## A new planar left-handed metamaterial composed of metal-dielectric-metal structure

Optics Express, Vol. 16, Issue 12, pp. 8617-8622 (2008)

http://dx.doi.org/10.1364/OE.16.008617

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### Abstract

An improved planar structure of left-handed (LH) metamaterial is presented, and then designed and analyzed in microwave regime. In the anticipated LH frequency regime, the LH property is validated from the phenomena of backward wave propagation and negative refraction. To characterize the electromagnetic property of the planar metamaterial, we introduce the wedge method by constructing a wedge-shaped bulk LH metamaterial by stacking the planar LH metamaterials. The effective refractive index estimated by the wedge method is in excellent agreement with that retrieved by the inversion method from the transmission and reflection spectra.

© 2008 Optical Society of America

*d*=0.5 mm. The two copper layers have the same thickness of

_{S}*d*=18

_{C}*µ*m. Our designed pattern can be manufactured through conventional commercial photolithography technique. The patterns of the two copper layers have the same shapes and no lateral displacement with each other, as shown in Fig. 1(b). In a single unit cell, the copper pattern is composed of one central and four corner squares, with the dimensions of

*b*×

*b*and

*a*×

*a*, where

*b*=7.8 mm and

*a*=1.625 mm, as shown in Fig. 1(c). In particular, there is an overlapping region with the dimension of

*g*×

*g*between the central and corner squares. The transmission spectra of the single-piece planar structure are calculated by FEM, at five different values of

*g*=-0.1,-0.05,0,0.05, and 0.1 mm.

*g*<0 (without overlapping between the central and corner copper squares) and

*g*≥0 (with overlapping). The transmission spectrum is slightly changed as

*g*varies, within the range of either

*g*<0 or

*g*≥0.

*g*<0 and

*g*≥0 will give rise to what inherent difference in physical property. Based on the inversion method [14

14. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B **65**, 195104 (2002). [CrossRef]

15. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E **71**, 036617 (2005). [CrossRef]

*r*

_{11}and

*t*

_{21}) calculated by FEM, we retrieve the effective parameters (refractive index

*n*, permittivity

*ε*, and permeability

*μ*) of the single-piece planar metamaterial in terms of an effective homogeneous medium. The retrieved results reveal that when

*g*≥0, the planar metamaterial exhibits the LH property within the frequency regime we anticipated; in contrast, the LH property disappears when

*g*<0, because in this case the discontinuous copper layers cannot provide the negative electric response frequency regime to be the same as the negative magnetic response. Our attentions below focus on the case of

*g*=0 for simplicity and without the lack of generality, so the dimension of the unit cell should be

*D*×

*D*with

*D*=

*b*+2

*a*. Moreover, we restrict that the area of the cental copper square is larger than the total area of the four corner copper squares, i.e.

*b*>2

*a*.

*g*=0 (

*b*=7.8 mm,

*a*=1.625 mm, and

*D*=11.05 mm). Figure 3(a) plots the reflection and transmission (R-T) coefficients (

*r*

_{11}and

*t*

_{21}) calculated by using FEM as a function of frequency. The valley

*V*located at

_{m}*ω*=13.88 GHz in

_{m}*t*

_{21}indicates the magnetic resonance. Figures 3(b)–(d) show the retrieved effective

*n*,

*ε*, and

*μ*, respectively, by the inversion method [14

14. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B **65**, 195104 (2002). [CrossRef]

15. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E **71**, 036617 (2005). [CrossRef]

*d*=2.2 mm. Therefore, the single-piece planar metamaterial we designed can equivalently considered to be a homogeneous metamaterial slab with an effective

_{e}*n*,

*ε*,

*μ*, and thickness

*d*=2.2 mm, as the inset shown in Fig. 3(d). In addition, inasmuch as we adopt the very low-loss PCB in the microwave regime, our designed metamaterial has the high figure of merit (FOM) beyond 10 within the LH band from 14.1 to 14.3 GHz (in particular, at

_{e}*f*=14.194 GHz, the highest value of FOM is about 15.6 and the effective

*n*is -1.35).

*d*in the normal direction of the piece, and the period in the normal direction is also

_{e}*d*. Therefore, this stacked structure is equivalent to a thick homogeneous metamaterial slab with the effective

_{e}*n*,

*ε*,

*μ*, and thickness 10

*d*, from the effective medium model, as depicted in Fig. 4.

_{e}*f*=14.172 and

*f*=16.77 GHz for simulations, the results of the electric field distributions at different moments are shown by the upper and lower panels in Fig. 5, respectively. One can find that the phase velocity (or wavefront

**K**) propagates in the opposite direction to the energy flow (or Poynting vector

**S**), implying that the phase velocity (or the effective

*n*) is negative at

*f*=14.172. In contrast, the phase velocity propagates in the same direction as the energy flow, suggesting that the phase velocity (or the effective

*n*) is positive at

*f*=16.77. The results furnished by FEM verify that the planar metamaterial we designed exhibits the LH and RH property at

*f*=14.172 and

*f*=16.77 GHz, respectively, which are in excellent agreement with the results retrieved by the inversion method. It should be pointed that the effective homogeneous metamaterial slab has

*n*=-1.51 at

*f*=14.172 GHz and

*n*=1.04 at

*f*=16.77 GHz, respectively.

3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verificaiton of a negative index of refraction,” Science **292**, 77 (2001). [CrossRef] [PubMed]

17. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbachand, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. **90**, 107401 (2003). [CrossRef] [PubMed]

18. P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Sneider, and D. W. Prather, “Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals,” Phys. Rev. Lett. **92**, 127401 (2004). [CrossRef] [PubMed]

19. Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Sneider, and D. W. Prather, “Three-Dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies,” Phys. Rev. Lett. **95**, 153901(2005). [CrossRef] [PubMed]

*f*=14.2 GHz at the interface between our designed metamaterial and vacuum, which shows indeed the LH property. Through our analysis on the transmitted field in vacuum in the far-field regime, we can easily determine the angle of refraction

*β*and then to calculate the effective

*n*by the Snell’s law (the angle of incidence

*α*is 11.26°). Moreover, the effective

*n*values at four different frequencies are also estimated by the wedge method, as shown by circles in Fig. 6(b). It can be found that the effective

*n*estimated by the wedge configuration (by TEM) is in good agreement with that retrieved by the inversion method.

3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verificaiton of a negative index of refraction,” Science **292**, 77 (2001). [CrossRef] [PubMed]

3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verificaiton of a negative index of refraction,” Science **292**, 77 (2001). [CrossRef] [PubMed]

*D*will results in the relatively small blue shift of the resonance frequency of the negative magnetic response, when the size

*b*of the central copper square in the unit cell is invariable. When the period

*D*of the unit cell is fixed, the increase of the dimension of the central copper square in the unit cell will give rise to the large red shift of the resonance frequency of the negative magnetic response. In addition, inasmuch as the periodic boundary conditions are utilized, the EM property of the single unit cell can completely describe that of the infinite period planar metamaterial. The periodicity plays a role of translational symmetry (long-range order) as that in the atomic crystal. We find that the breakage in periodicity leads to the shift of the LH frequency band, although the shift is not so large.

## References and links

1. | V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of |

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

3. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verificaiton of a negative index of refraction,” Science |

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

5. | C. Caloz, C. C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configuations,” J. Appl. Phys. |

6. | J. F. Zhou, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B(R) |

7. | V. A. Podolskiy, A. K. Sarycher, and V. M. Shalaev, “Plasmon modes in metal nanowires and left-handed materials,” J. Nonlinear Opt. Phys. Mater. |

8. | V. A. Podolskiy, A. K. Sarycher, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express |

9. | S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Bruek, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. |

10. | V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. |

11. | G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science |

12. | G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. |

13. | S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks,” Opt. Express |

14. | D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B |

15. | D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E |

16. | P. Vodo, W. T. Lu, Y. Huang, and S. Sidhar, “Negative refraction and plano-concave lens focusing in one-dimensional photonic crystals,” Appl. Phys. Lett. |

17. | C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbachand, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. |

18. | P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Sneider, and D. W. Prather, “Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals,” Phys. Rev. Lett. |

19. | Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Sneider, and D. W. Prather, “Three-Dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies,” Phys. Rev. Lett. |

**OCIS Codes**

(260.2110) Physical optics : Electromagnetic optics

(260.2065) Physical optics : Effective medium theory

(350.3618) Other areas of optics : Left-handed materials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: March 19, 2008

Revised Manuscript: April 16, 2008

Manuscript Accepted: April 18, 2008

Published: May 28, 2008

**Citation**

Ming Kang, Nian-Hai Shen, Jing Chen, Jian Chen, Ya-Xian Fan, Jianping Ding, Hui-Tian Wang, and Peiheng Wu, "A new planar left-handed metamaterial composed of metal-dielectric-metal structure," Opt. Express **16**, 8617-8622 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8617

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### References

- V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ??? and ???," Sov. Phys. Usp. 10, 509-514 (1968). [CrossRef]
- D. R. Smith, W. J. Padilla, D. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184 (2000). [CrossRef] [PubMed]
- R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verificaiton of a negative index of refraction," Science 292, 77 (2001). [CrossRef] [PubMed]
- J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000). [CrossRef] [PubMed]
- C. Caloz, C. C. Chang, and T. Itoh, "Full-wave verification of the fundamental properties of left-handed materials in waveguide configuations," J. Appl. Phys. 90, 5483 (2001). [CrossRef]
- J. F. Zhou, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B (R) 73, 041101 (2006). [CrossRef]
- V. A. Podolskiy, A. K. Sarycher, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65 (2002). [CrossRef]
- V. A. Podolskiy, A. K. Sarycher, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735 (2003). [CrossRef] [PubMed]
- S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Bruek, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]
- V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356 (2005). [CrossRef]
- G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892 (2006). [CrossRef] [PubMed]
- G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800 (2006). [CrossRef] [PubMed]
- S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks," Opt. Express 14, 6778 (2006). [CrossRef] [PubMed]
- D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002). [CrossRef]
- D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005). [CrossRef]
- P. Vodo, W. T. Lu, Y. Huang, and S. Sidhar, "Negative refraction and plano-concave lens focusing in onedimensional photonic crystals," Appl. Phys. Lett. 89, 084104 (2006). [CrossRef]
- C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbachand, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell???s law," Phys. Rev. Lett. 90, 107401 (2003). [CrossRef] [PubMed]
- P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Sneider, and D. W. Prather, "Negative Refraction and Left-Handed Electromagnetism in Microwave Photonic Crystals," Phys. Rev. Lett. 92, 127401 (2004). [CrossRef] [PubMed]
- Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Sneider, and D. W. Prather, "Three-Dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett. 95, 153901(2005). [CrossRef] [PubMed]

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