## Zero loss magnetic metamaterials using powered active unit cells

Optics Express, Vol. 17, Issue 18, pp. 16135-16143 (2009)

http://dx.doi.org/10.1364/OE.17.016135

Acrobat PDF (660 KB)

### Abstract

We report the design and experimental measurement of a powered active magnetic metamaterial with tunable permeability. The unit cell is based on the combination of an embedded radiofrequency amplifier and a tunable phase shifter, which together control the response of the medium. The measurements show that a negative permeability metamaterial with zero loss or even gain can be achieved through an array of such metamaterial cells. This kind of active metamaterial can find use in applications that are performance limited due to material losses.

© 2009 Optical Society of America

## 2. Principle

**B**, and the

**H**-field is, in the absence of magneto-electric coupling:

**M**is the magnetization vector. The relative permeability tensor can be determined from this equation taking into account that

**B**=

*µ*

_{0}

*µ*̿

_{r}**H**. If

**B**,

**H**, and

**M**are colinear, as is the case in our analysis, only one component of the permeability tensor is relevant and is given by

*M*, i.e. magnetic moment per unit volume created in response to the external

*H*-field, is written in the form

*M*=|

*M*|

*e*

*, where the phase*

^{iφ}*φ*is the phase of the magnetisation relative to the applied

*H*-field. As noted in [14] controlling this phase enables direct control of the real and imaginary parts of the permeability. Our design exploits this observation. Following the architecture proposed in [14], our unit cell design comprises basic components such as a loop that senses the incident magnetic field, an amplifier that boosts the sensed signal, and a driven loop that creates the required magnetisation vector (see Eq. 2). In addition to these elements, several significant improvements have been employed to obtain a more practical design.

22. H.-T. Chen, W. J. Padilla1, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices, Nature **444**, 597–600 (2006).
[PubMed]

23. O. Paul, C. Imhof, B. Lgel, S. Wolff, J. Heinrich, S. Hfling, A. Forchel, R. Zengerle, R. Beigang, and M. Rahm, “Polarization-independent active metamaterial for high-frequency terahertz modulation,” Opt. Express **17**, 819–827 (2009).
[PubMed]

*φ*term in Eq. (2), and therefore the real and imaginary parts of the effective permeability. This tunability proves important in creating a metamaterial with zero magnetic loss.

## 3. Realization and parameter characterization

*w*=60 mm,

*h*=50 mm, and

*l*=40 mm, where

*w*and

*h*are the width and the height (both transverse to the direction of the wave propagation),

*l*is the length (along the wave propagation direction), and they are about 1/8, 1/10, and 1/12 of a free space wavelength around the operating frequency, respectively.

*µ*of a bulk medium made of our active unit cells. However, such quantitative calculations are beyond the scope of this paper and provide little additional insight into how the cell behaves. Instead we use a well established experimental method to recover the effective permeability of the fabricated cells.

_{r}28. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. **32**, 1671–1673 (2007).
[PubMed]

## 4. Measured EM parameters and their special features

*V*) on the phase shifter ranged from 0V to 12V, with a step of 1.5V (9 states available for the active unit cell). A subset of retrieved permeabilities for various phase shifter biases are shown in Fig. 2. At all bias values, the unit cell exhibits a significant magnetic response slightly above the self resonant frequency of the passive SRRs due to the coupling between the SRR and the metallic loop. In each case the magnitude of the susceptibility is essentially resonant, falling as frequency moves away from a single maximum. Passive metamaterials allow only one susceptibility phase distribution, resulting in losses at all frequencies. In contrast, the combination of the amplifier and the phase shifter enable control over the relative phase of the current in the output loop with respect to the input voltage (and thus the applied magnetic field), and this clearly changes the magnetic response. For example, at the lower bias voltages, the magnetic response is predominantly positive (

_{b}*µ*′

*>1) with some frequencies exhibiting loss (*

_{r}*µ*″

*<0) and others gain (*

_{r}*µ*″

*>0). As*

_{r}*V*increases, the real permeability exhibits a bandwidth of strong negative response and the character of the imaginary permeability changes as well.

_{b}*V*=4.5 V and

_{b}*V*=12 V, are examined in detail in Fig. 3. All combinations of real and imaginary magnetic susceptibility signs are obtained: (A)

_{b}*µ*′

*<1 and*

_{r}*µ*″

*<0, (B)*

_{r}*µ*′

*<1 and*

_{r}*µ*″

*>0, (C)*

_{r}*µ*′

*>1 and*

_{r}*µ*″

*>0, and (D)*

_{r}*µ*′

*>1 and*

_{r}*µ*″

*<0. The zero magnetic loss frequencies where*

_{r}*µ*′

*<1 and*

_{r}*µ*″

*=0 and*

_{r}*µ*′

*>1 and*

_{r}*µ*″

*=0 (as shown in Fig. 3(b)) are denoted by dashed lines. The case of*

_{r}*µ*′

*<1 and*

_{r}*µ*″

*=0 is particularly interesting, for it can be used to realize negative permeability with zero loss from arrays of such unit cells, as demonstrated later in the paper.*

_{r}*µ*″

*=0. At the first, the electric antiresonance has little effect, and the imaginary part of permittivity is zero, resulting in a material that not only has zero magnetic loss but also zero total loss. At the second, the effective electric response of the cell is significant and exhibits a negative imaginary permittivity. This results in a material that is magnetically lossless but not lossless overall.*

_{r}*S*

_{11}|

^{2}+|

*S*

_{11}|

^{2}>1 in the bandwidth where

*Im*(

*µ*)>0.

_{r}*V*≈6 V for a strong negative permeability response with some fine tuning to make the response of each cell approximately identical (Fig. 5(a)). The three cells were then all placed in the waveguide with a spacing of 52 mm between the cells in the transverse direction (see the dashed lines in Fig. 1(b)).

_{b}## 5. Conclusion

## References and links

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

2. | S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. |

3. | Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, “Directive emission based on anisotropic metamaterials,” Phys. Rev. A |

4. | J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science |

5. | 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 |

6. | S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E |

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

8. | S. A. Tretyakov, “Meta-materials with wideband negative permittivity and permeability,” Microwave Opt. Technology Lett. |

9. | A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, “Creating stable gain in active metamaterials,” J. Opt. Soc. Am. B |

10. | R. R. A. Syms, L. Solymar, and I. R. Young, “Three-frequency parametric amplification in magneto-inductive ring resonators,” Metamaterials |

11. | A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B |

12. | B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E |

13. | P. Kinsler, “Refractive index and wave vector in passive and active media,” Phys. Rev. A |

14. | B. I. Popa and S. A. Cummer, “An architecture for active metamaterial particles and experimental validation at RF,” Microwave Opt. Technology Lett. |

15. | Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, “Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials,” Opt. Express |

16. | H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong,“Experimental retrieval of the effective parameters of metamaterials based on a waveguide method,” Opt. Express |

17. | A. Sellier, S. N. Burokur, B. Kant, and A. de Lustrac,“Negative refractive index metamaterials using only metallic cut wires,” Opt. Express |

18. | O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett. |

19. | D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. |

20. | T. Hand and S. A. Cummer, “Characterization of tunable metamaterial elements using MEMS switches,” IEEE Ant. Wireless Propagation Lett. |

21. | D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, “Active left-handed material collaborated with microwave varactors,” Appl. Phys. Lett. |

22. | H.-T. Chen, W. J. Padilla1, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices, Nature |

23. | O. Paul, C. Imhof, B. Lgel, S. Wolff, J. Heinrich, S. Hfling, A. Forchel, R. Zengerle, R. Beigang, and M. Rahm, “Polarization-independent active metamaterial for high-frequency terahertz modulation,” Opt. Express |

24. | 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 |

25. | X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E |

26. | C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B |

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

28. | U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. |

29. | T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E |

30. | M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E |

31. | H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, “Equivalent circuit model for left-handed metamaterials,” J. Appl. Phys. |

32. | B.-I. Popa and S. A. Cummer, “Direct measurement of evanescent wave enhancement inside passive metamaterials,” Phys. Rev. E |

**OCIS Codes**

(350.4010) Other areas of optics : Microwaves

(160.1245) Materials : Artificially engineered materials

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: June 9, 2009

Revised Manuscript: August 14, 2009

Manuscript Accepted: August 21, 2009

Published: August 26, 2009

**Citation**

Yu Yuan, Bogdan-Ioan Popa, and Steven A. Cummer, "Zero loss magnetic metamaterials using powered active unit cells," Opt. Express **17**, 16135-16143 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-18-16135

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### References

- J. B. Pendry,"Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000). [PubMed]
- S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002). [PubMed]
- Y. Yuan, L. Shen, L. Ran, T. Jiang, J. Huangfu, and J. A. Kong, "Directive emission based on anisotropic metamaterials," Phys. Rev. A 77, 053821 (2008).
- J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006). [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, 977-980 (2006). [PubMed]
- S. A. Cummer, B.-I. Popa, D. Schurig, D. R. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006).
- H. Chen, B.-I. Wu, B. Zhang, and J. A. Kong, "Electromagnetic wave interactions with a metamaterial cloak, " Phys. Rev. Lett. 99, 063903 (2007). [PubMed]
- S. A. Tretyakov, "Meta-materials with wideband negative permittivity and permeability," Microwave Opt. Technology Lett. 31, 163-165 (2001).
- A. D. Boardman, Y. G. Rapoport, N. King, and V. N. Malnev, "Creating stable gain in active metamaterials," J. Opt. Soc. Am. B 24, 53-61 (2007).
- R. R. A. Syms, L. Solymar, and I. R. Young, "Three-frequency parametric amplification in magneto-inductive ring resonators," Metamaterials 2, 122-134 (2008).
- A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, "Self-consistent calculation of metamaterials with gain, " Phys. Rev. B 79, 241104(R) (2009).
- B. Nistad, and J. Skaar, "Causality and electromagnetic properties of active media," Phys. Rev. E 78, 036603 (2008).
- P. Kinsler, "Refractive index and wave vector in passive and active media," Phys. Rev. A 79, 023839 (2009).
- B. I. Popa and S. A. Cummer, "An architecture for active metamaterial particles and experimental validation at RF," Microwave Opt. Technol. Lett. 49, 2574-2577 (2007).
- Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. A. Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220-2227 (2006). [PubMed]
- H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong,"Experimental retrieval of the effective parameters of metamaterials based on a waveguide method," Opt. Express 14, 12944-12949 (2006). [PubMed]
- A. Sellier, S. N. Burokur, B. Kant, and A. de Lustrac,"Negative refractive index metamaterials using only metallic cut wires," Opt. Express 17, 6301-6310 (2009). [PubMed]
- O. Reynet and O. Acher, "Voltage controlled metamaterial," Appl. Phys. Lett. 84, 1198-1200 (2004).
- D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).
- T. Hand and S. A. Cummer, "Characterization of tunable metamaterial elements using MEMS switches," IEEE Ant. Wireless Propag. Lett. 6, 401-404 (2007).
- D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B.-I. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
- H.-T. Chen, W. J. Padilla1, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices, Nature 444, 597-600 (2006). [PubMed]
- O. Paul, C. Imhof, B. Lgel, S. Wolff, J. Heinrich, S. Hfling, A. Forchel, R. Zengerle, R. Beigang, and M. Rahm, "Polarization-independent active metamaterial for high-frequency terahertz modulation," Opt. Express 17, 819-827 (2009). [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).
- X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004).
- C. R. Simovski, and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111 (2007).
- D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
- U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm," Opt. Lett. 32, 1671-1673 (2007). [PubMed]
- T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602(R) (2003).
- M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, "Effect of microscopic disorder on magnetic properties of metamaterials," Phys. Rev. E 73, 056605 (2006).
- H. Chen, L. Ran, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Equivalent circuit model for left-handed metamaterials," J. Appl. Phys. 100, 024915 (2006)
- B.-I. Popa and S. A. Cummer, "Direct measurement of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617 (2006).

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