volume | PIER Journals

Abstract

This paper presents a dispersive finite difference time domain (FDTD) method suitable for the analysis of electromagnetic field rotator (and cloaking) devices. The method employs a coordinate transformation which accurately accounts for the radial dependence of the permittivity and permeability tensors, with Drude material models applied to the respective diagonal elements. The key aspect of the present formulation is the inclusion of the radial dependence of the plasma frequency, which makes this formalism quite attractive for the modeling of a general class of cloaking and field rotator geometries. Firstly, the method is validated by comparing its results with a previously published simulation of a cloaking device. Then, it is applied for the first time to the analysis of dispersive effects on the performance of field rotators.

1. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, June 2006.
doi:10.1126/science.1125907

2. Schurig, D., J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science, Vol. 314, 977-980, Nov. 2006.
doi:10.1126/science.1133628

3. Schurig, D., J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express, Vol. 14, 9794-9804, Oct. 2006.
doi:10.1364/OE.14.009794

4. Zhang, J. J., Y. Luo, H. S. Chen, and B.-I. Wu, "Sensitivity of transformation cloak in engineering," Progress In Electromagnetics Research, Vol. 84, 93-104, 2008.
doi:10.2528/PIER08071301

5. Tsang, M. and D. Psaltis, "Magnifying perfect lens and superlens design by coordinate transformation," Phys. Rev. B, Vol. 77, 035122, 2008.
doi:10.1103/PhysRevB.77.035122

6. Kildishev, A. V. and E. E. Narimanov, "Impedance-matched hyperlens," Opt. Letters, Vol. 32, 3432-3434, Nov. 2007.
doi:10.1364/OL.32.003432

7. Rahm, M., D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations," Phot. Nanostruc. Fund. and Appl., Vol. 6, 87-95, Aug. 2007.
doi:10.1016/j.photonics.2007.07.013

8. Yaghjian, A. D. and S. Maci, "Alternative derivation of electromagnetic cloaks and concentrators," arXiv:0710.2933, 2007.

9. Luo, Y., H. Chen, J. Zhang, L. Ran, and J. A. Kong, "Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations," Phys. Rev. Appl., Vol. 77, 125127/1-125127/8, Mar. 2008.

10. Chen, H. and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Letters, Vol. 90, 241105/1-241105/3, June 2007.

11. Chen, H., Z. Liang, P. Yao, X. Jiang, H. Ma, and C. T. Chan, "Extending the bandwidth of electromagnetic cloaks," Phys. Review B, Vol. 76, 241104/1-241104/4, Dec. 2007.

12. Silva-Macedo, J. A., M. A. Romero, and B.-H. V. Borges, "Improved FDTD formalism for electromagnetic cloaking applications," 13th IEEE Conference on Electromagnetic Field Computation --- CEFC 2008, 464, May 2008.

13. Zhao, Y., C. Argyropoulos, and H. Yang, "Dispersive finite-difference time-domain simulation of electromagnetic cloaking devices," Antennas andPr opagation Conference, 2008. LAPC 2008. Loughborough, 429-432, March 2008.
doi:10.1109/LAPC.2008.4516958

14. Argyropoulos, C., Y. Zhao, and Y. Hao, "A radial-dependent dispersive finite-difference time-domain method for evaluation of electromagnetic cloaks," arXiv:0805.2050v1, May 14 2008.

15. Prokopidis, K. P., E. P. Kosmidou, and T. D. Tsiboukis, "An FDTD algorithm for wave propagation in dispersive media using higher-order schemes," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 9, 1171-1194, 2004.
doi:10.1163/1569393042955306

16. Taflove, A. and S. C. Hagness, Computational Electrodynamics the Finite-difference Time Domain Method, Artech House, 2005.

Dr. Jorge Andrey Silva-Macêdo

Dr. Murilo Araujo Romero

Dr. Ben-Hur Viana Borges