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Abstract
We report a planar metamaterial consisting of double-layer Archimedean spirals for circular dichroism (CD) study in the infrared band. A maximum CD value of about 0.5 is designed by optimizing the zoom coefficient, thickness and size combination of the upper and bottom spirals. Different from almost all previous works, the mechanism of CD of our proposed double-layer Archimedean planar metamaterial is due to the anisotropic absorption of the in-plane gap plasmon excited in the metal-dielectric-metal structure. Our model shows good CD performance and may find useful applications in biomedicine, optoelectronics, and optical communication based on the in-plane gap plasmon.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Circular dichroism (CD) is a fundamental characteristic of the chiral materials, which show anisotropic absorption for right handed circularly polarized (RCP) and left handed circularly polarized (LCP) incident light. Based on the natural or artificial chiral materials, CD spectroscopic technique has been reported in structural analysis of protein, DNA detection, and optoelectronics, etc [1–3]. Natural chiral optical crystals (such as quartz, benzil, and NaBrO3) and bio-/chemical molecules normally exhibit relatively weak CD effect. As a comparison, artificial metamaterials which show intriguing phenomena [4–6], such as extraordinary transmission, negative refractive index, and zero index, have also been demonstrated to show giant CD in the three-dimensional (3D) chiral metamaterials [7–9]. For example, Gansel et al. [7] have demonstrated broadband and giant CD in gold helix 3D metamaterials which can be applied as circular polarizers.
Recently, the CD effect from planar chiral metamaterials has also been extensively studied at microwave, terahertz, infrared, and even optical frequencies [10–26]. Due to out-of-plane isotropy, single-layer planar chiral metamaterials are usually hard to generate obvious CD. In order to improve the CD of planar chiral metamaterials, an efficient way is using unit cell without in-plane mirror symmetry (such as split ring resonators) [12,13] or using quasi-3D chiral metamaterials based on stacked layers of planar structures [14–26]. In particular, there are three main kinds of quasi-3D chiral metamaterials have been reported. Type-I is based on a symmetric tri-layer metal-dielectric-metal (MDM) structure, where all three layers have uniform planar metamaterial patterns [14–16], such as gammadion spirals. Type-II is based on a quasi-symmetric multi-layer structure, where different layers have uniform planar metamaterial patterns but with rotational or mirror symmetry [17–25]. Type-III is based on an asymmetric multi-layer structure, where the metamaterial arrays differ by spatial constitution (size, position, and orientation) and there is no rotational-symmetric or mirror-symmetric relationship between the constituent layers. In previous works, the former two types have been widely studied and strong CD has been demonstrated in them [14,19,25], while the third type is less concerned and the reported CD effect is still weak [26].
In this paper, we would like to present the study on a new kind of Type-III quasi-3D chiral metamaterial and numerically demonstrate its strong CD based on the excitation of in-plane gap plasmon.
2. Structure and design methods
Figure 1(a) shows the schematic of the planar metamaterial in our study. The planar metamaterial consists of double-layer Ag Archimedean spirals with different sizes on the SiO2 substrate. The periodic constant is 500 nm and the array’s size is 5 μm × 5μm in x-y plane. In order to construct a stable structure, the bottom spiral is embedded in a polymer with refractive index (RI) of 1.5.
Fig. 1 (a) Schematic of the planar metamaterial constructed by double-layer Archimedean spirals with different sizes. (b) Diagram of the Archimedean spiral.
As shown in Fig. 1(b), the Archimedean spiral is a curve whose radius varies linearly with the angle of rotation. The mathematical expression of Archimedean spiral can be described as:
where r and W are the starting radius and width of the spiral, L is the pitch, m is the order of spiral and φ is the rotation angle. The Archimedean spirals in Fig. 1(a) are left-handed and they have a common origin and a same thickness T. We assume their order m = 1 and the maximum angle of rotation is 2π. The widths and pitches of the bottom and upper Archimedean spirals satisfy the following relationships:where α (0<α<1) is the zoom coefficient.A commercial three-dimensional finite-difference time-domain (3D-FDTD) software package, “Lumerical FDTD Solutions”, was employed to study the planar metamaterials. In FDTD simulations, the periodic boundary condition was used along both the x and y directions, and the perfectly matched layer (PML) absorbing boundary condition was used along the z direction. The gird size (Δx, Δy, Δz) set in this case is 4 nm. The complex dielectric constants for Ag and SiO2 are from Palik.
3. Results and discussion
3.1 Transmission spectra of the double-layer Archimedean planar metamaterial
First of all, we have studied the transmission spectra of the planar metamaterial illuminated by different circularly polarized beams. Figure 2 shows the transmission response of the double-layer planar chiral metamaterial under right-handed polarized (RCP) light and left-handed polarized (LCP) light illumination, respectively. The geometrical parameters of the optimal planar metamaterial are Λ = 500 nm, rupper = Wupper = Lupper = 25 nm, rbottom = Wbottom = Lbottom = 40 nm, α = 0.625, and T = 120 nm. As a comparison, the transmission response of the constituent upper and bottom Archimedean spirals under different circularly polarized light illumination were also calculated, as presented in Figs. 2(a)-(b).
Fig. 2 (a,b) Transmission spectra of upper and bottom spirals for different circularly polarized beams. The inset shows the magnetic field distribution at response positions. (c,d) Comparison of transmission spectra of double-layer spirals and single upper or bottom spiral for the same circular polarized beam.
From Fig. 2(a), it can be clearly found that the transmission curve of RCP almost coincides with that of LCP when the upper spiral works alone. There is only a slight difference at the transmission dip 1' located around 1600 nm. Even so, the magnetic field intensity distribution in the inset can demonstrate that the left-handed spiral shows stronger interaction of RCP than that of LCP, which is in agreement with the responses in transmission curves. For the bottom spiral with a larger size, the transmittance curves are red shifted and more apparent difference (about 0.01) between RCP and LCP can be observed at the transmission dip 2' located around 3000 nm. The enhanced anisotropic response can also be confirmed from the magnetic field intensity distribution in Fig. 2(b). However, such transmission difference is still quite small for CD application which usually requires a difference with one order enhancement. As a result, for a single Archimedean spiral, it is hard to generate significant transmission difference between RCP and LCP by only modulating the spiral’s size.
As a comparison, when both upper and bottom spirals work together, as shown in Figs. 2(c)-(d), much more apparent transmission difference can be observed between RCP and LCP at two main resonant positions 1 (1415 nm) and 2 (1966 nm). In particular, at position 1 we can see a transmission peak for RCP and a transmission dip for LCP. This is quite useful for the enhancement of transmission difference. At position 2, the transmission dips for RCP and LCP also show significant difference. By plotting the transmission curve of double-layer spirals and that of a single spiral together, it is not difficult to find that the resonant positions 1 and 2 are actually the coupling results of the resonant positions 1' and 2' of the upper and bottom spirals, during which process the mode coupling results in a blue shift of resonant positions. More detailed working mechanism of the Archimedean planar metamaterial will be specifically discussed in section 3.3.
3.2 Chiral characteristics of the double-layer Archimedean planar metamaterial
Figure 3(a) compares the transmission curves of the Archimedean planar metamaterial. The transmittance for the RCP and LCP are represented by T+ and T-, respectively. In order to further characterize the transmission difference, we calculated the CD, ellipticity and polarization rotation angle of the structure.
Fig. 3 Chiral characteristics of the Archimedean planar metamaterial: (a) transmission spectra, (b) CD, (c) ellipticity η and (d) polarization rotation angle θ.
The standard definition of CD is equal to |A+ A-|, where A+ and A- are the absorption for RCP and LCP through the metamaterials, given by A+ = 1T+ R+ and A- = 1T- R-, respectively. In general, the reflection spectra for RCP and LCP through the metamaterials are identical, so the CD is also defined as [14]:
The value of CD directly indicates the difference response of LCP and RCP through metamaterials: the larger of the value, the stronger of the difference will be. As shown in Fig. 3(b), the CD value at 1415 nm and 1966 nm is 0.36 and 0.37, respectively, which are about 40 times than that of a single bottom spiral. At the same time, peak 1 is sharper than peak 2, which is more useful in the sensing and lasing applications.
The ellipticity (η) and the angle of polarization rotation (θ) are two important parameters representing the optical activity [27] of chiral materials, which can be described as [15]:
where t+ and t- represent the transmission coefficient of RCP and LCP waves, respectively. The chirality of a metamaterial is proportional to the absolute value of η and θ, while the sign of η and θ can reflect the dominated contribution from RCP and LCP waves. As shown in Fig. 3(c), at resonant position 1, a positive value of η indicates a stronger LCP interaction than RCP; and vice versa for a negative value of η at resonant position 2. As shown in Fig. 3(d), a negative value of θ at resonant position 1 and a positive value of θ at resonant position 2 indicate a dominated rotation contribution from RCP and LCP waves, respectively, which is consistent with the results obtained by ellipticity analysis.3.3 Enhancement mechanism of the double-layer Archimedean planar metamaterial
In order to explain the mechanism of the strong CD from the double-layer Archimedean planar metamaterial, we calculated the magnetic field distributions at resonant positions 1 (1415 nm) and 2 (1966 nm) in Fig. 3(a). As shown in Fig. 4(a), in the X-Y plane of the interface between upper and bottom spirals, we can see three main hot spots for both LCP and RCP at 1415 nm. The intensity of hot spots for LCP is obviously stronger than that for RCP. From the corresponding magnetic field vector distributions in the X-Y plane, we can find that the magnetic field vectors for either LCP or RCP show identical left-handed characteristics at three hot spots. These evidences cannot only demonstrate that the Archimedean planar metamaterial behaviors more like a left-handed chiral structure at resonant position 1, but also explain why we can see a transmission peak in Fig. 3(a). By further comparing the magnetic field intensity distributions in the sliced X-Z and Y-Z planes, we can clearly observe that all three hot spots are mainly localized in the gaps between two spirals, which suggests that the anisotropic absorption of gap plasmon [28–30] excited in the in-plane Ag/polymer/Ag MDM structure is the fundamental reason for the enhancement CD in the Archimedean planar metamaterial. As a comparison, as shown in Fig. 4(b), two main hot spots can be observed at 1966 nm. The intensity of hot spots for RCP is much stronger than that for LCP. The magnetic field vector distributions at hot spots show consistent chiral characteristics to the incident wave, which results in transmission dips for both LCP and RCP at 1966 nm. The corresponding magnetic field intensity distributions in the sliced X-Z and Y-Z planes also demonstrate the hot spots are due to the gap plasmon.
Fig. 4 Magnetic field intensity and vector distributions for LCP and RCP light at (a) 1415 nm and (b) 1966 nm, respectively.
Consequently, the double-layer Archimedean planar metamaterial studied in this paper shows a different working mechanism as compared to all previously reported planar chiral metamaterials. In previous works, the working mechanism of Type-I planar chiral metamaterials is based on the anisotropic absorption of gap plasmon excited in the out-of-plane MDM structure and the corresponding CD is sensitive to the thickness of the dielectric layer, while the mechanism of Type-II can be explained by the Lagrange or plasmonic Born−Kuhn models [31,32] and the corresponding CD is sensitive to the rotational angle of the metallic layers. It should be noted that the Type-III planar metamaterial in Ref [26]. is also based on the excitation of out-of-plane gap plasmon.
3.4 Dependences of the CD on the structural parameters of the double-layer Archimedean planar metamaterial
For the application purpose, it is worthy to discuss the dependences of the CD on the structural parameters of Archimedean spirals. The first investigated parameter is the zoom coefficient. As shown in Fig. 5(a), for the bottom spiral with a fixed Wbottom of 40 nm, the maximum CD values of resonant positions 1 and 2 were simultaneously obtained when Wupper is 25 nm. The corresponding zoom coefficient of 0.625 is quite close to the well-known golden section ratio of 0.618 [33], implying unexplainable mathematical mystery inside the physical phenomenon. Based on a fixed zoom coefficient (α = 0.625), we then considered the influences from other two basic geometric parameters, i.e., the thicknesses and sizes of spirals. Figure 5(b) shows the CD as a function of spirals’ thicknesses varying from 60 nm to 240 nm for the spirals’ size combination of 40-25. As the thickness increases, the maximum CD values of resonant positions 1 and 2 are 0.38 and 0.41 at thickness of 160 nm and 200 nm, respectively. For a practical application which requires ultra-compact structure and high performance, an optimal thickness range from 140 nm and 200 nm is recommended, during which a good balance between CD value and total thickness can be obtained. Figure 5(c) shows the CD as a function of spirals’ sizes with different combinations when the thickness is 120 nm. It can be clearly found that the peak positions are consistently red shifted as the sizes increase, which is in good agreement with the prediction of Mie scattering theory [34,35]. The maximum CD values of resonant positions 1 and 2 are 0.43 and 0.39 for the size combination of 56-35 and 48-30, respectively. An optimal size combination range from 40 to 25 to 64-40 is recommended for obtaining high CD and practical fabrication purpose based on the widely used EBL method. Moreover, based on the size combination of 56-35, the CD values of resonant positions 1 and 2 can reach as high as 0.45 and 0.46 when the thickness is 160 nm and 200 nm, respectively.
Fig. 5 (a) CD value as a function of the upper spiral’s width when the width of the bottom spiral is 40 nm and T = 120 nm. (b) CD value as a function of the spirals’ thicknesses when α = 0.625 for the spirals’ size combination of 40-25. (c) CD value as a function of the spirals’ size combinations when α = 0.625 and T = 120 nm. (d-f) RCP and LCP transmission spectra when the mupper-mbottom combination is 1-2, 2-1, and 2-2 respectively for the spirals with size combination of 40-25 and T = 120 nm.
There are also some other advanced geometric parameters of the Archimedean spirals, such as m and φ, may strongly modulate the chiral characteristics of the double-layer structure. For example, as shown in Figs. 5(d)-(f), when mupper-mbottom combination is 1-2, 2-1, and 2-2 respectively, the spirals with size combination of 40-25 show quite different RCP and LCP transmission responses. We can find that the increase of spiral’s order will bring more resonant positions in the transmission spectra. In particular, the structure with order combination of 2-2 shows two main areas having distinct transmission difference for RCP and LCP wave. Area I shows a maximum CD value of 0.4 at 1100 nm, which is due to the co-contribution from order combination of 1-2 and 2-1. As a comparison, area II shows a broadband response with a CD value higher than 0.15 from 1350 nm to 1790 nm, which is quite similar to the response of order combination of 1-2. Moreover, we also considered to change the RI of surrounding medium of the bottom spiral. As shown in Fig. 6, strong CD can still be observed when the polymer is replaced by air (n = 1), while the performance is becoming much worse when the polymer is replaced by silicon (n = 3.4). As a result, in practical applications, surrounding material with relatively low RI is recommended for packing purpose.
Fig. 6 (a,b) RCP and LCP transmission spectra when the surrounding material is replaced by air (n = 1) and silicon (n = 3.4) for the spirals with size combination of 56-35 and T = 160 nm.
At last, we would like to compare the performance of our proposed double-layer Archimedean planar metamaterial with other planar metamaterial models. As shown in Table 1, our model shows not only significantly improved CD as compared to the same Type-III model in Ref [26], but also comparable CD as compared to that of Type-I and Type-II models, making it become an alternative choice for practical applications.
Table 1. A comparison of the CD from different types of quasi-3D planar metamaterials
4. Conclusions
In conclusion, we have investigated the CD of planar metamaterial constructed by double-layer Archimedean spirals with different sizes. It is found that strong CD of the Archimedean planar metamaterial can be obtained when the zoom coefficient of upper and bottom spirals is equal to 0.625. By further designing the spirals’ thicknesses and size combination, a maximum CD value as high as 0.46 can be obtained, which is more than 40 times of the single spiral and about 5 times of the same Type-III planar metamaterial in the reference. We account the enhancement mechanism of the double-layer Archimedean planar metamaterial for the anisotropic absorption of in-plane gap plasmon excited in the Ag/polymer/Ag MDM structure. Our proposed structure may find potential applications in circularly polarized beam generation [36], filtering [37], analyzer [38], lasing [39], imaging [40], and sensing based on the in-plane gap plasmon, which is more convenient for strong light-matter interaction in nanoscale volumes than the out-of-plane gap plasmon.
Funding
National Natural Science Foundation of China (NSFC) (61675096, 61205042); Natural Science Foundation of Jiangsu Province (BK2014021828).
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