Abstract

Stacked layers of metal meshes embedded in a dielectric substrate are routinely used for providing spectral selection at THz frequencies. Recent work has shown that particular geometries allow the refractive index to be tuned to produce practical artificial materials. Here we show that by spatially grading in the plane of the mesh we can manufacture a Graded Index (GrIn) thin flat lens optimized for use at THz frequencies. Measurements on a prototype lens show we are able to obtain the parabolic profile of a Woods type lens which is dependent only on the mesh parameters. This technique could realize other exotic optical devices.

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References

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    [CrossRef]

2010 (2)

2009 (1)

2006 (4)

C. Tucker and P. A. R. Ade, “Thermal filtering for large aperture cryogenic detector arrays,” Proc. SPIE6275, 62750T (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

P. A. R. Ade, G. Pisano, S. Weaver, and C. Tucker, “A review of metal mesh filters,” Proc. SPIE6275, 62750U (2006).
[CrossRef]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2000 (1)

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

1982 (1)

S. Lee, G. Zarrillo, and C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antenn. Propag.30(5), 904–909 (1982).
[CrossRef]

1981 (1)

1980 (1)

1973 (1)

C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microw. Theory21(1), 1–6 (1973).
[CrossRef]

1967 (2)

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys.7(1), 37–55 (1967).
[CrossRef]

R. Ulrich, “Effective low-pass filters for far infrared frequencies,” Infrared Phys.7(2), 65–74 (1967).
[CrossRef]

1965 (1)

Ade, P. A. R.

J. Zhang, P. A. R. Ade, P. Mauskopf, L. Moncelsi, G. Savini, and N. Whitehouse, “New artificial dielectric metamaterial and its application as a terahertz antireflection coating,” Appl. Opt.48(35), 6635–6642 (2009).
[CrossRef] [PubMed]

C. Tucker and P. A. R. Ade, “Thermal filtering for large aperture cryogenic detector arrays,” Proc. SPIE6275, 62750T (2006).
[CrossRef]

P. A. R. Ade, G. Pisano, S. Weaver, and C. Tucker, “A review of metal mesh filters,” Proc. SPIE6275, 62750U (2006).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Beigang, R.

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Chen, C.

C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microw. Theory21(1), 1–6 (1973).
[CrossRef]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Fischer, D. J.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Harkrider, C. J.

Krolla, B.

Law, C.-L.

S. Lee, G. Zarrillo, and C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antenn. Propag.30(5), 904–909 (1982).
[CrossRef]

Lee, S.

S. Lee, G. Zarrillo, and C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antenn. Propag.30(5), 904–909 (1982).
[CrossRef]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Mauskopf, P.

McKnight, R.

Moller, K.

Moncelsi, L.

Moore, D. T.

Neu, J.

Paul, O.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Pisano, G.

P. A. R. Ade, G. Pisano, S. Weaver, and C. Tucker, “A review of metal mesh filters,” Proc. SPIE6275, 62750U (2006).
[CrossRef]

Rahm, M.

Reinhard, B.

Richards, P. L.

Savini, G.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Timusk, T.

Tucker, C.

P. A. R. Ade, G. Pisano, S. Weaver, and C. Tucker, “A review of metal mesh filters,” Proc. SPIE6275, 62750U (2006).
[CrossRef]

C. Tucker and P. A. R. Ade, “Thermal filtering for large aperture cryogenic detector arrays,” Proc. SPIE6275, 62750T (2006).
[CrossRef]

Ulrich, R.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys.7(1), 37–55 (1967).
[CrossRef]

R. Ulrich, “Effective low-pass filters for far infrared frequencies,” Infrared Phys.7(2), 65–74 (1967).
[CrossRef]

Weaver, S.

P. A. R. Ade, G. Pisano, S. Weaver, and C. Tucker, “A review of metal mesh filters,” Proc. SPIE6275, 62750U (2006).
[CrossRef]

Whitehouse, N.

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Zarrillo, G.

S. Lee, G. Zarrillo, and C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antenn. Propag.30(5), 904–909 (1982).
[CrossRef]

Zhang, J.

Appl. Opt. (4)

IEEE Trans. Antenn. Propag. (1)

S. Lee, G. Zarrillo, and C.-L. Law, “Simple formulas for transmission through periodic metal grids or plates,” IEEE Trans. Antenn. Propag.30(5), 904–909 (1982).
[CrossRef]

IEEE Trans. Microw. Theory (1)

C. Chen, “Transmission of microwave through perforated flat plates of finite thickness,” IEEE Trans. Microw. Theory21(1), 1–6 (1973).
[CrossRef]

Infrared Phys. (2)

R. Ulrich, “Effective low-pass filters for far infrared frequencies,” Infrared Phys.7(2), 65–74 (1967).
[CrossRef]

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Infrared Phys.7(1), 37–55 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

Nat. Mater. (1)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater.9(5), 387–396 (2010).
[CrossRef] [PubMed]

Nature (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. Lett. (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett.58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Proc. SPIE (2)

C. Tucker and P. A. R. Ade, “Thermal filtering for large aperture cryogenic detector arrays,” Proc. SPIE6275, 62750T (2006).
[CrossRef]

P. A. R. Ade, G. Pisano, S. Weaver, and C. Tucker, “A review of metal mesh filters,” Proc. SPIE6275, 62750U (2006).
[CrossRef]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

Other (8)

HFSS, “High Frequency Structural Simulator”, ANSYS corp., www.ansys.com .

B. Born and W. Wolf, Principles of Optics, 6th Ed. (Cambridge University Press, 1980)

E. Marchand, Gradient Index Optics (New York Academic Press, New York, 1978).

C. Gomez-Reino, M. Perez, and C. Bao, Gradient Index Optics (Springer, 2010).

N. Marcuvitz, Waveguide Handbook,M.I.T. Radiation Laboratory Series (McGraw Hill, 1951).

R. W. Wood, Physical Optics 71 (The MacMillan Company, 1905)

S. Tretyakov, Analytical modeling in Applied Electromagnetics (Artech House Publishers, 2003)

P. A. R. Ade, Astronomical and Atmospheric Studies at Far Infrared Wavelengths (University of London, 1973).

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Figures (5)

Fig. 1
Fig. 1

Modeled index of refraction with HFSS, best analytical fit function (dotted line) and parametric approximation adopted in the patterning algorithm used in the master generation as discussed below.

Fig. 2
Fig. 2

Composite figure with different parts of the single grid-mesh showing the variation of square size and filling factor with position.

Fig. 3
Fig. 3

Picture of the GrIn lens formed from the hot-pressed grids. Detailed structure is difficult to observe not only due to the small structure size but also due to the alignment of subsequent grids.

Fig. 4
Fig. 4

The ratio of spectral transmission data of the Grin Lens compared to the PE lens is shown in black dots. The same measurement performed with a central obscuration shows identical transmission above 420 GHz proving that at higher frequencies there is no transmission within the radius of the obscuration, and also that at these frequencies, the lens is perfectly functional. The lower efficiency at lower frequencies where no cut-off is present (of the red curve compared to the black) can be explained with the ratio of geometrical area corona remaining from the central obscuration. The plateau value of efficiency reached is lower than the optimal efficiency of the black curve in the same region for a de-focused position of the lens due to a longer focal distance.

Fig. 5
Fig. 5

Normalized comparison of lens beam profiles. (Square and Triangle graphs): Cross-scan of canonical polyethylene lens. (Circle-line graph): Cross-scan of Gradient Index lens at the same position. The relative beam-width measured is larger in the GrIn lens (9.2mm) compared to the (7.5mm) of the PE lens due to the longer focal length. The red and blue points indicate separate scan averages in opposite directions (F = Left to Right, B = Right-to-Left).

Equations (3)

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n( a/g )= p 1 ln( a/g )+ p 2
n= n 0 r 2 2df
Δn=n( 0 )n( Δr )= ( Δr ) 2 df

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