Higher extinction ratio circular polarizers with hetero-structured double-helical metamaterials

doi:10.1364/OE.19.010886

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Higher extinction ratio circular polarizers with hetero-structured double-helical metamaterials

Yang Yu, Zhenyu Yang, Shengxi Li, and Ming Zhao »View Author Affiliations

Optics Express, Vol. 19, Issue 11, pp. 10886-10894 (2011)
http://dx.doi.org/10.1364/OE.19.010886

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– Abstract
1. Introduction
2. Simulation models
3. Simulation results and analyses
4. Conclusions
– References and links

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Abstract

We have recently shown circular polarizers with the homo-structured double-helical metamaterials, which have broader operation bands than those of the single-helical structures [Opt. Lett. 35, 2588 (2010)]. However, trying to get more operation bands deteriorates the extinction ratio. In this paper, we proposed circular polarizers with hetero-structured double-helical metamaterials. The extinction ratios of these circular polarizers are two times higher than those with homo-structured double-helical metamaterials. Furthermore, we qualitatively explained the phenomenon of the higher extinction ratio from the viewpoint of the interaction between the two helix-wires in a double-helical unit.

1. Introduction

Chirality is inherently a three-dimensional (3D) phenomenon and occurs, for example, for DNA, cholesteric liquid crystals, screws, and circular metal helices. In the last few years, there has been growing interest in the study of the chiral metamaterials in the research community both theoretically and experimentally due to the exciting potential applications ranging from giant optical activity [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]

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]

] to negative index of refraction [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

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

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]

–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

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]

] succeeded in developing a broadband circular polarizer using gold single-helical metamaterials. The devices offer giant circular dichroism in an operation band of 3-6 μm. Compared with other optical devices, the circular polarizers with the helical metamaterials have advantages of broad wavelength ranges and compact structures which are convenient to be integrated [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]

]. Recently, it was reported that a new type of circular polarizers with homo-structured double-helical metamaterials have operation bands more than 50% broader than the single-helical structures [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 Y. F. Lu, “Similar structures, different characteristics: optical performances of circular polarizers with single- and double-helical metamaterials,” J. Lightwave Technol. 28, 3415–3421 (2010).

]. However, trying to get more operation bands deteriorates the extinction ratio.

In this letter, we proposed double-helical circular polarizers with hetero-structured helical metamaterials, and the interaction between the two helix wires was discussed. We used the finite difference time domain (FDTD) method to study the optical properties of the metamaterials. From the simulation results, it is found that the double-helical circular polarizers with hetero-structured metamaterials have extinction ratios two times higher than those with homo-structured metamaterials. This phenomenon of the higher extinction ratio can be explained qualitatively through the interaction between the two helix-wires in a double-helical unit.

There are some performance parameters used in this paper. To make them clear, Table 1 summarizes the definitions for each of them. In this paper, the homo-structured helical metamaterials is for the structure in which the two helix-wires in a double-helical unit are the same materials, and the hetero-structured is for the structure in which the two helix-wires in a double-helical unit are different materials.

Table 1 Definitions of the Double-Helical Circular Polarizer’s Performance Parameters ^a

	Definitions (take left-circular helix as example)
T(LCP)	$I_{t r}^{L C P} / I_{i n}^{L C P}$
T(RCP)	$I_{t r}^{R C P} / I_{i n}^{R C P}$
Extinction ratio	$T (R C P) / T (L C P)$
Operation band	The wavelength range on which the extinction ratio is above 10:1

^a T(LCP): average transmittances of LCP light; T(RCP): average transmittances of RCP light;

I_{i n}^{L C P}

: intensity of incident LCP light;

I_{i n}^{R C P}

: intensity of incident RCP light;

I_{t r}^{L C P}

: intensity of transmitted LCP light;

I_{t r}^{R C P}

: intensity of transmitted RCP light.

2. Simulation models

Figure 1 shows the structure of the circular polarizers with homo-structured (Fig. 1(a)) and hetero-structured (Fig. 1(b)) double-helical metamaterials, in which DW, NH, SG, LH, and DH stand for the diameter of the wire, the number of the helix periods, the spacing of the grid, the length of the helix period, and the diameter of the helix, respectively (Fig. 1(c)). The helical nanowire structure is supported by a silica substrate. The refractive index of silica is configured for 1.45. The excitation sources were two circularly polarized states of light, left-handed circular polarization (LCP) and right- handed circular polarization (RCP), which respectively illuminated the helical strucuture along the positive Z direction. A broadband Gaussian-modulated pulsed light source is used as the excitation source. The Lorentz-Drude model was used to describe the metal material [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]

]. The boundary conditions along Z direction are the perfectly matched layers (PML) [14

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

]. And along X and Y directions, the periodic boundary conditions (PBC) [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]

] are used due to the periodicity of the metamaterials.

Fig. 1 Schematic diagrams of the hetero- and homo-structured helical optical circular polarizers.

3. Simulation results and analyses

3.1 Optical performances of hetero- and homo-structured helical circular polarizers

Circular polarizers with different homo-structured double-helical metamaterials: argentum (Ag), aluminium (Al) and platinum (Pt), and hetero-structured double-helical metamaterials: Ag-Pt and Al-Pt were simulated. The parameters of the structure are as follows: LH = 200 nm, SG = 1.8 μm, NH = 3, DH = 0.92 μm, and DW = 0.54 μm. The simulation results are shown in Fig. 2 and the related optical parameters, the average transmittances for the RCP and LCP light and the average extinction ratios in the operation band are compared in Table 2 .

Fig. 2 Optical performances of the homo and hetero-structured double-helical circular polarizers.

Table 2 Optical Performances of the Homo and Hetero-Structured Double-Helical Circular Polarizers ^a

	OB (μm)	T (RCP)	T(LCP)	AER
Ag-Ag	0.62-1.27	52%	2.8%	21:1
Al-Al	0.44-1.12	48%	1.8%	31:1
Pt-Pt	0.55-1.15	22%	0.8%	31:1
Ag-Pt	0.46-1.15	40%	1.4%	37:1
Al-Pt	0.48-1.07	30%	0.8%	43:1

^a OB: Operation band, T (RCP): Average transmittances of RCP Light, T (LCP): Average transmittances of LCP Light, AER: Average extinction ratio.

Figures 2(a), 2(b), and 2(c) show the optical performances of the homo-structured double-helical optical circular polarizers; Figs. 2(d) and 2(e) show the optical performances of the hetero-structured double-helical circular polarizers. It is very clear that the transmittances of the light decrease from Fig. 2(a) to Fig. 2(c), and the transmittances of the light in Fig. 2(d) are higher than those in Fig. 2(e). Moreover, the extinction ratios of the optical polarizers with hetero-structured double-helical matematerials are higher than those with homo-structured double-helical matematerials.

These phenomena can be explained from the antenna theory. The motif of our metamaterial structures is similar to the helical antennas with the so-called end-fire geometry. Such helical antennas are widely used in microwave wireless local-area networks (WLAN) [16

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.

]. In the analysis of antenna, there are electric currents on the helical wires when light transmitted through the helix. For the double-helical structure, we think that the two helix-wires in a double-helical unit are in parallel connection, and the equivalent resistivity of the double-helical wire can be expressed as:

ρ = \frac{ρ_{1} \cdot ρ_{2}}{ρ_{1} + ρ_{2}}

(1)

Where ρ ₁ and ρ ₂ are the resistivity of the two helix wires, respectively. The equivalent resistivities of the double-helical metamaterials are shown in Table 3 . Following antenna theory [16

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.

] and our previous work [12

,17

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

], we know that the current decreased with increasing of the resistivity, which led to the declining of the light transmittances. Therefore, the transmittances of the light decreased from Fig. 2(a) to Fig. 2(c), and the transmittances of the light in Fig. 2(d) are higher than those in Fig. 2(e).

Table 3 The Equivalent Resistivity of the Double-Helical Optical Circular Polarizers

	Ag-Ag	Al-Al	Pt-Pt	Ag-Pt	Al-Pt
$ρ (Ω \cdot m)$	0.793 × 10⁻⁸	1.329 × 10⁻⁸	5.300 × 10⁻⁸	1.380 × 10⁻⁸	2.123 × 10⁻⁸

Furthermore, when the value of LH is not too large, the electric currents of the two helix-wires in a double-helical unit had the contrary directions, which generated two attractive interaction forces between the two helix-wires (shown in Figs. 3(a) and 3(b)). This made the electric current flow to the inner wall of the helix, which was equivalent to decrease the DH. From our previous work [12

], it has been observed that the decreasing of the DH led to the increasing of the transmittances of the light. The interaction force of hetero-structured double-helical polarizer was larger than the homo-structured one, which made the electric current of the two helix-wires flow more inner (shown in Figs. 3(c) and 3(d)). When the RCP light transmitted though the polarizers, the current magnitude in the helix-wires were large, and the function of the interaction force was obvious. Therefore, compared with the homo-structured double-helical polarizer, the RCP light transmittance of the hetero-structured one was enhanced greatly. However, the current magnitude was very small when the LCP light transmitted through the polarizers, and the interaction force between the two helix-wires was very weak. Therefore, the electric current still flowed in the outer radius of the helix. Thus, the LCP light transmittance of the hetero-structured double-helical polarizer was not increased much. In summary, the extinction ratio obtained a very big promotion.

Fig. 3 Difference between the homo- and hetero-structured double-helical circular polarizers. F₁, F₂: interaction force; I₁, I_2: current magnitude of the helix-wires; CP: current’s path; OW: outer wall of the helix; IW: inner wall of the helix.

3.2 Influence of different parameters

3.2.1 Comparison of different number of helix-period

In the following simulation, Al and Pt were used as the helical materials for the hetero-structured double-helical circular polarizers. Figure 4 and Table 4 show the optical performances of Al-Pt hetero-structured double-helical circular polarizers with different number of helix-period. All other parameters are fixed to their respective values in Fig. 2(a).

Fig. 4 Optical performances of Al-Pt hetero-structured double-helical polarizers with different number of helix-period.

Table 4 Optical Performances of Al-Pt Hetero-Structured Double-Helical Polarizers with Different Number of Helix-Period ^a

	OB (μm)	T (RCP)	T(LCP)	AER
NH = 1	AER<10:1, the polarizer does not work			<10:1
NH = 2	0.53-1.05	37%	2%	20:1
NH = 3	0.48-1.21	28%	0.8%	42:1
NH = 4	0.47-1.24	21%	0.5%	73:1

^a NH: Number of helix-period, OB: Operation band, T (RCP): Average transmittances of RCP Light, T (LCP): Average transmittances of LCP Light, AER: Average extinction ratio.

It is clear that the extinction ratio is significantly enhanced with the increase of the number of helix-period. When the number of helix-period is increased, the resistance of the helix-wires is enhanced. Therefore, the transmittances of RCP and LCP light decreased. However, since the decreasing rate of the LCP light is much higher than the RCP light, the extinction ratio is enhanced with the increase of the number of helix-period. On the other hand, too large NH will lead to great deteriorations of transmittances and difficulties of fabrication processes. Therefore, a number of helix-period of 4 is properly selected for the hetero-structured double-helical circular polarizer.

3.2.2 Comparison of different length of helix-period

Figure 5 and Table 5 show the optical performances of Al-Pt hetero-structured double-helical polarizers with different length of helix-period. All other parameters are fixed to their respective values in Fig. 2(a). From the simulation results, it becomes obvious that the increase of the length of helix-period leads to the red shift of the operation region. It is because that the current directions in each helical wire are almost opposite. When the value of LH is small, the interaction force between the two helix-wires is attractive. Thus, the electrical current flows in the inner radius of the helix. However, when the value of LH is large, the directions of the currents tend to be uniform. The interaction force becomes repulsive, and the current flows in the outer radius of the helix. Therefore, increasing LH effectively increases the DH. Based on the antenna theory, the increasing of the DH leads to the red shift of the operation band [12

]. Moreover, the resistance of the helix-wires was enhanced with the increasing of LH, which led to the increasing of the extinction ratio.

Fig. 5 Optical performances of hetero-structured double-helical polarizers with different length of helix-period.

Table 5 Optical Performances of Al-Pt Hetero-Structured Double-Helical Polarizers with Different Length of Helix-Period ^a

	OB (μm)	T (RCP)	T(LCP)	AER
LH = 200 nm	0.48-1.21	28%	0.8%	42:1
LH = 350 nm	0.62-1.56	28%	0.7%	64:1

^a LH: Length of helix-period, OB: Operation band, T (RCP): Average transmittances of RCP Light, T (LCP): Average transmittances of LCP Light, AER: Average extinction ratio.

3.2.3 Optimized hetero-structured double-helical circular polarizer

We also simulated structures with different DW, DH and SG. However, these three parameters had less effect on the increasing of the optical performance than that of LH and NH. Therefore, we did not list all in detail. Finally, by properly selecting the parameters of helix metamaterials including: LH = 350 nm, SG = 1.8 μm, NH = 4, DH = 0.92 μm, and DW = 0.54 μm, we proposed an Al-Pt hetero-structured double-helical circular polarizer. As shown in Fig. 6 , it can reach an average extinction ratio 100:1 in the wavelength range from 0.51 μm to 1.42 μm.

Fig. 6 Optical performances of hetero-structured double-helical polarizers with ideal parameters.

4. Conclusions

In summary, the circular polarizers with hetero-structured double-helical metamaterials were studied. It was found that the circular polarizers with hetero-structured double-helical metamaterials have average extinction ratios two times higher than those with homo-structured double-helical metamaterials. The relationship between the resistivity and the transmittance was discussed, and the interaction between the two helix wires were analyzed to explain the higher extiction ratios of the hetero-structured double-helical circular polarizers. Although the proposed structures need to be fabricated to experimentally realize the circular polarizers, the hetero-structured metamaterials will provide a new type of method for improving the polarizers’ performances.

Acknowledgments

This work was supported 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.	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]
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, 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 Y. F. Lu, “Similar structures, different characteristics: optical performances of circular polarizers with single- and double-helical metamaterials,” J. Lightwave Technol. 28, 3415–3421 (2010).
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]
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.	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.
17.	Z. Yang, M. Zhao, and P. Lu, “Improving the signal-to-noise ratio for circular polarizers consisting of helical metamaterials,” Opt. Express 19(5), 4255–4260 (2011). [CrossRef] [PubMed]

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

ToC Category:
Metamaterials

History
Original Manuscript: April 1, 2011
Manuscript Accepted: May 12, 2011
Published: May 19, 2011

Citation
Yang Yu, Zhenyu Yang, Shengxi Li, and Ming Zhao, "Higher extinction ratio circular polarizers with hetero-structured double-helical metamaterials," Opt. Express 19, 10886-10894 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10886

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References

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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
Z. Y. Yang, M. Zhao, and Y. F. Lu, “Similar structures, different characteristics: optical performances of circular polarizers with single- and double-helical metamaterials,” J. Lightwave Technol. 28, 3415–3421 (2010).
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]
J. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]
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]
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.
Z. Yang, M. Zhao, and P. Lu, “Improving the signal-to-noise ratio for circular polarizers consisting of helical metamaterials,” Opt. Express 19(5), 4255–4260 (2011). [CrossRef] [PubMed]

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