Finite-Difference Frequency-Domain Method Analysis of Periodic Nano-Plasmonic Waveguides

Recently, guiding electromagnetic (EM) waves with a mode at subwavelength scale has attracted great attention, in particular, at optical wavelengths. The related phenomenon is that of surface plasmon polaritons (SPPs) that are bound non-radiative surface waves propagating at metaldielectric interfaces with the fields decaying exponentially away from the interface [1]. Structures supporting such subwavelength waveguiding modes, which can be called plasmonic waveguides, are essential components in future miniaturized light circuitry. Longitudinally uniform nanoplasmonic waveguides with various transverse structures have been proposed and studied [2-5], such as metallic nanowires [4] and V-shaped grooves [5]. In this paper, we consider longitudinally periodic waveguiding structures [6]. Real metals are lossy materials. Computation of band diagrams for periodic metallic structures including such real metal effects as an eigenvalue problem is known to be difficult, in particular for the transverse-electric (TE) mode, although a few methods have been developed leading to nonlinear eigenvalue problems, such as that based on multiple multipole expansions [7]. On the other hand, the finite-difference time-domain (FDTD) method based on the Yee mesh has been a popular numerical technique for the band-diagram calculation [8] because of its flexibility and easiness in dealing with dispersive materials. However, the conventional FDTD method employs orthogonal and staggered grids, and modifications at material interfaces are needed in order to improve numerical accuracy and mode-finding resolution in the calculation of band diagrams [9-10], which requires more complicated mathematical algorithms in treating material interfaces. In this paper, based on the finite-difference frequency-domain (FDFD) method using the Yee mesh, we formulate a standard eigenvalue problem for computing band diagrams or mode dispersion curves of two-dimensional (2-D) waveguiding structures with 1-D periodicity and involving lossless dispersive metallic materials such as silver nanorods. High enough numerical accuracy is obtained without using complicated algorithms to treat material interfaces, and the mode solutions are found to agree with the FDTD analysis results [6].