In order to discuss the modulation effect of the rotation angle on the transmission spectra more clearly, Type N4 with rotation angle of 0°, 10°, 40°, and 80° are demonstrated in Fig. 2. Here, tRCP and tLCP represent the co-polarized transmission coefficient of RCP and LCP waves respectively. When the rotation angle is set to 0° (i.e., Fig. 2(a)), significant asymmetric transmission can be observed in short wavelength band (3.3-3.95 μm), middle wavelength band (3.95-4.26 μm), and long wavelength band (4.26-5 μm). When the rotation angle is set to 10° (Fig. 2(b)), a large asymmetric transmission can be observed in the middle and long wavelength bands. When the rotation angle is set to 40° (Fig. 2(c)), asymmetric transmission can be observed only in middle wavelength band. And when the rotation angle is set to 80° (Fig. 2(d)), strong asymmetric transmission can be seen in short and middle wavelength bands. It should be noted that when the wavelength is less than 3.7 μm, there is nearly no asymmetric transmission in the metamaterial of Type N4.
To further investigate the modulation effect of rotation angle on chirality, the asymmetric transmission has been assessed by the CD (CD= |tRCP|2-|tLCP|2)(Jing, et al. 2018; S. Li, et al. 2020; Z. Wang, et al. 2017). As much as 0.609, 0.843, and 0.727 of the CD responses can be reached in three wavelength bands respectively. The CD spectra of four different rotation angles are shown in Fig. 2(e), where four different combinations of CD response in transmission spectra are marked as Mode 1, Mode 2, Mode 3, and Mode 4. Since the rotation period of the proposed metamaterial is 90°, the corresponding change of CD responses under the rotation angle from 0° to 90° have been simulated in Fig. 2(f), where the four modes mentioned before are marked by dash lines in the figure. This simulation can help to fully discover the impact of rotation angle on CD spectrum. It can be seen that when the rotation angle is adjusted periodically, the modes of proposed metamaterial can be switched cyclically.
As shown in Fig. 3(a), different folds of rotational symmetric structures are further studied. CD responses of three-fold rotational symmetric nano-structure can be modulated with the changing of rotation angle, which is same as Type N4. Five-fold rotational symmetry, as shown as Type N5, it can be observed that the CD responses in the short wavelength band can be modulated by rotation angle which is like Type N3 and Type N4. However, the CD responses in middle and long wavelength band will not be modulated. So, the responses which are not able to be modulated are defined as constant responses and the responses able to be modulated by rotation angle can be defined as switchable responses. To further investigate the relationship between the fold of rotational symmetry and CD responses, the CD spectra of the nano-structures with six and eight fold of rotational symmetry have been simulated, as shown in Fig. 3(c) and (d), where the CD spectra are almost unchanged with different rotation angles.
Therefore, with the fold of rotational symmetry increasing, the modulation effect of the rotation angle on the CD spectra will disappear gradually. In the wavelength band between 3.3 to 5 μm, rotation angle cannot change the CD spectra effectively when the fold of rotational symmetry exceeds five.
Selective absorption of circularly polarized waves is realized in this paper, as shown in Fig. 4. The absorption of LCP and RCP waves (ALCP and ARCP) (Cao, et al. 2013; Ouyang, et al. 2018; L. Wang, et al. 2019)can be calculated as:
Here, the RRL (RLR) is the cross-polarized reflectance of LCP (RCP) wave, and RLL (RRR) is the co-polarized reflectance of LCP (RCP) wave. The TRL (TLR) is the cross-polarized transmittance of LCP (RCP) wave, and TLL (TRR) is the co-polarized transmittance of LCP (RCP) wave.
The parameters of the different fold of rotational symmetric nano-structures are optimized to obtain their high selective absorption. Absorption of RCP waves can obtain 0.650, 0.987, 0.973, and 0.994 in Fig. 4(a), (b), (d), and (e) respectively. Absorption of LCP waves can obtain 0.915 in Fig. 4(c). Meanwhile, absorptive circular dichroism (CDAb) spectra, which is calculated by
are used to discuss the selective absorption of circularly polarized waves. Here, ARCP (ALCP) is the absorption of RCP (LCP) waves. As shown in Fig. 4(f), relatively high CDAb up to 0.867 is observed in Type N4. It should be noted that the absorption in Type N3, Type N4, and Type N5 can also be modulated by rotation angle which same as Fig. 3. So it is not being discussed in Fig. 4.
In addition, two reconfigure strategies are studied for more flexible designs. For Type N4S1 shown in Fig. 5, the direction of blades in both layers are different from Type N4, when the upper nano-structure is rotated clockwise (θ<0°), CD spectra are shown in Fig. 5(a), opposite to Fig. 2(e). Similarly, Mode -1, Mode -2, Mode -3, and Mode -4 are used to mark the occasions for rotation angles of 0°, -10°, -40°, and -80° respectively.
By changing the direction of blades in upper layer’s nano-structure of Type N4 only, a unit as Type N4S2 shown in Fig. 5 has been investigated. Metamaterial of this design has significantly different CD spectra as shown in Fig. 5(b). Following the previous discusses, four different modes, three wavelength bands; short and middle wavelength bands; single wavelength band; middle and long wavelength bands, are analyzed in the figure corresponding to the rotation angles of 0°, 10°, 30°, and 80° respectively. It should be noted that different fold of rotational symmetric nano-structures which are discussed in Fig. 3 and 4 are able to follow these two reconfigure strategies for more different responses.
To explain the underlying physical mechanism of the proposed metamaterial, the charge distribution of three different modes at middle and long wavelength bands are simulated, as shown in Fig. 6. For Mode 1, when the metamaterial is excited by RCP waves at 4.04 μm, the local electric dipoles in the two horizontal nano-rods of lower layer are mainly left pointing and both of the vertical nano-rods of the lower layer have local electric dipoles pointing upward. Similarly, local electric dipoles in the upper layer are pointing right in the horizontal nano-rods and pointing upward in the vertical nano-rods. To simplify the analysis, equivalent electric dipoles (M. Zhang, et al. 2018) have been provided as a reference and marked with solid arrows. It can be observed that the angle between the two equivalent electric dipoles is obtuse. For a Born–Kuhn model (X. Yin, et al. 2013), those two dipoles with an obtuse angle between them can form a bonding mode. In Mode 1, it can be found that the equivalent electric dipoles of the upper and lower layers are parallel when the charge distribution excited by LCP waves. That is, from the Born–Kuhn model, those two dipoles with the same pointing direction can form an antibonding mode.
To explain why modes switching can be implemented by angle rotation in the proposed metamaterial, the charge distribution at 4.58 μm of Mode 2 and Mode 3 are studied. Under the excitation of different circularly polarized waves, the local electric dipoles of Mode 2 at 4.58 μm build two different hybrid modes and the local electric dipoles of Mode 3 at 4.58 μm build two bonding modes, where the former one has strong CD response, but the latter one almost has no CD response. Furthermore, same method is used to analysis Type N8, it is found that the rotation angle between upper and lower nano-structures is not enough to change the hybrid modes. And the same hybrid modes lead to the insensitivity of the CD spectra to the rotation angle.
In plasma resonances excited by electromagnetic waves, bonding mode has lower resonance energy than antibonding mode, similar to molecular orbital theory (Q. Li and Zhang 2016; Prodan and Nordlander 2004). More specifically, the phenomenon that bonding modes have higher transmission coefficient than antibonding modes’ as shown in Fig. 2 is consistent with the theories. In a summary, the hybrid mode excited by different circularly polarized waves can be adjusted by changing the rotation angle. The CD responses are very weak when the same hybrid modes are excited by different circularly polarized waves. Otherwise, if different hybrid modes excited by different circularly polarized waves, the relatively strong CD responses will appear.
It should be noted that when the rotation angle is 0°, the separate two layer of gold structure is no longer 3D chiral. However, each layer of gold structure is placed on a substrate of different thicknesses and different materials, and the gold structure of lower layer is wrapped by polymer film. The whole metamaterial unit (gold structure-polymer-gold structure wrapped by polymer-silica) is still 3D chiral(Arteaga, et al. 2016).
To reveal the advantages of this work more completely, a compassion table is established (Table. 1). As for transmitted CD, it can be seen that in the series of rotational symmetric metamaterials we discussed, different types possess different maximum transmitted CD and different number of modes can be modulated. Among the different types mentioned in this article, Type N4 has the largest number of modes and can achieve the strongest transmitted circular dichroism response. And through the reconfigure strategies which are proposed in Fig. 5, much more modes of transmitted CD can be realized. As for absorptive CD, it can also be found that strong absorptive CD are realized in Type N4 which is relatively high in the similar chiral absorbers(M. Li, et al. 2014; L. Wang, et al. 2019).
Table. 1 Some types mentioned in this work and comparison with some other chiral metamaterials
Metamaterial
|
Number of modes
|
Single wavelength band
|
Dual-wavelength bands
|
Triple-wavelength bands or more
|
Transmitted circular dichroism
|
Absorptive circular dichroism
|
(Yan, et al. 2017)
|
1
|
√
|
|
|
0.75
|
|
(Cao, et al. 2014)
|
1
|
|
|
√
|
0.17
|
|
(M. Li, et al. 2014)
|
1
|
√
|
|
|
|
0.76
|
(L. Wang, et al. 2019)
|
3
|
|
√*
|
|
|
0.79
|
Type N3
|
3
|
√
|
√
|
√
|
0.75
|
0.49
|
Type N4
|
4
|
√
|
√*
|
√
|
0.84
|
0.87
|
Type N5
|
3
|
|
√
|
√*
|
0.54
|
0.57
|
Type N6
|
1
|
|
|
√
|
0.63
|
0.70
|
Type N8
|
1
|
|
|
√
|
0.74
|
0.77
|
* More than one mode and all of them are dual-wavelength bands (triple-wavelength bands or more).