OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 16 — Aug. 1, 2011
  • pp: 15119–15126

General conformal transformation method based on Schwarz-Christoffel approach

Linlong Tang, Jinchan Yin, Guishan Yuan, Jinglei Du, Hongtao Gao, Xiaochun Dong, Yueguang Lu, and Chunlei Du  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 15119-15126 (2011)
http://dx.doi.org/10.1364/OE.19.015119


View Full Text Article

Enhanced HTML    Acrobat PDF (1104 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A general conformal transformation method (CTM) is proposed to construct the conformal mapping between two irregular geometries. In order to find the material parameters corresponding to the conformal transformation between two irregular geometries, two polygons are utilized to approximate the two irregular geometries, and an intermediate geometry is used to connect the mapping relations between the two polygons. Based on these manipulations, the approximate material parameters for TE and TM waves are finally obtained by calculating the Schwarz-Christoffel (SC) mappings. To demonstrate the validity of the method, a phase modulator and a plane focal surface Luneburg lens are designed and simulated by the finite element method. The results show that the conformal transformation can be expanded to the cases that the transformed objects are with irregular geometries.

© 2011 OSA

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(230.0230) Optical devices : Optical devices
(260.2110) Physical optics : Electromagnetic optics
(260.2710) Physical optics : Inhomogeneous optical media

ToC Category:
Physical Optics

History
Original Manuscript: May 10, 2011
Revised Manuscript: June 24, 2011
Manuscript Accepted: June 26, 2011
Published: July 21, 2011

Citation
Linlong Tang, Jinchan Yin, Guishan Yuan, Jinglei Du, Hongtao Gao, Xiaochun Dong, Yueguang Lu, and Chunlei Du, "General conformal transformation method based on Schwarz-Christoffel approach," Opt. Express 19, 15119-15126 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15119


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
  3. 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(5801), 977–980 (2006). [CrossRef] [PubMed]
  4. M. Rahm, 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. 100(6), 063903 (2008). [CrossRef] [PubMed]
  5. M. Tsang and D. Psaltis, “Magnifying perfect lens and superlens design by coordinate transformation,” Phys. Rev. B 77(3), 035122 (2008). [CrossRef]
  6. G. Yuan, X. Dong, Q. Deng, H. Gao, C. Liu, Y. Lu, and C. Du, “A design method to change the effective shape of scattering cross section for PEC objects based on transformation optics,” Opt. Express 18(6), 6327–6332 (2010). [CrossRef] [PubMed]
  7. N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17(17), 14872–14879 (2009). [CrossRef] [PubMed]
  8. Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27(5), 968–972 (2010). [CrossRef] [PubMed]
  9. J. P. Turpin, A. T. Massoud, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Conformal mappings to achieve simple material parameters for transformation optics devices,” Opt. Express 18(1), 244–252 (2010). [CrossRef] [PubMed]
  10. M. Schmiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81(3), 033837 (2010). [CrossRef]
  11. C. Ren, Z. Xiang, and Z. Cen, “Design of acoustic devices with isotropic material via conformal transformation,” Appl. Phys. Lett. 97(4), 044101 (2010). [CrossRef]
  12. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008). [CrossRef] [PubMed]
  13. T. A. Driscoll, “A MATLAB toolbox for Schwarz-Christoffel mapping,” ACM Trans. Math. Softw. 22(2), 168–186 (1996). [CrossRef]
  14. T. A. Driscoll and L. N. Trefethen, Schwartz-Christoffel Mapping (Cambridge University Press, 2002).
  15. P. Henrici, Applied and Computational Complex Analysis, Volume 3: Discrete Fourier Analysis, Cauchy Integrals, Construction of Conformal Maps, Univalent Functions (Wiley, 1986).
  16. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011), doi:. [CrossRef] [PubMed]
  17. A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express 19(6), 5156–5162 (2011). [CrossRef] [PubMed]

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