## Metamaterial electromagnetic concentrators with arbitrary geometries

Optics Express, Vol. 17, Issue 22, pp. 19656-19661 (2009)

http://dx.doi.org/10.1364/OE.17.019656

Acrobat PDF (270 KB)

### Abstract

The electromagnetic concentrators play an important role in the harnessing of light in solar cells or similar devices, where high field intensities are required. The material parameters for two-dimensional (2D) metamaterial-assisted electromagnetic concentrators with arbitrary geometries are derived based on transformation-optical approach. Enhancements in field intensities of the 2D concentrator have been shown by full-wave simulation. All theoretical and numerical results validate the material parameters for the 2D concentrator with irregular cross section we developed.

© 2009 OSA

## 1. Introduction

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science **312**(5781), 1780–1782 (2006). [CrossRef] [PubMed]

6. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. **8**(7), 568–571 (2009). [CrossRef] [PubMed]

7. P. Alitalo and S. Tretyakov, “Electromagnetic cloaking with metamaterials,” Mater. Today **12**(3), 22–29 (2009). [CrossRef]

8. Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. **102**(25), 253902 (2009). [CrossRef] [PubMed]

9. M. Rahm, 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,” Photonics and Nanostructures-Fundamentals and Applications **6**, 89 (2008). [CrossRef]

10. 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]

11. H. Y. Chen, X. D. Luo, H. R. Ma, and C. T. Chan, “The anti-cloak,” Opt. Express **16**(19), 14603–14608 (2008). [CrossRef] [PubMed]

12. T. Yang, H. Y. Chen, X. D. Luo, and H. R. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express **16**(22), 18545–18550 (2008). [CrossRef] [PubMed]

13. J. Ng, H. Y. Chen, and C. T. Chan, “Metamaterial frequency-selective superabsorber,” Opt. Lett. **34**(5), 644–646 (2009). [CrossRef] [PubMed]

14. Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. **102**(9), 093901 (2009). [CrossRef] [PubMed]

15. A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. **102**(23), 233901 (2009). [CrossRef] [PubMed]

9. M. Rahm, 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,” Photonics and Nanostructures-Fundamentals and Applications **6**, 89 (2008). [CrossRef]

16. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express **16**(26), 21793–21800 (2008). [CrossRef] [PubMed]

9. M. Rahm, 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,” Photonics and Nanostructures-Fundamentals and Applications **6**, 89 (2008). [CrossRef]

17. C. Li, K. Yao, and F. Li, “Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries,” Opt. Express **16**(23), 19366–19374 (2008). [CrossRef]

## 2. Theoretical model

_{1}, S

_{2}and S

_{3}. The space is compressed into S

_{1}at the expense of an expansion of space in regions S

_{2}and S

_{3}. Here,

17. C. Li, K. Yao, and F. Li, “Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries,” Opt. Express **16**(23), 19366–19374 (2008). [CrossRef]

18. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express **14**(21), 9794–9804 (2006). [CrossRef] [PubMed]

19. C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express **16**(17), 13414 (2008). [CrossRef] [PubMed]

## 3. Simulation results and discussion

**6**, 89 (2008). [CrossRef]

## 6. Conclusion

## Acknowledgments

## References and links

1. | J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science |

2. | U. Leonhardt, “Optical conformal mapping,” Science |

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 |

4. | U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science |

5. | R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science |

6. | J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. |

7. | P. Alitalo and S. Tretyakov, “Electromagnetic cloaking with metamaterials,” Mater. Today |

8. | Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. |

9. | M. Rahm, 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,” Photonics and Nanostructures-Fundamentals and Applications |

10. | 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. |

11. | H. Y. Chen, X. D. Luo, H. R. Ma, and C. T. Chan, “The anti-cloak,” Opt. Express |

12. | T. Yang, H. Y. Chen, X. D. Luo, and H. R. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express |

13. | J. Ng, H. Y. Chen, and C. T. Chan, “Metamaterial frequency-selective superabsorber,” Opt. Lett. |

14. | Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. |

15. | A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. |

16. | K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express |

17. | C. Li, K. Yao, and F. Li, “Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries,” Opt. Express |

18. | D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express |

19. | C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express |

**OCIS Codes**

(220.1770) Optical design and fabrication : Concentrators

(230.0230) Optical devices : Optical devices

(050.1755) Diffraction and gratings : Computational electromagnetic methods

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: August 10, 2009

Revised Manuscript: September 20, 2009

Manuscript Accepted: October 5, 2009

Published: October 15, 2009

**Citation**

Jingjing Yang, Ming Huang, Chengfu Yang, Zhe Xiao, and Jinhui Peng, "Metamaterial electromagnetic concentrators with arbitrary geometries," Opt. Express **17**, 19656-19661 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19656

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### References

- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
- U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
- 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]
- U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science 323(5910), 110–112 (2009). [CrossRef]
- R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009). [CrossRef] [PubMed]
- J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009). [CrossRef] [PubMed]
- P. Alitalo and S. Tretyakov, “Electromagnetic cloaking with metamaterials,” Mater. Today 12(3), 22–29 (2009). [CrossRef]
- Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009). [CrossRef] [PubMed]
- M. Rahm, 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,” Photonics and Nanostructures-Fundamentals and Applications 6, 89 (2008). [CrossRef]
- 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]
- H. Y. Chen, X. D. Luo, H. R. Ma, and C. T. Chan, “The anti-cloak,” Opt. Express 16(19), 14603–14608 (2008). [CrossRef] [PubMed]
- T. Yang, H. Y. Chen, X. D. Luo, and H. R. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express 16(22), 18545–18550 (2008). [CrossRef] [PubMed]
- J. Ng, H. Y. Chen, and C. T. Chan, “Metamaterial frequency-selective superabsorber,” Opt. Lett. 34(5), 644–646 (2009). [CrossRef] [PubMed]
- Y. Lai, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102(9), 093901 (2009). [CrossRef] [PubMed]
- A. Alù and N. Engheta, “Cloaking a sensor,” Phys. Rev. Lett. 102(23), 233901 (2009). [CrossRef] [PubMed]
- K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16(26), 21793–21800 (2008). [CrossRef] [PubMed]
- C. Li, K. Yao, and F. Li, “Two-dimensional electromagnetic cloaks with non-conformal inner and outer boundaries,” Opt. Express 16(23), 19366–19374 (2008). [CrossRef]
- D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006). [CrossRef] [PubMed]
- C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express 16(17), 13414 (2008). [CrossRef] [PubMed]

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