## Far field free-space measurement of three dimensional hole –in –Teflon invisibility cloak |

Optics Express, Vol. 21, Issue 5, pp. 5941-5948 (2013)

http://dx.doi.org/10.1364/OE.21.005941

Acrobat PDF (1744 KB)

### Abstract

In this paper, we report a fabrication of a three-dimensional (3D) carpet cloak that works for any polarization in free space. Two-dimensional (2D) conformal mapping is first employed and the 3D structure is generated by a rotation of the 2D cloak. The structure of the cloak is hole-in-dielectric. The triangular invisible region has a height of 36 mm (one third of the height of the whole device) and a width of 240 mm. The cloaking effect is examined in free space by measuring the scattering parameters. The results show our device has very good cloaking performance in a wide frequency range from 4 to10 GHz.

© 2013 OSA

## 1. Introduction

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

13. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature **470**(7334), 369–373 (2011). [CrossRef] [PubMed]

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]

2. U. Leonhardt, “Optical conformal mapping,” Science **312**(5781), 1777–1780 (2006). [CrossRef] [PubMed]

16. H. Y. Chen, U. Leonhardt, and T. Tyc, “Conformal cloak for waves,” Phys. Rev. A **83**(5), 055801 (2011). [CrossRef]

17. T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A **86**(4), 043827 (2012). [CrossRef]

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]

18. Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt. **13**(2), 024002 (2011). [CrossRef]

## 2. 2D model design and simulation

*n*close to unit replaced simply by air. The reason behind is due to comparable operation wavelength with respect to the sizes of our device and cloaked region, which incurs small wavefront distortion by the outer layer approximation. Here we choose a rectangular geometry for the device with a triangular bump at the bottom. Things put inside the empty bump are invisible to an outside observer. Saw-tooth like boundaries is used to approximate the straight bump edges. Figure 1(a) gives the calculated index profile. Their values vary from 0.6 to 2.2. But only two unit blocks at the bottom apexes of the triangular bump have an index less than 1. Thus we approximate them by air. In addition the region far away from the cloaked bump with index close to 1 is also approximated by empty air. Consequently, only a relatively small region needs to be filled by dielectric media with indices all larger than unity. In implementation we discretize the cloaks into blocks of square unit cells. Each square has a dimension of 6 × 6 mm

^{2}. As shown in Fig. 1(b), the whole 2D cloaking device was divided into 41 × 18 unit squares and their local indices change from 1 to 1.7.

*θ*starts clockwise from the

*y*axis as schematically shown in the middle inset of Fig. 2. A Gaussian beam is incident from the top left at a fixed angle of 45° from the

*y*axis. The scattering patterns are calculated at 10 GHz. For the case of a flat conducting ground as shown in Fig. 2(a), simulation shows a typical mirror reflection. For the case of a naked triangle metal bump as shown in Fig. 2(b), the incident beam was irregularly scattered and had a very wide outward reflection angles. Two reflection peaks around 15°and 70° can be discriminated as also evidenced from the inset field profile. For the case with an ideal continuous cloak as shown in Fig. 2(c), simulation shows a single reflection beam at 45° and proves a perfect carpet cloaking. Discretization is necessary to implement the cloaking device. This may cause structural imperfection and degrade the overall cloaking performance. As shown in Fig. 2(d), simulation did show a broadened reflection peak around 45°. But consider the finite sample size with the wavelength reaching almost 5 times of the unit cell size, such a cloaking performance is still reasonable acceptable. The increased noise level in this case is mainly caused by the internal boundary scattering after discretizing the device.

## 3. Implementation of the 3D cloak

*r*). Also, each 6 × 6 mm

^{2}unit cell approximately becomes a 6 × 6 × 6 mm

^{3}cubic unit cell in the 3D space. Transverse electric (TE) and transverse magnetic (TM) polarization are both considered in our experiment, respectively corresponding to

*E*-field parallel and perpendicular to the axe of empty holes in the unit cells used in our structure. A software HFSS is used to calculate the hole diameters for each refractive index for both polarizations. As the refractive index is required from 1 to 1.7, we use Teflon (

*n*= 1.45) and Delrin (

*n*= 1.92) as the embedding materials.

^{3}, where hole in dielectric elements occupies the whole cubic unit cell element. In order to achieve the refractive index close to 1 for regions near the edge of cloak, a 6 × 6 × 2 mm

^{3}brick is also used with a hole in each dielectric element. The calculated refractive indices as a function of hole radius of the three types of unit cells are presented in Figs. 3(a) to 3(c). The unit cell of 6 × 6 × 2 mm

^{3}Teflon is used for regions with

*n*close to 1, 6 × 6 × 6 mm

^{3}Teflon is used for regions with both

*n*> 1.15 and

*n*< 1.45; 6 × 6 × 6 mm

^{3}Delrin is used for

*n*>1.45. Figures 3(a) to 3(c) show that all the three unit cells have almost the same profile for both polarizations with the variation less than 5%. Figures 4(a) to 4(d) show the different views of the assembled 3D cloaking device. In assembling thin foam with

*ε*= 1.05 is used to separate each dielectric disk layer.

## 4. Far-field free space measurement

*θ*at incident angles of 35° and 45°, respectively. Our measurement frequency is from 4 to 10 GHz. Here we selectively show the results at four frequency points, i.e., 4 GHz, 7 GHz, 8 GHz and 10 GHz. Each figure gives both TE and TM polarization results together with that for a flat ground for comparison purpose. From these reflection curves, we can see our cloaking device performs very well in the measured frequency range. The reflected wave profiles for both TE and TM polarizations can nearly agree with that reflected from a flat ground. However discrepancies are also observed in particular at higher frequencies (8-10 GHz). This could be due to the large unit size employed in our structures. At 7 GHz, the wavelength (4.5 cm) is 7.5 times the dimension of the unit cell used. This touches the limit of the effective medium theory based in our medium design, which usually requires a wavelength-to-unit length ratio larger than 10. In addition, the broadened reflection peaks are consistent with the above simulations for a real device made of discrete index profile, which causes impedance-mismatched internal boundary scattering. Such negative influence can be minimized using smaller unit cells.

## 5. Conclusion

## Acknowledgment

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

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

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

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

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

9. | T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science |

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

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

12. | H.F. Ma and T. j. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nature Comm. |

13. | M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature |

14. | U. Leonhardt and T. G. Philbin, “Chapter 2 Transformation optics and the geometry of light,” Prog. Opt. |

15. | U. Leonhardt and T. G. Philbin, “Geometry and light: the science of invisibility,” (Dover, Mineola, 2010). |

16. | H. Y. Chen, U. Leonhardt, and T. Tyc, “Conformal cloak for waves,” Phys. Rev. A |

17. | T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A |

18. | Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt. |

19. | H. F. Ma, W. X. Jiang, X. M. Yang, X. Y. Zhou, and T. J. Cui, “Compact-sized and broadband carpet cloak and free-space cloak,” Opt. Express |

20. | Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A |

21. | R. F. Huang, S. Matitsine, L. Liu, L. B. Kong, R. Kumaran, and R. Balakrishnan, “Broadband free space material measurement system,” 33rd Annual Symposium of the Antenna Measurement Techniques Association (AMTA) Englewood, Colorado, USA, 2011, pp. 477–482. |

**OCIS Codes**

(220.0220) Optical design and fabrication : Optical design and fabrication

(230.3205) Optical devices : Invisibility cloaks

**ToC Category:**

Optical Devices

**History**

Original Manuscript: November 21, 2012

Revised Manuscript: January 16, 2013

Manuscript Accepted: January 20, 2013

Published: March 4, 2013

**Citation**

Ning Wang, Yungui Ma, Ruifeng Huang, and C. K. Ong, "Far field free-space measurement of three dimensional hole –in –Teflon invisibility cloak," Opt. Express **21**, 5941-5948 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5941

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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]
- J. S. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008). [CrossRef] [PubMed]
- U. Leonhardt and T. Tyc, “Broadband invisibility by non-Euclidean cloaking,” Science323(5910), 110–112 (2009). [CrossRef] [PubMed]
- J. Valentine, J. S. 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. Photonics3(8), 461–463 (2009). [CrossRef]
- 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]
- T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010). [CrossRef] [PubMed]
- X. Z. Chen, Y. Luo, J. J. Zhang, K. Jiang, J. B. Pendry, and S. A. Zhang, “Macroscopic invisibility cloaking of visible light,” Nat Commun2, 176 (2011), doi:. [CrossRef] [PubMed]
- B. L. Zhang, Y. Luo, X. G. Liu, and G. Barbastathis, “Macroscopic invisibility cloak for visible light,” Phys. Rev. Lett.106(3), 033901 (2011). [CrossRef] [PubMed]
- H.F. Ma and T. j. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nature Comm. 1, 124 (2011), Doi: 10.1038/ncomms1023 (2010). [CrossRef]
- M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature470(7334), 369–373 (2011). [CrossRef] [PubMed]
- U. Leonhardt and T. G. Philbin, “Chapter 2 Transformation optics and the geometry of light,” Prog. Opt. 53, 69–152 (2009).
- U. Leonhardt and T. G. Philbin, “Geometry and light: the science of invisibility,” (Dover, Mineola, 2010).
- H. Y. Chen, U. Leonhardt, and T. Tyc, “Conformal cloak for waves,” Phys. Rev. A83(5), 055801 (2011). [CrossRef]
- T. Xu, Y. C. Liu, Y. Zhang, C. K. Ong, and Y. G. Ma, “Perfect invisibility cloaking by isotropic media,” Phys. Rev. A86(4), 043827 (2012). [CrossRef]
- Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches,” J. Opt.13(2), 024002 (2011). [CrossRef]
- H. F. Ma, W. X. Jiang, X. M. Yang, X. Y. Zhou, and T. J. Cui, “Compact-sized and broadband carpet cloak and free-space cloak,” Opt. Express17(22), 19947–19959 (2009). [CrossRef] [PubMed]
- Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A27(5), 968–972 (2010). [CrossRef] [PubMed]
- R. F. Huang, S. Matitsine, L. Liu, L. B. Kong, R. Kumaran, and R. Balakrishnan, “Broadband free space material measurement system,” 33rd Annual Symposium of the Antenna Measurement Techniques Association (AMTA) Englewood, Colorado, USA, 2011, pp. 477–482.

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