Abstract
This paper shows how to analyze plasmonic metal-insulator-metal waveguides using the full modal structure of these guides. The analysis applies to all frequencies, particularly including the near infrared and visible spectrum, and to a wide range of sizes, including nanometallic structures. We use the approach here specifically to analyze waveguide junctions. We show that the full modal structure of the metal-insulator-metal MIM waveguides—which consists of real and complex discrete eigenvalue spectra, as well as the continuous spectrum—forms a complete basis set. We provide the derivation of these modes using the techniques developed for Sturm-Liouville and generalized eigenvalue equations. We demonstrate the need to include all parts of the spectrum to have a complete set of basis vectors to describe scattering within MIM waveguides with the mode-matching technique. We numerically compare the mode-matching formulation with finite-difference frequency-domain analysis and find very good agreement between the two for modal scattering at symmetric MIM waveguide junctions. We touch upon the similarities between the underlying mathematical structure of the MIM waveguide and the PT symmetric quantum-mechanical pseudo-Hermitian Hamiltonians. The rich set of modes that the MIM waveguide supports forms a canonical example against which other more complicated geometries can be compared. Our work here encompasses the microwave results but extends also to waveguides with real metals even at infrared and optical frequencies.
Highlights
Waveguides have long been used to controllably direct energy flow between different points in space
We will provide the detailed mathematical framework to analyze the modal structure of the MIM waveguide and emphasize how it is a hybrid between the parallel plate and the dielectric slab waveguides
FIG. 12. ͑Color online Magnetic field Hy at the junction of two MIM waveguides as a result of the scattering of the main mode of the left waveguide traveling toward the right—the inset shows the schematic of the geometry
Summary
Waveguides have long been used to controllably direct energy flow between different points in space. At optical frequencies below the plasma oscillation frequency, electrons go through a negligible number of collisions during an electromagnetic cycle, and this time acceleration of electrons is proportional to the applied field strength, which results in a permittivity that can be substantially a large real negative number. The full set of modes that the MIM waveguide supports—real and complex discrete modes as well as a continuous set of modes—has only very recently been published.[23] For other geometries, it has been shown that, in general, waveguides support real, complex, and continuous sets of modes.[24,25,26,27,28] In this work, we will provide the detailed mathematical framework to analyze the modal structure of the MIM waveguide and emphasize how it is a hybrid between the parallel plate and the dielectric slab waveguides.
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