The interaction of an evanescent wave and plasmonic nanostructures are simulated in Finite Element Method. Specifically, the optical absorption cross section (Cabs) of a silver nanoparticle (AgNP) and a gold nanoparticle (AuNP) in the presence of metallic (gold) and dielectric (silicon) atomic force microscope (AFM) probes are numerically calculated in COMSOL. The system was illuminated by a transverse magnetic polarized, total internally reflected (TIR) waves or propagating surface plasmon (SP) wave. Both material nanoscale probes localize and enhance the field between the apex of the tip and the particle. Based on the absorption cross section equation the author was able to demonstrate the increment of absorption cross section when the Si tip was brought closer to the AuNP, or when the Si tip apex was made larger. However, the equation was not enough to predict the absorption modification under metallic tips, especially for a AgNP's Cabs; neither it was possible to estimate the optical absorption based on the localized enhanced field caused by a gold tip. With the help of the driven damped harmonic oscillator equation, the Cabs of nanoparticles was explained. In addition, this model was applicable for both TIR and Surface Plasmon Polaritons illuminations. Fitting the numerical absorption data to a driven damped harmonic oscillator (HO) model revealed that the AFM tip modifies both the driving force (F0), consisting of the free carrier charge and the driving field, and the overall damping of the oscillator beta. An increased F0 or a decreased beta will result in an increased Cabs and vice versa. Moreover, these effects of F0 and beta can be complementary or competing, and they combine to either enhance or suppress absorption. Hence, a significantly higher beta with a small increment in F0 will result in an absorption suppression. Therefore, under a Si tip, Cabs of a AuNP is enhanced while Cabs of a AgNP is suppressed. In contrast, a Au tip suppresses the Cabs for both Au and Ag NPs. As an extension of this absorption model, further investigation of the guided mode and a close by nanostructure is proposed, where the scattered wave off the structure attenuates the guided mode with destructive interference.

Gegenstand der Untersuchungen dieser Arbeit ist die analytische und numerische Studie der plasmonischen Eigenschaften vorhanden in Silbernanodrähten von verschiedener horizontaler Geometrie aufgrund verschiedener Modelle der optischen Antwort der Leitungselektronen. Nach einer hierarchischen Anordnung von linearen Volumen-Materialmodellen, welche innerhalb der plasmonischen Literatur genutzt werden, untersuchen wir die Verwicklung von (nicht)lokaler und dispersiver Antwort mit geometrischen Parametern von Monomeren und Dimeren. Unsere analytischen Studien fokussieren sich auf einzelne zylindrische Drähte, wobei wir das Auftreten von Radius-abhängiger Dämpfung in lokalisierten Oberflächenplasmonen nachweisen, ähnlich dem Konzept der begrenzten mittleren freien Weglänge diskutiert von Kreibig und Mitarbeitern. Weiterhin wird ein Streuproblem mit transversaler Nichtlokalität und "No-slip"- Randbedingung gelöst, gefolgt von einer Diskussion einer Randbedingung, welche zwischen “No-Slip”- und “Slip”-Bedinung interpoliert. Aus numerischer Sicht wird die Streuung an abgerundeten und gleichseitigen dreieckigen und Bowtie-Drähten behandelt mit Fokus auf einer vollanalytischen Beschreibung der Eckenrundung mittels Bézier- Kurven. Dies enthüllt den Krümmungsradius als neuen geometrischen Parameter. Das Variieren der Lückenbreite und Eckenrundung führt zu Verstärkungsfaktoren, welche relevant für oberflächenverstärkte Raman-Streuung einzelner Moleküle sind, in ausgezeichneten räumlichen Bereichen abhängig von der Art der Resonanz. Innerhalb der Extinktionsspektren von dreieckigen und Bowtie-Drähten erscheint eine Sequenz von nichtlokalen Maxima. Diese Sequenz ist am sensitivsten in Bezug auf die Änderung der Krümmung. Die Identifikation der (Hybrid-)Resonanzen basiert auf simulierten Ladungsdichteverteilungen. / Subject of this thesis is the analytical and numerical study of the plasmonic properties present in silver nanowires of different horizontal geometries due to different models of optical response of conduction electrons. Following a hierarchical arrangement of linear bulk material models, used throughout the plasmonic literature, we investigate the intertwining of (non)local and dispersive response with geometrical parameters of monomers and dimers. Our analytical studies focus on single cylindrical wires, revealing the occurrence of radius-dependent damping of localized surface plasmons similar to the concept of limited-mean-free-path discussed by Kreibig and coworkers. Further, a scattering problem with transverse nonlocality and s no-slip condition is solved followed by a discussion of a boundary condition interpolating between the slip and no-slip conditions. On a numerical level, the scattering by rounded and equilateral triangular and bowtie nanowires is treated based on a full analytical description of the corner rounding via Bézier curves revealing the radius of curvature as a new geometrical degree of freedom. Tuning of gap size and corner rounding reveals enhancement factors relevant for surface-enhanced Raman scattering of single molecules in distinguished spatial domains dependent on the type of resonance. Within the extinction spectra a nonlocal peak sequence emerges. This sequence is most sensitive to curvature variations and arises in the triangular monomer and bowtie dimer. The identification of (hybrid) resonances is based on charge density simulations.