Contour-path effective permittivities for the two-dimensional finite-difference time-domain method
Optics Express, Vol. 13, Issue 25, pp. 10367-10381 (2005)
http://dx.doi.org/10.1364/OPEX.13.010367
Acrobat PDF (219 KB)
Abstract
Effective permittivities for the two-dimensional Finite-Difference Time-Domain (FDTD) method are derived using a contour path approach that accounts for the boundary conditions of the electromagnetic field at dielectric interfaces. A phenomenological formula for the effective permittivities is also proposed as an effective and simpler alternative to the previous result. Our schemes are validated using Mie theory for the scattering of a dielectric cylinder and they are compared to the usual staircase and the widely used volume-average approximations. Significant improvements in terms of accuracy and error fluctuations are demonstrated, especially in the calculation of resonances.
© 2005 Optical Society of America
1. Introduction
1 . Proceedings of the Fifth International Symposium on Photonic and Electromagnetic Crystal Structures (PECS-V) ( Kyoto, Japan , March 7 – 11 , 2004 ); H. Benisty , S. Kawakami , D.J. Norris , and C.M. Soukoulis , eds, Phot. Nanostructures Fund. Appl . 2 , 57 – 159 ( 2004 ); [CrossRef]
1 . C. Jagadish , D.G. Deppe , S. Noda , T.F. Krauss , and O.J. Painter , eds, IEEE J. Sel. Top. Area Commun. 23 , 1305 – 1423 ( 2005 ).
2 . Special issue on nanostructured optical meta-materials: beyond photonic band gap effects , N. Zheludev and V. Shalaev , eds., J. Opt. A: Pure and Applied Optics , 7 , S1 – S254 ( 2005 ). [CrossRef]
7 . K.K. Mei , A. Cangellaris , and D.J. Angelakos , “ Conformal Time Domain Finite-Difference Method ,” Radio Sci. 19 , 1145 – 1147 ( 1984 ). [CrossRef]
8 . R. Holland , “ Finite-Difference Solution of Maxwell’s Equations in Generalized Nonorthogonal Coordinates ,” IEEE Trans. Nucl. Sci. NS-30 , 4589 – 4591 ( 1983 ). [CrossRef]
9 . M. Fusco , “ FDTD Algorithm in Curvilinear Coordinates ,” IEEE Trans. Antennas Propag. 38 , 76 – 89 ( 1990 ). [CrossRef]
10 . V. Shankar , A. Mohammadian , and W.F. Hall , “ A Time-Domain Finite-Volume Treatment for the Maxwell Equations ,” Electromagnetics 10 , 127 – 145 ( 1990 ). [CrossRef]
11 . N.K. Madsen and R.W. Ziolkowski , “ A Three-Dimensional Modified Finite Volume Technique for Maxwell’s Equations ,” Electromagnetics 10 , 147 – 161 ( 1990 ). [CrossRef]
12 . P.H. Harms , J.-F. Lee , and R. Mittra , “ A Study of the Nonorthogonal FDTD Method Versus the Conventional FDTD Technique for Computing Resonant Frequencies of Cylindrical Cavities ,” IEEE Trans. Microwave Theory Tech. 40 , 741 – 476 ( 1992 ). [CrossRef]
15 . C.J. Railton , I.J. Craddock , and J.B. Schneider , “ Improved locally distorted CPFDTD algorithm with provable stability ,” Electron. Lett. 31 , 1585 – 1586 ( 1995 ). [CrossRef]
13 . T.G. Jurgens , A. Taflove , K. Umashankar , and T.G. Moore , “ Finite-Difference Time-Domain Modeling of Curved Surfaces ,” IEEE Trans. Antennas Propag. 40 , 357 – 365 ( 1992 ). [CrossRef]
14 . T.G. Jurgens and A. Taflove , “ Three-Dimensional Contour FDTD Modeling of Scattering from Single and Multiple Bodies ,” IEEE Trans. Antennas Propag. 41 , 1703 – 1708 ( 1993 ). [CrossRef]
15 . C.J. Railton , I.J. Craddock , and J.B. Schneider , “ Improved locally distorted CPFDTD algorithm with provable stability ,” Electron. Lett. 31 , 1585 – 1586 ( 1995 ). [CrossRef]
15 . C.J. Railton , I.J. Craddock , and J.B. Schneider , “ Improved locally distorted CPFDTD algorithm with provable stability ,” Electron. Lett. 31 , 1585 – 1586 ( 1995 ). [CrossRef]
16 . Y. Hao and C.J. Railton , “ Analyzing Electromagnetic Structures with Curved Boundaries on Cartesian FDTD Meshes ,” IEEE Trans. Microwave Theory Tech. 46 , 82 – 88 ( 1998 ). [CrossRef]
17 . T.I. Kosmanis and T.D. Tsiboukis , “ A Systematic and Topologically Stable Conformal Finite-Difference Time-Domain Algorithm for Modeling Curved Dielectric Interfaces in Three Dimensions ,” IEEE Trans. Microwave Theory Tech. 51 , 839 – 847 ( 2003 ). [CrossRef]
18 . I.S. Kim and W.J.R. Hoefer , “ A Local Mesh Refinement Algorithm for the Time Domain-Finite Difference Method Using Maxwell’s Curl Equations ,” IEEE Trans. Microwave Theory Tech. 38 , 812 – 815 ( 1990 ). [CrossRef]
19 . S.S. Zivanovic , K.S. Yee , and K.K. Mei , “ A Subgridding Method for the Time-Domain Finite-Difference Method to Solve Maxwell’s Equations ,” IEEE Trans. Microwave Theory Tech. 39 , 471 – 479 ( 1991 ). [CrossRef]
20 . J.G. Maloney and G.S. Smith , “ The Efficient Modeling of Thin Material Sheets in the Finite-Difference Time-Domain (FDTD) Method ,” IEEE Trans. Antennas Propag. 40 , 323 – 330 ( 1992 ). [CrossRef]
21 . N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD Analysis of Dielectric Resonators with Curved Surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef]
22 . T. Hirono , Y. Shibata , W.W. Lui , S. Seki , and Y. Yoshikuni , “ The Second-Order Condition for the Dielectric Interface Orthogonal to the Yee-Lattice Axis in the FDTD Scheme ,” IEEE Microwave Guided Wave Lett. 10 , 359 – 361 ( 2000 ). [CrossRef]
23 . K.-P. Hwang and A.C. Cangellaris , “ Effective Permittivities for Second-Order Accurate FDTD Equations at Dielectric Interfaces ,” IEEE Microwave Wireless Comp. Lett. 11 , 158 – 160 ( 2001 ). [CrossRef]
24 . S. Dey and R. Mittra , “ A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators ,” IEEE Trans. Microwave Theory Tech. 47 , 1737 – 1739 ( 1999 ). [CrossRef]
25 . W. Yu and R. Mittra , “ On the modeling of periodic structures using the finite-difference time-domain algorithm ,” Microw. Opt. Technol. Lett. 24 , 151 – 155 ( 2000 ). [CrossRef]
26 . P. Yang , G.W. Kattawar , K.-N. Liou , and J.Q. Lu , “ Comparison of Cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles ,” Appl. Opt. 43 , 4611 – 4624 ( 2004 ). [CrossRef] [PubMed]
27 . P. Yang , K.N. Liou , M.I. Mishchenko , and B.-C. Gao , “ Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols , Appl. Opt. 39 , 3727 – 3737 ( 2000 ). [CrossRef]
28 . W. Yu and R. Mittra , “ A Conformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces ,” IEEE Microwave Wireless Comp. Lett. 11 , 25 – 27 ( 2001 ). [CrossRef]
29 . W. Sun and Q. Fu “ Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices ,” Appl. Opt. 39 , 5569 ( 2000 ). [CrossRef]
22 . T. Hirono , Y. Shibata , W.W. Lui , S. Seki , and Y. Yoshikuni , “ The Second-Order Condition for the Dielectric Interface Orthogonal to the Yee-Lattice Axis in the FDTD Scheme ,” IEEE Microwave Guided Wave Lett. 10 , 359 – 361 ( 2000 ). [CrossRef]
23 . K.-P. Hwang and A.C. Cangellaris , “ Effective Permittivities for Second-Order Accurate FDTD Equations at Dielectric Interfaces ,” IEEE Microwave Wireless Comp. Lett. 11 , 158 – 160 ( 2001 ). [CrossRef]
30 . J.-Y. Lee and N.-H. Myung , “ Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces ,” Microw. Opt. Technol. Lett. 23 , 245 – 249 ( 1999 ). [CrossRef]
31 . J. Nadobny , D. Sullivan , W. Wlodarczyk , P. Deuflhard , and P. Wust , “ A 3-D Tensor FDTD-Formulation for Treatment of Slopes Interfaces in Electrically Inhomogeneous Media ,” IEEE Trans. Antennas Propag. 51 , 1760 – 1770 ( 2003 ). [CrossRef]
32 . K.H. Dridi , J.S. Hesthaven , and A. Ditkowski , “ Staircase-Free Finite-Difference Time-Domain Formulation for General Materials in Complex Geometries ,” IEEE Trans. Antennas Propag. 49 , 749 – 756 ( 2001 ). [CrossRef]
33 . A. Ditkowski , K. Dridi , and J.S. Hesthaven , “ Convergent Cartesian Grid Methods for Maxwell’s Equations in Complex Geometries ,” J. Comp. Phys. 170 , 39 – 80 ( 2001 ). [CrossRef]
34 . M. Fujii , D. Lukashevich , I. Sakagami , and P. Russer , “ Convergence of FDTD and Wavelet-Collocation Modeling of Curved Dielectric Interface with the Effective Dielectric Constant Technique ,” IEEE Microwave Wireless Comp. Lett. 13 , 469 – 471 ( 2003 ). [CrossRef]
35 . T. Xiao and Q.H. Liu , “ A Staggered Upwind Embedded Boundary (SUEB) Method to Eliminate the FDTD Staircasing Error ,” IEEE Trans. Antennas Propag. 52 , 730 – 740 ( 2004 ). [CrossRef]
24 . S. Dey and R. Mittra , “ A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators ,” IEEE Trans. Microwave Theory Tech. 47 , 1737 – 1739 ( 1999 ). [CrossRef]
2. The Effective Permittivities
37 . A. Bossavit , “ Generalized finite differences in computational electromagnetics ,” Progress in Electromagnetic Research, PIER 32 , 45 – 64 ( 2001 ). [CrossRef]
20 . J.G. Maloney and G.S. Smith , “ The Efficient Modeling of Thin Material Sheets in the Finite-Difference Time-Domain (FDTD) Method ,” IEEE Trans. Antennas Propag. 40 , 323 – 330 ( 1992 ). [CrossRef]
21 . N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD Analysis of Dielectric Resonators with Curved Surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef]
22 . T. Hirono , Y. Shibata , W.W. Lui , S. Seki , and Y. Yoshikuni , “ The Second-Order Condition for the Dielectric Interface Orthogonal to the Yee-Lattice Axis in the FDTD Scheme ,” IEEE Microwave Guided Wave Lett. 10 , 359 – 361 ( 2000 ). [CrossRef]
23 . K.-P. Hwang and A.C. Cangellaris , “ Effective Permittivities for Second-Order Accurate FDTD Equations at Dielectric Interfaces ,” IEEE Microwave Wireless Comp. Lett. 11 , 158 – 160 ( 2001 ). [CrossRef]
21 . N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD Analysis of Dielectric Resonators with Curved Surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef]
22 . T. Hirono , Y. Shibata , W.W. Lui , S. Seki , and Y. Yoshikuni , “ The Second-Order Condition for the Dielectric Interface Orthogonal to the Yee-Lattice Axis in the FDTD Scheme ,” IEEE Microwave Guided Wave Lett. 10 , 359 – 361 ( 2000 ). [CrossRef]
23 . K.-P. Hwang and A.C. Cangellaris , “ Effective Permittivities for Second-Order Accurate FDTD Equations at Dielectric Interfaces ,” IEEE Microwave Wireless Comp. Lett. 11 , 158 – 160 ( 2001 ). [CrossRef]
22 . T. Hirono , Y. Shibata , W.W. Lui , S. Seki , and Y. Yoshikuni , “ The Second-Order Condition for the Dielectric Interface Orthogonal to the Yee-Lattice Axis in the FDTD Scheme ,” IEEE Microwave Guided Wave Lett. 10 , 359 – 361 ( 2000 ). [CrossRef]
23 . K.-P. Hwang and A.C. Cangellaris , “ Effective Permittivities for Second-Order Accurate FDTD Equations at Dielectric Interfaces ,” IEEE Microwave Wireless Comp. Lett. 11 , 158 – 160 ( 2001 ). [CrossRef]
21 . N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD Analysis of Dielectric Resonators with Curved Surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef]
30 . J.-Y. Lee and N.-H. Myung , “ Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces ,” Microw. Opt. Technol. Lett. 23 , 245 – 249 ( 1999 ). [CrossRef]
31 . J. Nadobny , D. Sullivan , W. Wlodarczyk , P. Deuflhard , and P. Wust , “ A 3-D Tensor FDTD-Formulation for Treatment of Slopes Interfaces in Electrically Inhomogeneous Media ,” IEEE Trans. Antennas Propag. 51 , 1760 – 1770 ( 2003 ). [CrossRef]
30 . J.-Y. Lee and N.-H. Myung , “ Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces ,” Microw. Opt. Technol. Lett. 23 , 245 – 249 ( 1999 ). [CrossRef]
3. Numerical Tests and Discussion
40 . A. Kirchner , K. Busch , and C.M. Soukoulis , “ Transport properties of random arrays of dielectric cylinders ,” Phys. Rev. B 57 , 277 – 288 ( 1998 ). [CrossRef]
4. Conclusion
33 . A. Ditkowski , K. Dridi , and J.S. Hesthaven , “ Convergent Cartesian Grid Methods for Maxwell’s Equations in Complex Geometries ,” J. Comp. Phys. 170 , 39 – 80 ( 2001 ). [CrossRef]
Acknowledgments
References and links
1 . | Proceedings of the Fifth International Symposium on Photonic and Electromagnetic Crystal Structures (PECS-V) ( Kyoto, Japan , March 7 – 11 , 2004 ); H. Benisty , S. Kawakami , D.J. Norris , and C.M. Soukoulis , eds, Phot. Nanostructures Fund. Appl . 2 , 57 – 159 ( 2004 ); [CrossRef] C. Jagadish , D.G. Deppe , S. Noda , T.F. Krauss , and O.J. Painter , eds, IEEE J. Sel. Top. Area Commun. 23 , 1305 – 1423 ( 2005 ). |
2 . | Special issue on nanostructured optical meta-materials: beyond photonic band gap effects , N. Zheludev and V. Shalaev , eds., J. Opt. A: Pure and Applied Optics , 7 , S1 – S254 ( 2005 ). [CrossRef] |
3 . | Proceedings of the EOS Topical Meeting on Advanced Optical Imaging Techniques , ( London, UK , June 29 - July 1, 2005 ). |
4 . | M.V.K. Chari and S.J. Salon , Numerical methods in electromagnetism ( Academic Press, San Diego, CA , 2000 ) |
5 . | K.S. Yee , “ Numerical Solution of Initial Boundary Value Problems involving Maxwell’s Equations in Isotropic Media ,” IEEE Trans. Antennas Propag. AP-14 , 302 – 307 ( 1966 ). |
6 . | A. Taflove and S.C. Hagness , Computational Electrodynamics: The Finite-Difference Time-Domain Method ( Artech House, Norwood, MA , 2005 ). |
7 . | K.K. Mei , A. Cangellaris , and D.J. Angelakos , “ Conformal Time Domain Finite-Difference Method ,” Radio Sci. 19 , 1145 – 1147 ( 1984 ). [CrossRef] |
8 . | R. Holland , “ Finite-Difference Solution of Maxwell’s Equations in Generalized Nonorthogonal Coordinates ,” IEEE Trans. Nucl. Sci. NS-30 , 4589 – 4591 ( 1983 ). [CrossRef] |
9 . | M. Fusco , “ FDTD Algorithm in Curvilinear Coordinates ,” IEEE Trans. Antennas Propag. 38 , 76 – 89 ( 1990 ). [CrossRef] |
10 . | V. Shankar , A. Mohammadian , and W.F. Hall , “ A Time-Domain Finite-Volume Treatment for the Maxwell Equations ,” Electromagnetics 10 , 127 – 145 ( 1990 ). [CrossRef] |
11 . | N.K. Madsen and R.W. Ziolkowski , “ A Three-Dimensional Modified Finite Volume Technique for Maxwell’s Equations ,” Electromagnetics 10 , 147 – 161 ( 1990 ). [CrossRef] |
12 . | P.H. Harms , J.-F. Lee , and R. Mittra , “ A Study of the Nonorthogonal FDTD Method Versus the Conventional FDTD Technique for Computing Resonant Frequencies of Cylindrical Cavities ,” IEEE Trans. Microwave Theory Tech. 40 , 741 – 476 ( 1992 ). [CrossRef] |
13 . | T.G. Jurgens , A. Taflove , K. Umashankar , and T.G. Moore , “ Finite-Difference Time-Domain Modeling of Curved Surfaces ,” IEEE Trans. Antennas Propag. 40 , 357 – 365 ( 1992 ). [CrossRef] |
14 . | T.G. Jurgens and A. Taflove , “ Three-Dimensional Contour FDTD Modeling of Scattering from Single and Multiple Bodies ,” IEEE Trans. Antennas Propag. 41 , 1703 – 1708 ( 1993 ). [CrossRef] |
15 . | C.J. Railton , I.J. Craddock , and J.B. Schneider , “ Improved locally distorted CPFDTD algorithm with provable stability ,” Electron. Lett. 31 , 1585 – 1586 ( 1995 ). [CrossRef] |
16 . | Y. Hao and C.J. Railton , “ Analyzing Electromagnetic Structures with Curved Boundaries on Cartesian FDTD Meshes ,” IEEE Trans. Microwave Theory Tech. 46 , 82 – 88 ( 1998 ). [CrossRef] |
17 . | T.I. Kosmanis and T.D. Tsiboukis , “ A Systematic and Topologically Stable Conformal Finite-Difference Time-Domain Algorithm for Modeling Curved Dielectric Interfaces in Three Dimensions ,” IEEE Trans. Microwave Theory Tech. 51 , 839 – 847 ( 2003 ). [CrossRef] |
18 . | I.S. Kim and W.J.R. Hoefer , “ A Local Mesh Refinement Algorithm for the Time Domain-Finite Difference Method Using Maxwell’s Curl Equations ,” IEEE Trans. Microwave Theory Tech. 38 , 812 – 815 ( 1990 ). [CrossRef] |
19 . | S.S. Zivanovic , K.S. Yee , and K.K. Mei , “ A Subgridding Method for the Time-Domain Finite-Difference Method to Solve Maxwell’s Equations ,” IEEE Trans. Microwave Theory Tech. 39 , 471 – 479 ( 1991 ). [CrossRef] |
20 . | J.G. Maloney and G.S. Smith , “ The Efficient Modeling of Thin Material Sheets in the Finite-Difference Time-Domain (FDTD) Method ,” IEEE Trans. Antennas Propag. 40 , 323 – 330 ( 1992 ). [CrossRef] |
21 . | N. Kaneda , B. Houshmand , and T. Itoh , “ FDTD Analysis of Dielectric Resonators with Curved Surfaces ,” IEEE Trans. Microwave Theory Tech. 45 , 1645 – 1649 ( 1997 ). [CrossRef] |
22 . | T. Hirono , Y. Shibata , W.W. Lui , S. Seki , and Y. Yoshikuni , “ The Second-Order Condition for the Dielectric Interface Orthogonal to the Yee-Lattice Axis in the FDTD Scheme ,” IEEE Microwave Guided Wave Lett. 10 , 359 – 361 ( 2000 ). [CrossRef] |
23 . | K.-P. Hwang and A.C. Cangellaris , “ Effective Permittivities for Second-Order Accurate FDTD Equations at Dielectric Interfaces ,” IEEE Microwave Wireless Comp. Lett. 11 , 158 – 160 ( 2001 ). [CrossRef] |
24 . | S. Dey and R. Mittra , “ A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators ,” IEEE Trans. Microwave Theory Tech. 47 , 1737 – 1739 ( 1999 ). [CrossRef] |
25 . | W. Yu and R. Mittra , “ On the modeling of periodic structures using the finite-difference time-domain algorithm ,” Microw. Opt. Technol. Lett. 24 , 151 – 155 ( 2000 ). [CrossRef] |
26 . | P. Yang , G.W. Kattawar , K.-N. Liou , and J.Q. Lu , “ Comparison of Cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles ,” Appl. Opt. 43 , 4611 – 4624 ( 2004 ). [CrossRef] [PubMed] |
27 . | P. Yang , K.N. Liou , M.I. Mishchenko , and B.-C. Gao , “ Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols , Appl. Opt. 39 , 3727 – 3737 ( 2000 ). [CrossRef] |
28 . | W. Yu and R. Mittra , “ A Conformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces ,” IEEE Microwave Wireless Comp. Lett. 11 , 25 – 27 ( 2001 ). [CrossRef] |
29 . | W. Sun and Q. Fu “ Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices ,” Appl. Opt. 39 , 5569 ( 2000 ). [CrossRef] |
30 . | J.-Y. Lee and N.-H. Myung , “ Locally tensor conformal FDTD method for modeling arbitrary dielectric surfaces ,” Microw. Opt. Technol. Lett. 23 , 245 – 249 ( 1999 ). [CrossRef] |
31 . | J. Nadobny , D. Sullivan , W. Wlodarczyk , P. Deuflhard , and P. Wust , “ A 3-D Tensor FDTD-Formulation for Treatment of Slopes Interfaces in Electrically Inhomogeneous Media ,” IEEE Trans. Antennas Propag. 51 , 1760 – 1770 ( 2003 ). [CrossRef] |
32 . | K.H. Dridi , J.S. Hesthaven , and A. Ditkowski , “ Staircase-Free Finite-Difference Time-Domain Formulation for General Materials in Complex Geometries ,” IEEE Trans. Antennas Propag. 49 , 749 – 756 ( 2001 ). [CrossRef] |
33 . | A. Ditkowski , K. Dridi , and J.S. Hesthaven , “ Convergent Cartesian Grid Methods for Maxwell’s Equations in Complex Geometries ,” J. Comp. Phys. 170 , 39 – 80 ( 2001 ). [CrossRef] |
34 . | M. Fujii , D. Lukashevich , I. Sakagami , and P. Russer , “ Convergence of FDTD and Wavelet-Collocation Modeling of Curved Dielectric Interface with the Effective Dielectric Constant Technique ,” IEEE Microwave Wireless Comp. Lett. 13 , 469 – 471 ( 2003 ). [CrossRef] |
35 . | T. Xiao and Q.H. Liu , “ A Staggered Upwind Embedded Boundary (SUEB) Method to Eliminate the FDTD Staircasing Error ,” IEEE Trans. Antennas Propag. 52 , 730 – 740 ( 2004 ). [CrossRef] |
36 . | C.F. Bohren and D.R. Huffman , Absorption and Scattering of Light by Small Particles ( Wiley Interscience, New York , 1983 ). |
37 . | A. Bossavit , “ Generalized finite differences in computational electromagnetics ,” Progress in Electromagnetic Research, PIER 32 , 45 – 64 ( 2001 ). [CrossRef] |
38 . | K.L. Shlager and J.B. Schneider , “ Comparison of the Dispersion Properties of Several Low-Dispersion Finite-Difference Time-Domain Algorithms ,” IEEE Trans. Antennas Propag. 51 , 642 – 652 ( 2003 ). [CrossRef] |
39 . | J.A. Roden and S.D. Gedney , “ Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media ,” Microw. Opt. Technol. Lett. 27 , 334 – 339 ( 2000 ). [CrossRef] |
40 . | A. Kirchner , K. Busch , and C.M. Soukoulis , “ Transport properties of random arrays of dielectric cylinders ,” Phys. Rev. B 57 , 277 – 288 ( 1998 ). [CrossRef] |
OCIS Codes
(000.4430) General : Numerical approximation and analysis
(260.5740) Physical optics : Resonance
(290.0290) Scattering : Scattering
ToC Category:
Research Papers
Citation
Ahmad Mohammadi, Hamid Nadgaran, and Mario Agio, "Contour-path effective permittivities for the two-dimensional finite-difference time-domain method," Opt. Express 13, 10367-10381 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-25-10367
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References
- Proceedings of the Fifth International Symposium on Photonic and Electromagnetic Crystal Structures (PECSV) (Kyoto, Japan, March 7-11, 2004); H. Benisty, S. Kawakami, D.J. Norris, and C.M. Soukoulis, eds, Phot. Nanostructures Fund. Appl. 2, 57-159 (2004); C. Jagadish, D.G. Deppe, S. Noda, T.F. Krauss, and O.J. Painter, eds, IEEE J. Sel. Top. Area Commun. 23, 1305-1423 (2005). [CrossRef]
- Special issue on nanostructured optical meta-materials: beyond photonic band gap effects, N. Zheludev, and V. Shalaev, eds., J. Opt. A: Pure and Applied Optics, 7, S1-S254 (2005). [CrossRef]
- Proceedings of the EOS Topical Meeting on Advanced Optical Imaging Techniques, (London, UK, June 29 - July 1, 2005).
- M.V.K. Chari, and S.J. Salon, Numerical methods in electromagnetism (Academic Press, San Diego, CA, 2000)
- K.S. Yee, "Numerical Solution of Initial Boundary Value Problems involving Maxwell's Equations in Isotropic Media," IEEE Trans. Antennas Propag. AP-14, 302-307 (1966).
- A. Taflove, and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 2005).
- K.K. Mei, A. Cangellaris, and D.J. Angelakos, "Conformal Time Domain Finite-Difference Method," Radio Sci. 19, 1145-1147 (1984). [CrossRef]
- R. Holland, "Finite-Difference Solution of Maxwell's Equations in Generalized Nonorthogonal Coordinates," IEEE Trans. Nucl. Sci. NS-30, 4589-4591 (1983). [CrossRef]
- M. Fusco, "FDTD Algorithm in Curvilinear Coordinates," IEEE Trans. Antennas Propag. 38, 76-89 (1990). [CrossRef]
- V. Shankar, A. Mohammadian, andW.F. Hall, "A Time-Domain Finite-Volume Treatment for the Maxwell Equations," Electromagnetics 10, 127-145 (1990). [CrossRef]
- N.K. Madsen, and R.W. Ziolkowski, "A Three-Dimensional Modified Finite Volume Technique for Maxwell's Equations," Electromagnetics 10, 147-161 (1990). [CrossRef]
- P.H. Harms, J.-F. Lee, and R. Mittra, "A Study of the Nonorthogonal FDTD Method Versus the Conventional FDTD Technique for Computing Resonant Frequencies of Cylindrical Cavities," IEEE Trans. Microwave Theory Tech. 40, 741-476 (1992). [CrossRef]
- T.G. Jurgens, A. Taflove, K. Umashankar, and T.G. Moore, "Finite-Difference Time-Domain Modeling of Curved Surfaces," IEEE Trans. Antennas Propag. 40, 357-365 (1992). [CrossRef]
- T.G. Jurgens, and A. Taflove, "Three-Dimensional Contour FDTD Modeling of Scattering from Single and Multiple Bodies," IEEE Trans. Antennas Propag. 41, 1703-1708 (1993). [CrossRef]
- C.J. Railton, I.J. Craddock, and J.B. Schneider, "Improved locally distorted CPFDTD algorithm with provable stability," Electron. Lett. 31, 1585-1586 (1995). [CrossRef]
- Y. Hao, and C.J. Railton, "Analyzing Electromagnetic Structures with Curved Boundaries on Cartesian FDTD Meshes," IEEE Trans. Microwave Theory Tech. 46, 82-88 (1998). [CrossRef]
- T.I. Kosmanis, and T.D. Tsiboukis, "A Systematic and Topologically Stable Conformal Finite-Difference Time- Domain Algorithm for Modeling Curved Dielectric Interfaces in Three Dimensions," IEEE Trans. Microwave Theory Tech. 51, 839-847 (2003). [CrossRef]
- I.S. Kim, and W.J.R. Hoefer, "A Local Mesh Refinement Algorithm for the Time Domain-Finite Difference Method Using Maxwell's Curl Equations," IEEE Trans. Microwave Theory Tech. 38, 812-815 (1990). [CrossRef]
- S.S. Zivanovic, K.S. Yee, and K.K. Mei, "A Subgridding Method for the Time-Domain Finite-Difference Method to Solve Maxwell's Equations," IEEE Trans. Microwave Theory Tech. 39, 471-479 (1991). [CrossRef]
- J.G. Maloney, and G.S. Smith, "The Efficient Modeling of Thin Material Sheets in the Finite-Difference Time- Domain (FDTD) Method," IEEE Trans. Antennas Propag. 40, 323-330 (1992). [CrossRef]
- N. Kaneda, B. Houshmand, and T. Itoh, "FDTD Analysis of Dielectric Resonators with Curved Surfaces," IEEE Trans. Microwave Theory Tech. 45, 1645-1649 (1997). [CrossRef]
- T. Hirono, Y. Shibata, W.W. Lui, S. Seki, and Y. Yoshikuni, "The Second-Order Condition for the Dielectric Interface Orthogonal to the Yee-Lattice Axis in the FDTD Scheme," IEEE Microwave Guided Wave Lett. 10, 359-361 (2000). [CrossRef]
- K.-P. Hwang, and A.C. Cangellaris, "Effective Permittivities for Second-Order Accurate FDTD Equations at Dielectric Interfaces," IEEE Microwave Wireless Comp. Lett. 11, 158-160 (2001). [CrossRef]
- S. Dey, and R. Mittra, "A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonators," IEEE Trans. Microwave Theory Tech. 47, 1737-1739 (1999). [CrossRef]
- W. Yu, and R. Mittra, "On the modeling of periodic structures using the finite-difference time-domain algorithm," Microw. Opt. Technol. Lett. 24, 151-155 (2000). [CrossRef]
- P. Yang, G.W. Kattawar, K.-N. Liou, and J.Q. Lu, "Comparison of Cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles," Appl. Opt. 43, 4611-4624 (2004). [CrossRef] [PubMed]
- P. Yang, K.N. Liou, M.I. Mishchenko, and B.-C. Gao, "Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols," Appl. Opt. 39, 3727-3737 (2000). [CrossRef]
- W. Yu, and R. Mittra, "A Conformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces," IEEE Microwave Wireless Comp. Lett. 11, 25-27 (2001). [CrossRef]
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