Journal
PHYSICAL REVIEW B
Volume 79, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.79.035120
Keywords
finite difference methods; frequency-domain analysis; MIM devices; modal analysis; optical waveguides; plasmons; Sturm-Liouville equation
Funding
- DARPA MTO
- Interconnect Focus Center
- Focus Center Research Program
- DARPA
- Semiconductor Research Corporation program
- USAFOSR Plasmon Enabled Nanophotonic Circuits MURI Program
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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.
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