Stacked planar chiral metamaterials which combine the fabrication convenience of planar metamaterials and good chirality of stereo metamaterials have recently drawn a lot of attention. In this paper, we present a study on the CD performance in the double-layer and multi-layer closely stacked Archimedean planar metamaterials (SAPMs), which will simultaneously support localized modes in the interface of two spirals and non-localized conductive modes in the whole structure, as well as show particular twist-angle dependent CD performance and broadband CD performance due to the coaction of localized modes and non-localized modes. We give reasonable explanations on the CD performance of SAPMs by employing the plasmonic Lagrange model and the equivalent model. We also discuss the optimization of structural parameters and application challenge of our proposed model.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
A chiral object is defined as one for which the structure and its mirror image are not superimposable. Natural chiral optical crystals (such as quartz, benzil, and NaBrO3) and bio-/chemical molecules normally show different optical responses to the right handed circularly polarized (RCP) and left handed circularly polarized (LCP) incident light. Such anisotropic optical response is defined as the circular dichroism (CD) effect. Unfortunately, the CD effect is generally very weak in natural chiral materials due to the large mismatch between their atomic feature sizes and optical wavelengths. As a comparison, artificial chiral metamaterials with designed structures can significantly improve the CD performance which has been experimentally demonstrated at microwave, terahertz, infrared, and even optical frequencies. The underlying mechanism is generally related to the strong electromagnetic coupling in the artificial chiral metamaterials . Since the electromagnetic coupling is complicated and diverse in different artificial chiral metamaterials, universal and solid interpretations are yet to be clearly provided.
Compared with three-dimensional chiral metamaterials , planar chiral metamaterials are relatively convenient in fabrication. However, due to isotropic response and limit thickness, the electromagnetic coupling along the axial direction of planar chiral metamaterials is much weaker than three-dimensional ones, resulting in inferior performance in both maximum CD value and bandwidth . An efficient way to solve this problem is using stacked planar chiral metamaterials which can be regarded as a quasi-type of three-dimensional chiral metamaterials but retain the fabrication convenience of the planar type. In the past decade, several typical stacked planar chiral metamaterials have been reported [4–6]. The first one (Type-I) is a triple-layer metal-dielectric-metal (MDM) structure with uniform pattern in each layer [7–11]. The second one (Type-II) is usually a double layer structure constructed by two same planar chiral metamaterials with a twist angle or mirror symmetry [12–24]. The third but not the last one (Type-III) is usually a double layer or multi-layer structure constructed by different planar chiral metamaterials without any rotational or mirror symmetry [25,26]. Usually, there is a layer distance between the stacked planar chiral metamaterials and the CD performance related to the interlayer electromagnetic coupling can be modulated by changing the layer distance and twist angle between stacked layers [12,27].
Except for these typical structures, we have recently reported a new double-layer planar chiral metamaterial constructed by two closely stacked Archimedean spirals with a certain scaling . We find that the connected spirals can support strong localized gap plasmon modes in the interface of two spirals and generate giant CD performance due to the near-field in-plane coupling, which has also been demonstrated later in the gap of coupled plasmonic ‘atoms’ in different single-layer planar metamaterials [29–31]. In other words, we can tailor the CD performance based on the high field localization in the interface or gap of two plasmonic ‘atoms’. This allows us to achieve a good degree of control over the localized surface plasmon effects on the CD performance. Different from the single-layer planar metamaterials, the planar metamaterials closely stacked in the vertical direction with different sizes or rotation angles will bring additional degrees to control the localized surface plasmon, while the influence of conducting effect of the whole structure on the CD performance should be considered as well. Following such idea, in the present contribution, we would like to study the CD performance of the chiral metamaterial stacked by two or more Archimedean spirals with a twist angle. We will show that the twist-angle dependent CD performance and the underlying mechanism are quite different when different layer distances are considered in the stacked planar chiral metamaterials. In particular, we will demonstrate that the stacked Archimedean spirals without a layer distance can provide giant and broadband CD performance due to the coaction of localized gap plasmon modes and non-localized conductive modes.
2. Model and methods
Figure 1(a) shows the schematic of the stacked planar chiral metamaterial studied in this work. Take the double layer as an example, the planar chiral metamaterial consists of double-layer twisted Archimedean Ag spirals vertically arranged on the SiO2 substrate. The periodic constant in the x and y directions is defined as Px and Py, respectively. For the purpose of potential applications in biomolecules detection and optical communication, we focus our study in the infrared band and the silver is chosen due to its good plasmonic performance in the infrared band.
Figures 1(b) shows the diagram of the unit cell. Both top and bottom Archimedean spirals have same geometry parameters which can be described by the mathematical expression:$\phi$ is the rotation angle. In addition, the thickness of each spiral is t. As shown in Fig. 1(c), θ represents the twist angle of the top spiral with respect to the bottom one. A negative θ corresponds to a clockwise twist angle and vice versa.
A commercial three-dimensional finite-difference time-domain (3D-FDTD) software package, “Lumerical FDTD Solutions”, was employed to study the transmission spectra of stacked planar chiral 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 was set as 5 nm along the x, y and z directions. The complex dielectric constants for Ag and SiO2 were fitted based on the Palik database. A plane-wave source with a size of Px*Py was used in the simulation and a frequency-domain power monitor with the same size was set 50 nm away from the 500 nm-thick SiO2 substrate. The transmission was calculated as the ratio of the total power on the monitor to the source’s power. The CD value was calculated as the transmittance difference between LCP and RCP beams, i.e., CD = ΔT = TL-TR.
3. Results and discussion
3.1 Twist-angle dependent transmission and CD spectra of double-layer stacked Archimedean planar metamaterials
We studied the twist-angle dependent transmission and CD spectra of the double-layer stacked Archimedean planar metamaterials (SAPM) illuminated by different circularly polarized beams. The geometrical parameters of the double-layer SAPM in study are Px = Py = 500 nm, r = W = L = 40 nm, t = 120 nm. When the twist angle θ21 is changed from 0 to 360°, Fig. 2(a) shows the dependencies of the maximum absolute value of CD and the corresponding resonant wavelength on the twist angle. It can be seen that the maximum CD value shows two peaks at about 150° and 210° (i.e. −150°), respectively. The maximum CD value also shows nearly symmetrical distribution with respect to the twist angle of 180°.
Figure 2(b) shows the transmission spectra of the double-layer SAPM when θ21 = ±150°. For the case of θ21 = 150°, the transmission spectra for the RCP and LCP beams cross each other at 1156 nm. We define the left and right areas of the intersection as the short-wavelength (marked by green color) and long-wavelength areas, respectively. Two resonances in the short-wavelength area show stronger response to the RCP beam than the LCP beam, while another two resonances in the long-wavelength area show opposite response. The most significant transmission difference appears at resonance 2 (979 nm). For the case of θ21 = -150°, the transmission spectra are similar to the case of θ21 = 150° but the responses of RCP and LCP beams are reversed. Resonance 1 (911 nm) shows the most significant transmission difference.
Figures 2(c) and 2(d) show the twist-angle dependent CD spectra of the double-layer SAPM. The maximum CD value reaches as high as about ±0.8 at ±150° in the short-wavelength area. Resonance 3 (star sign) and resonance 4 (square sign) in the long-wavelength area keep redshifting and reach maximum at ±150° and ±90°, respectively. It is clear to find that 180° is a critical twist angle which separates the negative and positive CD values in the long-wavelength area.
3.2 Underlying mechanism
In this section, we will comprehensively study the mechanism of twist-angle dependent CD performance in the double-layer SAPM. First, we have investigated the mode profile of resonances in Fig. 2(b). Figure 3 shows the magnetic field and surface current distributions at resonance 2 (979 nm), resonance 3 (1600 nm), and resonance 4 (3191 nm) for the case of θ21 = 150°. The hot spots at resonances 2 are mainly distributed on the interface of two spirals and the surface current distributions are messy throughout the double-layer SAPM. The hot spot’s intensity for RCP beam is much stronger than that for LCP beam. As a comparison, the hot spots at resonances 3 and 4 can also be found on the top surface of the upper spiral and the inside walls of both spirals. Meanwhile, the surface current gradually shows continuous and circular distributions throughout the double-layer SAPM. For the case of θ21 = -150°, the magnetic field and surface current distributions at resonance 1′ (911 nm), resonance 3′ (1572 nm), and resonance 4′ (3313 nm) are presented in Fig. 4. Similar to the case of θ21 = 150°, the hot spots at resonances 1′ are mainly distributed on the interface of two spirals, while the hot spots at resonances 3′ and 4′ can also be found on the top surface of the upper spiral and the inside walls of both spirals. Different from the case of θ21 = 150°, the circular directions of surface current at resonances 3′ and 4′ are opposite to those at resonances 3 and 4. As a result, resonances in the short-wavelength and long-wavelength areas behave as localized and non-localized modes, respectively. The localized modes are actually gap plasmon modes due to the near-field in-plane coupling [28–31], while the non-localized modes behave like conductive coupling modes with continuous surface current along the whole connected spiral. In particular, the non-localized modes for the cases of θ21 = 150° and θ21 = -150° show opposite circular directions of surface current, which can be used to explain why their responses to RCP and LCP beams are reversed.
Totally different from the single spiral whose CD performance is only decided by its geometric chirality, the CD performance of double-layer SAPM is mainly related to the localized and non-localized modes which are actually the coupling results of two spirals. Consequently, the layer distance is a critical factor which can influence their coupling. Generally, the localized gap plasmon mode can be excited in a small range of layer distance through near-filed coupling, while the non-localized conductive mode should be excited without a layer distance. In order to understand how the layer distance will influence the coupling of spirals and their CD spectra, we then calculated the layer-distance dependent transmission spectra of the double-layer SAPM when the twist angle was fixed to be 150°. As shown in Fig. 5(a), when the layer distance is in a far-field coupling region (e.g., d = 900 nm), we can observe two main resonances in the long-wavelength area and more resonances in the short-wavelength area. Figures 5(e)–5(g) compare the transmission spectra of individual/coupled spirals with or without a substrate at d = 900 nm. It is not difficult to find that resonance 2 in the long-wavelength area is an original eigen mode of two individual spirals without a substrate and the resonance 1 of spiral 1 is actually due to the substrate effect which can result in a redshift of resonant modes in either short-wavelength or long-wavelength areas. The coupled spirals without a substrate only show quite weak CD performance even if there is a large twist angle between them, while relatively apparent CD performance in Fig. 5(a) obviously arises from the substrate effect. When the layer distance is decreased from 900 nm to 150 nm and 5 nm respectively, i.e., the near-field coupling region, the splitting of resonances 1 and 2 becomes more and more distinct and the CD performance is gradually improved. When there is no layer distance between two spirals, i.e., a conductive coupling case, resonances 1 and 2 show the largest separation and the best CD performance. It is interesting that the substrate effect no longer contributes to the separation of resonances 1 and 2 by comparing Figs. 5(d) and 5(h). Actually, when two spirals touch each other, the whole structure should be regarded as a single three-dimensional (3D) spiral rather than two individual planar spirals with a certain coupling distance. As a result, the resonances 1 and 2 in Figs. 5(d) and 5(h) should be conductive eigen modes of the 3D spiral rather than the original eigen modes of two individual planar spirals. Moreover, it is worth to mention that the double-layer SAPM does not support clear surface plasmon polariton (SPP) resonance in the spectra. The giant CD of our model is due to the strong interlayer near-field coupling and conductive coupling of two spirals.
We further calculated the twist-angle dependent CD contour maps of the double-layer SAPM with different layer distances. For both far-field coupling (d = 900 nm) and near-field coupling (d = 5 nm) cases, it can be clearly found that the contour maps show a periodical phase change when the twist angle is increased by 90 degrees each time [ Figs. 6(a) and 6(b)]. As a comparison, for the conductive coupling case (d = 0 nm) [Fig. 6(c)], the twist angle difference which can result in a periodical phase change becomes 180 degrees. Meanwhile, for the far-field coupling case, the wavelength of each resonance almost keep constant as the twist angle changes, while the wavelength of each resonance for either near-field coupling case or conductive coupling case is sensitive to the twist angle, especially in the long-wavelength area.
The different twist-angle dependent CD contour maps of the double-layer SAPM with different layer distances correspond to different mode coupling mechanism. For the far-field and near-field coupling cases, we employ the plasmonic Lagrange model  to qualitatively explain the CD performance in Figs. 6(a) and 6(b). In particular, the Lagrangian of two spirals with a certain twist angle and layer distance can be described as:
For the conductive coupling case, we employ the equivalent model to simply explain the twist-angle dependent CD performance in Fig. 6(c). When 0°<θ21<180°, the double-layer SAPM is equivalent to a right-handed 3D chiral metamaterial. As the twist angle increases, the total length of surface current will increase and thus the resonant wavelength will keep redshifting. Similarly, when −180°<θ21<0°, the double-layer SAPM is equivalent to a left-handed 3D chiral metamaterial and thus an opposite CD value can be obtained. In particular, 180° is a critical twist angle which can result in a phase change between the left-handed and right-handed three-dimensional chiral metamaterials. Therefore, the CD performance in the long-wavelength area shows nearly symmetrical distribution with respect to the twist angle of 180° because the non-localized modes in the long-wavelength area are conductive coupling modes.
3.3 Application and extension
In the practical application, the optimization of structural parameters should be considered for obtaining good CD performance. As shown in Fig. 7(a), the double-layer SAPM shows the maximum CD value when the thickness of spiral is about 120 nm. In the range of 80-160 nm, the CD performance of the double-layer SAPM is relatively stable. When the thickness of spiral is 120 nm, as shown in Fig. 7(b), the optimized width of the spiral is in the range of 40-50 nm. As shown in Fig. 7(c), when the order of spiral increases from 1 to 1.5 and 2, the CD performance is getting worse. The periodical constant of the array should also influence the CD performance. By doing more simulations, we have found that the maximum CD value will decrease and the peak will be redshifted as the periodical constant increases from 400 nm to 700 nm.
At the same time, it is worth to discuss the fabrication challenge of the double-layer SAPM. In our model, in order to clearly understand the mode coupling mechanism, the upper spiral is directly placed on the bottom spiral without a supporting layer. However, such structure is almost impossible to be fabricated based on conventional methods. A simple way to solve this problem is adding a coating on the bottom spiral as illustrated in the inset of Fig. 7(d). First, the bottom spiral can be fabricated by employing the conventional electron-beam lithography (EBL) and lift-off technique on the Ag/SiO2 substrate. Then, the bottom spiral can be covered by a layer of polymer (n=1.5) and followed by a second layer of Ag film. At last, the upper spiral will be fabricated again by the EBL and lift-off technique to obtain the final double-layer SAPM. It should be noted that it is difficult to accurately controlling the thickness of polymer and let it perfectly equal to the thickness of the bottom spiral during the spin-on coating. Instead, there will be a small gap between the bottom and upper spirals. Figure 7(d) shows the influence of polymer gap on the CD performance of the double-layer SAPM. It can be found that when the polymer gap is zero, the CD performance of the double-layer SAPM is different from the case without a polymer coating. Meanwhile, even when a small polymer gap of 5 nm is introduced, the CD performance of the double-layer SAPM is totally different from the case without a polymer gap, which is agreement with the behaviors in Figs. 5(c) and 5(d). However, the existence of polymer gap does not influence the maximum CD value of the double-layer SAPM. When the polymer gap is changed from 5 nm to 40 nm, the double-layer SAPM still has good CD performance. Such robust performance gives a high tolerance to the spin-on procedure. Except for the gap, the alignment of the two layers during the EBL process will also influence the CD performance of the double-layer SAPM. The alignment is usually done by employing metal marks in the fabrication of bottom spirals. As shown in Figs. 7(e) and 7(f), by doing more simulations, we have found that the CD performance of our design is still stable for a rotational alignment error in the range of ±5° or a translational alignment error in the range of ±5 nm.
Based on the twist-angle dependent CD performance of the double-layer SAPM, we have also done some extended researches on the CD performance of triple-layer and multi-layer SAPMs. For the triple-layer case, we calculated the transmission spectra considering different combinations of θ32-θ21 with the same absolute twist angle of 150°. As shown in Fig. 8(b), the triple-layer SAPM with different combinations of θ32-θ21 always has an additional resonance 5 in the long-wavelength area as compared to the double-layer case. Meanwhile, we can find that good CD performance only occurs when θ32 = θ21. The sign of CD value is opposite when θ32 = θ21 = 150° and θ32 = θ21 = -150°, respectively. Actually, according to the equivalent model, the triple-layer SAPM with opposite twist angles between each neighboring layers can be regarded as a combination of two double-layer SAPMs with opposite chirality [Fig. 8(a)], while the triple-layer SAPM with consistent twist angles between each neighboring layers can be regarded as a combination of two double-layer SAPMs with consistent chirality. As a result, the chirality of the triple-layer SAPM would be canceled or enhanced after a combination of two double-layer SAPMs. Moreover, from the magnetic field and surface current distributions at resonance 5 (3547 nm) for the case of θ32 = θ21 = 150°, we can find that the additional resonance actually behaves as a new conductive mode of the whole 3D spiral.
The triple-layer SAPM case indicates that we can create more CD peaks in the spectra by adding more spirals with a consistent twist angle between neighboring layers. For examples, we calculated the transmission spectra of 4-layer, 5-layer, 6-layer, 7-layer SAPMs with a fixed twist angle of 150° between neighboring layers. As shown in Fig. 9(a), as compared to the triple-layer SAPM, the multiple-layer SAPMs show more irregular sub resonances in the short-wavelength area, while more and more resonances in the long-wavelength area can be generated as the layer number increases. These behaviors are beneficial to support broadband CD performance in multi-layer SAPMs. As shown in Fig. 9(b), if we set ±0.27 as the threshold value, the 5-layer and 6-layer SAPMs show the best broadband positive and negative CD performance with a bandwidth of 550 nm and 800 nm, respectively, while the 7-layer SAPM shows the largest sum of negative CD values in the long-wavelength area. In the practical application, the triple-layer and multiple-layer SAPMs can be fabricated by using similar fabrication methods as mentioned above for the double-layer SAPM.
To conclude, based on the idea of simultaneously controlling the field localization effect in the interface of two spirals and the conducting effect of the whole structure, we have investigated the twist-angle dependent CD performance in the double-layer and multi-layer SAPMs. For the double-layer SAPM, a maximum CD value of about ±0.8 can be obtained when the twist angle between two layers is 150° and −150°, respectively. The multi-layer SAPMs show broadband CD performance when the twist angle between each two neighboring layers is fixed to be 150° or −150°. Such good and broadband CD performance of the connected double-layer SAPM are closely related to the localized gap plasmon modes at the interface of two individual spirals and non-localized conductive modes in the whole connected spiral. In particular, the localized and non-localized modes show a periodical phase change in the CD contour maps when the twist angle is increased by 180 degrees each time. When the layer number is gradually increased, the superposition of localized modes will happen in the short-wavelength area and more non-localized conductive modes will be generated in the long-wavelength area. We have employed the plasmonic Lagrange model and the equivalent model to give reasonable explanations on the above CD performance. The SAPMs with enhanced and broadband CD performance may find potential applications in biomolecules detection [32,33], circularly polarized beam generation [34,35], filtering , analyzer , lasing , and imaging .
National Natural Science Foundation of China (61205042, 61675096); Natural Science Foundation of Jiangsu Province (BK20141393, BK2020010119); Six Talent Climax Foundation of Jiangsu (XYDXX-027); Fundamental Research Funds for the Central Universities (30919011106); Open Research Fund of State Key Laboratory of Bioelectronics (Sk1b2021p06).
The authors declare no conflicts of interest.
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