Figure 2(a) presents the simulated co-polarization transmission coefficients (t++(ω), t−−(ω)) and reflection coefficients (r++(ω), r−−(ω)) for normal incident LCP and RCP lights. Two chiral plasmonic resonance modes (mode 1 and mode 2) are evidently at frequencies of f1 = 288.5 THz and f2 = 404 THz, respectively. It can be observed that the co-polarization reflection coefficients (r++(ω), r−−(ω)) for LCP and RCP lights are equal; and both of them are less 0.4 across the whole interested frequency range. In addition, the magnitudes of r++(ω) and r−−(ω) are decreased to about 0.15 around resonance frequencies, meaning that the relative impedance of the PMSA are nearly matched to free space for both RCP and LCP lights at resonances. It also can be seen that the co-polarization transmission coefficients (t++(ω), t−−(ω)) for RCP and LCP lights are different significantly at resoances due to the chiral nature of the proposed PMSA. Around the lower frequency point, the magnitude of t++(ω) for the RCP light is about 0.93, which is much higher than that for the LCP light, and the one for the LCP is only about 0.075. Around the higher frequency point, the magnitude of t−−(ω) for the LCP light is decreased to minimal value of 0.018, while the one for the LCP is up to maximal value of about 0.92. It means that only the RCP light can be selected to pass through the PMSA while the LCP light is forbidden to transmit mostly at the lower frequency. While only the LCP light can be selected to pass through the PMSA while the RCP light is forbidden to transmit mostly at the higher frequency. This will cause the different distortion and absorption for the RCP and LCP lights going through the PMSA slab, implying a high efficiency chiral-selective absorption and giant CD effect at resonances.
Figure 2(b) shows the chiral-selective absorbance spectra (A+(ω), A−(ω)) for both incident LCP and RCP lights. It can be observed that the chiral-selective absorbance for LCP and RCP lights is up to maximal value of about 93.2% and 91.6%, while the one for RCP and LCP lights is decreased to only about 8.7% and 4.8% around the above two resonances, respectively. Obviously, the designed PMSA has the high absorption level for an LCP light whereas the weak absorption for RCP light around the lower frequency. On the other hand, the PMSA becomes strongly absorptive for RCP light while quite weak absorption for LCP light around the higher frequency. It means a chiral-selective absorption for two CP lights with particular handedness while reflecting the other one at different resonance frequency. It is worth highlighting that the PMSA has the two chiral-selective strong absorption frequency band just using a single size chiral nanostructure, which is much superior compared with the previous chiral absorbers for one absorption required different size ones for each CP light [22, 23, 26, 28, 30, 34]. Thus, the designed chiral nanostructure can act serve as a perfect LCP light absorber at the lower frequency and perfect RCP light absorber at the higher frequency. The characteristic of high chiral-selective absorption for CP lights will result in a giant CD effect.
The chiral-selective absorption or transmission difference between the LCP and RCP lights can be characterized by CD parameter Δ. Figure 3(a) presents the CD spectrum of the PMSA, where the main peaks of CD parameter are about 0.85 and 0.91 at two selectively resonance frequencies, respectively; which is much greater than the current reported chiral nanostructures [14–28, 34–40]. The giant CD effect is caused by the strong chirality of the PMSA. Obviously, owing to the giant CD effect, the proposed PSMA can be applied as a transparent circular polarizer. To study its CP purity of the PSMA applied as a circular polarizer, we give the ellipticity angle η and polarization azimuth rotation angle θ as shwon in Fig. 3(b). It can be observed that the value of the η is about 40.4◦ and − 43.9◦, while the one of the θ is about 0◦ at the lower and higher frequencies, respectively. It means that the transmitted lights exhibit prominent RCP and LCP characteristics after lights passing through the PMSA slab at the lower and higher frequencies, respectively. It should be noticed that this PMSA based circular polarizer with the higher CP purity is valid for any arbitrarily polarization lights due to its high C4 symmetry of the unit-cell. Thus, the homogenous circular polarizer is realized with our prposed PMSA.
To fully understand the chiral-selective absorption and giant CD effect of the PMSA, we retrieved the refractive index Re(n), Re(n−), Re(n+) and chiral parameter Re(κ) using a standard retrieval procedure from the transmission and reflection coefficients of CP lights [41, 42], as shwon in Figs. 4(a) and (b). It is clearly that there are two resonances related to the strong chirality for the designed PMSA. The lower frequency resonance occurs around 288.5 THz and the higher one happens around 404 THz, which are consistent with where the chiral-selective absorption and CD peaks. As shown in Fig. 4(a), the Re(n) is negative with maximal magnitudes of -2.3 and − 1.1, and the Re(κ) is up to maximal magnitudes of 6.4 and − 5.1 around above two resonance frequencies, respectively. It is clear that the chiral parameter κ also contributes to the negative refractive index of RCP and LCP lights. The strong chirality can easily push the refractive index of the RCP/LCP light to become negative at resonance frequencies due to the relation of n± = n ± κ. Thus, as shown in Fig. 4(b), the Re(n−) for LCP light and Re(n+) for RCP light is negative from 286.2 THz to 291 THz, and 400.2 THz to 404 THz, respectively. In addition, the Re(n−) and Re(n+) are up to the maximal negative values of -8.6 and − 6.3 at above two resonance frequencies, respectively. It reveals that the high chrial-selective absorption as well as giant CD effect of the proposed PMSA are associated with the negative refractive property of the LCP and RCP lights.
To further unveil the origin of the chiral-selective absorption associated with the giant CD effect of the proposed PMSA, we studied the electric field (Ez) distributions of the unit-cell driven by the incident RCP and LCP lights at 288.5 THz and 404 THz, respectively. The excitation of surface plasmons resonance will produce oscillating dipole fields due to the semicircle nanostructure with small diameters relative to the incident wavelength of the different CP lights [43–46]. When RCP or LCP light excites the semicircle nanostructure, a chiral-selective absorption and giant CD effect will occur, and the electric field and magnetic field components of each layer are different due to the chirality [46–51].
Figure 5 show the electric field (Ez) distributions of the proposed PMSA drived by RCP and LCP lights at different resonance frequencies. The detail plot of the electric field (Ez) distributions on the semicircle nanostructure clearly shows the nature of each sruface plasmonics mode. The red and blue region on the top and bottom layers of the semicircle nanostructure present the positive and negative charge accumulations provided under RCP and LCP light excitation. It can be seen that the positive and negative charges are separated and mainly accumulated at the corners of the each semicircle nanostructure, acting like an electric dipole. It can be observed that the electric dipole power is much more than the magnetic dipole power for the designed semicircle nanostructure, thus, the electric dipole oscillations are predominant. The chiral-selective absorption and giant CD effect will be generated at resonance frequencies owing to the obvious dipole power difference under LCP and RCP excitation. Here, we use a simplified method with equivalent electric dipole moments, which considers the charge vibrations of four semicircle nanostructure per layer to one dipole vibration [46–48]. According to Born-Kuhn theory model [48, 49], when the mode is hybridized from two dipoles with the same electric field direction, namely bonding mode, while the one is hybridized from two dipoles with 90° or cross direction, known as antibonding mode. As shown in Figs. 5(a1,b1), under RCP light at resonance frequency f1 = 288.5 THz, the electric dipole fields in top and bottom layers shows the cross directions and form a antibonding mode based on the Born-Kuhn model, resulting in high transmission of RCP light. As shown in Figs. 5 (c1,d1), under LCP light, it can be seen that it is hybrid from the bonding mode between the upper and lower layers, with the same direction of the equivalent electric dipole moments, resulting in high absorption level of LCP light. Thus, at the lower frequency, the bonding and antibonding modes cause different resonance energy and thus different transmission and absorption of chiral nanostructures under LCP and RCP lights (See Fig. 2). As shown in Figs. 5(a2,b2) and (c2,d2), under RCP light and LCP lights at resonance frequency f2 = 404 THz, the electric dipole fields in top and bottom layers shows the same and cross directions, and form bonding and antibonding modes, respectively; resulting in high absorption level for RCP light and high transmission for LCP light. Thus, it can be seen that two chiral-selective absorption and CD effect are mainly attributed to the bonding and antibonding modes induced by hybrid coupling of the top and bottom layer electric dipole moments.
In the following, we investigate the influences of the geometric parameters of the unit-cell on the chiral-selective absorption properties of the proposed PMSA. Figure 6 shows the simulated chiral-selective absorbance spectra for these different geometric parameters (r, w, tm, and ts) of the unit-cell. For the proposed chiral nanostructure, the parameter-depended chiral-selective absorbance will show some interesting spectral variation characteristics since the influence process is complex and multi-factor competitive. In this study, the geometric parameters of the control group are r = 70 nm, w = 40 nm, tm=30 nm, and ts=120 nm, and changing one parameter at a time.
The semicircle nanostructure with the different r (r = 65 nm, 70 nm, 75 nm, and 80 nm) were firstly calculated, while the other parameters are fixed. As shown in Fig. 6(a), when increasing r, the resonance frequencies for both LCP and RCP waves decrease gradually, which can be interpreted by the equivalent LC resonance circuit theory [52, 53]. The resonance frequencies for both LCP and RCP lights can be expressed as\(f=\frac{1}{{2\pi \sqrt {LC} }}\), where equivalent capacitance C and inductance L are mainly determined by the geometric parameters of the proposed PMSA. The L will increase with the increase of the r, thus resulting in the decrease of the resonance frequencies. In addition, when increasing r, the absorbance of the LCP light will decrease gradually while the one of the RCP light will be nearly unchanged. Figure 6(b) shows the absorbance spectra of the LCP and RCP lights when changing the w from 30 nm to 45 nm by a step of 5 nm, while the other parameters are kept unchanged. It can be seen that the resonance frequencies for both LCP and RCP lights will increase gradually with the increase of the w. Obviously, the decrease of the resonance frequencies is mainly due to the increase of the C. The absorbance of the LCP light will firstly increase and the then decrease slightly, while the one of the RCP light will decrease gradually when increasing r. As shown in Fig. 6(c), we present the absorbance spectra of the LCP and RCP lights with varying tm from 20 nm to 50 nm by a step of 10 nm and other parameters fixed. There are similar cases to the change of w, when increasing tm, the resonance frequency for LCP light decrease significantly, and the one for RCP light decrease slightly. In this case, the L will decrease with the increasing of the tm, thus resulting in the increase of the resonance frequencies. In addition, the absorbance of the LCP light will increase gradually, while the one of the RCP light will firstly increase and then decrease when increasing tm. Finally, we present the absorbance spectra of the LCP and RCP lights with different ts (ts = 110 nm, 120 nm, 130 nm, and 140 nm), and other parameters are kept unchanged, as shown in Fig. 6(d). It can be observed that the resonance frequencies for both LCP and RCP lights decrease when increasing ts. In this case, the C will decrease when increasing ts, thus resulting in the increase of the resonance frequencies. In addition, when increasing ts, the absorbance of the LCP will increase gradually, while the one of the RCP light will decrease slightly. It can be concluded that the resonance frequencies and absorption level for both RCP and LCP lights are sensitive to the geometric parameters of the unit-cell of the designed PMSA. Thus, the chiral-selective absorption properties of the proposed PMSA can be adjusted dynamically by varying geometric parameters.