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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17539–17945
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Polarization characteristics of the metallic structure with elliptically helical metamaterials

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


Optics Express, Vol. 19, Issue 18, pp. 17539-17945 (2011)
http://dx.doi.org/10.1364/OE.19.017539


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Abstract

Abstract: In the last few years, there has been growing interest in the research of the polarizing optics consisting of sub-wavelength metamaterials due to the advantages of broad wavelength ranges, high temperature durability, and compact structures. So far, the metallic structure with the sub-wavelength metamaterials has been proved to achieve the linearly and the circularly polarized light. Therefore, there should be one question raised easily: Is it possible for the metallic structure with sub-wavelength metamaterials to generate the elliptically polarized light? To answer this question, we proposed a metallic structure with elliptically helical nanowires, and analyzed the polarization states of the transmitted light using FDTD method. It is confirmed that this metallic structure does have a giant elliptical dichroism. Furthermore, we also compared the distinct optical performances of elliptical single-, double-, three-, and four-helixes, and made a qualitative explanation for them.

© 2011 OSA

1. Introduction

Polarization of light has been of interest for over a century, in applications across many fields of science and technology. Polarized lights can be classified into the following three types: linearly polarized light, circularly polarized light, and elliptically polarized light [1

1. E. Hecht, Optics (Addison-Wesley, San Francisco, 2002, 4th edition). [PubMed]

]. In the last few years, the metallic structure with sub-wavelength metamaterials has been proved to achieve the linearly [2

2. J. J. Wang, F. Walters, X. M. Liu, P. Sciortino, and X. G. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90(6), 061104 (2007). [CrossRef]

7

7. C. Lei, W. Jian Jim, F. Walters, D. Xuegong, M. Buonanno, S. Tai, and L. Xiaoming, “Large flexible nanowire grid visible polarizer made by nanoimprint lithography,” Appl. Phys. Lett. 90(6), 063111 (2007). [CrossRef]

] and the circularly polarized light [8

8. 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]

12

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

]. Compared with traditional crystal and cube polarizers, the polarizers with the sub-wavelength metamaterials have advantages of broad wavelength ranges, high temperature durability, and compact structures which are convenient to be integrated with other optical devices [3

3. J. J. Wang, L. Chen, X. M. Liu, P. Sciortino, F. Liu, F. Walters, and X. G. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint lithography,” Appl. Phys. Lett. 89(14), 141105 (2006). [CrossRef]

, 7

7. C. Lei, W. Jian Jim, F. Walters, D. Xuegong, M. Buonanno, S. Tai, and L. Xiaoming, “Large flexible nanowire grid visible polarizer made by nanoimprint lithography,” Appl. Phys. Lett. 90(6), 063111 (2007). [CrossRef]

].

From the view of the mathematical description, both the linearly and the circularly polarized light are special cases of the elliptically polarized light [1

1. E. Hecht, Optics (Addison-Wesley, San Francisco, 2002, 4th edition). [PubMed]

]. There should be one question raised easily: Is it possible for the metallic structure with sub-wavelength metamaterials to generate the elliptically polarized light? If it is, this will create much broader potential applications, such as two-dimensional polarization encoding in quantum information processing [13

13. J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39(10), 1549–1554 (2000). [CrossRef] [PubMed]

], coherent population trapping (CPT) of atoms driven by elliptically polarized light [14

14. A. V. Taichenachev, A. M. Tumaikin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69(3), 033410 (2004). [CrossRef]

] and researches on nonlinear polarization rotation in some cubic crystals [15

15. A. Jullien, O. Albert, G. Chériaux, J. Etchepare, S. Kourtev, N. Minkovski, and S. M. Saltiel, “Nonlinear polarization rotation of elliptical light in cubic crystals, with application to cross-polarized wave generation,” J. Opt. Soc. Am. B 22(12), 2635–2641 (2005). [CrossRef]

].

For this purpose, we studied the possibility of the metallic structure generating elliptically polarized light using the finite-difference time-domain (FDTD) method. From the simulation results, it is confirmed that the elliptically polarized light can be realized through such metallic structure with elliptical helixes. And we also made careful analysis of the polarization states of the output light through different elliptically helical structures.

2. Simulation models

Figure 1
Fig. 1 Schematic diagram of the metallic structure consisting of elliptically helical nanowires.
shows the schematic diagram of the metallic structure with elliptically single-helical nanowires. The parameters of the elliptically helical nanowire include diameters of wires (DW), numbers of helix-period (NH), lengths of helix-period (LH), long-axis of elliptical helix (LEH), short-axis of elliptical helix (SEH), and spacing of grids in long-axis direction (SGL) and in short-axis direction (SGS). The axial ratio (ratio of the length of the major semiaxis to that of the minor semiaxis) is 2:1. The metal is aluminum (Al). The elliptically helical nanowires are supported by a silica substrate with refractive index of 1.5. The excitation sources are orthogonal left-elliptically polarized (LEP) light and right-elliptically polarized (REP) light propagating along z axis in free space. They are represented with the following Jones vectors [1

1. E. Hecht, Optics (Addison-Wesley, San Francisco, 2002, 4th edition). [PubMed]

]:LEP:15[12i]       REP:15[2i]

A broadband Gaussian-modulated pulsed light source is used as the excitation source. The perfectly matched layers (PML) [16

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

] are along the z axis. The boundaries along x and y axes are confined with the periodic boundary conditions [17

17. 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]

] owing to the periodicity of the structure. During the calculation, the dielectric function of the metal Al is described by the Lorentz-Drude model [18

18. 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]

].

There are some performance parameters used in this paper. To make them clear, Table 1

Table 1. Definitions of the metallic structure’s performance parameters

table-icon
View This Table
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summarizes the definitions for each of them.

3. Simulation results and analyses

Firstly, we simulated an elliptically single-helical metamaterials with the parameters’ values: DW = 30 nm, NH = 3, LH = 200 nm, LEH = 80 nm, SEH = 40 nm, SGL = 310 nm, and SGS = 170 nm. Figure 2(a)
Fig. 2 (a) Optical performance of the elliptically single-helical metamaterials; (b) The polarization state of the transmitted LEP light represented on the Poincaré sphere.
shows the transmittance and the extinction ratio of the structure. According to the definitions in Table 1, the operation region is 680-1100 nm. In the region, the average transmittance of LEP light is 74% and the average extinction ratio is 11.1 dB. It is obvious that this metamaterials has a giant elliptical dichroism. To analyze the polarization states of the transmitted LEP light in detail, the Poincaré sphere [19

19. I. D. Rukhlenko, C. Dissanayake, and M. Premaratne, “Visualization of electromagnetic-wave polarization evolution using the Poincaré sphere,” Opt. Lett. 35(13), 2221–2223 (2010). [CrossRef] [PubMed]

] is plotted in Fig. 2(b), in which these red points refer to different wavelengths. The coordinates of the points on the Poincaré sphere, their corresponding polarization states and the conversions of LEP are listed in Table 2

Table 2. The polarization states of the transmitted LEP light

table-icon
View This Table
| View All Tables
. From the calculation results, it is clear that the axial ratios of the transmitted LEP light are all around 2:1, which is the same as that of the incident LEP light.

Next, the structures with elliptically double-, three- and four-helical nanowires were simulated. Figure 3(a)
Fig. 3 Comparison of the optical performances of the elliptically double-, three- and four- helical nanowires metamaterials.
, 3(b), and 3(c) show the schematic diagrams of structures with elliptically double-, three-, and four-helical nanowires, respectively. The parameters of the elliptically multi-helical nanowires are the same as those of the single-helical ones above. Figures 3(d), 3(e) and 3(f) are optical performances of such elliptically double-, three- and four-helical structures, respectively. It is obvious that these multi-helical structures do also have giant elliptical dichroism, which is similar to the single-helical ones.

However, along with studying the polarization state of the transmitted light in detail, different characteristics occur. Figures 4(a)
Fig. 4 The polarization state of the transmitted LEP light represented on the Poincaré sphere. (a) Double-helix; (b) Three-helix; (c) Four-helix.
, 4(b) and 4(c) are the polarization states of the transmitted LEP light represented on the Poincaré sphere for the elliptically double-, three- and four-helical nanowires, respectively. The coordinates of the points on the Poincaré sphere, their corresponding polarization states and the conversions of LEP are listed in Table 3

Table 3. The polarization states of the transmitted light of the the structures with elliptically double-, three- and four-helical nanowires

table-icon
View This Table
| View All Tables
. From the results, it is found that the axial ratios of the transmitted LEP light decrease with the increasing of the number of wires in one helix.

These phenomena can be explained in the language of the antenna theory. When the electromagnetic wave propagates through the helical metamaterials, electrical currents will occur in the surfaces of the helical wires. In our case, when the LEP light source propagates through the elliptically helical nanowires, the electrical currents will be on the surfaces of them. We think that there is a certain relationship between the existence of the current and the transmitted light’s polarization states: The handedness of the transmitted light is orthogonal to that of the current’s path. Generally, the path of the current depends on two factors: One is the interaction between the neighbouring helical structures, which we call outer interactions; the other is that among the different helical wires within one multi-helix, which we call inner interactions. With the increase of the number of wires in one helix, the currents’ paths will be more and more dominated by the inner interaction. Therefore, we pay more attention to the inner interaction here. Figure 5
Fig. 5 The schematic diagram of the inner interaction for elliptical multi-helix and the paths of currents
shows the sketch map of the inner interaction for the elliptically multi-helix and the paths of the currents. We take an elliptical double-helix as an example here. The inclination angles of different position on the elliptical helix are not uniform: On both sides of the major axis, the inclination angles (θ) reach minimum (shown in Fig. 5(a)); but on both sides of the minor axis, the inclination angles (Φ) reach maximum (shown in Fig. 5(b)). It’s obvious that the angle Φ is much bigger than θ. Therefore, the paths of the current flowing through the sides of minor axis are much steeper than that flowing through the sides of major axis (shown in Fig. 5(c)).

For the currents flowing through the sides of minor axis, their vertical components are predominant, which leads to repulsive forces between them. And for the currents flowing through the sides of major axis, their horizontal components are predominant, which leads to attractive forces between them. These two forces make the currents’ paths have the following properties: On both sides of the major axis, the current has a trend flowing along the inner surface of the elliptical helix; on both sides of the minor axis, the current has a trend flowing along the outer surface (shown in Fig. 5(d)). Therefore, when the number of wires in one helix increases, the inner interactions will become stronger, and the axial ratio of the transmitted light decreased.

4. Conclusions

In summary, this paper starts with such a question: Is it possible for the metallic structure with sub-wavelength metamaterials to generate the elliptically polarized light? To answer this question, we proposed a metallic structure with elliptically helical nanowires, and analyzed the polarization states of the transmitted light using FDTD method. It is confirmed that this metallic structure does have a giant elliptical dichroism. Furthermore, we also compared the distinct optical performances of elliptically single-, double-, three-, and four-helixes, and made a qualitative explanation for them based on the antenna theory. Finally, it can be expected that with the affirmative answer of our question the metallic structure with sub-wavelength metamaterials will have applications in much broader potential areas such as optical communications, optical computings, and optical sensors.

Acknowledgments

We acknowledge support by the Natural Science Foundation of China (NSFC) (Nos. 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 Special Funds of Central Colleges Basic Scientific Research Operating Expenses (No. 2010MS063).

References and links

1.

E. Hecht, Optics (Addison-Wesley, San Francisco, 2002, 4th edition). [PubMed]

2.

J. J. Wang, F. Walters, X. M. Liu, P. Sciortino, and X. G. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett. 90(6), 061104 (2007). [CrossRef]

3.

J. J. Wang, L. Chen, X. M. Liu, P. Sciortino, F. Liu, F. Walters, and X. G. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint lithography,” Appl. Phys. Lett. 89(14), 141105 (2006). [CrossRef]

4.

J. J. Wang, W. Zhang, X. G. Deng, J. D. Deng, F. Liu, P. Sciortino, and L. Chen, “High-performance nanowire-grid polarizers,” Opt. Lett. 30(2), 195–197 (2005). [CrossRef] [PubMed]

5.

Z. Y. Yang, M. Zhao, N. L. Dai, G. Yang, H. Long, Y. H. Li, and P. X. Lu, “‘Broadband polarizers using dual-layer metallic nanowire grids,” IEEE Photon. Technol. Lett. 20(9), 697–699 (2008). [CrossRef]

6.

Z. Y. Yang and Y. F. Lu, “Broadband nanowire-grid polarizers in ultraviolet-visible-near-infrared regions,” Opt. Express 15(15), 9510–9519 (2007). [CrossRef] [PubMed]

7.

C. Lei, W. Jian Jim, F. Walters, D. Xuegong, M. Buonanno, S. Tai, and L. Xiaoming, “Large flexible nanowire grid visible polarizer made by nanoimprint lithography,” Appl. Phys. Lett. 90(6), 063111 (2007). [CrossRef]

8.

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]

9.

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]

10.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010). [CrossRef]

11.

Z. Y. Yang, M. Zhao, P. X. Lu, and Y. F. Lu, “Ultrabroadband optical circular polarizers consisting of double-helical nanowire structures,” Opt. Lett. 35(15), 2588–2590 (2010). [CrossRef] [PubMed]

12.

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

13.

J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39(10), 1549–1554 (2000). [CrossRef] [PubMed]

14.

A. V. Taichenachev, A. M. Tumaikin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A 69(3), 033410 (2004). [CrossRef]

15.

A. Jullien, O. Albert, G. Chériaux, J. Etchepare, S. Kourtev, N. Minkovski, and S. M. Saltiel, “Nonlinear polarization rotation of elliptical light in cubic crystals, with application to cross-polarized wave generation,” J. Opt. Soc. Am. B 22(12), 2635–2641 (2005). [CrossRef]

16.

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

17.

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]

18.

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]

19.

I. D. Rukhlenko, C. Dissanayake, and M. Premaratne, “Visualization of electromagnetic-wave polarization evolution using the Poincaré sphere,” Opt. Lett. 35(13), 2221–2223 (2010). [CrossRef] [PubMed]

20.

J. D. Kraus and R. J. Marhefka, Antennas: for All Applications (McGraw-Hill, New York, 2003, 3rd edition).

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

ToC Category:
Metamaterials

History
Original Manuscript: June 30, 2011
Revised Manuscript: July 25, 2011
Manuscript Accepted: July 25, 2011
Published: August 22, 2011

Citation
Lin Wu, ZhenYu Yang, Ming Zhao, Yang Yu, ShengXi Li, QianPeng Zhang, and XiuHua Yuan, "Polarization characteristics of the metallic structure with elliptically helical metamaterials," Opt. Express 19, 17539-17945 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17539


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References

  1. E. Hecht, Optics (Addison-Wesley, San Francisco, 2002, 4th edition). [PubMed]
  2. J. J. Wang, F. Walters, X. M. Liu, P. Sciortino, and X. G. Deng, “High-performance, large area, deep ultraviolet to infrared polarizers based on 40 nm line/78 nm space nanowire grids,” Appl. Phys. Lett.90(6), 061104 (2007). [CrossRef]
  3. J. J. Wang, L. Chen, X. M. Liu, P. Sciortino, F. Liu, F. Walters, and X. G. Deng, “30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by UV-nanoimprint lithography,” Appl. Phys. Lett.89(14), 141105 (2006). [CrossRef]
  4. J. J. Wang, W. Zhang, X. G. Deng, J. D. Deng, F. Liu, P. Sciortino, and L. Chen, “High-performance nanowire-grid polarizers,” Opt. Lett.30(2), 195–197 (2005). [CrossRef] [PubMed]
  5. Z. Y. Yang, M. Zhao, N. L. Dai, G. Yang, H. Long, Y. H. Li, and P. X. Lu, “‘Broadband polarizers using dual-layer metallic nanowire grids,” IEEE Photon. Technol. Lett.20(9), 697–699 (2008). [CrossRef]
  6. Z. Y. Yang and Y. F. Lu, “Broadband nanowire-grid polarizers in ultraviolet-visible-near-infrared regions,” Opt. Express15(15), 9510–9519 (2007). [CrossRef] [PubMed]
  7. C. Lei, W. Jian Jim, F. Walters, D. Xuegong, M. Buonanno, S. Tai, and L. Xiaoming, “Large flexible nanowire grid visible polarizer made by nanoimprint lithography,” Appl. Phys. Lett.90(6), 063111 (2007). [CrossRef]
  8. 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]
  9. 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]
  10. G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater.20(7), 1038–1052 (2010). [CrossRef]
  11. Z. Y. Yang, M. Zhao, P. X. Lu, and Y. F. Lu, “Ultrabroadband optical circular polarizers consisting of double-helical nanowire structures,” Opt. Lett.35(15), 2588–2590 (2010). [CrossRef] [PubMed]
  12. Z. Y. Yang, M. Zhao, and P. X. Lu, “How to improve the signal-to-noise ratio for circular polarizers consisting of helical metamaterials?” Opt. Express19(5), 4255–4260 (2011). [CrossRef] [PubMed]
  13. J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt.39(10), 1549–1554 (2000). [CrossRef] [PubMed]
  14. A. V. Taichenachev, A. M. Tumaikin, V. I. Yudin, and G. Nienhuis, “Steady state of atoms in a resonant field with elliptical polarization,” Phys. Rev. A69(3), 033410 (2004). [CrossRef]
  15. A. Jullien, O. Albert, G. Chériaux, J. Etchepare, S. Kourtev, N. Minkovski, and S. M. Saltiel, “Nonlinear polarization rotation of elliptical light in cubic crystals, with application to cross-polarized wave generation,” J. Opt. Soc. Am. B22(12), 2635–2641 (2005). [CrossRef]
  16. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys.114(2), 185–200 (1994). [CrossRef]
  17. 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]
  18. 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]
  19. I. D. Rukhlenko, C. Dissanayake, and M. Premaratne, “Visualization of electromagnetic-wave polarization evolution using the Poincaré sphere,” Opt. Lett.35(13), 2221–2223 (2010). [CrossRef] [PubMed]
  20. J. D. Kraus and R. J. Marhefka, Antennas: for All Applications (McGraw-Hill, New York, 2003, 3rd edition).

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