Yüzey plazmon polaritonlarının dispersiyon mühendisliği

Surface plasmon polaritons (SPPs) and their features have been scrutinized and documented in the scientific literature for decades. Experimental configurations that can excite and exploit SPP modes have been developed. The characteristic phenomena related to SPPs such as local field enhancement, electromagnetic energy confinement, increased absorption of incident light have formed the basis of many novel applications. Significant improvements in spectroscopic methods, sensors, solar cells, nanoparticle-based targeted disease solutions have been enabled by the use of SPPs. However, this fast pace of advancement in the field seems to have left behind several important pieces missing in its theoretical foundations. The purpose of this thesis is to uncover these pieces, investigate them in detail, resolve some of the current discussions in the literature, and finally show how a thorough understanding of SPP modes opens up new venues for improvement in essentially any plasmonic system. In this thesis, the SPP modes in layered media are analyzed by taking into account all facets of the electromagnetic response of the plasmonic structure, without any prior assumptions about whether the modes are physical/proper or unphysical/improper. It is shown that all extrema defining the response of the structure, including the ones that are seemingly unphysical and usually dismissed as such in other studies, are responsible for the SPP phenomena and experimental measurements in realistic scenarios. This is achieved by a detailed investigation of the Riemann sheets that show up in the evaluation of the electromagnetic response of plasmonic structures, and by establishing connections between the modes on different Riemann sheets. Based on this exhaustive analysis of SPP modes, optimal values for parameters such as the metal film thickness and the dielectric constant are discussed for various experimental purposes. Surface plasmon dispersion relation is also analyzed and shown to support a much richer domain of SPP modes than what is commonly assumed in the literature. In this thesis, we refrain from prematurely applying any conditions that originate from pre-existing physical intuitions and only rely on the mathematical restrictions that are imposed by the boundary conditions of the problem. This enables the expansion of the dispersion relation to the third dimension as a surface rather than just a curve, resulting in SPP modes with simultaneous complex frequencies and complex wave vectors. The connection between the SPP modes on this dispersion surface and the temporal and spatial boundary conditions is also established. These results are applied to two popular examples in plasmonics: A metal-dielectric-metal plasmonic waveguide and the super lens which provides resolution beyond the diffraction limit. In each case, it is shown that the features such as image resolution, mode propagation length and field confinement can be dramatically improved using the dispersion surface compared to conventional approaches.