Calculation of Complex Propagation Constants of Surface Plasmon Polariton Rectangular Waveguide by The Method of Lines

摘要

The construction of optical circuits on subwavelength or nanometric scales has attracted much attention of many researchers recently. The size and density of optical devices employing conventional dielectric optical waveguide and photonic crystals will in principle be limited by the diffraction limit of light. In contrast, the size of optical waveguide using Surface Plasmon Polariton (SPP) can be decreased significantly as compared to the above-mentioned conventional diffraction-limited optical device. So, the SPP is expected to be employed as one of the types of nanometric optical wire in nanometric scale integrated optical circuits. Many interesting experimental or theoretical works that treated practical and concrete nanometric optical circuits using SPP have been reported so far [1]-[5]. One of the fundamental SPP waveguide is the hollow rectangular metallic optical waveguide. So far, some interesting phenomena have been reported in comparison with rectangular waveguide made of perfect electric conductor (PEC) used in the microwave technology [6]-[9]. The permittivity of the metallic material that supports SPP has a complex value in the optical frequency region. It is difficult to obtain the rigorous and analytical solution of the guided-mode for the SPP waveguide of rectangular cross section. The approximate values of propagation constant can be obtained effective-index method (EIM) [6], [7]. The numerical techniques are effective and several papers have treated numerical study of the SPP rectangular waveguide [10]-[12]. However, the basic characteristics of complex propagation constants of SPP rectangular waveguide have not been sufficiently investigated in detail. In this paper, we present the numerical study about the complex propagation constants of SPP rectangular waveguide by the Method of Lines (MoL) with high accuracy [13]-[15]. We calculate the dependences of complex propagation constants on the waveguide sizes and wavelength. The fundamental, important and interesting characteristics of SPP rectangular waveguide have been revealed.