OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 1 — Jan. 1, 2013
  • pp: 140–148

Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach

Yong Yoon Lee and Doyeol Ahn  »View Author Affiliations

JOSA B, Vol. 30, Issue 1, pp. 140-148 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1181 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A dispersive full-wave finite-difference time-domain model is used to study the performance of bipolar cylindrical invisibility cloaking devices. We have considered two different cloaking structures generated by the mapping of the σ axis and the mapping of the τ axis of bipolar coordinates. The permittivity and permeability tensors for the cloaking devices are obtained from an effective medium approach in general relativity. The σ-axis mapped bipolar cylindrical cloak is found to be imperfect, and the cloaking performance is found to depend on the polarization of the incident waves, the direction of propagation of the waves, and the loss tangents of the metamaterial. Only the case of TM waves for the specific propagation direction shows good cloaking performance. On the other hand, the τ-mapped cloaking device shows good cloaking performance for all polarizations and directions of propagation. However, this structure has a singular boundary at the inner radius. Realistic cloaking materials with loss still show a cloak that is working, but attenuated backscattering waves exist.

© 2012 Optical Society of America

OCIS Codes
(000.2780) General : Gravity
(350.6980) Other areas of optics : Transforms
(160.3918) Materials : Metamaterials
(260.2710) Physical optics : Inhomogeneous optical media
(230.3205) Optical devices : Invisibility cloaks

ToC Category:

Original Manuscript: September 19, 2012
Revised Manuscript: October 22, 2012
Manuscript Accepted: November 1, 2012
Published: December 13, 2012

Yong Yoon Lee and Doyeol Ahn, "Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach," J. Opt. Soc. Am. B 30, 140-148 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef]
  2. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006). [CrossRef]
  3. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006). [CrossRef]
  4. J. Yang, M. Huang, C. Yang, Z. Xiao, and J. Peng, “Metamaterial electromagnetic concentrators with arbitrary geometries,” Opt. Express 17, 19656–19661 (2009). [CrossRef]
  5. H. Chen, C. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010). [CrossRef]
  6. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006). [CrossRef]
  7. D. Ahn, “Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity,” J. Mod. Opt. 58, 700–710 (2011). [CrossRef]
  8. Y. Y. Lee and D. Ahn, “Dispersive finite-difference time-domain analysis of the elliptic cylindrical cloak,” J. Korean Phys. Soc. 60, 1349–1360 (2012). [CrossRef]
  9. I. Tamm, “Electrodynamics of an anisotropic medium in the special theory of relativity,” J. Russ. Phys. Chem. Soc. 56, 248 (1924).
  10. J. Plebanski, “Electromagnetic waves in gravitational fields,” Phys. Rev. 118, 1396–1408 (1960). [CrossRef]
  11. A. Lakhtakia and T. G. Mackay, “Toward gravitationally assisted negative refraction of light by vacuum,” J. Phys. A 37, L505–L510 (2004). [CrossRef]
  12. T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005). [CrossRef]
  13. T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009). [CrossRef]
  14. M. W. Mccall, “On negative refraction in classical vacuum,” J. Mod. Opt. 54, 119–128 (2007). [CrossRef]
  15. M. W. McCall, “Classical gravity does not refract negatively,” Phys. Rev. Lett. 98, 091102 (2007). [CrossRef]
  16. H. Chen and C. Chan, “‘Cloaking at a distance’ from folded geometries in bipolar coordinates,” Opt. Lett. 34, 2649–2651 (2009). [CrossRef]
  17. U. Leonhardt and T. Tyc, “Broadband invisibility by nonEuclidean cloaking,” Science 323, 110–112 (2009). [CrossRef]
  18. J. Perczel, T. Tyc, and U. Leonhardt, “Invisibility cloaking without superluminal propagation,” New J. Phys. 13, 083007 (2011). [CrossRef]
  19. E. Cojocaru, “Exact analytical approaches for elliptic cylindrical invisibility cloaks,” J. Opt. Soc. Am. B 26, 1119–1128 (2009). [CrossRef]
  20. Y. Luo, J. Zhang, H. Chen, L. Ran, B. I. Wu, and J. A. Kong, “A rigorous analysis of plane-transformed invisibility cloaks,” IEEE Trans. Antennas Propag. 57, 3926–3933 (2009). [CrossRef]
  21. D. H. Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008). [CrossRef]
  22. W. X. Jiang, T. T. Cui, G. X. Yu, X. Q. Lin, Q. Cheng, and J. Y. Chin, “Arbitrarily elliptical-cylindrical invisibe cloaking,” J. Phys. D 41, 085504 (2008). [CrossRef]
  23. H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008). [CrossRef]
  24. J. Jin, J. Jin, and J. M. Jin, The Finite Element Method in Electromagnetics (Wiley, 1993).
  25. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 1995).
  26. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).
  27. Y. Hao and R. Mittra , FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2009).
  28. E. Lifshitz, L. Pitaevskii, and L. Landau, Electrodynamics of Continuous Media (Butterworth-Heinemann, 1984), Vol. 8.
  29. J. Pendry, A. Holden, W. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996). [CrossRef]
  30. J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]
  31. Y. Zhao, C. Argyropoulos, and Y. Hao, “Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures,” Opt. Express 16, 6717–6730 (2008). [CrossRef]
  32. Z. Liang, P. Yao, X. Sun, and X. Jiang, “The physical picture and essential elements of the dynamical process for dispersive cloaking structures,” Appl. Phys. Lett. 92, 131118 (2008). [CrossRef]
  33. C. Argyropoulos, E. Kallos, and Y. Hao, “Dispersive cylindrical cloaks under nonmonochromatic illumination,” Phys. Rev. E 81, 016611 (2010). [CrossRef]
  34. C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antennas Propag. 57, 1432–1441 (2009). [CrossRef]
  35. Y. Y. Lee and D. Ahn, “Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak,” J. Korean Phys. Soc. 60, 1349–1360 (2012). [CrossRef]
  36. B. Kante, D. Germain, and A. Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104(R) (2009). [CrossRef]
  37. D. Schurig, 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 314, 977–980 (2006). [CrossRef]
  38. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369(2009). [CrossRef]
  39. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571(2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited