Domain Decomposition Scheme in Newmark-Beta-FDTD for Dispersive Grating Calculation
Keywords:Domain decomposition, extraordinary optical transmission (EOT), Newmark-Beta-FDTD, surface plasmons
In this work, an efficient domain decomposition scheme is introduced into the unconditionally stable finite-difference time-domain (FDTD) method based on the Newmark-Beta algorithm. The entire computational domain is decomposed into several subdomains, and thus the large sparse matrix equation produced by the implicit FDTD method can be divided into some independent small ones, resulting in a fast speed lower-upper decomposition and backward substitution. The domain decomposition scheme with different subdomain schemes and different subdomain numbers is studied. With a generalized auxiliary differential equation (ADE) technique, the extraordinary optical transmission through a periodic metallic grating with bumps and cuts is investigated with the domain decomposition Newmark-Beta-FDTD. Compared with the traditional ADE-FDTD method and the ADENewmark- Beta-FDTD method, the results from the proposed method show its accuracy and efficiency.
T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraodinary optical transmission through sub-wavelength hole arrays,” Nature, vol. 391, no. 6668, pp. 667-669, Feb. 1998.
C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature, vol. 445, no. 7123, pp. 39-46, Jan. 2007.
J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonance on metallic gratings with very narrow slits,” Phy. Rev. Lett., vol. 83, no. 14, pp. 2845-2848, Oct. 1999.
H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Exp., vol. 12, no. 16, pp. 3629-3651, Aug. 2004.
A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method. Norwood, MA: Artech House, 2000.
T. Namiki, “A new FDTD algorithm based on alternating-direction implicit method,” IEEE Trans. Microw. Theory Techn., vol. 47, no. 10, pp. 2003- 2007, Oct. 1999.
L. Gao, B. Zhang, and D. Liang, “The splitting finite difference time-domain methods for Maxwell’s equations in two dimensions,” J. Comput. Appl. Math., vol. 205, no. 1, pp. 207-230, Aug. 2007.
E. L. Tan, “Unconditionally stable LOD-FDTD method for 3-D Maxwell’s equations,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 2, pp. 85-87, Feb. 2007.
G. Sun and C. W. Truneman, “Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 5, pp. 2275-2284, May 2006.
S. B. Shi, W. Shao, X. K. Wei, X. S. Yang, and B. Z. Wang, “A new unconditionally stable FDTD method based on the Newmark-Beta algorithm,” IEEE Microw. Theory Techn., vol. 64, no. 12, pp. 4082-4090, Dec. 2016.
M. N. Vouvakis, Z. Cendes, and J. F. Lee, “A FEM domain decomposition method for photonic and electromagnetic band gap structures,” IEEE Trans. Antennas Propag., vol. 54, no. 2, pp. 721-733, Feb. 2006.
B. Z. Wang, R. Mittra, and W. Shao, “A domain decomposition finite-difference utilizing characteristic basis functions for solving electrostatic problems,” IEEE Trans. Electromagn. Compat., vol. 50, no. 4, pp. 946-952, Nov. 2008.
G. Q. He, W. Shao, X. H. Wang, and B. Z. Wang, “An efficient domain decomposition LaguerreFDTD method for two-dimensional scattering problems,” IEEE Trans. Antennas Propag., vol. 64, no. 5, pp. 2639-2645, May 2013.
D. Sullivan, “Nonlinear FDTD formulations using Z transforms,” IEEE Trans. Microw. Theory Techn., vol. 43, no. 3, pp. 676-682, Mar. 1995.
R. J. Luebbers and F. Hunsberger, “FDTD for Nthorder dispersive media,” IEEE Trans. Antennas Propag., vol. 40, no. 11, pp. 1297-1301, Nov. 1992.
S. B. Shi, W. Shao, T. L. Liang, L. Y. Xiao, X. S. Yang, and H. Ou, “Efficient frequency-dependent Newmark-Beta-FDTD method for periodic grating calculation,” IEEE Photonics J., vol. 8, no. 6, pp. 1-9, Dec. 2016.
T. N. Phillips, “Preconditioned iterative methods for elliptic problems on decomposed domains,” Int. J. Comput. Math., vol. 44, pp. 5-18, 1992.
E. D. Palik, Handbook of Optical Constants in Solids. Academic, 1982.
A. P. Hibbins, M. J. Lockyear, and J. R. Sambles, “The resonant electromagnetic fields of an array of metallic slits acting as Fabry-Pérot cavities,” J. Appl. Phys., vol. 99, no. 12, pp. 1-5, June 2006.