## Weaving the invisible thread: design of an optically invisible metamaterial fibre |

Optics Express, Vol. 18, Issue 17, pp. 18095-18105 (2010)

http://dx.doi.org/10.1364/OE.18.018095

Acrobat PDF (4049 KB)

### Abstract

We present the design of an invisible metamaterial fibre operating at optical frequencies, which could be fabricated by adapting existing fibre drawing techniques. The invisibility is realised by matching the refractive index of the metamaterial fibre with the surroundings. We present a general recipe for the fabrication of such fibres, and numerically characterise a specific example using hexagonally arranged silver nanowires in a silica background. We find that invisibility is highly sensitive to details of the metamaterial boundary, a problem that is likely to affect most invisibility and cloaking schemes.

© 2010 OSA

## 1. Introduction

1. J. Ward, “Towards invisible glass,” Vacuum **22**(9), 369–375 (1972). [CrossRef]

2. R. L. Fante, M. T. McCormack, T. D. Syst, and M. A. Wilmington, “Reflection properties of the Salisbury screen,” IEEE Trans. Antenn. Propag. **36**(10), 1443–1454 (1988). [CrossRef]

3. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **72**(1), 016623 (2005). [CrossRef] [PubMed]

5. B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. **103**(15), 153901 (2009). [CrossRef] [PubMed]

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

10. N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express **15**(10), 6314–6323 (2007). [CrossRef] [PubMed]

11. W.-H. Sun, Y. Lu, R.-W. Peng, L.-S. Cao, D. Li, X. Wu, and M. Wang, “Omnidirectional transparency induced by matched impedance in disordered metamaterials,” J. Appl. Phys. **106**(1), 013104 (2009). [CrossRef]

12. Y. Fang and S. He, “Transparent structure consisting of metamaterial layers and matching layers,” Phys. Rev. A **78**(2), 023813 (2008). [CrossRef]

14. J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express **16**(9), 5983–5990 (2008). [CrossRef] [PubMed]

15. A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. **96**(19), 191101 (2010). [CrossRef]

16. M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, and P. S. J. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B **77**(3), 033417 (2008). [CrossRef]

17. Y. Ruan, H. Ebendorff-Heidepriem, and T. M. Monro, “Subwavelength soft glass fibres with extremely small hole size for field enhancement,” in *Proceedings of the Australasian Conference on Optics, Lasers and Spectroscopy and Australian Conference on Optical Fibre Technology* (Adelaide, Australia, 2009).

18. J. C. Knight, “Photonic crystal fibres,” Nature **424**(6950), 847–851 (2003). [CrossRef] [PubMed]

^{3}in volume) and volume production (one preform can in principle be used to make kilometers of fibre). In contrast, the lithographic techniques used for producing metamaterials at operating frequencies from the terahertz to the visible are generally quite expensive, and produce no more than a few cm

^{2}of metamaterial at a time [19

19. A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials (Amst.) **2**(1), 1–17 (2008). [CrossRef]

20. M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express **17**(17), 14851–14864 (2009). [CrossRef] [PubMed]

21. E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. **10**(1), 1–5 (2010). [CrossRef]

*λ*= 633nm for a He:Ne laser) with normal incidence. Our design method is based on matching the effective optical parameters for a metamaterial of 2-dimensional patterned nanocylinders of sub-wavelength pitch to its surroundings. We characterise our invisible fibre via the total scattering cross section

*σ*, showing that

_{T}*σ*has a minimum when the real part of the metamaterial effective refractive index matches the surroundings. Taking the example of a fibre to be invisible at 633nm using silver nanocylinders in a silica cylinder of radius

_{T}*R*= 1μm, we study the behaviour of

*σ*with wavelength, incident angle, and polarisation. In this case more than a 95% reduction in

_{T}*σ*can be achieved over ~13nm bandwidth when compared to dielectric and conducting cylinders of the same size, as well as a 95% reduction in

_{T}*σ*for angles that are ± 10° to normal incidence at 633nm. We find that invisibility is highly sensitive to changes in the metamaterial boundary, with best results when the

_{T}*total*filling fraction – including the metamaterial boundaries – matches the bulk filling fraction. Thus, particular attention should be paid to the fibre preform design process. At larger fibre diameters our invisible metamaterial becomes a near-perfect absorber, due its low reflectance and inherently lossy nature.

## 2. Material design – bulk properties

### 2.1 Principle

*n*= 1 and

*z*= 1 is invisible in vacuum, since

*r*= 0 and

*t = exp(iωL/c)*. Natural materials possess an impedance and refractive index that are not unity at optical wavelengths, and are thus visible; typically bulk metals possess a permittivity

*ε*< 0 and dielectrics possess

_{m}*ε*> 1, with

_{d}*μ*= 1 for both.

*ε*given bywhere

_{eff}*f*is the area filling fraction of the metal (see, for example, Ref [24

24. R. C. McPhedran, N. A. Nicorovici, and L. C. Botten, “The TEM mode and homogenization of doubly periodic structures,” J. Electromagn. Waves Appl. **11**(7), 981–1012 (1997). [CrossRef]

*ε*and

_{m}*ε*at a given wavelength, it is possible to compute the filling fraction at which the composite medium is invisible by solving for

_{d}*ε*= 1 in Eq. (3), yielding

_{eff}*μ*= 1), for

_{eff}*f*satisfying Eq. (4) the effective index and impedance take the values

*n*= 1 and

_{eff}*z*= 1 respectively, as required.

_{eff}*λ*= 633nm using silver (

*ε*= −17.7 + 0.49

_{Ag}*i*from interpolated values of Ref [25

25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

*ε*= 2.123 from the Sellmeier equation [26

_{silica}26. I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. **55**(10), 1205–1208 (1965). [CrossRef]

*ε*= 1.00 + 0.03

_{eff}*i*when

*f*= 0.0567. For a hexagonal lattice of cylinders with radius

*r*and centre-to-centre pitch

*d*, i.e.

*r*= 30nm (the smallest drawn feature reported [17

17. Y. Ruan, H. Ebendorff-Heidepriem, and T. M. Monro, “Subwavelength soft glass fibres with extremely small hole size for field enhancement,” in *Proceedings of the Australasian Conference on Optics, Lasers and Spectroscopy and Australian Conference on Optical Fibre Technology* (Adelaide, Australia, 2009).

*d*= 120nm, in which case

*λ*/

*d*~4 and the electrostatic approximation is not appropriate.

27. R. C. McPhedran, C. G. Poulton, N. A. Nicorovici, and A. B. Movchan, “Low frequency corrections to the static effective dielectric constant of a two-dimensional composite material,” Proc. R. Soc. Lond. A **452**(1953), 2231–2245 (1996). [CrossRef]

### 2.2 Higher order corrections

*r*and

*t*and inverting Eqs. (1) and (2), for different slabs of lengths

*L = d, 2d, 3d*. Following the procedure outlined in [23], using Eq. (5) and (6) we verify that

*z*is independent of

*L*, and unambiguously retrieve

*n*(and thus

*ε*and

*μ*) at a given wavelength.

*r*and

*t*for uniform slabs of hexagonally arranged silver cylinders in a silica background under TE polarisation. Fields around each cylinder are expanded in a multipole basis, where analytic expressions are derived for the cylindrical boundary conditions [28

28. L. C. Botten, N. A. P. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, “Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method,” J. Opt. Soc. Am. A **17**(12), 2165–2176 (2000). [CrossRef]

29. R. C. McPhedran, N. A. Nicorovici, L. C. Botten, and K. A. Grubits, “Lattice sums for gratings and arrays,” J. Math. Phys. **41**(11), 7808–7816 (2000). [CrossRef]

26. I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. **55**(10), 1205–1208 (1965). [CrossRef]

25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

*r*,

*t,*and extract

*n*,

*z*, as a function of

*f*for two fixed unit cell lengths,

*d*= 10nm and

*d*= 100nm. The results are shown in Fig. 3(a) and 3(b): whereas for smaller lattices (

*d*= 10nm, i.e.

*λ*/

*d*~60), calculations are in excellent agreement with the quasistatic theory of Eq. (3), for larger lattices (

*d*= 100nm, i.e.

*λ*/

*d*~6) a significant correctionto the first order theory is required. Analytical work on the homogenisation of arrays of metallic cylinders [27

27. R. C. McPhedran, C. G. Poulton, N. A. Nicorovici, and A. B. Movchan, “Low frequency corrections to the static effective dielectric constant of a two-dimensional composite material,” Proc. R. Soc. Lond. A **452**(1953), 2231–2245 (1996). [CrossRef]

*z*≠ 1/

*n*.

*f =*0.0659 yields an effective index of 1.00 + 0.01

*i*at

*λ*= 633nm for a lattice constant of

*d*= 100nm, corresponding to a cylinder diameter of 2

*r*= 27nm, which can potentially be achieved using fibre drawing techniques.

*d*= 10nm,

*f*= 0.0567 and for

*d*= 100nm,

*f*= 0.0659. In the former case [Fig. 3(c)], all optical parameters are unity at 633nm by design. In the latter case [Fig. 3(d)], the presence of a magnetic response makes it impossible to simultaneously match the refractive index and the impedance to the surroundings. As we will see next, this does not compromise device performance at the desired wavelength. We now characterise its visibility in detail in a fibre geometry.

## 3. Numerical simulations and analysis

30. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. De Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B **19**(10), 2322–2330 (2002). [CrossRef]

31. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B **19**(10), 2331–2340 (2002). [CrossRef]

32. D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A **11**(9), 2526–2538 (1994). [CrossRef]

*R*made out of the metamaterial characterised in Section 2.2. This method allows to characterise visibility via semi-analytical calculations of the scattering cross section (SCS) for any linear polarisation state, azimuthal angle, and incident angle with respect to the cylinder axis [represented by

*δ*,

*φ*and

*θ*respectively, as shown in the schematic of Fig. 4(a) ]. The scattering cross section

*σ*is defined as the total scattered power per unit length at large distances, normalised to the incident power density. In polar coordinates

*(ρ,α)*this is written aswhere

**E**and

^{0}**E**are the incident and scattered electric field, respectively. One then obtains the total SCS

^{S}*σ*by integrating over all angles,

_{T}*W*a complex-valued parameter defined as the width of an ideal shadow which produces the same forward-scattered field as the cylinder being observed [33

_{eq}33. P. S. Kildal, A. A. Kishk, and A. Tengs, “Reduction of forward scattering from cylindrical objects using hardsurfaces,” IEEE Trans. Antenn. Propag. **44**(11), 1509–1520 (1996). [CrossRef]

*σ*= 2

_{T}*Re(W*. It follows, for example, that at a given wavelength a perfectly conducting cylinder of radius R possesses

_{eq})*σ*2 in the limit of

_{T}/2R =*R*→∞, whereas a perfectly absorbing cylinder possesses

*σ*/

_{T}*2R =*1 in the same limit. We refer to the vast literature on the scattering cross section for further details [34].

*σ*at optical wavelengths for a fibre composed of the metamaterial presented in Section 2.2, formed by 361 hexagonally arranged silver cylinders with radius

_{T}*r*= 13.5nm and pitch

*d*= 100nm within a silica cylinder of radius

*R*= 1μm in vacuum. We consider normal incidence, with the electric field parallel to the cylinders (TE polarisation,

*θ*= 90°,

*δ*= 90°). The results are shown in Fig. 4(b): the metamaterial fibre has

*σ*/

_{T}*2R*= −12.6dB at

*λ*= 633nm, corresponding to more than a 97% reduction in shadow when compared to equivalent silver or silica cylinders of the same size. Furthermore, the metamaterial fibre has

*σ*/

_{T}*2R*< 0.1 over a 13nm bandwidth (95% reduction in shadow). Additionally, an effective reduction of

*σ*occurs over ~100nm with respect to either of its constituent materials. The inset of Fig. 4(b) presents the normalised total SCS at normal incidence for

_{T}*λ*= 633nm, as a function of the azimuthal angle

*φ*, demonstrating −12 ± 0.6 dB reduction of total SCS at all angles. The corresponding contour plot of the electric field at

*λ*= 633nm for these three cylinders is shown in Fig. 5(a) –5(c); the designed fibre indeed appears invisible, exhibiting low scattering and loss.

*σ*for the same cylinder possessing an effective

_{T}*ε*and

*μ*retrieved in Section 2.2 [Fig. 3(d)], finding excellent agreement with the full multipole calculation [Fig. 4(b)]. The minimum SCS occurs at a wavelength when

*Re(n)*= 1 (minimum phase change), as opposed to when

*Re(z)*= 1 (minimum reflection). Thus, the interference due to a phase change through the fibre, due to a small perturbation in

*n*, has a more significant effect on

*σ*than a reflection due to a small perturbation in

_{T}*z.*This is further illustrated in Fig. 5(d) and 5(e), which compares the scattered electric field magnitude

**|E**| for the metamaterial fibre at λ = 593nm (

^{S}*Re(z)*= 1.00,

*Re(n)*= 1.08) and

*λ*= 633nm (

*Re(z)*= 1.07,

*Re(n)*= 1.00).

## 4. Incident angle, polarisation, and size dependence

*σ*on polarisation and incident angle with respect to the cylinder axis (

_{T}*δ*and

*θ*respectively). Thus far we have considered the case

*δ*= 90°,

*θ*= 90°, corresponding to TE polarisation at normal incidence. Figure 6(a) shows a density plot of total scattering cross section as a function of incident angle, while maintaining the polarisation (i.e. we fix

*δ*= 90° and vary

*θ*). Note that

*σ*< −10dB for

_{Τ}*θ*= 90 ± 10° with respect to the normal at

*λ*= 633nm. As we increase the incident angle, the regions of minimum scattering move to longer wavelengths, and for

*θ*= 90 ± 50° there exists a wavelength range where

*σ*/

_{T}*2R*< 1 over a bandwidth of ~10nm.

*θ*= 90° and vary

*δ*). As expected, the regions of smallest scattering correspond to TE polarisation. As the electric field along the fibre decreases, so does the

*σ*. For purely TM polarisation (magnetic field directed along the wires), the cylinder behaves like a dielectric.

_{T}*n*= 1.00 + 0.01

*i*at

*λ*= 633nm, corresponding to a loss of 0.43dB/μm; achieving a low-loss transparent metamaterial is thus only truly possible at smaller fibre radii. We now examine the influence of metamaterial fibre dimensions on the total scattering cross section.

*R*,

*σ*

_{T}/

*2R*reaches unity, thus behaving like a near-perfect absorber. In contrast, the normalised SCS for silver and silica cylinders tends to 2 at large radii, as expected.

*R*, using the multipole method. The fibres are silica cylinders of radius R centred in the origin, containing silver nanocylinders with

*r*= 13.5nm arranged in a hexagonal array of pitch

*d*= 100nm, such that nanocylinder distance from the origin is

*ρ*<

*R-r*. Since the number of cylinders

*N*increases stepwise with

*R*, the total filling fraction

*f*=

_{T}*Nr*when increasing

^{2}/R^{2}*R*is not constant, and goes through discontinuities. When

*f*differs from the ideal value of

_{T}*f*, regions at the boundary exist for which the local effective index near the boundary of the metamaterial fibre is not unity, causing increased scattering. Minimal

*σ*is thus achieved at values of

_{T}*R*for which

*f*= 0.659. In particular, we observe the lowest normalised SCS of−24dB for a metamaterial cylinder of

_{T}*R*= 230nm. Despite possessing significantly lower SCS compared to silver and silica cylinders of the same size,

*σ*is strongly sensitive to total filling fraction, since scattering occurs when the local filling fraction at the metamaterial boundary significantly deviates from that required by design. For example, the inset of Fig. 7 shows a contour plot of the electric field for

_{T}*R*= 470nm (containing 73 nanocylinders, thus

*f*= 0.602 and

_{T}*σ*/

_{T}*2R*= −6.2dB) and

*R*= 480nm (containing 85 nanocylinders, thus

*f*= 0.672 and a much reduced normalised total SCS,

_{T}*σ*/

_{T}*2R*= −19.4dB).

*R*= 3μm already contains 3241 silver nanocylinders. Due to memory constraints, we could not perform a full calculation of the metamaterial total SCS for

*R*> 3μm.

## 6. Conclusions and future outlook

14. J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express **16**(9), 5983–5990 (2008). [CrossRef] [PubMed]

15. A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. **96**(19), 191101 (2010). [CrossRef]

17. Y. Ruan, H. Ebendorff-Heidepriem, and T. M. Monro, “Subwavelength soft glass fibres with extremely small hole size for field enhancement,” in *Proceedings of the Australasian Conference on Optics, Lasers and Spectroscopy and Australian Conference on Optical Fibre Technology* (Adelaide, Australia, 2009).

## Acknowledgements

## References and links

1. | J. Ward, “Towards invisible glass,” Vacuum |

2. | R. L. Fante, M. T. McCormack, T. D. Syst, and M. A. Wilmington, “Reflection properties of the Salisbury screen,” IEEE Trans. Antenn. Propag. |

3. | A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

4. | A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express |

5. | B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. |

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

7. | 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 |

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

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

10. | N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express |

11. | W.-H. Sun, Y. Lu, R.-W. Peng, L.-S. Cao, D. Li, X. Wu, and M. Wang, “Omnidirectional transparency induced by matched impedance in disordered metamaterials,” J. Appl. Phys. |

12. | Y. Fang and S. He, “Transparent structure consisting of metamaterial layers and matching layers,” Phys. Rev. A |

13. | C. Yang, J. Yang, M. Huang, J. Shi, and J. Peng, “Electromagnetic cylindrical transparent devices with irregular cross section,” Radioengineering |

14. | J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express |

15. | A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. |

16. | M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, and P. S. J. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B |

17. | Y. Ruan, H. Ebendorff-Heidepriem, and T. M. Monro, “Subwavelength soft glass fibres with extremely small hole size for field enhancement,” in |

18. | J. C. Knight, “Photonic crystal fibres,” Nature |

19. | A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials (Amst.) |

20. | M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express |

21. | E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. |

22. | A. Tuniz, P. Chen, B. T. Kuhlmey, and S. C. Fleming, “Design of an optical hyperlens with metallic nanocylinders,” in |

23. | P. Markos, and C. M. Soukoulis, |

24. | R. C. McPhedran, N. A. Nicorovici, and L. C. Botten, “The TEM mode and homogenization of doubly periodic structures,” J. Electromagn. Waves Appl. |

25. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

26. | I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. |

27. | R. C. McPhedran, C. G. Poulton, N. A. Nicorovici, and A. B. Movchan, “Low frequency corrections to the static effective dielectric constant of a two-dimensional composite material,” Proc. R. Soc. Lond. A |

28. | L. C. Botten, N. A. P. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, “Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method,” J. Opt. Soc. Am. A |

29. | R. C. McPhedran, N. A. Nicorovici, L. C. Botten, and K. A. Grubits, “Lattice sums for gratings and arrays,” J. Math. Phys. |

30. | T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. De Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B |

31. | B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B |

32. | D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A |

33. | P. S. Kildal, A. A. Kishk, and A. Tengs, “Reduction of forward scattering from cylindrical objects using hardsurfaces,” IEEE Trans. Antenn. Propag. |

34. | E. F. Knott, J. F. Shaeffer, and M. T. Tuley, |

**OCIS Codes**

(060.2400) Fiber optics and optical communications : Fiber properties

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: June 30, 2010

Revised Manuscript: August 4, 2010

Manuscript Accepted: August 5, 2010

Published: August 6, 2010

**Citation**

Alessandro Tuniz, Boris T. Kuhlmey, Parry Y. Chen, and Simon C. Fleming, "Weaving the invisible thread: design of an optically invisible metamaterial fibre," Opt. Express **18**, 18095-18105 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-18095

Sort: Year | Journal | Reset

### References

- J. Ward, “Towards invisible glass,” Vacuum 22(9), 369–375 (1972). [CrossRef]
- R. L. Fante, M. T. McCormack, T. D. Syst, and M. A. Wilmington, “Reflection properties of the Salisbury screen,” IEEE Trans. Antenn. Propag. 36(10), 1443–1454 (1988). [CrossRef]
- A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005). [CrossRef] [PubMed]
- A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express 15(6), 3318–3332 (2007). [CrossRef] [PubMed]
- B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Experimental verification of plasmonic cloaking at microwave frequencies with metamaterials,” Phys. Rev. Lett. 103(15), 153901 (2009). [CrossRef] [PubMed]
- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (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,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]
- J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009). [CrossRef] [PubMed]
- T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]
- N. A. Nicorovici, G. W. Milton, R. C. McPhedran, and L. C. Botten, “Quasistatic cloaking of two-dimensional polarizable discrete systems by anomalous resonance,” Opt. Express 15(10), 6314–6323 (2007). [CrossRef] [PubMed]
- W.-H. Sun, Y. Lu, R.-W. Peng, L.-S. Cao, D. Li, X. Wu, and M. Wang, “Omnidirectional transparency induced by matched impedance in disordered metamaterials,” J. Appl. Phys. 106(1), 013104 (2009). [CrossRef]
- Y. Fang and S. He, “Transparent structure consisting of metamaterial layers and matching layers,” Phys. Rev. A 78(2), 023813 (2008). [CrossRef]
- C. Yang, J. Yang, M. Huang, J. Shi, and J. Peng, “Electromagnetic cylindrical transparent devices with irregular cross section,” Radioengineering 19, 136–140 (2010).
- J. Hou, D. Bird, A. George, S. Maier, B. T. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008). [CrossRef] [PubMed]
- A. Tuniz, B. T. Kuhlmey, R. Lwin, A. Wang, J. Anthony, R. Leonhardt, and S. C. Fleming, “Drawn metamaterials with plasmonic response at terahertz frequencies,” Appl. Phys. Lett. 96(19), 191101 (2010). [CrossRef]
- M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, and P. S. J. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008). [CrossRef]
- Y. Ruan, H. Ebendorff-Heidepriem, and T. M. Monro, “Subwavelength soft glass fibres with extremely small hole size for field enhancement,” in Proceedings of the Australasian Conference on Optics, Lasers and Spectroscopy and Australian Conference on Optical Fibre Technology (Adelaide, Australia, 2009).
- J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003). [CrossRef] [PubMed]
- A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials (Amst.) 2(1), 1–17 (2008). [CrossRef]
- M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17(17), 14851–14864 (2009). [CrossRef] [PubMed]
- E. J. Smith, Z. Liu, Y. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010). [CrossRef]
- A. Tuniz, P. Chen, B. T. Kuhlmey, and S. C. Fleming, “Design of an optical hyperlens with metallic nanocylinders,” in Proceedings of META '10, 2nd International Conference on Metamaterials, Photonc Crystals and Plasmonics (Cairo, Egypt, 2010).
- P. Markos, and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, 2008), Chap. 14.
- R. C. McPhedran, N. A. Nicorovici, and L. C. Botten, “The TEM mode and homogenization of doubly periodic structures,” J. Electromagn. Waves Appl. 11(7), 981–1012 (1997). [CrossRef]
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
- I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” J. Opt. Soc. Am. 55(10), 1205–1208 (1965). [CrossRef]
- R. C. McPhedran, C. G. Poulton, N. A. Nicorovici, and A. B. Movchan, “Low frequency corrections to the static effective dielectric constant of a two-dimensional composite material,” Proc. R. Soc. Lond. A 452(1953), 2231–2245 (1996). [CrossRef]
- L. C. Botten, N. A. P. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, “Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method,” J. Opt. Soc. Am. A 17(12), 2165–2176 (2000). [CrossRef]
- R. C. McPhedran, N. A. Nicorovici, L. C. Botten, and K. A. Grubits, “Lattice sums for gratings and arrays,” J. Math. Phys. 41(11), 7808–7816 (2000). [CrossRef]
- T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. De Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002). [CrossRef]
- B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19(10), 2331–2340 (2002). [CrossRef]
- D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11(9), 2526–2538 (1994). [CrossRef]
- P. S. Kildal, A. A. Kishk, and A. Tengs, “Reduction of forward scattering from cylindrical objects using hardsurfaces,” IEEE Trans. Antenn. Propag. 44(11), 1509–1520 (1996). [CrossRef]
- E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar cross section (New York: SciTech Publishing, 2004), Chapter 3.

## 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.