## Simplified ground plane invisibility cloak by multilayer dielectrics |

Optics Express, Vol. 18, Issue 24, pp. 24477-24485 (2010)

http://dx.doi.org/10.1364/OE.18.024477

Acrobat PDF (1135 KB)

### Abstract

Most implementations of the ground plane invisibility cloak are based on the isotropic design through the quasi-conformal transformation. However recent theoretical analysis predicts the unavoidable lateral shift of the scattering fields associated with these cloaks making them detectable. In this paper, we propose an alternative method to design the ground plane invisibility clock with electromagnetic beam modulation blocks through simple coordinate transformation discussed in our previous work. The ground plane cloak obtained with the rigorous transformation optics possesses moderate anisotropic distributions of material parameters, but results in no lateral shift of the scattering fields. To realize the design, a possible scheme is suggested by discretizing the ground plane cloak to several homogeneous sub-blocks. These sub-blocks can be realized with multilayer isotropic dielectrics with alignment angles that are determined by the effective medium theory. Thus the non-magnetic ground plane invisibility cloak can be constructed by several multilayered normal dielectrics aligned in different angles. The performance of the proposed cloak and its practical implementation is validated by full-wave electromagnetic simulations with both near field distributions and far field scattering patterns under different EM wave incident angles. The proposed cloak is composed of normal dielectric multilayers, thus can leads to easy experimental demonstration of non-magnetic ground plane cloak in the frequency range from microwave to optical.

© 2010 OSA

## 1. Introduction

18. X. Xu, Y. Feng, and T. Jiang, “Electromagnetic beam modulation through transformation optical structures,” N. J. Phys. **10**(11), 115027 (2008). [CrossRef]

8. 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]

13. 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. S. Xi, H. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wirel. Compon. Lett. **19**(3), 131–133 (2009). [CrossRef]

29. 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. B. Zhang, T. Chan, and B. I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. **104**(23), 233903 (2010). [CrossRef] [PubMed]

## 2. Beam modulation blocks designed from transformation optics

18. X. Xu, Y. Feng, and T. Jiang, “Electromagnetic beam modulation through transformation optical structures,” N. J. Phys. **10**(11), 115027 (2008). [CrossRef]

*y*coordinate has been transformed in a uniform linear proportion within the cloak area, similar with the so-called “transfinite transformation” discussed in [23

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

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

*η*represents the modulation coefficient,

**J**indicates the Jacobian matrix, with the element of

*x*

_{3}coordinate), it is also possible to remove the requirement of magnetic response of the material, which is difficult for natural materials, especially in optical frequency range. Therefore, we could reduce the material parameters for a perfect cloak to the non-magnetic form by keeping the following product unchanged similar to the procedure used in [6

6. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterial,” Nat. Photonics **1**(4), 224–227 (2007). [CrossRef]

*x*

_{1}–

*x*

_{2}plane), and

## 3. Design and performance of the ground plane cloak

*η*= 3/4,

*a*= 4

*λ*,

*b*= 4

*λ*(

*λ*denotes the working wavelength) and the host medium with

*ε*= 2.2,

*μ*= 1, the material parameters for the cloak covering the bump could be directly retrieved from Eq. (2) following the TO procedure described in [4

4. U. Leonhardt, “Notes on conformal invisibility devices,” N. J. Phys. **8**(7), 118 (2006). [CrossRef]

5. 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]

*x*

_{1}–

*x*

_{2}plane) with a waist of 3

*λ*impinges along the direction with an azimuth angle

*φ*= 135°. Figure 2 shows the near field transverse magnetic field distributions for four different cases: the flat PEC ground plane [Fig. 2(a)], the reflective PEC bump on the ground plane [Fig. 2(b)], the bump covered with perfect ground plane cloak [Fig. 2(c)], and the bump covered with non-magnetic cloak [Fig. 2(d)]. As indicated in the results, the field scattered by the reflective PEC bump [Fig. 2(b)] is quite irregular, while in the cases where the bump is covered with either perfect or non-magnetic ground plane cloak [Fig. 2(c) or 2(d)], the magnetic scattering field is confined highly in the specular direction, mimicking that in the case of a flat reflective PEC ground plane [Fig. 2(a)].

30. B. Zhang, T. Chan, and B. I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. **104**(23), 233903 (2010). [CrossRef] [PubMed]

## 4. Practical implementation of the ground plane cloak

24. 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]

24. 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]

28. S. Xi, H. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wirel. Compon. Lett. **19**(3), 131–133 (2009). [CrossRef]

29. 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]

*r*of the alternating dielectrics, the permittivity of the two dielectric

*ε*and

_{a}*ε*, and the alignment angle

_{b}*θ*. They are connected in the following equations. The anisotropic in-plane permittivity for each sub-divided block is determined by

*θ*is the alignment angle of the multilayered dielectric structure with respect to the

*x′*

_{1}axis, and

*eigen-permittivitiy*, while

*eigen-permittivitiy*from the alternating dielectric multilayers composed of two natural dielectrics with permittivity

*ε*and

_{a}*ε*. We have

_{b}*r*, permittivity

*ε*and

_{a}*ε*, and the alignment angle

_{b}*θ*can be determined through Eqs. (3)–(5).

*r*= 1 for simplicity. The thickness of each layer is set to

*λ*/20 as to abide the essential condition of EMT. The moderate permittivity of the dielectric layers in the cloak can be easily realized with normal dielectrics as indicated in Table 1. The cloak performance is verified again through FEM-based simulations as shown in Fig. 4(b) and 4(c). We compare both the case where the cloak is composed with eight block of homogeneous anisotropic medium [Fig. 4(b)] and the case where the eight blocks in the cloak are realized by aligned multilayered dielectrics. These two implementations both inherit the performance of an ideal ground plane cloak, which confirms the design procedure. Note that slight reflection might occur at the incidence plane due to impedance mis-matching when the spatial variant cloak is sub-divided coarsely, which could be minimized by finer sub-division. We also find very slight lateral shift between the power flow path and the specular ray trace. We attribute this slight excursion to the coarse sub-division, for the reason that the lateral deviation is only about

*λ*/10, much less than the characteristic lateral shift in the isotropic cloak derived from quasi-conformal mapping, which is in the order of the bump height (one wavelength) [30

30. B. Zhang, T. Chan, and B. I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. **104**(23), 233903 (2010). [CrossRef] [PubMed]

*φ*= 120° is shown in Fig. 6 with both the near field distribution and far field scattering pattern. These results are very similar to those in Fig. 5 with the incident azimuth angle of 135°, except the reflected lobe direction.

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]

6. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterial,” Nat. Photonics **1**(4), 224–227 (2007). [CrossRef]

## 5. Conclusion

## Acknowledgements

## 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, “Notes on conformal invisibility devices,” N. J. Phys. |

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

6. | W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterial,” Nat. Photonics |

7. | F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. |

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

9. | H. S. Chen, B.-I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. |

10. | Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. |

11. | W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. |

12. | X. Xu, Y. Feng, L. Zhao, T. Jiang, C. Lu, and Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. |

13. | 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. |

14. | C. Li, X. Liu, and F. Li, “Experimental observation of invisibility to a broadband electromagnetic pulse by a cloak using transformation media based on inductor-capacitor networks,” Phys. Rev. B |

15. | A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett. |

16. | 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. |

17. | 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. |

18. | X. Xu, Y. Feng, and T. Jiang, “Electromagnetic beam modulation through transformation optical structures,” N. J. Phys. |

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

20. | H. Ma, S. Qu, Z. Xu, and J. Wang, “General method for designing wave shape transformers,” Opt. Express |

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

22. | Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. |

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

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

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

26. | L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics |

27. | E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A |

28. | S. Xi, H. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wirel. Compon. Lett. |

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

30. | B. Zhang, T. Chan, and B. I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. |

31. | G. Dupont, S. Guenneau, and S. Enoch, “Electromagnetic analysis of arbitrarily shaped pinched carpets,” Phys. Rev. A |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(260.2065) Physical optics : Effective medium theory

(160.3918) Materials : Metamaterials

(230.3205) Optical devices : Invisibility cloaks

**ToC Category:**

Physical Optics

**History**

Original Manuscript: August 18, 2010

Revised Manuscript: October 26, 2010

Manuscript Accepted: October 28, 2010

Published: November 9, 2010

**Citation**

Xiaofei Xu, Yijun Feng, Zhenzhong Yu, Tian Jiang, and Junming Zhao, "Simplified ground plane invisibility cloak by multilayer dielectrics," Opt. Express **18**, 24477-24485 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-24-24477

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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, “Notes on conformal invisibility devices,” N. J. Phys. 8(7), 118 (2006). [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]
- W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterial,” Nat. Photonics 1(4), 224–227 (2007). [CrossRef]
- F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32(9), 1069–1071 (2007). [CrossRef] [PubMed]
- 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]
- H. S. Chen, B.-I. Wu, B. L. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 113903 (2007).
- Z. Ruan, M. Yan, C. W. Neff, and M. Qiu, “Ideal cylindrical cloak: perfect but sensitive to tiny perturbations,” Phys. Rev. Lett. 99(11), 113903 (2007). [CrossRef] [PubMed]
- W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, and G. W. Milton, “Nonmagnetic cloak with minimized scattering,” Appl. Phys. Lett. 91(11), 111105 (2007). [CrossRef]
- X. Xu, Y. Feng, L. Zhao, T. Jiang, C. Lu, and Z. Xu, “Designing the coordinate transformation function for non-magnetic invisibility cloaking,” J. Phys. D Appl. Phys. 41(21), 215504 (2008). [CrossRef]
- 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. Li, X. Liu, and F. Li, “Experimental observation of invisibility to a broadband electromagnetic pulse by a cloak using transformation media based on inductor-capacitor networks,” Phys. Rev. B 81(11), 115133 (2010). [CrossRef]
- A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett. 33(1), 43–45 (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]
- 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]
- X. Xu, Y. Feng, and T. Jiang, “Electromagnetic beam modulation through transformation optical structures,” N. J. Phys. 10(11), 115027 (2008). [CrossRef]
- T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: enhancement of scattering with complementary media,” Opt. Express 16(22), 18545–18550 (2008). [CrossRef] [PubMed]
- H. Ma, S. Qu, Z. Xu, and J. Wang, “General method for designing wave shape transformers,” Opt. Express 16(26), 22072–22082 (2008). [CrossRef] [PubMed]
- Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, 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]
- Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95(19), 193506 (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,” 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]
- L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009). [CrossRef]
- E. Kallos, C. Argyropoulos, and Y. Hao, “Ground-plane quasicloaking for free space,” Phys. Rev. A 79(6), 063825 (2009). [CrossRef]
- S. Xi, H. Chen, B. Wu, and J. A. Kong, “One-directional perfect cloak created with homogeneous material,” IEEE Microw. Wirel. Compon. Lett. 19(3), 131–133 (2009). [CrossRef]
- 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]
- B. Zhang, T. Chan, and B. I. Wu, “Lateral shift makes a ground-plane cloak detectable,” Phys. Rev. Lett. 104(23), 233903 (2010). [CrossRef] [PubMed]
- G. Dupont, S. Guenneau, and S. Enoch, “Electromagnetic analysis of arbitrarily shaped pinched carpets,” Phys. Rev. A 82(3), 033840 (2010). [CrossRef]

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