{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T15:20:38Z","timestamp":1719069638333},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2012,3,14]],"date-time":"2012-03-14T00:00:00Z","timestamp":1331683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"We present a new effective permittivity (EP) model to accurately calculate surface plasmons (SPs) using the finite-difference time-domain (FDTD) method. The computational representation of physical structures with curved interfaces causes inherent errors in FDTD calculations, especially when the numerical grid is coarse. Conventional EP models improve the errors, but they are not effective for SPs because the SP resonance condition determined by the original permittivity is changed by the interpolated EP values. We perform FDTD simulations using the proposed model for an infinitely-long silver cylinder and gold sphere, and the results are compared with Mie theory. Our model gives better accuracy than the conventional staircase and EP models for SPs.<\/jats:p>","DOI":"10.3390\/mi3010168","type":"journal-article","created":{"date-parts":[[2012,3,14]],"date-time":"2012-03-14T18:17:19Z","timestamp":1331749039000},"page":"168-179","source":"Crossref","is-referenced-by-count":14,"title":["Effective Permittivity for FDTD Calculation of Plasmonic Materials"],"prefix":"10.3390","volume":"3","author":[{"given":"Naoki","family":"Okada","sequence":"first","affiliation":[{"name":"Department of Computer Science, Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan"}]},{"given":"James B.","family":"Cole","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2012,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3966","DOI":"10.1103\/PhysRevLett.85.3966","article-title":"Negative refraction makes a perfect lens","volume":"85","author":"Pendry","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0925-4005(98)00321-9","article-title":"Surface plasmon resonance sensors: Review","volume":"54","author":"Homola","year":"1999","journal-title":"Sens. Actuat. B Chem."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Maier, S.A. (2007). Plasmonics: Fundamentals and Applications, Springer.","DOI":"10.1007\/0-387-37825-1"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zouhdi, S., Sihvola, A., and Vinogradov, A.P. (2008). Metamaterials and Plasmonics: Fundamentals, Modeling, Applications, Springer.","DOI":"10.1007\/978-1-4020-9407-1"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1038\/459504a","article-title":"Metamaterials: Ideal focus","volume":"459","author":"Brumfiel","year":"2009","journal-title":"Nature"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cai, W., and Shalaev, V. (2009). Optical Metamaterials: Fundamentals and Applications, Springer.","DOI":"10.1007\/978-1-4419-1151-3"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Solymar, L., and Shamonina, E. (2009). Waves in Metamaterials, Oxford University Press.","DOI":"10.1093\/oso\/9780199215331.001.0001"},{"key":"ref_8","unstructured":"Capolino, F. (2009). Applications of Metamaterials, CRC Press."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sarid, D., and Challener, W. (2010). Modern Introduction to Surface Plasmons: Theory, Mathematica Modeling, and Applications, Cambridge University Press.","DOI":"10.1017\/CBO9781139194846"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/TAP.1966.1138693","article-title":"Numerical solution of initial boundary value problems involving maxwell\u2019s equations in isotropic media","volume":"14","author":"Yee","year":"1966","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1109\/TMTT.1975.1128640","article-title":"Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell\u2019s equations","volume":"23","author":"Taflove","year":"1975","journal-title":"IEEE Trans. Microwave Theory Tech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1109\/TEMC.1980.303879","article-title":"Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic-penetration problems","volume":"22","author":"Taflove","year":"1980","journal-title":"IEEE Trans. Electromagnet. Compat."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Taflove, A., and Hagness, S.C. (2005). Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House. [3rd ed.].","DOI":"10.1002\/0471654507.eme123"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/TAP.2002.801268","article-title":"High-accuracy Yee algorithm based on nonstandard finite differences: New developments and verifications","volume":"50","author":"Cole","year":"2002","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4589","DOI":"10.1109\/TNS.1983.4333176","article-title":"Finite-difference solution of Maxwell\u2019s equations in generalized nonorthogonal coordinates","volume":"30","author":"Mei","year":"1983","journal-title":"IEEE Trans. Nuclear Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1029\/RS019i005p01145","article-title":"Conformal time domain finite difference method","volume":"19","author":"Mei","year":"1984","journal-title":"Radio Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/8.43592","article-title":"FDTD algorithm in curvilinear coordinates","volume":"38","author":"Fusco","year":"1990","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/8.138836","article-title":"Finite-difference time-domain modeling of curved surfaces","volume":"40","author":"Jurgens","year":"1992","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1109\/8.273315","article-title":"Three-dimensional contour FDTD modeling of scattering from single and multiple bodies","volume":"41","author":"Jurgens","year":"1993","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1109\/22.130985","article-title":"A local mesh refinement algorithm for the time domain-finite difference method using Maxwell\u2019s curl equations","volume":"38","author":"Kim","year":"1990","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1109\/22.75289","article-title":"A subgridding method for the time-domain finite-difference method to solve Maxwell\u2019s equations","volume":"39","author":"Zivanovic","year":"1991","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1109\/8.558656","article-title":"FDTD local grid with material traverse","volume":"45","author":"Chevalier","year":"1997","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1109\/22.622937","article-title":"FDTD analysis of dielectric resonators with curved surfaces","volume":"45","author":"Kaneda","year":"1997","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1109\/75.867850","article-title":"The second-order condition for the dielectric interface orthogonal to the Yee-lattice axis in the FDTD scheme","volume":"10","author":"Hirono","year":"2000","journal-title":"IEEE Microw. Guid. Wave Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1109\/7260.916329","article-title":"Effective permittivities for second-order accurate FDTD equations at dielectric interfaces","volume":"11","author":"Hwang","year":"2001","journal-title":"IEEE Microw. Wirel. Compon. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"10367","DOI":"10.1364\/OPEX.13.010367","article-title":"Contour-path effective permittivities for the two-dimensional finite-difference time-domain method","volume":"13","author":"Mohammadi","year":"2005","journal-title":"Opt. Express"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1364\/JOSAB.27.000631","article-title":"Simulation of whispering gallery modes in the Mie regime using the nonstandard finite-difference time domain algorithm","volume":"27","author":"Okada","year":"2010","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_28","unstructured":"Capolino, F. (2011). Light Scattering Reviews 6, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/8.135475","article-title":"The efficient modeling of thin material sheets in the finite-difference time-domain (FDTD) method","volume":"40","author":"Maloney","year":"1992","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1109\/22.788616","article-title":"A conformal finite-difference time-domain technique for modeling cylindrical dielectric resonators","volume":"47","author":"Dey","year":"1999","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3141","DOI":"10.1364\/AO.38.003141","article-title":"Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition","volume":"38","author":"Sun","year":"1999","journal-title":"Appl. Opt."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1002\/(SICI)1098-2760(20000205)24:3<151::AID-MOP2>3.0.CO;2-8","article-title":"On the modeling of periodic structures using the finite-difference time-domain algorithm","volume":"24","author":"Yu","year":"2000","journal-title":"Microw. Opt. Tech. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3727","DOI":"10.1364\/AO.39.003727","article-title":"Efficient finite-difference time-domain scheme for light scattering by dielectric particles: Application to aerosols","volume":"39","author":"Yang","year":"2000","journal-title":"Appl. Opt."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/7260.905957","article-title":"A conformal finite difference time domain technique for modeling curved dielectric surfaces","volume":"11","author":"Yu","year":"2001","journal-title":"IEEE Microw. Wirel. Compon. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4611","DOI":"10.1364\/AO.43.004611","article-title":"Comparison of cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles","volume":"43","author":"Yang","year":"2004","journal-title":"Appl. Opt."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3070","DOI":"10.1109\/TAP.2007.908370","article-title":"Finite-difference time-domain study of guided modes in nano-plasmonic waveguides","volume":"55","author":"Zhao","year":"2007","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Barber, P.W., and Hill, S.C. (1989). Light Scattering by Particles: Computational Methods, World Scientific.","DOI":"10.1142\/9789814317689"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4370","DOI":"10.1103\/PhysRevB.6.4370","article-title":"Optical constants of the noble metals","volume":"6","author":"Johnson","year":"1972","journal-title":"Phys. Rev. B"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Etchegoin, P.G., Ru, E.C.L., and Meyer, M. (2006). An analytic model for the optical properties of gold. J. Chem. Phys., 125.","DOI":"10.1063\/1.2360270"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1088\/1464-4258\/9\/7\/029","article-title":"Implementation of the critical points model in the recursive convolution method for modeling dispersive media with the finite-difference time domain method","volume":"9","author":"Vial","year":"2007","journal-title":"J. Opt. A: Pure Appl. Opt."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1109\/15.57116","article-title":"A frequency-dependent finite-difference time-domain formulation for dispersive materials","volume":"32","author":"Luebbers","year":"1990","journal-title":"IEEE Trans. Electromagnet. Compat."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1109\/8.509882","article-title":"Piecewise linear recursive convolution for dispersive media using FDTD","volume":"44","author":"Kelley","year":"1996","journal-title":"IEEE Trans. Antennas Propag."}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/3\/1\/168\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T00:19:40Z","timestamp":1717114780000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/3\/1\/168"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,14]]},"references-count":42,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,3]]}},"alternative-id":["mi3010168"],"URL":"https:\/\/doi.org\/10.3390\/mi3010168","relation":{},"ISSN":["2072-666X"],"issn-type":[{"value":"2072-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,14]]}}}