## Controlling electromagnetic scattering of a cavity by transformation media |

Optics Express, Vol. 20, Issue 6, pp. 6777-6787 (2012)

http://dx.doi.org/10.1364/OE.20.006777

Acrobat PDF (2920 KB)

### Abstract

Based on the transformation media theory, we proposed a way to control the scattering of a cavity, or trench, located on a metallic plane. Specifically, we show how is possible to design transformation medium to fill up a cavity with arbitrary cross section, which is capable of enhancing the specularly reflection wave. As the inverse problem, we also address the design of transformation medium coating, which is laid on the metallic plane, to mimic the scattering of the cavity. Based on the effective medium theory, the transformation medium for the case of a polygonal cavity can be realized by oblique layered structures, and each layered structure is consisting of two kinds of isotropic dielectrics, thus leading an ease of practical fabrication.

© 2012 OSA

## 1. Introduction

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

5. C. W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **80**(1), 016604 (2009). [CrossRef] [PubMed]

7. C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antenn. Propag. **57**(5), 1432–1441 (2009). [CrossRef]

8. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. **101**(20), 203901 (2008). [CrossRef] [PubMed]

9. 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]

11. B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. **106**(3), 033901 (2011). [CrossRef] [PubMed]

12. W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. **92**(26), 264101 (2008). [CrossRef]

13. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. **90**(24), 241105 (2007). [CrossRef]

14. 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]

15. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express **16**(15), 11555–11567 (2008). [CrossRef] [PubMed]

16. A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express **19**(6), 5156–5162 (2011). [CrossRef] [PubMed]

17. D.-H. Kwon and D. H. Werner, “Flat focusing lens designs having minimized reflection based on coordinate transformation techniques,” Opt. Express **17**(10), 7807–7817 (2009). [CrossRef] [PubMed]

18. 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]

20. Z. L. Mei, J. Bai, and T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys. **13**(6), 063028 (2011). [CrossRef]

21. K. Zhang, Q. Wu, F.-Y. Meng, and L. W. Li, “Arbitrary waveguide connector based on embedded optical transformation,” Opt. Express **18**(16), 17273–17279 (2010). [CrossRef] [PubMed]

22. C. García-Meca, M. M. Tung, J. V. Galán, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Squeezing and expanding light without reflections via transformation optics,” Opt. Express **19**(4), 3562–3575 (2011). [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]

9. 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]

23. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. **84**(18), 4184–4187 (2000). [CrossRef] [PubMed]

10. X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun **2**, 176 (2011). [CrossRef] [PubMed]

11. B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. **106**(3), 033901 (2011). [CrossRef] [PubMed]

24. Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express **15**(18), 11133–11141 (2007). [CrossRef] [PubMed]

25. M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. **103**(2), 024301 (2009). [CrossRef] [PubMed]

26. C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **79**(4), 047602 (2009). [CrossRef] [PubMed]

28. X. Xu, Y. Feng, Y. Hao, J. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett. **95**(18), 184102 (2009). [CrossRef]

30. J. Zhang, L. Liu, Y. Luo, S. Zhang, and N. A. Mortensen, “Homogeneous optical cloak constructed with uniform layered structure,” Opt. Express **19**(9), 8625–8631 (2011). [CrossRef]

33. I. Gallina, G. Castaldi, and V. Galdi, “Transformation optics-inspired metamaterial coatings for controlling the scattering response of wedge/corner-type structures,” Microw. Opt. Technol. Lett. **51**, 2709–2712 (2009). [CrossRef]

34. Z. Liang and J. Li, “Bending a periodically layered structure for transformation acoustics,” Appl. Phys. Lett. **98**(24), 241914 (2011). [CrossRef]

## 2. Theory

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

8. 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. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. **90**(24), 241105 (2007). [CrossRef]

22. C. García-Meca, M. M. Tung, J. V. Galán, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Squeezing and expanding light without reflections via transformation optics,” Opt. Express **19**(4), 3562–3575 (2011). [CrossRef] [PubMed]

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

## 3. Design and performance of transformation medium

21. K. Zhang, Q. Wu, F.-Y. Meng, and L. W. Li, “Arbitrary waveguide connector based on embedded optical transformation,” Opt. Express **18**(16), 17273–17279 (2010). [CrossRef] [PubMed]

## 4. Practical implementation of the transformation medium

35. B. Wood, J. B. Pendry, and D. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B **74**(11), 115116 (2006). [CrossRef]

## 4. Conclusions

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

5. | C. W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

6. | S. A. Cummer, B.-I. Popa, and D. R. Smith, “Full-wave simulation of electromagnetic cloaking structures,” Phys. Rev. Lett. |

7. | C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antenn. Propag. |

8. | J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. |

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

10. | X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun |

11. | B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett. |

12. | W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. |

13. | H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. |

14. | 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. |

15. | M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express |

16. | A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express |

17. | D.-H. Kwon and D. H. Werner, “Flat focusing lens designs having minimized reflection based on coordinate transformation techniques,” Opt. Express |

18. | 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. |

19. | W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. |

20. | Z. L. Mei, J. Bai, and T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys. |

21. | K. Zhang, Q. Wu, F.-Y. Meng, and L. W. Li, “Arbitrary waveguide connector based on embedded optical transformation,” Opt. Express |

22. | C. García-Meca, M. M. Tung, J. V. Galán, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Squeezing and expanding light without reflections via transformation optics,” Opt. Express |

23. | D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. |

24. | Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express |

25. | M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. |

26. | C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

27. | C. W. Qiu, L. Hu, and S. Zouhdi, “Isotropic non-ideal cloaks providing improved invisibility yb adaptive segmentation and optimal refractive index profile from ordering isotropic materials,” Opt. Express |

28. | X. Xu, Y. Feng, Y. Hao, J. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett. |

29. | X. Xu, Y. Feng, Z. Yu, T. Jiang, and J. Zhao, “Simplified ground plane invisibility cloak by multilayer dielectrics,” Opt. Express |

30. | J. Zhang, L. Liu, Y. Luo, S. Zhang, and N. A. Mortensen, “Homogeneous optical cloak constructed with uniform layered structure,” Opt. Express |

31. | H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Appl. Phys. B |

32. | I. Gallina, G. Castaldi, and V. Galdi, “Transformation thin planar retro directive reflector,” IEEE Microw. Wirel. Compon. Lett. |

33. | I. Gallina, G. Castaldi, and V. Galdi, “Transformation optics-inspired metamaterial coatings for controlling the scattering response of wedge/corner-type structures,” Microw. Opt. Technol. Lett. |

34. | Z. Liang and J. Li, “Bending a periodically layered structure for transformation acoustics,” Appl. Phys. Lett. |

35. | B. Wood, J. B. Pendry, and D. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(230.0230) Optical devices : Optical devices

**ToC Category:**

Physical Optics

**History**

Original Manuscript: December 22, 2011

Revised Manuscript: February 19, 2012

Manuscript Accepted: March 4, 2012

Published: March 8, 2012

**Citation**

Shenyun Wang and Shaobin Liu, "Controlling electromagnetic scattering of a cavity by transformation media," Opt. Express **20**, 6777-6787 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6777

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### References

- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
- U. Leonhardt, “Optical conformal mapping,” Science312(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,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
- D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express14(21), 9794–9804 (2006). [CrossRef] [PubMed]
- C. W. Qiu, A. Novitsky, H. Ma, and S. Qu, “Electromagnetic interaction of arbitrary radial-dependent anisotropic spheres and improved invisibility for nonlinear-transformation-based cloaks,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(1), 016604 (2009). [CrossRef] [PubMed]
- S. A. Cummer, B.-I. Popa, and D. R. Smith, “Full-wave simulation of electromagnetic cloaking structures,” Phys. Rev. Lett.74, 036621 (2006).
- C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antenn. Propag.57(5), 1432–1441 (2009). [CrossRef]
- J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008). [CrossRef] [PubMed]
- R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009). [CrossRef] [PubMed]
- X. Chen, Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun2, 176 (2011). [CrossRef] [PubMed]
- B. Zhang, Y. Luo, X. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett.106(3), 033901 (2011). [CrossRef] [PubMed]
- W. X. Jiang, T. J. Cui, Q. Cheng, J. Y. Chin, X. M. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett.92(26), 264101 (2008). [CrossRef]
- H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett.90(24), 241105 (2007). [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]
- M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express16(15), 11555–11567 (2008). [CrossRef] [PubMed]
- A. Di Falco, S. C. Kehr, and U. Leonhardt, “Luneburg lens in silicon photonics,” Opt. Express19(6), 5156–5162 (2011). [CrossRef] [PubMed]
- D.-H. Kwon and D. H. Werner, “Flat focusing lens designs having minimized reflection based on coordinate transformation techniques,” Opt. Express17(10), 7807–7817 (2009). [CrossRef] [PubMed]
- 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]
- W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett.98, 204101 (2011).
- Z. L. Mei, J. Bai, and T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys.13(6), 063028 (2011). [CrossRef]
- K. Zhang, Q. Wu, F.-Y. Meng, and L. W. Li, “Arbitrary waveguide connector based on embedded optical transformation,” Opt. Express18(16), 17273–17279 (2010). [CrossRef] [PubMed]
- C. García-Meca, M. M. Tung, J. V. Galán, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Squeezing and expanding light without reflections via transformation optics,” Opt. Express19(4), 3562–3575 (2011). [CrossRef] [PubMed]
- D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett.84(18), 4184–4187 (2000). [CrossRef] [PubMed]
- Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express15(18), 11133–11141 (2007). [CrossRef] [PubMed]
- M. Farhat, S. Guenneau, and S. Enoch, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett.103(2), 024301 (2009). [CrossRef] [PubMed]
- C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.79(4), 047602 (2009). [CrossRef] [PubMed]
- C. W. Qiu, L. Hu, and S. Zouhdi, “Isotropic non-ideal cloaks providing improved invisibility yb adaptive segmentation and optimal refractive index profile from ordering isotropic materials,” Opt. Express18, 14950–14959 (2010).
- X. Xu, Y. Feng, Y. Hao, J. Zhao, and T. Jiang, “Infrared carpet cloak designed with uniform silicon grating structure,” Appl. Phys. Lett.95(18), 184102 (2009). [CrossRef]
- X. Xu, Y. Feng, Z. Yu, T. Jiang, and J. Zhao, “Simplified ground plane invisibility cloak by multilayer dielectrics,” Opt. Express18(24), 24477–24485 (2010). [CrossRef] [PubMed]
- J. Zhang, L. Liu, Y. Luo, S. Zhang, and N. A. Mortensen, “Homogeneous optical cloak constructed with uniform layered structure,” Opt. Express19(9), 8625–8631 (2011). [CrossRef]
- H. Chen and C. T. Chan, “Electromagnetic wave manipulation by layered systems using the transformation media concept,” Appl. Phys. B78, 054204 (2008).
- I. Gallina, G. Castaldi, and V. Galdi, “Transformation thin planar retro directive reflector,” IEEE Microw. Wirel. Compon. Lett.7, 603–605 (2008).
- I. Gallina, G. Castaldi, and V. Galdi, “Transformation optics-inspired metamaterial coatings for controlling the scattering response of wedge/corner-type structures,” Microw. Opt. Technol. Lett.51, 2709–2712 (2009). [CrossRef]
- Z. Liang and J. Li, “Bending a periodically layered structure for transformation acoustics,” Appl. Phys. Lett.98(24), 241914 (2011). [CrossRef]
- B. Wood, J. B. Pendry, and D. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B74(11), 115116 (2006). [CrossRef]

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