief overview of the basic properties of surface waves and plasmon
polaritons and the relevant underlying physics. We then focus on the ultrafast and
nonlinear behaviour, which just as for linear SPPs is a convolution of the intrinsic elementary electronic properties of metals with extrinsic size and geometry-dependent
structural resonances. Ultrafast and nonlinear optics involving SPPs are particularly
sensitive to the combination and relative roles of intrinsic and extrinsic effects. The
goal here is to provide a microscopic discussion of the dynamic processes of SPPs
and the parameters that govern their spectral, spatial, and temporal characteristics
linked to the ultrafast electron dynamics of metals.
The nonlinear SPP response is of interest for the generation of optical frequency
components by parametric generation or nonlinear wave-mixing, optical saturation
and gain, and strong light-matter interaction, taking advantage of the nonlinearity
of the medium in combination with resonant or non-resonant field enhancement
and optical antenna effects. The study of the ultrafast dynamics of SPPs also
opens new experimental approaches for controlling the light-matter interaction and
super-resolution microscopy simultaneously on femtosecond time and nanometer
length scales as determined by the elementary processes in (homogeneous and
heterogeneous) media.
7.1.2 Linear Optical Polarization
We first discuss some basics of the light-matter interaction to define the relevant
nomenclature. The induced optical polarization of a (nonmagnetic) medium subject
to an incident electromagnetic field is given by
P(ω) = ε 0 χ(ω)E(ω)
(7.1)
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