2009-11-18
Determination the Material Parameters for Arbitrary Cloak Based on Poisson's Equation
By
Progress In Electromagnetics Research M, Vol. 9, 177-184, 2009
Abstract
We propose a general method to determine the material parameters for arbitrary shapes of cloak based on the Poisson's equation to map the coordinate transformation. As a result, we can obtain the diverse deformation material properties and then the field distribution. This method, compared with the previous technique presented in literature, can determine the countless transformation forms, so it may provide the opportunity to choose the optimization transformation and the material parameter map which is easily to be fabricated using the metamaterial technology.
Citation
Jia-Jun Ma, Xiang-Yu Cao, Kan-Min Yu, and Tao Liu, "Determination the Material Parameters for Arbitrary Cloak Based on Poisson's Equation," Progress In Electromagnetics Research M, Vol. 9, 177-184, 2009.
doi:10.2528/PIERM09091405
References

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

2. Leonhardt, U., "Optical conformal mapping," Science, Vol. 312, 1777-1780, 2006.
doi:10.1126/science.1126493        Google Scholar

3. Cummer, S. A., B. I. Popa, D. S. Schurig, and D. R. Smith, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E, Vol. 74, 036621, 2006.
doi:10.1103/PhysRevE.74.036621        Google Scholar

4. Rahm, M., D. Schurig, D. A. Roberts, S. A. Cummer, and D. R. Smith, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations," Photon. Nanostruct. Fundam. Appl., Vol. 6, No. 87, 2008.        Google Scholar

5. Kwon, D. H. and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett., Vol. 92, 013505, 2008.
doi:10.1063/1.2830698        Google Scholar

6. Ma, H., S. B. Qu, Z. Xu, J. Q. Zhang, B. W. Chen, and J. F.Wang, "Material parameter equation for elliptical cylindrical cloaks," Phys. Rev. A, Vol. 77, 013825, 2008.
doi:10.1103/PhysRevA.77.013825        Google Scholar

7. Rahm, M., D. A. Roberts, J. B. Pendry, and D. R. Smith, "Transformation-optical design of adaptive beam bends and beam expanders," Opt. Express, Vol. 16, 11555, 2008.
doi:10.1364/OE.16.011555        Google Scholar

8. Lin, L., W. Wang, J. H. Cui, C. Du, and X. G. Luo, "Design of electromagnetic refractor and phase transformaer using coordinate transformation theory," Opt. Express, Vol. 16, 6815, 2008.
doi:10.1364/OE.16.006815        Google Scholar

9. Rahm, M., S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett., Vol. 100, 063903, 2008.
doi:10.1103/PhysRevLett.100.063903        Google Scholar

10. Jiang, W. X., J. Y. Chin, Z. Li, Q. Cheng. R. P. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E, Vol. 77, 066607, 2008.        Google Scholar

11. Jiang, W. X., T. J. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, "Arbitrarily elliptical-cylindrical invisible cloaking," Appl. Phys., Vol. 41, 085504, 2008.        Google Scholar

12. Ma, H., S. B. Qu, Z. Xu, and J. F. Wang, "Numerical method for designing approximate cloaks with arbitrary shapes," Phys. Rev. E, Vol. 78, 036608, 2008.
doi:10.1103/PhysRevE.78.036608        Google Scholar

13. Hu, J., X. M. Zhou, and G. K. Hu, "Design method for electromagnetic cloak with arbitrary shapes based on Laplace's equation," Opt. Express, Vol. 17, 1308, 2009.
doi:10.1364/OE.17.001308        Google Scholar

14. Cai, W. S., U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Nonmagnetic cloak with minimized scattering," Appl. Phys. Lett., Vol. 91, 111105, 2007.
doi:10.1063/1.2783266        Google Scholar