Nonlinear Surface Plasmon Polaritons: Analytical and Numerical Studies
Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
This dissertation contains analytical and numerical studies of nonlinear
surface-plasmon polaritons (SPPs). In our studies, we consider SPP propagation
at the interface between a noble metal with a cubic optical nonlinearity and an
optically linear dielectric.
We first consider a sum-frequency generation process during the nonlinear
interaction, where a nonlinear polarization with tripled frequency is generated from
the incident fundamental SPP. Using the non-depletion approximation, the solution
of the nonlinear wave equation shows a third harmonic generation process from the
incident SPP wave. The solution is bound in the dielectric while freely propagating
in the metal. For realistic noble metals with absorption, we use silver for its
transparency window around the plasma frequency. In this window, absorption
losses are reduced and the resultant signal has a good transmittance within the
metal. The energy conversion efficiency from the incident SPP wave to the THG signal is about 0.1% for excitation using a standard continuous wave laser with
visible light intensity I = 103W/cm2. Once generated, the propagation angle of the
signal is fully determined by the optical properties of the dielectric and the metal layers. We next consider a nonlinear polarization with the same frequency as
the incident light. In this process the third order nonlinearity of the metal
is described by a nonlinear optical refractive-index. With the slowly varying
amplitude approximation, the nonlinear wave equation takes the form of a
nonlinear temporal Schr¨odinger (NLS) equation. The solution to the NLS equation
for the nonlinear SPP is a temporal dark soliton (TDS). In addition to analytical
studies, computational methods are also used. With no metal loss, the numerical
solution shows stable propagation of a TDS, when the initial pulse has a tanh
envelope satisfying the threshold peak amplitude. For an arbitrary input pulse,
instabilities such as background-oscillations and multi-peak breakups occur. With
metal loss, the input optical pulse decays while maintaining a single pulse shape
when the initial amplitude satisfies the same tanh envelope condition as in the
lossless case. For an arbitrary pulse, background-oscillations or pulse-breakups
occur after a short time of propagation.
Description
Keywords
Nolinear, Optics, Plasmonics, Soliton, SPP