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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 1552–1560
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What makes single-helical metamaterials generate “pure” circularly polarized light?

Lin Wu, ZhenYu Yang, Ming Zhao, Peng Zhang, ZeQing Lu, Yang Yu, ShengXi Li, and XiuHua Yuan  »View Author Affiliations


Optics Express, Vol. 20, Issue 2, pp. 1552-1560 (2012)
http://dx.doi.org/10.1364/OE.20.001552


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Abstract

Circular polarizers with left-handed helical metamaterials can transmit right-handed circularly polarized (RCP) light with few losses. But a certain amount of left-handed circularly polarized (LCP) light will occur in the transmitted light, which is the noise of the circular polarizer. Therefore, we defined the ratio of the RCP light intensity to the LCP light intensity as the signal-to-noise (S/N) ratio. In our previous work, it’s found that circular polarizers with multi-helical metamaterials have two orders higher S/N ratios than that of single-helical metamaterials. However, it has been a great challenge to fabricate such multi-helical structures with micron or sub-micron feature sizes. Is it possible for the single-helical metamaterials to obtain equally high S/N ratios as the multi-helical ones? To answer this question, we systematically investigated the influences of structure parameters of single-helical metamaterials on the S/N ratios using the finite-different time-domain (FDTD) method. It was found that the single-helical metamaterials can also reach about 30dB S/N ratios, which are equal to the multi-helical ones. Furthermore, we explained the phenomenon by the antenna theory and optimized the performances of the single-helical circular polarizers.

© 2012 OSA

1. Introduction

In the last few years, there has been growing interest in the study of the chiral metamaterials both theoretically and experimentally due to the exciting potential applications such as giant optical activity [1

1. Y. Q. Ye and S. L. He, “90° polarization rotator using a bilayered chiral metamaterial with giant optical activity,” Appl. Phys. Lett. 96(20), 203501 (2010). [CrossRef]

,2

2. M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34(16), 2501–2503 (2009). [CrossRef] [PubMed]

], negative index of refraction [3

3. Z. F. Li, H. Caglayan, E. Colak, J. F. Zhou, C. M. Soukoulis, and E. Ozbay, “Coupling effect between two adjacent chiral structure layers,” Opt. Express 18(6), 5375–5383 (2010). [CrossRef] [PubMed]

5

5. Z. F. Li, R. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, ““Chiral metamaterials with negative refractive index based on four “U” split ring resonators,” Appl. Phys. Lett. 97(8), 081901 (2010). [CrossRef]

] and circular dichroism [6

6. H. S. Oh, S. Liu, H. S. Jee, A. Baev, M. T. Swihart, and P. N. Prasad, “Chiral poly(fluorene-alt-benzothiadiazole) (PFBT) and nanocomposites with gold nanoparticles: plasmonically and structurally enhanced chirality,” J. Am. Chem. Soc. 132(49), 17346–17348 (2010). [CrossRef] [PubMed]

8

8. D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express 16(16), 11802–11807 (2008). [CrossRef] [PubMed]

]. In the recent past, Gansel [9

9. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef] [PubMed]

,10

10. J. K. Gansel, M. Wegener, S. Burger, and S. Linden, “Gold helix photonic metamaterials: a numerical parameter study,” Opt. Express 18(2), 1059–1069 (2010). [CrossRef] [PubMed]

] succeeded in developing a circular polarizer using gold single-helical metamaterials. Compared with other familiar methods, this polarizer has advantages of broad wavelength ranges and compact structures which are convenient to be integrated with other optical devices. However, due to the high intensity conversions between left-handed circualrly polarized (LCP) light and right-handed circualrly polarized (RCP) light, when the incident light is RCP light, the transmitted light contains both RCP (regarded as signal) and LCP (regarded as noise) light. Therefore, we defined the ratio of the RCP light intensity to the LCP light intensity as the signal-to-noise (S/N) ratio. The single-helixes, mentioned in the Gansel’s reports, have rather low S/N ratios (~10 dB), which means the ellipticity of the transmitted wave will deviate from 1. In consequence, the low S/N ratios will make the transmitted light not a perfect circularly polarized light and restrict the potential applications of the devices. Recently, we proposed a new type of circular polarizers with multi-helical metamaterials which have about 30dB S/N ratios [11

11. Z. Y. Yang, M. Zhao, and P. X. Lu, “Improving the signal-to-noise ratio for circular polarizers consisting of helical metamaterials” Opt. Express 19(5), 4255–4260 (2011). [CrossRef] [PubMed]

]. But it’s a great challenge to fabricate such multi-helical structures with micron or sub-micron feature sizes. It seems that there is a contradiction between the improvement of the S/N ratio and the simplification of the structure. So there should be one question raised easily: Is it possible for the single-helical metamaterials to obtain equally high S/N ratios as the multi-helical ones?

In this work, we systematically investigated the influences of structure parameters on the S/N ratios of the single-helical metamaterials using the finite-different time-domain (FDTD) method. From the simulation results, we found that the S/N ratios do have significant relationship with the length of the helix (LH), the diameter of the helix (DH) and the spacing of the grid (SG). We also explained the phenomena by the antenna theory [12

12. J. D. Kraus and R. J. Marhefka, “The helical antenna: axial and other modes, Part II,” in Antennas: For All Applications, 3rd ed. (McGraw-Hill, 2003), pp. 251–258.

]. Through the optimization, these single-helical metamaterials can reach the same S/N ratios as the multi-helical ones (~30dB). There are some performance parameters used in this paper. To make them clear, Table 1

Table 1. Definitions of the Helical Metamaterials’ Performances

table-icon
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summarizes the definitions for each of them. The parameters S/N ratio and axial ratio indicate how perfect the transmitted circularly polarized light is. The higher S/N ratios are and the closer to 1 the axial ratios are, the more perfect or “purer” the transmitted circularly polarized light will be. The extinction ratios indicate the differences between the transmittances of RCP and LCP light. With higher extinction ratios, the helical metamaterials exhibit stronger circular dichroism.

2. Simulation model

Circular polarizers consisting of aluminum (Al) single-helical metamaterials were simulated using the FDTD method. Figure 1(a)
Fig. 1 Schematic diagrams of the optical circular polarizers using single-helical metamaterials.
shows the schematic diagrams of the circular polarizer. The helical nanowire structure is supported by the silica substrate. The refractive index of silica is configured for 1.45. The dielectric function of the Al materials is described by the Lorentz-Drude model [13

13. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

]. The broadband Gaussian-modulated pulsed left-handed circualrly polarized light and right-handed circualrly polarized light are used as the excitation source to irradiate the polarizers along the negtive Z direction respectively. The perfectly matched layers (PML) [14

14. J. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]

] is used as the boundary conditions along the Z direction. The boundaries along X and Y directions are confined with the periodic boundary conditions [15

15. P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antenn. Propag. 42(9), 1317–1324 (1994). [CrossRef]

] due to the periodicity of the structure.

Figures 1(b) and 1(c) show the parameters of helical structure array, which includes the length of the helix (LH), the diameter of the helix (DH), the number of helix-period (NH), the diameter of wire (DW), and the spacings of grid (SG).

3. Simulation results and analyses

3.1 Dependence on the Diameter of Wire and the Number of Helix-Period

The single-helical circular polarizers with different DWs and NHs were simulated respectively. Other parameters are LH = 200 nm, SG = 190 nm, DH = 100 nm. The parameters and the simulation results including the average axial ratios and the average S/N ratios are summarized in Table 2

Table 2. Parameters and Simulation Results of Single-helical Circular Polarizers with Different DWs or NHs

table-icon
View This Table
| View All Tables
and shown in Fig. 2
Fig. 2 The comparison of polarization states of the transmitted RCP light of single-helical circular polarizers with different DWs or NHs (represented on the Poincaré sphere).
. Figure 2(a) shows the transmittance spectrum for the structure of DW = 30 nm, and NH = 3. In the Figs. 2(b), 2(c), and 2(d), the Poincaré sphere [16

16. A. Drezet, C. Genet, J. Y. Laluet, and T. W. Ebbesen, “Optical chirality without optical activity: How surface plasmons give a twist to light,” Opt. Express 16(17), 12559–12570 (2008). [CrossRef] [PubMed]

] was used to analyze the polarization states of the transmitted RCP light. Five wavelengths (1.25μm, 1.07μm, 0.93μm, 0.83μm and 0.75μm) were chosen to been plotted on the Poincaré sphere (also plotted on the Fig. 2(a)), each point denotes the polarization states of the corresponding transmitted RCP light. Figures 2(b) and 2(c) show the comparison of the structures with same DWs of 30 nm but different NHs of 3 and 6; Figs. 2(b) and 2(d) compare the structures with same NH of 3 but different DWs of 30 nm and 60 nm. In the figures, these red points indicate the polarization states of the five different wavelengths. For a perfect RCP light, its corresponding point ought to be on the pole of the Poincaré sphere. The closer the red pionts are to the pole, the higher the S/N ratios of the polarizers are and the closer the axial ratios are to the value of 1. Comparing all the results, it is indicated that the average S/N ratios have no obvious changes with the different DWs and NHs.

3.2 Dependence on the Spacing of Grid

Both single-helical circular polarizers with SG = 190 nm and 390 nm were simulated. All other parameters are as follow: LH = 200 nm, DW = 30 nm, DH = 100 nm, NH = 3. The parameters and the simulation results including the average axial ratios and the average S/N ratios are summarized in Table 3

Table 3. Parameters and Simulation Eesults of Single-helical Circular Polarizers with Different SGs

table-icon
View This Table
| View All Tables
and shown in Figs. 3(a)
Fig. 3 The comparison of polarization states of the transmitted RCP light of single-helical circular polarizers with different SGs. (represented on the Poincaré sphere)
and 3(b). It’s clear that the red points in Fig. 3(b) are much closer to the pole than that in Fig. 3(a), which means that increasing the spacing of grid can improve the average S/N ratio evidently.

3.3 Dependence on the Length of Helix and the Diameter of Helix

In this section, the helical circular polarizers with different LHs and DHs were simulated respectively. Other parameters are as follow: DW = 30 nm, NH = 3, SG = 190 nm. The parameters and the simulation results including the average axial ratios and the average S/N ratios are listed in Table 4

Table 4. The parameters and simulation results of single-helical circular polarizers with different LHs or DHs

table-icon
View This Table
| View All Tables
and shown in Figs. 5(a)
Fig. 5 The comparison of polarization states of the transmitted RCP light of single-helical metamaterials with different LHs or DHs (represented on the Poincaré sphere).
, 5(b) and 5(c). These figures show the polarization states of transmitted RCP lights on Poincaré sphere. Figures 5(a) and 5(b) are the comparison of LH = 200 nm and LH = 600 nm. Figures 5(a) and 5(c) are the comparison of DH = 100 nm and DH = 50 nm. It’s obvious that the red points in Fig. 5(b) and 5(c) are closer to the pole than that in Fig. 5(a). From the results, it is clear that increasing the LH and decreasing the DH can both greatly improve the S/N ratios.

Figure 6
Fig. 6 Currents’ paths on the surfaces of the helical metamaterials with different LHs or DHs.
shows the schematic diagram of the currents’ paths on the surfaces of the three single-helix with different LHs or DHs. Comparing the red lines in Figs. 6(a), 6(b) and 6(c), the current flowing along the helixes with longer helixes or shorter diameters of helixes is much steeper. For the current in Fig. 6(a), its horizontal components are predominant, so the interactions between the helix cells are strong, which will result in that the horizontal projection can’t be a perfect circle (shown in Fig. 6(d)). Whereas for the current in Figs. 6(b) and 6(c), its horizontal components are not predominant any more, so the currents don’t have much impact on neighbouring currents, which lead to a perfect circular horizontal projection of the current’s path (shown in Figs. 6(e) and (f)). Therefore, increasing the LH and decreasing the DH can also great improve the S/N ratios.

3.4 Optimized helical circular polarizers

4. Conclusion

In summary, we investigated the influences of the single-helical metamaterals’ structure parameters on the S/N ratios systematically and explained the phenomena in the language of antenna theory. The influences of the structure parameters on the S/N ratios are summarized in Table 5

Table 5. Influences of Structure Parameters on S/N Ratios of Single-helical Metamaterials

table-icon
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| View All Tables
. It was found that by properly designing the structure these single-helical circular polarizers can also reach a high S/N ratio of about 30 dB. Comparing with the multi-helical metamaterials, these single-helical ones have great advantages in fabrication. Although the extinction ratios can’t keep up with the multi-helical ones yet, it’s a sure fire way to fabricate high performance circular polarizers with helical metamaterials.

Acknowledgment

We acknowledge support by the Natural Science Foundation of China (NSFC) (Nos. 11104094, 61007019 and 50735007), Doctoral Fund of Ministry of Education of China (No. 200804871147), the Natural Science Foundation of Hubei Province of China (No. 2008CDB004), and the Fundamental Research Funds for the Central Universities (HUST:Nos. 2010MS063 and 2011TS060).

References and links

1.

Y. Q. Ye and S. L. He, “90° polarization rotator using a bilayered chiral metamaterial with giant optical activity,” Appl. Phys. Lett. 96(20), 203501 (2010). [CrossRef]

2.

M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34(16), 2501–2503 (2009). [CrossRef] [PubMed]

3.

Z. F. Li, H. Caglayan, E. Colak, J. F. Zhou, C. M. Soukoulis, and E. Ozbay, “Coupling effect between two adjacent chiral structure layers,” Opt. Express 18(6), 5375–5383 (2010). [CrossRef] [PubMed]

4.

J. F. Zhou, J. F. Dong, B. N. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B 79(12), 121104 (2009). [CrossRef]

5.

Z. F. Li, R. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, ““Chiral metamaterials with negative refractive index based on four “U” split ring resonators,” Appl. Phys. Lett. 97(8), 081901 (2010). [CrossRef]

6.

H. S. Oh, S. Liu, H. S. Jee, A. Baev, M. T. Swihart, and P. N. Prasad, “Chiral poly(fluorene-alt-benzothiadiazole) (PFBT) and nanocomposites with gold nanoparticles: plasmonically and structurally enhanced chirality,” J. Am. Chem. Soc. 132(49), 17346–17348 (2010). [CrossRef] [PubMed]

7.

M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]

8.

D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express 16(16), 11802–11807 (2008). [CrossRef] [PubMed]

9.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef] [PubMed]

10.

J. K. Gansel, M. Wegener, S. Burger, and S. Linden, “Gold helix photonic metamaterials: a numerical parameter study,” Opt. Express 18(2), 1059–1069 (2010). [CrossRef] [PubMed]

11.

Z. Y. Yang, M. Zhao, and P. X. Lu, “Improving the signal-to-noise ratio for circular polarizers consisting of helical metamaterials” Opt. Express 19(5), 4255–4260 (2011). [CrossRef] [PubMed]

12.

J. D. Kraus and R. J. Marhefka, “The helical antenna: axial and other modes, Part II,” in Antennas: For All Applications, 3rd ed. (McGraw-Hill, 2003), pp. 251–258.

13.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

14.

J. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]

15.

P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antenn. Propag. 42(9), 1317–1324 (1994). [CrossRef]

16.

A. Drezet, C. Genet, J. Y. Laluet, and T. W. Ebbesen, “Optical chirality without optical activity: How surface plasmons give a twist to light,” Opt. Express 16(17), 12559–12570 (2008). [CrossRef] [PubMed]

17.

L. Wu, Z. Y. Yang, M. Zhao, Y. Yu, S. X. Li, Q. P. Zhang, and X. H. Yuan, “Polarization characteristics of the metallic structure with elliptically helical metamaterials,” Opt. Express 19(18), 17539–17545 (2011). [CrossRef] [PubMed]

18.

Z. Y. Yang, M. Zhao, and P. X. Lu, “A numerical study on helix nanowire metamaterials as optical circular polarizers in the visible region,” IEEE Photon. Technol. Lett. 22(17), 1303–1305 (2010). [CrossRef]

OCIS Codes
(260.5430) Physical optics : Polarization
(160.1585) Materials : Chiral media
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: November 7, 2011
Revised Manuscript: December 13, 2011
Manuscript Accepted: December 31, 2011
Published: January 10, 2012

Citation
Lin Wu, ZhenYu Yang, Ming Zhao, Peng Zhang, ZeQing Lu, Yang Yu, ShengXi Li, and XiuHua Yuan, "What makes single-helical metamaterials generate “pure” circularly polarized light?," Opt. Express 20, 1552-1560 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1552


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References

  1. Y. Q. Ye and S. L. He, “90° polarization rotator using a bilayered chiral metamaterial with giant optical activity,” Appl. Phys. Lett.96(20), 203501 (2010). [CrossRef]
  2. M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett.34(16), 2501–2503 (2009). [CrossRef] [PubMed]
  3. Z. F. Li, H. Caglayan, E. Colak, J. F. Zhou, C. M. Soukoulis, and E. Ozbay, “Coupling effect between two adjacent chiral structure layers,” Opt. Express18(6), 5375–5383 (2010). [CrossRef] [PubMed]
  4. J. F. Zhou, J. F. Dong, B. N. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B79(12), 121104 (2009). [CrossRef]
  5. Z. F. Li, R. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, ““Chiral metamaterials with negative refractive index based on four “U” split ring resonators,” Appl. Phys. Lett.97(8), 081901 (2010). [CrossRef]
  6. H. S. Oh, S. Liu, H. S. Jee, A. Baev, M. T. Swihart, and P. N. Prasad, “Chiral poly(fluorene-alt-benzothiadiazole) (PFBT) and nanocomposites with gold nanoparticles: plasmonically and structurally enhanced chirality,” J. Am. Chem. Soc.132(49), 17346–17348 (2010). [CrossRef] [PubMed]
  7. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett.32(7), 856–858 (2007). [CrossRef] [PubMed]
  8. D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express16(16), 11802–11807 (2008). [CrossRef] [PubMed]
  9. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325(5947), 1513–1515 (2009). [CrossRef] [PubMed]
  10. J. K. Gansel, M. Wegener, S. Burger, and S. Linden, “Gold helix photonic metamaterials: a numerical parameter study,” Opt. Express18(2), 1059–1069 (2010). [CrossRef] [PubMed]
  11. Z. Y. Yang, M. Zhao, and P. X. Lu, “Improving the signal-to-noise ratio for circular polarizers consisting of helical metamaterials” Opt. Express19(5), 4255–4260 (2011). [CrossRef] [PubMed]
  12. J. D. Kraus and R. J. Marhefka, “The helical antenna: axial and other modes, Part II,” in Antennas: For All Applications, 3rd ed. (McGraw-Hill, 2003), pp. 251–258.
  13. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt.37(22), 5271–5283 (1998). [CrossRef] [PubMed]
  14. J. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys.114(2), 185–200 (1994). [CrossRef]
  15. P. Harms, R. Mittra, and W. Ko, “Implementation of the periodic boundary condition in the finite-difference time-domain algorithm for FSS structures,” IEEE Trans. Antenn. Propag.42(9), 1317–1324 (1994). [CrossRef]
  16. A. Drezet, C. Genet, J. Y. Laluet, and T. W. Ebbesen, “Optical chirality without optical activity: How surface plasmons give a twist to light,” Opt. Express16(17), 12559–12570 (2008). [CrossRef] [PubMed]
  17. L. Wu, Z. Y. Yang, M. Zhao, Y. Yu, S. X. Li, Q. P. Zhang, and X. H. Yuan, “Polarization characteristics of the metallic structure with elliptically helical metamaterials,” Opt. Express19(18), 17539–17545 (2011). [CrossRef] [PubMed]
  18. Z. Y. Yang, M. Zhao, and P. X. Lu, “A numerical study on helix nanowire metamaterials as optical circular polarizers in the visible region,” IEEE Photon. Technol. Lett.22(17), 1303–1305 (2010). [CrossRef]

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