## Experimental determination and numerical simulation of the properties of negative index of refraction materials

Optics Express, Vol. 11, Issue 7, pp. 688-695 (2003)

http://dx.doi.org/10.1364/OE.11.000688

Acrobat PDF (634 KB)

### Abstract

Negative index of refraction materials have been postulated for many years but have only recently been realized in practice. In the microwave region these materials are constructed of rings and wires deposited on a dielectric substrate to form a unit cell. We have constructed, experimentally characterized and simulated several of these structures operating in the 10 – 15 GHz range. Our simulations using Maxwell’s Equations solvers have included wire arrays, ring arrays and assemblies of unit cells comprised of rings and wires. We find good agreement between the numerical simulations and experimental measurements of the scattering parameters and index of refraction. The procedure was to first model ring and wire structures on the unit cell level to obtain scattering parameters from which effective ε, μ and n were retrieved. Next an assembled array of unit cells forming a 12° wedge was used for the Snell’s Law determination of the negative index of refraction. For the structure examined the computed value of n is within 20% of the one experimentally measured in the Snell’s Law experiment from 13.6 to 14.8 GHz.

© 2003 Optical Society of America

## 1. Introduction

2. D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “A composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. **84**, 4184 (2000). [CrossRef] [PubMed]

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

_{eff}and permeability μ

_{eff}are both negative. It has been shown that this results in a negative index of refraction,

*n*=- (με)

^{1/2}.

_{eff}, permeability μ⃑

_{eff}and index of refraction n, are obtained from the scattering parameters obtained using the simulation tools. We compare these numerical values of n to experimental results obtained using a Snell’s Law experiment. For the structure examined the computed value of n is within 20% of the one experimentally measured from 13.6 to 14.8 GHz.

## 2. Numerical simulations using Maxwell’s equations solvers

_{z}) and μ⃡=(1, μ

_{y}, 1). Here, the two concentric rectangular SRR generate the negative permeability μ

_{y}, while the metal strip in the z-direction (the wire) generates the negative permittivity ε

_{z}. The SRR and the wire are deposited on a dielectric substrate.

_{11}(reflection) and S

_{21}(transmission) in the direction of propagation, x, are computed. We then use DS to cascade multiple cells, thus obtaining the scattering parameters for an arbitrary number of cells in the direction of propagation. From the scattering parameters we can retrieve the effective ε

_{z}, μ

_{y}, n and Z of the NIM material.

## 3. Experimental and numerical results

### 3.1 Sample preparation and experimental measurements

_{21}and ~0.5% full scale for S

_{11}.

### 3.2 Scattering parameters

_{21}), of the wire matrix is shown as a function of the frequency for the grounded and floating wire cases. The agreement between the simulation and the experiment is quite good. Observe that in the grounded wire case the transmission is an increasing monotonic function of the frequency, as expected. For the floating wire case, the monotonic increase of the transmission is modulated. The discrete value of the frequency

*f*

_{n/2}, for a minimum is given by

*f*

_{n/2}=(

*c*/2

*L*

_{w})(

*n*-1). Here, c is the speed of light in vacuum,

*L*

_{w}is the length of the wire and n (

*n*≥2) is an even integer.

_{21}) parameters as a function of the frequency for the 901 HWD structure having both rings and wires. The band in which the structure displays negative index of refraction is between ~ 13.6 and ~ 14.8 GHz. The agreement between the measured and MWS computed modulus of S

_{21}appears to be satisfactory. In the numerical simulation the values for copper conductivity (5.8×10

^{7}S/m) and a substrate dielectric constant (2.2) approximately equal to the nominal value for Rogers 5880 have been used. A loss tangent of 0.0009 was used for the Rogers 5880 cards, no adhesive was used to hold the structure together. The Rohacell spacers expanded the unit cell y-dimension from 0.33 cm to 0.51cm

### 3.3 Power losses

*l*=1-(

*S*

_{11}

*S**

_{11}+

*S*

_{21}

*S**

_{21}). The sources of losses are in the finite conductivity of the metallic (copper) layer and in the dielectric loss of the substrate, along with other materials that may be used to construct the NIM.

*i*ε″, respectively. The dielectric losses are concentrated in the high field regions, as the numerical simulations clearly show in Fig. 4. Here the dissipated power density is given in false colors, in various locations of the 901 HWD structure. It is obvious from this result that the small gaps concentrate the fields increasing the losses. It is also noticeable that the losses are limited to narrow regions surrounding the gaps. The removal of the dielectric in the region of high fields significantly reduces the losses. This is clearly shown in Fig. 5(a) where the loss tangent of the adhesive used to hold the structure together is varied. Reduction of adhesive loss tangent significantly increases the transmission for the case where the adhesive is placed directly over the azimuthal ring gap. If the adhesive is placed away from the gaps, as indicated in Fig. 5(a), then it has little effect on the transmission properties of the structure. Thus, if it is necessary to place an adhesive over the ring gaps, then it is critical that this adhesive have a low loss tangent. It is preferable to use construction methods that do not require adhesives over the gap regions. We also note, that due to the high dielectric constant of some adhesive, the NIM passband can be shifted to lower frequencies.

^{7}S/m. The thickness of the metallic layer also affects the insertion loss. Approximately 5 skin depths, are needed to minimize the losses.

### 3.4 Snell’s Law experiment

9. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial,” App. Phys. Lett. **78**, 489 (2001). [CrossRef]

^{0}wedge were reported previously [10]. Here we report the results for a 12

^{0}wedge. This wedge was constructed using the low loss approaches discussed above. A Rogers substrate was used having copper wires and rings with Rohacell spacers without any adhesive at the Rogers / Rohacell interfaces. The structure was held together using shrink-wrap at the wedge external boundaries. An identical Teflon positive index material (PIM) wedge was used for calibration purposes. A focused beam illuminated the NIM and PIM wedges.

*E*

_{z}(

*r, f*), of the z-component of the electric field as function of the refraction angle

*r*, and frequency

*f*. The angle

*r*is measured from the normal of the wedge exit face. The refraction angle

*r*

_{Max}is defined as [∂

*E*

_{z}(

*r, f*)/∂

*r*]

_{r=rMax}=0. In Fig. 6 the Teflon wedge refracts the beam into positive angles. As expected, for the frequency range explored, the refraction angle

*r*

_{Max}is constant at ~17°. However,

*r*

_{Max}of the NIM wedge is strongly dependent on the frequency and appears at negative refractive angles.

*f*), for the 901 HWD NIM structure, from the simulated values of the scattering parameters. The values of

*r*

_{Max})/Sin (

*i*), using the experimentally observed position of the refraction angle

*r*

_{Max}. The results shown in Fig. 7 agree within 20% over the frequency range tested (~13.6 to 14.8 GHz).

## 4. Summary and conclusions

## Acknowledgments

## References and links

1. | V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. USPEK1 10, |

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

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

4. | T. Weiland, R. Schuhmann, R.B. Greegor, C.G. Parazzoli, A.M. Vetter, D.R. Smith, D.C. Vier, and S. Schultz, “Ab initio numerical simulation of left-handed metamaterials: comparison of calculation and experiment,” J. App. Phys. |

5. | Microwave Studio and Design Studio are registered trademarks of CST GmbH. |

6. | M. Byindir, K. Aydin, E. Ozbay, P. Markos, and C.M. Soukoulis, “Transmission properties of composite metamaterials in free space,” App. Phys. Lett. |

7. | P Markos and C. M. Soukoulis, “Transmission studies of left-handed materials,” Phys. Rev. B |

8. | R.B. Greegor, C.G. Parazzoli, K. Li, and M.H. Tanielian, “Origin of dissipative losses in negative index of refraction materials,” In press Appl. Phys. Lett. |

9. | R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a twodimensional, isotropic, left-handed metamaterial,” App. Phys. Lett. |

10. | C.G. Parazzoli, R.B. Greegor, K. Li, B.E.C. Koltenbah, and M.H. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s Law,” In press, Phys. Rev. Lett. |

**OCIS Codes**

(160.0160) Materials : Materials

(350.3850) Other areas of optics : Materials processing

**ToC Category:**

Focus Issue: Negative refraction and metamaterials

**History**

Original Manuscript: February 3, 2003

Revised Manuscript: March 15, 2003

Published: April 7, 2003

**Citation**

R. Greegor, C. Parazzoli, K. Li, B. Koltenbah, and M. Tanielian, "Experimental determination and numerical simulation of the properties of negative index of refraction materials," Opt. Express **11**, 688-695 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-7-688

Sort: Journal | Reset

### References

- V. G. Veselago, �??The electrodynamics of substances with simultaneously negative values of permittivity and permeability,�?? Sov. Phys. USPEK1 10, 509 (1968).
- D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, �??A composite medium with simultaneously negative permeability and permittivity,�?? Phys. Rev. Lett. 84, 4184 (2000). [CrossRef] [PubMed]
- R. A. Shelby, D. R. Smith, S. Schultz, �??Experimental verification of a negative index of refraction,�?? Science 292, 77 (2001). [CrossRef] [PubMed]
- T. Weiland, R. Schuhmann, R.B. Greegor, C.G. Parazzoli, A.M. Vetter, D.R. Smith, D.C. Vier and S. Schultz, �??Ab initio numerical simulation of left-handed metamaterials: comparison of calculation and experiment,�?? J. Appl. Phys. 90, 5419 (2001). [CrossRef]
- Microwave Studio and Design Studio are registered trademarks of CST GmbH.
- M. Byindir, K. Aydin, E. Ozbay, P. Markos and C.M. Soukoulis, �??Transmission properties of composite metamaterials in free space,�?? Appl. Phys. Lett. 81, 120 (2002). [CrossRef]
- P Markos and C. M. Soukoulis, �??Transmission studies of left-handed materials,�?? Phys. Rev. B 65, 033401 (2001). [CrossRef]
- R.B. Greegor, C.G. Parazzoli, K. Li and M.H. Tanielian, �??Origin of dissipative losses in negative index of refraction materials,�?? In press Appl. Phys. Lett. 82 (2003).
- R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz, �??Microwave transmission through a two dimensional , isotropic, left-handed metamaterial,�?? Appl. Phys. Lett. 78, 489 (2001). [CrossRef]
- C.G. Parazzoli, R.B. Greegor, K. Li, B.E.C. Koltenbah and M.H. Tanielian, �??Experimental verification and simulation of negative index of refraction using Snell�??s Law,�?? In press, Phys. Rev. Lett. 90(10), (2003).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.