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Assembling optically active and nonactive metamaterials with chiral units
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1.
1.V. M. Shalaev, Nature Photonics 1, 41 (2007).
http://dx.doi.org/10.1038/nphoton.2006.49
2.
2.D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Physical Review Letters 84, 4184 (2000).
http://dx.doi.org/10.1103/PhysRevLett.84.4184
3.
3.A. Andryieuski, C. Menzel, C. Rockstuhl, R. Malureanu, F. Lederer, and A. Lavrinenko, Physical Review B 82, 235107 (2010).
http://dx.doi.org/10.1103/PhysRevB.82.235107
4.
4.T. Koschny, L. Zhang, and C. M. Soukoulis, Physical Review B 71, 121103R (2005).
http://dx.doi.org/10.1103/PhysRevB.71.121103
5.
5.D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004).
http://dx.doi.org/10.1126/science.1096796
6.
6.J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Physical Review Letters 76, 4773 (1996).
http://dx.doi.org/10.1103/PhysRevLett.76.4773
7.
7.J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, Ieee Transactions on Microwave Theory and Techniques 47, 2075 (1999).
http://dx.doi.org/10.1109/22.798002
8.
8.R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
http://dx.doi.org/10.1126/science.1058847
9.
9.V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, Optics Letters 30, 3356 (2005).
http://dx.doi.org/10.1364/OL.30.003356
10.
10.C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Advanced Materials 18, 1941 (2006).
http://dx.doi.org/10.1002/adma.200600106
11.
11.J. F. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Physical Review B 73, 041101R (2006).
http://dx.doi.org/10.1103/PhysRevB.73.041101
12.
12.G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, Optics Letters 32, 53 (2007).
http://dx.doi.org/10.1364/OL.32.000053
13.
13.J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
http://dx.doi.org/10.1038/nature07247
14.
14.K. Lodewijks, N. Verellen, W. Van Roy, V. Moshchalkov, G. Borghs, and P. Van Dorpe, Applied Physics Letters 98, 091101 (2011).
http://dx.doi.org/10.1063/1.3560444
15.
15.X. Xiong, Z. W. Wang, S. J. Fu, M. Wang, R. W. Peng, X. P. Hao, and C. Sun, Applied Physics Letters 99, 181905 (2011).
http://dx.doi.org/10.1063/1.3656715
16.
16.J. B. Pendry, Physical Review Letters 85, 3966 (2000).
http://dx.doi.org/10.1103/PhysRevLett.85.3966
17.
17.N. Fang, and X. Zhang, Applied Physics Letters 82, 161 (2003).
http://dx.doi.org/10.1063/1.1536712
18.
18.N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
http://dx.doi.org/10.1126/science.1108759
19.
19.J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
http://dx.doi.org/10.1126/science.1125907
20.
20.R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, Science 323, 366 (2009).
http://dx.doi.org/10.1126/science.1166949
21.
21.F. Zhou, Y. J. Bao, W. Cao, C. T. Stuart, J. Q. Gu, W. L. Zhang, and C. Sun, Scientific Reports 1, 78 (2011).
http://dx.doi.org/10.1038/srep00078
22.
22.H. Liu, J. Ng, S. B. Wang, Z. F. Lin, Z. H. Hang, C. T. Chan, and S. N. Zhu, Physical Review Letters 106, 087401 (2011).
http://dx.doi.org/10.1103/PhysRevLett.106.087401
23.
23.S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Physical Review Letters 95, 137404 (2005).
http://dx.doi.org/10.1103/PhysRevLett.95.137404
24.
24.S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, Nature 466, 735 (2010).
http://dx.doi.org/10.1038/nature09278
25.
25.B. Kante, A. de Lustrac, and J. M. Lourtioz, Photonics and Nanostructures-Fundamentals and Applications 8, 112 (2010).
http://dx.doi.org/10.1016/j.photonics.2009.08.001
26.
26.A. Kamli, S. A. Moiseev, and B. C. Sanders, Physical Review Letters 101, 263601 (2008).
http://dx.doi.org/10.1103/PhysRevLett.101.263601
27.
27.J. B. Pendry, Science 306, 1353 (2004).
http://dx.doi.org/10.1126/science.1104467
28.
28.X. Xiong, W. H. Sun, Y. J. Bao, M. Wang, R. W. Peng, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, Physical Review B 81, 075119 (2010).
http://dx.doi.org/10.1103/PhysRevB.81.075119
29.
29.S. Zhang, Y. S. Park, J. S. Li, X. C. Lu, W. L. Zhang, and X. Zhang, Physical Review Letters 102, 023901 (2009).
http://dx.doi.org/10.1103/PhysRevLett.102.023901
30.
30.E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, Physical Review B 79, 035407 (2009).
http://dx.doi.org/10.1103/PhysRevB.79.035407
31.
31.J. F. Zhou, J. F. Dong, B. N. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, Physical Review B 79, 121104R (2009).
http://dx.doi.org/10.1103/PhysRevB.79.121104
32.
32.B. N. Wang, J. F. Zhou, T. Koschny, and C. M. Soukoulis, Applied Physics Letters 94, 151112 (2009).
http://dx.doi.org/10.1063/1.3120565
33.
33.X. Xiong, W. H. Sun, Y. J. Bao, R. W. Peng, M. Wang, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, Physical Review B 80, 201105R (2009).
http://dx.doi.org/10.1103/PhysRevB.80.201105
34.
34.X. Xiong, X. C. Chen, M. Wang, R. W. Peng, D. J. Shu, and C. Sun, Applied Physics Letters 98, 071901 (2011).
http://dx.doi.org/10.1063/1.3554704
35.
35.J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, Science 325, 1513 (2009).
http://dx.doi.org/10.1126/science.1177031
36.
36.J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
37.
37.D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Physical Review B 65, 195104 (2002).
http://dx.doi.org/10.1103/PhysRevB.65.195104
38.
38.M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, Applied Optics 24, 4493 (1985).
http://dx.doi.org/10.1364/AO.24.004493
39.
39.G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, Optics Letters 31, 1800 (2006).
http://dx.doi.org/10.1364/OL.31.001800
40.
40.S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, Physical Review Letters 105, 127401 (2010).
http://dx.doi.org/10.1103/PhysRevLett.105.127401
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Image of FIG. 1.

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FIG. 1.

(a) The elementary building block is a uniaxial gold helix with two and a half turns. The geometrical parameters of the helix are: length (L) = 1.6 mm, outer radius (R) = 0.8 mm, and inner radius (r) = 0.6 mm. (b) The transmission coefficients of an array of helices with x- polarized incidence. A resonant dip in t || and a peak in t appear at 11 GHz. (c) and (d) illustrate the phase difference δ and the azimuth angle of the principal axis of polarization of transmission wave θ as a function of frequency, respectively. (e) illustrates the calculated induced surface electric current distribution on the helix at 11GHz. (f) schematically shows the equivalent electric and magnetic dipoles induced on the helix. In our calculation, the substrate is set as Teflon and the refractive index is 1.63.

Image of FIG. 2.

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FIG. 2.

(a) The structure of the stacked and orthogonally rotated USR pairs with a = 4.0 μm, b = 1.0 μm, and g = 0.6 μm. The thickness of each U pattern is 100 nm. (b) The calculated transmission coefficients of USRs for normal incidence. In the calculation the ambient is set as vacuum and the polarization is along −45°. Two resonances can be detected at ω L (∼420 cm−1) and ω H (∼600 cm−1). (c) and (d): The diagram to show the phase difference δ and the azimuth angle of the principal axis of polarization of transmission wave θ as a function of frequency, respectively. (e) shows the induced surface electric current distribution on USRs at lower (ω L ) (left) and at higher (ω H ) (right) resonant frequencies, respectively. The small red arrows represent the surface current distribution. At the lower frequency ω L , the induced current on upper and lower layers flow in the same direction. At the higher resonant frequency ω H , the induced currents on these two layers flow in the opposite directions. (f) By setting x - and y -axis along the diagonal directions of USRs, the effective induced surface electric current can be projected in x- and y-directions, respectively. One may identify that at ω L and ω H , the electric and magnetic dipoles are induced, respectively.

Image of FIG. 3.

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FIG. 3.

(a) The schematics to show the arrangement of helices in a unit cell. Each helix is separated by 2.4 mm. (b) The plot to show the amplitudes of t ||, t , r || and r . Resonance appears at 11.2 GHz. (c) The plot to show the amplitude of t L, t R and r. (d) The diagram to show the phase difference δ between t , t || and the azimuth angle of the principle axis of polarization of transmission wave θ as a function of frequency, respectively.

Image of FIG. 4.

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FIG. 4.

The retrieved effective optical parameters of helix arrays. (a) illustrates the real parts of the refractive index for LCP and RCP light. (b)-(d) illustrate the real parts of the chiral parameter ξ, permittivity ɛ, and permeability μ, as a function of frequency, respectively.

Image of FIG. 5.

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FIG. 5.

(a) The picture of the helix array insert on a Teflon substrate. The inset is the picture of an individual helix. Each helix is separated by 2.4mm. The geometrical parameters of helix are the same as that listed in Fig. 3. (b) The schematics to show the measurement setup. (c) illustrates the experimental data of the transmission coefficients for LCP and RCP, respectively. (d) illustrates the measured phase difference δ between t , t || and the azimuth angle of the principle axis. (e)-(h) show the refractive index for LCP and RCP, the real parts of the chiral parameter ξ, permittivity ɛ, and permeability μ retrieved from the measured S-parameters, respectively.

Image of FIG. 6.

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FIG. 6.

The elementary building block is a uniaxial gold helix with three turns. The geometrical parameters of the helix are: length (L) = 1.6 mm, outer radius (R) = 0.8 mm, inner radius (r) = 0.6 mm. The lattice parameter is 5.6 mm in both x- and y- directions. (a) and (b) demonstrate the calculated induced surface current at 9 GHz on metallic helices when incident light is x -polarized (a) and y -polarized (b), respectively. (c) and (d) are the schematics to show the equivalent electric and magnetic dipoles on each helix at 9 GHz when incident light is x -polarized (c) and (d) y -polarized, respectively.

Image of FIG. 7.

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FIG. 7.

(a) and (b): the calculated transmission and reflection coefficients for x - and y -polarized incidence. (c) and (d): the retrieved effective permittivity (ɛ) and permeability (μ) for x - and y -polarized incidence, respectively. The shaded regions correspond to region with negative permittivity (ɛ)/permeability (μ).

Image of FIG. 8.

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FIG. 8.

(a) and (b): the calculated distribution of x -component of (a) electric and (b) magnetic fields an cross section z = 0 for x -polarized incidence at 9 GHz. (c) and (d): the calculated distribution of x -component of (c) electric and (d) magnetic fields an cross section z = 0 for y -polarized incidence.

Image of FIG. 9.

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FIG. 9.

(a) The helices of different handedness we use to fabricate the sample. The bar stands for 1.5 mm. (b) shows the helix array sample used for measurement. The substrate is Teflon and the geometrical parameters of the helix array are identical to that in Fig. 6. (c) and (d): the measured transmission (t) and reflection (r) coefficients for x - and y -polarized incidence, respectively. (e) and (f): the retrieved effective permittivity (ɛ) and permeability (μ) for x - and y -polarized incidence retrieved from measured S-parameters.

Image of FIG. 10.

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FIG. 10.

(a) The schematics to show the assembled USR unit cell, in which each building block is identical to that in Fig. 2(a). The distance between two adjacent USR is 2 μm. (b) The transmission (t ||, t ) and reflection (r ||, r ) amplitudes calculated with different output and input signal polarizations. Two resonances can be detected at ω L = 390 cm−1 and ω H = 590 cm−1, respectively. (c) The transmission and reflection amplitudes of left-handed and right-handed circular polarizations. (d) The phase difference δ between t || and t and the rotation angle θ of the major polarization axis of transmitted wave as a function of wave number, respectively. Reprinted with permission from X. Xiong et al., Phys. Rev. B81, 075119 (2010).10.1103/PhysRevB.81.075119 Copyright 2010 by the American Physical Society.

Image of FIG. 11.

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FIG. 11.

The retrieved effective optical parameters of USR arrays. (a) illustrates the real parts of the refractive index for LCP and RCP light, respectively. (b)-(d) illustrate the real parts of the chiral parameter ξ, the permittivity ɛ, and the permeability μ, respectively. Reprinted with permission from X. Xiong et al., Phys. Rev. B81, 075119 (2010).10.1103/PhysRevB.81.075119 Copyright 2010 by the American Physical Society.

Image of FIG. 12.

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FIG. 12.

(a) The scanning electron micrograph of the double-layered USR arrays. The double layer structure can be easily identified from the inset. (b) The schematics to show the measurement setup. In the measurement, the arms of USRs are set in parallel with x - and y -directions. The polarizer in front of and after the sample can be independently rotated with angle θ 1 and θ 2, respectively. (c) Experimentally measured transmission spectra with different polarization of θ 1 and θ 2. The red solid line: θ 1 = θ 2 = −45°; the blue solid line: θ 1 = θ 2 = 0; the black solid line: θ 1 = θ 2 = 45°; the red dash dot line: θ 1 = −45, θ 2 = 45°; the black dash line: θ 1 = 45, θ 2 = −45°; the blue dot line: θ 1 = 90°, θ 2 = 0. (d) Simulation of the transmission T || and T . In simulation damping constant ωτused in Drude model is doubled to fit the loss in real system. Reprinted with permission from X. Xiong et al., Phys. Rev. B81, 075119 (2010).10.1103/PhysRevB.81.075119 Copyright 2010 by the American Physical Society.

Image of FIG. 13.

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FIG. 13.

(a) The structure of stacked and orthogonally rotated USR pairs (U1 and U2). (b) The unit cell constructed with U1 and U2. The elements in the diagonal directions are identical. The geometrical parameter of each USR is identical to that in Fig. 2(a). (c) Transmission coefficients (|t|) with different polarization (θ = 0, x -polarization; θ = π/4; and θ = π/2, y -polarization). Two resonant dips locate at ω L and ω H , respectively. (d) The calculated surface current density excited on USRs at lower and higher resonant frequencies, respectively. The red small arrows represent the calculated local current distribution, and the highlighted arrows represent the effective current. In the calculation both the interlayer and the substrate are set as vacuum, and a = 4.0 μm, b = 1.0 μm, g = 600 nm for each building block in the unit cell. Reprinted with permission from X. Xiong et al., Phys. Rev. B80, 201105–R (2009).10.1103/PhysRevB.80.201105 Copyright 2009 by the American Physical Society.

Image of FIG. 14.

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FIG. 14.

By setting x - and y -axis along the diagonal directions of USRs, we project the induced surface current along x - and y -directions. (a) for x -polarized incident light, at ω L the induced electric fields contributed by U1 and U2 are canceled; whereas the induced magnetic fields sum up and are along the direction of the incident light. In this scenario magnetic response occurs. (b) for y -polarized incident light, at ω L the induced magnetic fields contributed by U1 and U2 are canceled; whereas the induced electric fields sum up and are along the direction of the incident light. In this scenario electric response occurs. (c) and (d) show the situations at high resonant frequency ω H , where electric ((c)) and magnetic ((d)) responses are induced, respectively. It should be noted that the induced magnetic fields in vertical direction,, either cancel out in the unit cell, or along the k vector of incident light. They do not add to the incident field H. Reprinted with permission from X. Xiong et al., Phys. Rev. B80, 201105–R (2009).10.1103/PhysRevB.80.201105 Copyright 2009 by the American Physical Society.

Image of FIG. 15.

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FIG. 15.

(a) The calculated transmission (|t|) and reflection (|r|) coefficients for x -polarized incident light. (b) The retrieved permittivity and permeability with x -polarized incident light. (c) The calculated transmission (|t|) and reflection (|r|) coefficients for y -polarized incident light. (d) The retrieved permittivity and permeability with y -polarized incident light. Reprinted with permission from X. Xiong et al., Phys. Rev. B80, 201105–R (2009).10.1103/PhysRevB.80.201105 Copyright 2009 by the American Physical Society.

Image of FIG. 16.

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FIG. 16.

(a) Scanning electron micrograph of USR array fabricated by alignment nesting lithography. The bar stands for 10 μm. The inset shows the detail micrograph of the unit of USRs. The arms of lower layer USRs look wider than that on the upper layer due to the coverage of Si3N4. (b) Experimentally measured transmission spectra with different polarization. The inset shows the schematics of measurement setup. Two resonance dips can be identified. (c) Retrieved permittivity (black solid line) and permeability (red solid lines) from the experimental data with different polarizations. The dashed lines are from the simulation, which act as the guide of eyes. Reprinted with permission from X. Xiong et al., Phys. Rev. B80, 201105–R (2009).10.1103/PhysRevB.80.201105 Copyright 2009 by the American Physical Society.

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/content/aip/journal/adva/2/4/10.1063/1.4773466
2012-12-28
2014-04-20

Abstract

Metamaterials constructed with chiral units can be either optically active or nonactive depending on the spatial configuration of the building blocks. For a class of chiral units, their effective induced electric and magnetic dipoles, which originate from the induced surface electric current upon illumination of incident light, can be collinear at the resonant frequency. This feature provides significant advantage in designing metamaterials. In this paper we concentrate on several examples. In one scenario, chiral units with opposite chiralities are used to construct the optically nonactive metamaterial structure. It turns out that with linearly polarized incident light, the pure electric or magnetic resonance (and accordingly negative permittivity or negative permeability) can be selectively realized by tuning the polarization of incident light for 90°. Alternatively, units with the same chirality can be assembled as a chiralmetamaterial by taking the advantage of the collinear induced electric and magnetic dipoles. It follows that for the circularly polarized incident light, negative refractive index can be realized. These examples demonstrate the unique approach to achieve certain optical properties by assembling chiral building blocks, which could be enlightening in designing metamaterials.

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Scitation: Assembling optically active and nonactive metamaterials with chiral units
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/4/10.1063/1.4773466
10.1063/1.4773466
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