## A chirality switching device designed with transformation optics |

Optics Express, Vol. 18, Issue 20, pp. 21419-21426 (2010)

http://dx.doi.org/10.1364/OE.18.021419

Acrobat PDF (1007 KB)

### Abstract

Based on transformation optics theory, we designed a chirality switching device, such that an object hidden inside would exhibit a reversed chirality (i.e., from left-handedness to right-handedness) for an observer at the far field. Distinct from a perfect mirror which also creates a chirality-reversed image, our device makes the original object completely invisible to the far field observer. Numerical simulations are employed to demonstrate the functionalities of the designed devices in both two- and three-dimensional spaces.

© 2010 OSA

## 1. Introduction

*optical*approach to “change” the chirality of an object. We show that an optical device can be designed, such that any object (with certain chirality) placed inside the device would exhibit a reversed chirality for an observer at the far field.

## 2. Operation, transformation, and device parameters

9. U. Leonhardt, “Optical Conformal Mapping,” Science **312**(5781), 1777–1780 (2006). [CrossRef] [PubMed]

10. H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and Metamaterials,” Nat. Mater. **9**(5), 387–396 (2010). [CrossRef] [PubMed]

*operation*performed in certain space region [11]. For instance, the operation adopted to design the field rotator [12

12. H. Y. Chen and C. T. Chan, “Transformation Media that Rotate Electromagnetic Fields,” Appl. Phys. Lett. **90**(24), 241105 (2007). [CrossRef]

*rotation*of 3D coordinate system by a specific angle; a field concentrator [13

13. M. Rahm, D. Schurig, D. A. Robertsa, S. A. Cummera, D. R. Smith, and J. B. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-invariant Coordinate Transformations of Maxwell’s Equations,” Phot. Nano.: Fund. Appl. **6**(1), 87–95 (2008). [CrossRef]

*stretching*operation; and one can easily identify the operations for the hyper-lens (

*stretching*) [14

14. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field Imaging Beyond the Diffraction Limit,” Opt. Express **14**(18), 8247–8256 (2006). [CrossRef] [PubMed]

*twisting*) [15

15. 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. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. **85**(18), 3966–3969 (2000). [CrossRef] [PubMed]

*operation*was identified by Leonhardt and Philbin as a space “

*folding*” [16

16. U. Leonhardt and T. G. Philbin, “General Relativity in Electrical Engineering,” N. J. Phys. **8**(10), 247 (2006). [CrossRef]

*n*in the physical space [10

10. H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and Metamaterials,” Nat. Mater. **9**(5), 387–396 (2010). [CrossRef] [PubMed]

*operation*” required to achieve the desired function. In addition, to make a good design, the

*operation*should follow some general rules. First, the operation should be performed uniformly if one wants to obtain a homogeneous transformation medium [10

10. H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and Metamaterials,” Nat. Mater. **9**(5), 387–396 (2010). [CrossRef] [PubMed]

17. L. Bergamin, “Electromagnetic Fields and Boundary Conditions at the Interface of Generalized Transformation Media,” Phys. Rev. A **80**(6), 063835 (2009). [CrossRef]

9. U. Leonhardt, “Optical Conformal Mapping,” Science **312**(5781), 1777–1780 (2006). [CrossRef] [PubMed]

*operation*defined in Fig. 2(a-d), we can easily get the coordinate transformation and material properties of the transformation medium based on the theory developed in [9

9. U. Leonhardt, “Optical Conformal Mapping,” Science **312**(5781), 1777–1780 (2006). [CrossRef] [PubMed]

*x,y,z*} and {

*u,v,w*} be the coordinate systems in physical and EM space, respectively, we summarized the coordinate transformations and the corresponding materials parameters in different regions [see definitions in Fig. 3(a) ] in Table 1 .

*n*= −1 medium in a rhombus shape (see property of region V in Table 1). However, we have mentioned that such a system

*alone*does not behave as a perfect mirror, as schematically shown in Fig. 1(b). The recipe here is to add four pieces of transformation media (regions I-IV) to surround such a rhombus

*n*= −1 area, which can help resolve the problems existing for a rhombus

*n*= −1 device alone. It is worth mentioning that, although

## 3. Numerical verifications

*optically*switch its chirality as a perfect mirror. In the following, we demonstrate two important characteristics for the proposed device:

- 1) for any true light source, the device effectively
*relocate*its position to the mirror-reflection symmetry point with respect to the central plane of the device, for an observer at the far field; - 2) for a ray (radiated from a true source) which originally propagates to left (right) direction, the device effectively
*redirect*its propagation to right (left) direction, again for an observer at the far field.

*a*= 6.25 [19] and assumed that the device medium properties were given by Table 1, and then placed a line source at a point (

*x*= 1.25,

*y*= 1.25,

*z*= 0) inside the device. The calculated radiation pattern (only

*E*component is shown) of this source is depicted in Fig. 3(a). While the field distribution inside the device is rather complex, we find surprisingly that the radiation pattern outside the device is quite regular. As a comparison, we show in Fig. 3(b) the radiation pattern of a line source placed at a point (

_{z}*x*= −1.25,

*y*= 1.25,

*z*= 0) with the device removed [20]. Comparison between Fig. 3(a) and Fig. 3(b) show that they are essentially the same, demonstrating that the proposed device can indeed effectively

*relocate*the position of a source to its mirror-reflection symmetry point.

*virtual*source, which is the mirror image of the original one, for a far field observer.

*z*coordinate into consideration, the design for 2D space extends to infinity along the

*z*axis. However, a real 3D device must be finite along all directions. Unfortunately, just truncating the device at some points at the

*z*axis does not work well since the upper and lower boundaries may cause undesirable reflections. This problem can be solved by taking advantage of the fact that the functionality of the 2D device is

*independent*of the value of

*a*(see Table 1). Therefore, shrinking the cross section of the device gradually to zero as |

*z*| increases to a certain value, we obtain a design for the 3D device which is finite along all directions. By doing so, all potential reflections could be eliminated since the device no longer tears up any boundary. Inset to Fig. 5(a) shows the designed 3D chirality-switching device, which is an octahedron with its material parameters obtained by substituting

*a*in Table 1 byfor the

*xy*plane at a particular

*z*point. Obviously, the total height of the 3D device is 2

*a*

_{0}.

## 4. Conclusions

## Acknowledgments

## References and links

1. | G. Q. Lin, Y. M. Li, and A. S. C. Chan, |

2. | U. J. Meierhenrich, |

3. | J. B. Pendry and S. A. Ramakrishna, “Focussing Light Using Negative Refraction,” J. Phys. Condens. Matter |

4. | In this paper, we consider only those sources emitting light rays symmetrically, i.e., for any ray emitted from the source, we can always find another emitted ray going to the opposite direction. |

5. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

6. | D. Maystre and S. Enoch, “Perfect lenses made with left-handed materials: Alice’s mirror?” J. Opt. Soc. Am. A |

7. | 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. |

8. | 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. |

9. | U. Leonhardt, “Optical Conformal Mapping,” Science |

10. | H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and Metamaterials,” Nat. Mater. |

11. | L. V. Ahlfors, |

12. | H. Y. Chen and C. T. Chan, “Transformation Media that Rotate Electromagnetic Fields,” Appl. Phys. Lett. |

13. | M. Rahm, D. Schurig, D. A. Robertsa, S. A. Cummera, D. R. Smith, and J. B. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-invariant Coordinate Transformations of Maxwell’s Equations,” Phot. Nano.: Fund. Appl. |

14. | Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field Imaging Beyond the Diffraction Limit,” Opt. Express |

15. | 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. |

16. | U. Leonhardt and T. G. Philbin, “General Relativity in Electrical Engineering,” N. J. Phys. |

17. | L. Bergamin, “Electromagnetic Fields and Boundary Conditions at the Interface of Generalized Transformation Media,” Phys. Rev. A |

18. | COMSOL Multi-physics 3.5, developed by COMSOL ©, network license (2008). |

19. | All lengths are rescaled by the working wavelengths taken in the simulations. |

20. | Here the shape of device is shown only for identifying the position. |

21. | The directional source is formed by an array of 6 × 6 line sources (with lattice constant 0.5.). The pumping fields of these sources are chosen as |

22. | The point source consists of three mutually orthogonal antennae, with pumping fields carefully adjusted to ensure that the resultant radiation pattern in free space exhibits a spherical symmetry. |

**OCIS Codes**

(230.0230) Optical devices : Optical devices

(260.2110) Physical optics : Electromagnetic optics

(160.3918) Materials : Metamaterials

**ToC Category:**

Physical Optics

**History**

Original Manuscript: August 5, 2010

Revised Manuscript: September 2, 2010

Manuscript Accepted: September 16, 2010

Published: September 23, 2010

**Citation**

Yuan Shen, Kun Ding, Wujiong Sun, and Lei Zhou, "A chirality switching device designed with transformation optics," Opt. Express **18**, 21419-21426 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-21419

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### References

- G. Q. Lin, Y. M. Li, and A. S. C. Chan, Principles and Applications of Asymmetric Synthesis, (John Wiley & Sons, New York, 2001), Chap. 1.
- U. J. Meierhenrich, Amino Acids and the Asymmetry of Life, (Springer, Berlin, 2008), Chap. 1.
- J. B. Pendry and S. A. Ramakrishna, “Focussing Light Using Negative Refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003). [CrossRef]
- In this paper, we consider only those sources emitting light rays symmetrically, i.e., for any ray emitted from the source, we can always find another emitted ray going to the opposite direction.
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
- D. Maystre and S. Enoch, “Perfect lenses made with left-handed materials: Alice’s mirror?” J. Opt. Soc. Am. A 21(1), 122–131 (2004). [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]
- 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]
- U. Leonhardt, “Optical Conformal Mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
- H. Chen, C. T. Chan, and P. Sheng, “Transformation Optics and Metamaterials,” Nat. Mater. 9(5), 387–396 (2010). [CrossRef] [PubMed]
- L. V. Ahlfors, Complex Analysis, (McGraw-Hill, New York, 1979), Chap. 3&8.
- H. Y. Chen and C. T. Chan, “Transformation Media that Rotate Electromagnetic Fields,” Appl. Phys. Lett. 90(24), 241105 (2007). [CrossRef]
- M. Rahm, D. Schurig, D. A. Robertsa, S. A. Cummera, D. R. Smith, and J. B. Pendry, “Design of Electromagnetic Cloaks and Concentrators Using Form-invariant Coordinate Transformations of Maxwell’s Equations,” Phot. Nano.: Fund. Appl. 6(1), 87–95 (2008). [CrossRef]
- Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field Imaging Beyond the Diffraction Limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]
- 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]
- U. Leonhardt and T. G. Philbin, “General Relativity in Electrical Engineering,” N. J. Phys. 8(10), 247 (2006). [CrossRef]
- L. Bergamin, “Electromagnetic Fields and Boundary Conditions at the Interface of Generalized Transformation Media,” Phys. Rev. A 80(6), 063835 (2009). [CrossRef]
- COMSOL Multi-physics 3.5, developed by COMSOL ©, network license (2008).
- All lengths are rescaled by the working wavelengths taken in the simulations.
- Here the shape of device is shown only for identifying the position.
- The directional source is formed by an array of 6 × 6 line sources (with lattice constant 0.5.). The pumping fields of these sources are chosen as (+1−1+1−1+1−1+1−2+2−2+2−1+1−2+4−4+2−1+1−2+4−4+2−1+1−2+2−2+2−1+1−1+1−1+1−1)
- The point source consists of three mutually orthogonal antennae, with pumping fields carefully adjusted to ensure that the resultant radiation pattern in free space exhibits a spherical symmetry.

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