Abstract

We experimentally verify the anomalous phase behavior in metamaterial structures with birefringent materials predicted by Mandatori, et. al. using form birefringent structures. Large birefringence as much as Δn/n = 0.7 has been achieved by surface-treated form birefringent discs, making compact single layer Mandatori structures viable. With a reduced model of a single layer birefringent structure, the relationship between design parameters (thickness and orientation angle) and device operation and performance parameters (such as the center operation frequency, bandwidth, effective negative index, negative group index of refraction, and the transmission throughput) are derived and verified experimentally. Tunable group index of refraction from strong slow light of ng = 29.6 to fast light of ng = -1.1 are measured experimentally.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction index at optical wavelengths," Science 315,47-49 (2007).
    [CrossRef] [PubMed]
  7. V. M. Shalaev, "Optical negative-index metamaterials," Nature Photonics 1,41-48 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (3)

2008 (2)

A. Mandatori, C. Sibilia, M. Bertolotti, and J. W. Haus, "Analysis of negative refraction from anomalous phase in transmission spectrum," Appl. Phys. Lett. 92,251117 (2008).
[CrossRef]

V. A. Markel, "Correct definition of the Poynting vector in electrically and magnetically polarizable medium reveals that negative refraction is impossible," Opt. Express 16,19152-19168 (2008).
[CrossRef]

2007 (4)

U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New J. Phys. 9,254 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction index at optical wavelengths," Science 315,47-49 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, "Optical negative-index metamaterials," Nature Photonics 1,41-48 (2007).
[CrossRef]

M. I. Stockman, "Criterion for negative refraction with low optical losses from a fundamental principle of causality," Phys. Rev. Lett. 98,177404 (2007).
[CrossRef]

2006 (1)

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312,1780-1782 (2006).
[CrossRef] [PubMed]

2005 (3)

A. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68,449-521 (2005).
[CrossRef]

Y. Lu, P. Wang, P. Yao, J. Xie, and M. Hai, "Negative refraction at the interface of uniaxial anisotropic media," Opt. Commun. 246,429-435 (2005).
[CrossRef]

A. Figotin and I. Vitebskiy, "Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers," Phys. Rev. E 72,036619 (2005).
[CrossRef]

2004 (2)

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70,165107 (2004).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305,788-792 (2004).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85,3966-3969 (2000).
[CrossRef] [PubMed]

1994 (1)

Bertolotti, M.

A. Mandatori, C. Sibilia, M. Bertolotti, and J. W. Haus, "Analysis of negative refraction from anomalous phase in transmission spectrum," Appl. Phys. Lett. 92,251117 (2008).
[CrossRef]

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70,165107 (2004).
[CrossRef]

Favaro, A.

Ferrari, J. A.

Figotin, A.

A. Figotin and I. Vitebskiy, "Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers," Phys. Rev. E 72,036619 (2005).
[CrossRef]

French, O.

Grann, E. B.

Hai, M.

Y. Lu, P. Wang, P. Yao, J. Xie, and M. Hai, "Negative refraction at the interface of uniaxial anisotropic media," Opt. Commun. 246,429-435 (2005).
[CrossRef]

Haus, J. W.

A. Mandatori, C. Sibilia, M. Bertolotti, and J. W. Haus, "Analysis of negative refraction from anomalous phase in transmission spectrum," Appl. Phys. Lett. 92,251117 (2008).
[CrossRef]

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70,165107 (2004).
[CrossRef]

Hopcraft, K. I.

Ingrey, P. C.

Jakeman, E.

Kinsler, P.

Leonhardt, U.

U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New J. Phys. 9,254 (2007).
[CrossRef]

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction index at optical wavelengths," Science 315,47-49 (2007).
[CrossRef] [PubMed]

Lu, Y.

Y. Lu, P. Wang, P. Yao, J. Xie, and M. Hai, "Negative refraction at the interface of uniaxial anisotropic media," Opt. Commun. 246,429-435 (2005).
[CrossRef]

Mandatori, A.

A. Mandatori, C. Sibilia, M. Bertolotti, and J. W. Haus, "Analysis of negative refraction from anomalous phase in transmission spectrum," Appl. Phys. Lett. 92,251117 (2008).
[CrossRef]

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70,165107 (2004).
[CrossRef]

Markel, V. A.

McCall, M. W.

Moharam, M. G.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312,1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305,788-792 (2004).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85,3966-3969 (2000).
[CrossRef] [PubMed]

Perciante, C. D.

Philbin, T. G.

U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New J. Phys. 9,254 (2007).
[CrossRef]

Pommet, D. A.

Ramakrishna, A. A.

A. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68,449-521 (2005).
[CrossRef]

Scalora, M.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70,165107 (2004).
[CrossRef]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312,1780-1782 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

V. M. Shalaev, "Optical negative-index metamaterials," Nature Photonics 1,41-48 (2007).
[CrossRef]

Sibilia, C.

A. Mandatori, C. Sibilia, M. Bertolotti, and J. W. Haus, "Analysis of negative refraction from anomalous phase in transmission spectrum," Appl. Phys. Lett. 92,251117 (2008).
[CrossRef]

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70,165107 (2004).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312,1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305,788-792 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction index at optical wavelengths," Science 315,47-49 (2007).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, "Criterion for negative refraction with low optical losses from a fundamental principle of causality," Phys. Rev. Lett. 98,177404 (2007).
[CrossRef]

Vitebskiy, I.

A. Figotin and I. Vitebskiy, "Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers," Phys. Rev. E 72,036619 (2005).
[CrossRef]

Wang, P.

Y. Lu, P. Wang, P. Yao, J. Xie, and M. Hai, "Negative refraction at the interface of uniaxial anisotropic media," Opt. Commun. 246,429-435 (2005).
[CrossRef]

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction index at optical wavelengths," Science 315,47-49 (2007).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305,788-792 (2004).
[CrossRef] [PubMed]

Xie, J.

Y. Lu, P. Wang, P. Yao, J. Xie, and M. Hai, "Negative refraction at the interface of uniaxial anisotropic media," Opt. Commun. 246,429-435 (2005).
[CrossRef]

Yao, P.

Y. Lu, P. Wang, P. Yao, J. Xie, and M. Hai, "Negative refraction at the interface of uniaxial anisotropic media," Opt. Commun. 246,429-435 (2005).
[CrossRef]

Zhukovsky, S.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70,165107 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

A. Mandatori, C. Sibilia, M. Bertolotti, and J. W. Haus, "Analysis of negative refraction from anomalous phase in transmission spectrum," Appl. Phys. Lett. 92,251117 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature Photonics (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nature Photonics 1,41-48 (2007).
[CrossRef]

New J. Phys. (1)

U. Leonhardt and T. G. Philbin, "Quantum levitation by left-handed metamaterials," New J. Phys. 9,254 (2007).
[CrossRef]

Opt. Commun. (1)

Y. Lu, P. Wang, P. Yao, J. Xie, and M. Hai, "Negative refraction at the interface of uniaxial anisotropic media," Opt. Commun. 246,429-435 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70,165107 (2004).
[CrossRef]

Phys. Rev. E (1)

A. Figotin and I. Vitebskiy, "Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers," Phys. Rev. E 72,036619 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

M. I. Stockman, "Criterion for negative refraction with low optical losses from a fundamental principle of causality," Phys. Rev. Lett. 98,177404 (2007).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85,3966-3969 (2000).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

A. A. Ramakrishna, "Physics of negative refractive index materials," Rep. Prog. Phys. 68,449-521 (2005).
[CrossRef]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling Electromagnetic Fields," Science 312,1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305,788-792 (2004).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refraction index at optical wavelengths," Science 315,47-49 (2007).
[CrossRef] [PubMed]

Other (1)

BenA.  Munk, Metamaterials: Critique and Alternatives (Wiley, Hoboken, N.J., 2009).

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Figures (9)

Fig. 1.
Fig. 1.

A single-layer Mandatori structure can be modeled as a birefringent filter with parallel polarizers.

Fig. 2.
Fig. 2.

(a) Accumulated optical phase v.s. thickness d that light passes through. The decreasing optical phase with thickness infers effective negative index of refraction. (b) Spectral phase v.s. optical frequency after light passes through a fixed thickness of the medium. Conventionally the negative slope of the spectral phase corresponds to a group delay. The anomalous spectral phase behavior exhibits a positive slope, implying a negative group delay.

Fig. 3.
Fig. 3.

(a) Form-birefringent ABS disc fabricated using 3-D rapid prototype machine. (b) The measured birefringence and its frequency dependence.

Fig. 4.
Fig. 4.

Enhanced birefringence of a surface-treated form-birefringent ABS disc. Index contrast of Δn/n = 0.7.

Fig. 5.
Fig. 5.

Experimental setup utilizing a free-space X-band architecture with a vector network analyzer (VNA).

Fig. 6.
Fig. 6.

Thickness dependence of the center operating frequency of the anomalous spectral phase. Different curves correspond to single-layer birefringent structures with different thicknesses. The shift of the center operating frequency agrees very well with the theoretical prediction.

Fig. 7.
Fig. 7.

(a) Azimuthal angle dependence of the anomalous spectral phase. The group index is tunable from positive values to negative values by the rotation of the birefringent layer. The sign change happens when the azimuth angle is close to 45 degrees. (b) The intensity transmission spectra.

Fig. 8.
Fig. 8.

Angle dependence of the anomalous spectral phase for a high Δn, 2.5 cm thick, surface treated form-birefringent ABS structure. The large slow light group delay with a bandwidth of 0.3 GHz around the center frequency of 10 GHz exhibits a group index of 29.6.

Fig. 9.
Fig. 9.

Typical transmission spectral phase spectra of a periodic multilayer birefringent structure: (a) Simulation. (b) Measurements. Both show the predicted anomalous spectral phase behavior.

Tables (1)

Tables Icon

Table 1. Center frequency dependence on thickness and the inferred index difference

Equations (7)

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ω m = m d Δ n
n g = n y ( 1 α 1 α Δ n n y )
Δ ω = ω 2 ω 1 = 2 c arccos α d Δ n
T = ( 1 α ) 2
n x = r n 2 + 1 r
n y = 1 r n 2 + 1 r
[ Δ n n y ] max = 1 2 ( n + 1 n ) 1

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