more accurate than those calculated using Stern's formula with a five times smaller mesh size.In Figure 7, for metal thickness below 50 nm, the propagation loss calculated by Stern's formula with a coarse mesh size ⌬ ϭ 50 nm becomes zero, which is due to its inability to simulate metal layers between two sample nodes. On the contrary, ST4 with the same order of coarse mesh can still calculate the SPP mode of thin metal film correctly. For metal thickness beyond 50 nm, ST4 achieves better accuracy in calculating propagation loss compared with Stern's formula for the same mesh size.
CONCLUSIONWith the analysis of SPP waveguides for nanoscale optical devices in mind, a fourth order accurate FD scheme capable of simulating multiple material interfaces between nodes has been developed. The effectiveness of this formula has been validated by evaluating the eigenmode characteristic of 2D and 3D SPP metallic waveguides using the ID-BPM procedure. In comparison with other FD formulas, numerical simulation with a given accuracy can be obtained using far fewer mesh points with a corresponding reduction of the computational resources required. REFERENCES 1. P. Berini, Plasmon-polariton waves guided by thin lossy metal film of finite width: Bound modes of symmetric structures, Phys Rev B Condens Matter 61 (2000), 10484-10503. 2. R. Zia, A. Chandran, and M.L. Brongersma, Dielectric waveguide model for guided surface polaritons, Opt Let 30 (2005), 1473-1475. 3. J.A. Dionne, L.A. Sweatlock, and H.A. Atwater, Planar metal plasmon waveguides: Frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model, Phys Rev B Condens Matter 72 (2005), 075405. 4. J. Shibayama, T. Yamazaki, J. Yamauchi, and H. Nakano, Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method, J Lightwave Technol 23 (2005), 1533-1539. 5. M.S. Stern, Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles, IEE Proc J 135 (1988), 56-63. 6. C. Vassallo, Interest of improved three-point formulas for finite difference modeling of optical devices, J Opt Soc Am 14 (1997), 3273-3284. 7. J. Yamauchi, M. Sekiguchi, O. Uchiyama, J. Shibayama, and H.Nakano, Modified finite-difference formula for the analysis of semivectorial modes in step-index optical waveguides, IEEE Photon Technol Lett 9 (1997), 961-963.