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Dynamically adjustable-induced THz circular dichroism and biosensing application of symmetric silicon-graphene-metal composite nanostructures

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Abstract

Induced circular dichroism (ICD) has been used to detect biomolecular conformations through the coupling between chiral molecules and achiral metal nanostructures with the localized surface plasmon (LSP). However, this ICD is always weak and cannot be dynamically adjusted. Here, we put dielectric and graphene nanostructures on a metal-substrate for restricting more light energies and obtaining dynamic adjustable performance. A composite nanostructure array composed of achiral silicon-nanorods on a metal-substrate and graphene-ribbons (ASMG) is theoretically investigated. Two strong ICD signals appear in the THz region. Near-field magnetic distributions of ASMG reveal that the two strong ICD signals are mainly due to the surface plasmon resonances (SPPs) on the metal-substrate and LSP in the graphene nanostructures, respectively. The ICD signals strongly depend on the geometric parameters of ASMG and are dynamically adjusted by just changing the Fermi levels of graphene-ribbons. In addition, left-handed ASMG and right-handed ASMG can be used to identify the chiral molecular solutions with different chiralities. The maximum enhancement factor of the chiral molecular solutions could reach up to 3500 times in the THz region. These results can help to design dynamically adjustable THz chiral sensors and promote their application in biological monitoring and asymmetric catalysis.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The original meaning of chirality is a geometric feature, which cannot superimposable with their mirror structures [1,2]. For example, our left and right hand are called the enantiomers. Chiral structures are ubiquitous, such as the galaxy, conchs, aloe polyphylla, DNA, and amino acids. Meanwhile, these structures show fascinating optical features, such as circular dichroism (CD), which is defined as the difference of absorbance between right circularly polarized (RCP, +) light and left circularly polarized (LCP, −) light [3,4]. CD spectrum has become an important means for detecting and analyzing chiral molecules. However, the weak coupling between incident lights and chiral molecules leads to weak CD signals [5,6]. Ag chiral nanostructures can enhance Raman optical activity [7]; artificial achiral metal nanostructures can interact strongly with incident lights, which leads to localized surface plasmon (LSP) on their surface [8,9]. These LSP can enhance the coupling between incident lights and chiral molecules, and induce the CD of chiral molecules from the UV band to the visible band. This CD is called induced circular dichroism (ICD) [1012]. ICD effect can be applied in the chiral catalysis [13,14] and chiral distinguishing of chiral molecules [15,16].

Recently, researchers have reported many works to illustrate the mechanism of ICD and enhance the CD of chiral molecules in theory and experiment [17,18]. In theory, ICD is attributed to electromagnetic coupling [19,20] between chiral molecules and achiral metal nanoparticles with LSP resonances [21,22], achiral metal nanogap with hotspots [23], or chiral metal nanostructures with superchiral fields [24]. In the experiment, ICD is also attributed to the chiral arrangement of metal nanoparticles due to the bonds formed by the charge transfers between metal nanoparticles and chiral molecules [25,26]. An unusual CD signal can be achieved by the conformation change of chemisorbed molecules when their interband absorption is enhanced [27]. Dynamically adjustable ICD is also achieved in the microns region by introducing graphene nanostructures into chiral molecules, as shown in our previous work [28].

The above research results supplemented the ICD mechanism and promoted the application of ICD in biosensing. However, these ICD signals based on achiral metal nanoparticles with LSP are weak and cannot be dynamically adjusted, which greatly limits the applications of the ICD. Dielectric nanostructures with the metal-substrates help restrict energies in a small area [29,30]. Graphene nanostructures show dynamic adjustable optical phenomenons in the THz region [3133] and enhance Raman Scattering [3436]. Chiral twisted bilayer graphene shows the linear and nonlinear optical absorption and asymmetrical electromagnetic interaction [37]. The composite nanostructure can provide a good opportunity for achieving strong and dynamic adjustable ICD signals in the THz region.

In this paper, we theoretically investigate a composite nanostructure composed of graphene-ribbons (GRs) and achiral silicon-nanorods on a metal-substrate (ASM). The finite element method is used to calculate the absorption and CD spectra of ASM, GRs, and ASM with GRs (ASMG). The ICD spectrum of ASMG shows a peak and a valley at 6.54 and 7.12 THz. The chirality of ASMG can be reversed by the reversing of the Fermi levels of GRs. Near-field magnetic distributions of ASMG reveal that the ICD signals 6.54 THz and 7.12 THz are mainly due to the surface plasmon resonances (SPPs) on the metal-substrate and LSP in GRs around Si-nanorods, respectively. The influences of the geometric parameters of ASMG on ICD are also investigated. The ICD of ASMG can be dynamically adjusted by just changing the Fermi levels of GRs. Besides, left-handed ASMG (L-ASMG) and right-handed ASMG (R-ASMG) can enhance the CD of different chiral molecules when they are immersed in different chiral molecular solutions. The enhancement factors of the chiral molecules could reach up to 3065 and 3500 times at 6.54 THz and 7.12 THz, respectively.

2. Structure and computational method

Figure 1 shows the proposed the ASMG array, whose cell is enclosed by the brown dotted lines in the bottom right corner. The periods of the ASMG arrays are labeled as Px and Py in x- and y-direction, respectively. Two Si nanorods are symmetrically placed on a Cu substrate covered by a SiO2 layer. The center distance of two Si nanorods is labeled as D. θ denotes the angle between Si nanorod and x-axis. The length, width, and height of Si nanorods are labeled as l, w, h, respectively. The thickness of the SiO2 layer is labeled as tSiO2. Two GRs are placed on the bottom center of the two Si nanorods. The width of two GRs is labeled as wG. Two adjacent graphene belts are set with different voltages, which leads to different Fermi energies of ${E_{fa}}$ and ${E_{fb}}$, respectively. ASMG array is normally excited by LCP (red) and RCP lights (green) along the -z-direction. The absorption spectra, CD spectra, and near field distribution of ASMG are simulated by frequency domain analysis in COMSOL Multiphysics. The periodic boundary conditions along the x- and y-directions are used in the unit cell of ASMG instead of the infinite array of ASMG. The absorption spectra of LCP light and RCP light are represented by A and A+, respectively. Here, the ICD spectra are achieved by ${A_ + }\; - \; {A_ - }$.

 figure: Fig. 1.

Fig. 1. Schematic of ASMG array and parameters definition.

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The Cu refractive index is taken in the experiment [38]. The refractive indices of Si and SiO2 can be obtained in [39] and [40], respectively. For simplicity, the tiny imaginary parts of the refractive indices of Si and SiO2 are ignored in THz region, and the real parts of the refractive indexes of Si and SiO2 are fixed as 3.7 and 1.45, respectively. The conductivity of graphene is related to the intra-band electron-photon scattering processes and inter-band transition, which is a function of the angular frequency of incident light [41,42].

$$\begin{aligned} \sigma (\omega ) &= \frac{{2i{e^2}{k_\textrm{B}}T}}{{\pi {\hbar ^2}(\omega + i{\tau ^{ - 1}})}}\ln \left[ {2\cosh \left( {\frac{{{E_\textrm{f}}}}{{2{k_\textrm{B}}T}}} \right)} \right]\\ &+ \frac{{{e^2}}}{{4\hbar }}\left\{ {\frac{1}{2}} \right. + \frac{1}{\pi }\arctan \left( {\frac{{\hbar \omega - 2{E_\textrm{f}}}}{{2{k_\textrm{B}}T}}} \right) - \frac{i}{{2\pi }}\ln \left[ {\frac{{{{({\hbar \omega + 2{E_\textrm{f}}} )}^2}}}{{{{({\hbar \omega - 2{E_\textrm{f}}} )}^2} + {{({2{k_\textrm{B}}T} )}^2}}}} \right], \end{aligned}$$
where ℏ, Ef, kB, and e correspond to the reduced Planck constant, Fermi energy, Boltzmann constant, and electron charge, respectively. The carrier relaxation $\tau = \rho {E_\textrm{f}}/ev_F^2$.  ρ, vF, and, T are the measured DC mobility, Fermi velocity, and temperature, respectively. In Eq. (1), $\rho = \textrm{ 10000 c}{\textrm{m}^\textrm{2}}/\textrm{V}$ and T = 300 K [43].

The chiral molecular solutions are set as isotropic and homogeneous chiral medium layers. Their chiral factors are described as Pasteur parameter κ. The permittivity ε and Pasteur parameter κ of chiral molecular solutions are the functions of the angular frequency of incident light [44,45].

$$\varepsilon = {\varepsilon _\textrm{b}} - \gamma (\frac{1}{{\hbar \omega - \hbar {\omega _0} + i\Gamma }} - \frac{1}{{\hbar \omega + \hbar {\omega _0} + i\Gamma }})$$
$$\kappa = \beta (\frac{1}{{\hbar \omega + \hbar {\omega _0} + i\Gamma }} + \frac{1}{{\hbar \omega - \hbar {\omega _0} + i\Gamma }}), $$
where ${\omega _0}$ is the angular frequency of the CD peak of chiral molecular solutions taken as 1×1016 rad/s (corresponding wavelength about at 190 nm). εb is the refractive index of background taken as 1.33 (water). Γ is the absorption broadening taken as 0.1 eV. γ and β are the amplitudes of absorption and chirality, respectively. For reducing the time of the simulations, γ ≈ 7 ×10−2 and β ≈ 6×10−4 [46]. Chiral molecular solutions show different effective refractive indices when they illuminated LCP and RCP lights, which is regarded as ${n_ \pm } = \sqrt {\varepsilon \mu } \pm \kappa$ [47].

3. Results and discussion

Figure 2(a) shows the calculated absorption spectra of ASM alone, GRs alone, and left-handed ASMG (L-ASMG) excited by LCP light and RCP light, respectively. The parameters of L-ASMG arrays are set as Px = 40 µm, Py = 25 µm, D = 20 µm, tSiO2 = 5 µm, l = 15 µm, w = 5 µm, h = 5 µm, and $\theta = 60^{\circ}$, ${E_{fa}} = \textrm{0.1 eV}$, ${E_{fb}} = \textrm{0.9 eV}$, and WG = 5 µm, respectively. The frequency ranges from 5.5 to 8.5 THz. When ASM alone and GRs alone are excited by LCP light and RCP light, the two absorption spectra are overlapping and present two resonant peaks at fCu = 6.53 THz and fGRs = 7.47 THz, respectively. However, the absorbance of ASM alone at fCu is a feeble 0.02, and the absorbance of GRs alone at fGRs is 0.15. The absorption spectra of composite L-ASMG under LCP light and RCP light are different and present two peaks at fI = 6.54 THz and fII = 7.12 THz. For L-ASMG, the LCP absorbance can reach 0.72 at fI and 0.26 at fII; the RCP absorbance can reach 0.33 at fI and 0.73 at fII. Figure 2(b) shows the calculated ICD spectra of ASM alone, GRs alone, L-ASMG, and R-ASMG, respectively. The ICD spectra of ASM alone and GRs alone are overlapping and equal to zero. It proves the achirality of ASM alone and GRs alone. The ICD of L-ASMG can reach -0.39 at fI and 0.47 at fII. R-ASMG can be achieved by reversing the Fermi energies of the GRs from ${E_{fa}} = 0.1 \textrm{eV}$ and ${E_{fb}} = 0.9 \textrm{eV}$ to ${E_{fa}} = 0.9 \textrm{eV}$ and ${E_{fb}} = 0.1 \textrm{eV}$. The ICD spectra of L-ASMG and R-ASMG are mirror images in the entire spectra. The absorption spectra for the GRs part of ASMG and the other ASM part are also calculated respectively. The absorbance of the GRs part is stronger than the one of the ASM part. It suggests that the increased absorption mainly distributes on GRs. ASMG without Cu-substrate can also show ICD effects, which are weaker than the ICD effects of ASMG. The substrate effect in this nanosystem is very important.

 figure: Fig. 2.

Fig. 2. (a) The absorption spectra of ASM alone, GRs alone, and L-ASMG; (b) ICD spectra of ASM alone, GRs alone, L-ASMG, and R-ASMG.

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The corresponding steady-state magnetic field distributions are calculated to investigate the origins of the two ICD signals in Fig. 2. Figure 3 shows the normalized steady-state magnetic field distributions excited by LCP (magenta arrow) and RCP (green arrow) lights at resonant frequencies for L-ASMG. Red and blue indicate the maximal and minimal magnetic field intensity, respectively. Figures 3(a)–3(d) exhibit the magnetic field distributions in the xy-plane. Figures 3(e)–3(h) exhibit the magnetic field distributions in the xz-plane. For the ICD of L-ASMG at fI, the magnetic fields under LCP and RCP lights form two banded magnetic fields, which is perpendicular to the x-direction, as shown in Fig. 3(a) and 3(b). The magnetic field of the left band in Fig. 3(a) is weaker than the one in Fig. 3(b), but the magnetic field of the right band in Fig. 3(a) is stronger than one one in Fig. 3(b). Figure 3(e) and 3(f) show that two magnetic field belts are confined mainly on the surface of Cu-substrate. The different components of the magnetic fields of L-ASMG excited by LCP and RCP lights at two resonant frequencies are calculated. The y-components of the magnetic fields also show two banded magnetic fields, which is perpendicular to the x-direction. Hence the ICD at fI is related to the SPPs in x-direction on the Cu-substrate surface. The main area of magnetic field distributions is enclosed in the box with a height of 45 µm, as shown in Fig. 3(e). For the ICD at fII, the magnetic fields of L-ASMG mainly distribute in the GRs around left Si nanorods under LCP light (Fig. 3(c) and 3(g)) and the GRs around right Si nanorods under RCP light (Fig. 3(d) and 3(h)). Hence the ICD at fII is related to the LSP of GRs around Si-nanorods.

 figure: Fig. 3.

Fig. 3. The magnetic field distributions (color distributions) of L-ASMG excited by LCP and RCP lights at two resonant frequencies.

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To verify the mechanism of ICD at fI and fII, Px is varied from 36 µm to 44 µm, and Py is varied from 21 µm to 29 µm, respectively. When each geometric parameter of L-ASMG is changed, the other geometric parameters are the same as Fig. 2. The ICD spectra of L-ASMG with different Px is calculated, as shown in Fig. 4(a). With the increase of Px, fI redshifts due to the increase of the resonant length of the SPPs on the Cu-substrate in the x-direction. The redshift of fII means that fII is mainly decided by the LSP of the GRs in the x-direction. The ICD at fII gradually decreases due to the decrease of the density of L-ASMG, while ICD at fI first increases then decreases. Specifically, the ICD reaches to max value at fI = 6.54 THz when Px = 40 µm. It is because the ICD at fI is attributed to the SPPs in x-direction on the Cu-substrate surface. The relationship between SPPs frequency fSPPs and incident frequency is as follows [48]:

$${f_{SPPs}} = \frac{{c\sqrt {{i^2} + {j^2}} }}{P}\sqrt {\frac{{{\varepsilon _d} + {\varepsilon _m}(f)}}{{{\varepsilon _d}{\varepsilon _m}(f)}}}. $$
where P, i, j, c, and ${\varepsilon _d}$ are period, integer, integer, the speed of light, and the dielectric constant of the interface medium, respectively. The dielectric constant of metal ${\varepsilon _m}(f)$ is a function of incident frequency. Here, the metal is Cu, the interface mediums include the SiO2 layer, Si nanorods, and air environment. In the THz region, ${\varepsilon _{Cu}}(f) \approx - 8052.6 + 22485i$. The absolute value of ${\varepsilon _{Cu}}(f)$ is much larger than the ones of ${\varepsilon _{Si{O_2}}}$, ${\varepsilon _{Si}},$ and ${\varepsilon _{air}}$. When $({i,j} )= ({0,1} )$, Eq. (4) is reduced as:
$${f_{SPPs\textrm{ - }x}} = \frac{c}{{{P_x}}}\sqrt {\frac{\textrm{1}}{{{{\bar{\varepsilon }}_d}}}} , $$
where ${\bar{\varepsilon }_d}$ is the average dielectric constant of the medium in the box with a height of 45 µm, as shown in Fig. 3(e). ${V_{Si}}$, ${V_{SiO2}}$, ${V_{air}}$, and ${V_{\textrm{total}}}$ mean the volume of Si nanorods, SiO2 layer, air, and total space of the box, respectively. ${\bar{\varepsilon }_d}$ is regarded as
$$\begin{aligned} {{\bar{\varepsilon }}_d} &= \frac{{{\varepsilon _{SiO2}}{V_{SiO2}} + {\varepsilon _{Si}}\textrm{2}{V_{Si}} + {\varepsilon _{air}}({V_{\textrm{total}}} - {V_{SiO2}} - \textrm{2}{V_{Si}})}}{{{V_{\textrm{total}}}}}\\ &= \frac{{{{1.45}^\textrm{2}}\!\ast\! {P_x}{P_y}\!\ast\! 5um\! +\! {{3.7}^\textrm{2}}\!\ast\! 2\!\ast\! 15um\!\ast\! 5um\!\ast\! 5um\! +\! {1^\textrm{2}}\!\ast\! ({P_x}{P_y}\!\ast\! \textrm{45}um - {P_x}{P_y}\!\ast\! 5um - 2\!\ast\! 15um\!\ast\! 5um\!\ast\! 5um)}}{{{P_x}{P_y}\!\ast\! \textrm{45}um}}\\ &\approx \textrm{1}\textrm{.33}\textrm{.} \end{aligned}$$
Taking ${\bar{\varepsilon }_d} \approx \textrm{1}\textrm{.33}$ and Px = 40 µm into Eq. (5), ${f_{SPPs\textrm{ - }x}} \approx 6.50\textrm{ THz}$, which is very close to the ${f_\textrm{I}} = 6.54\textrm{ THz}$. It proves that the ICD at fI is mainly attributed to the SPPs in x-direction on the Cu-substrate surface. The ICD spectra of L-ASMG with different Py is calculated, as shown in Fig. 4(b). With the increase of Py, the change of the ICD spectra is very small. It proves that fI and fII are mainly decided by the resonances in the x-direction.

 figure: Fig. 4.

Fig. 4. The ICD spectra of L-ASMG with different (a) Px, (b) Py, (c) D, and (d) tSiO2.

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To study the coupled mode of L-ASMG, the transverse coupling distance D is varied from 16 µm to 24 µm, and the longitudinal coupling distance tSiO2 is varied from 3 µm to 7 µm, respectively. The ICD spectra of L-ASMG with different D is calculated, as shown in Fig. 4(c). With the increase of D, the ICD spectra are almost unchangeable. It means that the ICD of L-ASMG is not related to the transverse coupling between the two GRs covered by Si-nanorods. The ICD spectra of L-ASMG with different tSiO2 is calculated, as shown in Fig. 4(d). With the increase of tSiO2, the ICD spectra show dramatic changes. It means that the ICD of L-ASMG is related to the longitudinal coupling between the two GRs covered by Si-nanorods and the Cu-substrate. fI and fII redshifts due to the increase of ${\bar{\varepsilon }_d}$. The ICD at fII gradually decreases due to the decrease of the longitudinal coupling. However, ICD at fI first increases then decreases. Specifically, the ICD reaches to max value when tSiO2 = 5 µm. At this time, the fI is close to ${f_{SPPs\textrm{ - }x}} \approx 6.50\textrm{ THz}$, which generates the SPPs in x-direction on the Cu-substrate surface.

To analyze the effects of Si nanorods on the ICD of L-ASMG, l is varied from 13 µm to 17 µm, w is varied from 3 µm to 7 µm, h is varied from 3 µm to 7 µm, and $\theta$ is varied from 10° to 80°, respectively. The ICD spectra of L-ASMG with different l, w, and h are calculated respectively, as shown in Fig. 5(a)–5(c). With the increase of l, w, and h, fI, and fII redshift due to the increase of ${\bar{\varepsilon }_d}$, according to Eq. (5). The ICD at fII gradually enhances due to the increase of the capturing LSP capacity with ${\bar{\varepsilon }_d}$ increase. ICD at fI first increases then decreases. Specifically, the ICD reaches to max value when l = 15 µm, w = 15 µm, h = 15 µm, respectively. At this time, these fI is close to ${f_{SPPs\textrm{ - }x}} \approx $6.50 THz, which generates the SPPs in the x-direction on the Cu-substrate surface. The ICD spectra of L-ASMG with different $\theta$ is calculated, as shown in Fig. 5(d). With the increase of $\theta$, fI blue shifts due to the decrease of ${\bar{\varepsilon }_d}$ in the x-direction, according to Eq. (5). The redshift of fII is due to the increase of the projection of Si nanorods on GRs. It increases the effective refractive index of the area around GRs leading to the resonant distance increase of LSP of GRs. The ICD at fI and fII first enhance and then weaken. It is because the asymmetry of L-AMGAs first increases and then decreases with $\theta$ increase.

 figure: Fig. 5.

Fig. 5. ICD spectra of L-ASMG with different parameters of the Si nanorods: (a) l, (b) w, (c) h, and (d) $\theta$.

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To analyze the effects of GRs on the ICD of L-ASMG, ${E_{fa}}$ is varied from 0.1 eV to 0.9 eV, ${E_{fb}}$ is varied from 0.1 eV to 0.9 eV, wG is varied from 3 µm to 7 µm, and the malposition (Mx) between Si nanorods and GRs is varied from −3 µm to 3 µm, respectively. The ICD spectra of L-ASMG with different ${E_{fa}}$ and ${E_{fb}}$ are calculated respectively, as shown in Fig. 6(a) and 6(b). With the increase of ${E_{fa}}$ and ${E_{fa}}$ of GRs, fI almost does not shift due to the ICD at fI related to the SPPs on Cu substrate, while fII blue shifts. The blue shift of fII is due to $\lambda \propto {\hbar ^2}c_{}^2/(4\pi {e^2}{E_f})$[49]. With the increase of ${E_{fa}}$, the $\Delta {E_f} = |{{E_{fb}} - {E_{fa}}} | = |0.9 \textrm{eV} - {E_{fa}} |$ decreases, which leads to the decrease of the asymmetry of L-ASMG and then reduces the ICD signals at fI and fII. With the increase of ${E_{fb}}$, the $\Delta {E_f} \textrm{ = }|{{E_{fb}} \textrm{ - }{E_{fa}} } |\textrm{ = }|{{E_{fb}} \textrm{ - 0}\textrm{.1 eV} } |$ increases, which leads to an increase of the asymmetry of L-ASMG and then enhances the ICD signals at fI and fII. The ICD spectra of L-ASMG with different wG is calculated respectively, as shown in Fig. 6(c). With the increase of wG, fI and fII almost does not shift. The ICD at fI is enhanced, which reaches the saturation when wG = 5 µm. The misplacement between Si nanorods and GRs is inevitable in the preparation of L-ASMG, as shown in Fig. 6(d). With the increase of Mx in a small range, the change of the ICD spectra is very small. It can resist the inaccuracy in the preparation of L-ASMG.

 figure: Fig. 6.

Fig. 6. ICD spectra of L-ASMG with different parameters of the GRs: (a) ${E_{fa}}$, (b) ${E_{fb}}$, (c) wG, and (d) Mx.

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In addition, L-ASMG and R-ASMG are immersed in different molecular solutions to analyze the effects of different molecules with different chirality on their CD. The parameters of ASMG are the same as in Fig. 2(b). The right-handed chiral molecular solution, left-handed chiral molecular solution, and achiral are labeled as $\textrm{ + }\kappa$, $\textrm{ - }\kappa$, and $\kappa \textrm{ = }0$, respectively. The CD spectra of $\textrm{ + }\kappa$, $\textrm{ - }\kappa$, L-ASMG/$\kappa \textrm{ = }0$, L-ASMG/$\textrm{ + }\kappa$, L-ASMG/$\textrm{ - }\kappa$, R-ASMG/$\kappa \textrm{ = }0$, R-ASMG/$\textrm{ + }\kappa$, and R-ASMG/$\textrm{ - }\kappa$ are calculated respectively, as shown in Fig. 7(a). The CD spectra are magnified in the gray dashed boxes. The CD of $\textrm{ + }\kappa$(black dashed line) and $\textrm{ - }\kappa$(red dashed line) are positive and negative, while the difference of their CD signals is very tiny. The CD spectra red shift compared with the one in Fig. 2. It is because the environment refractive index (${n_{solution}} \approx 1.33$) in Fig. 7 is higher than the one (${n_{air}}\textrm{ = }1$) in Fig. 2. The CD spectra of L-ASMG/$\textrm{ + }\kappa$ and L-ASMG/$\textrm{ - }\kappa$ locate in the top and bottom of the CD spectrum of L-ASMG/$\kappa \textrm{ = }0$. A similar phenomenon is also observed in the CD spectra of R-ASMG/$\textrm{ + }\kappa$, R-ASMG/$\textrm{ - }\kappa$, and R-ASMG/$\kappa \textrm{ = }0$. The phenomenon has been verified in the experiment [50,51]. Here, the enhancement factor of chiral molecules is calculated according to ${f_{ {\pm} \kappa }} = \textrm{(C}{\textrm{D}_{\textrm{R - A}\textrm{S}\textrm{MG/} \pm \kappa }} - \textrm{C}{\textrm{D}_{\textrm{L}\textrm{ - A}\textrm{S}\textrm{MG/} \pm \kappa }}\textrm{)/C}{\textrm{D}_{ {\pm} \kappa }}$, as shown in Fig. 7(b). The f spectra are associated with the ICD spectra of L-ASMG and R-ASMG. The f can reach 3067 at 6.06 THz and 3525 at 6.56 THz, which is larger than that reported in a previous study [47].

 figure: Fig. 7.

Fig. 7. (a) CD spectra of the different mixtures including achiral water, right-handed chiral molecular solution, left-handed chiral molecular solution, L-ASMG, and R-ASMG; (b) the CD enhancement factor f of chiral molecules.

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4. Conclusions

In this paper, we proposed a concise method for achieving strong dynamic adjustable ICD in the THz region by introducing dielectric and graphene nanostructures. The strong absorption and ICD spectra of ASMG are achieved in the THz region by the coupling between ASM and GRs. Opposite chirality of ASMG can be obtained just by reversing the Fermi levels of GRs. Near-field magnetic distributions of ASMG reveal that the two strong ICD signals at fI and fII are mainly due to SPPs on Cu substrate and LSP in GRs around silicon-nanorods, respectively. The ICD signals strongly depend on the geometric parameters of ASMG. Especially, the ICD signals are dynamically adjusted from 0 to 0.47 just by changing the Fermi levels of GRs. Besides, L-ASMG and R-ASMG can be used to identify the chiral molecules with different handedness, whose maximum enhancement factor could reach up to 3500 times in the THz region. These findings can help to design dynamic adjustable THz chiral sensors and promote their application in chiral molecular identification and asymmetric catalysis.

Funding

Xi'an University of Posts and Telecommunications (CXJJLY2018060, YJGJ201905); International Cooperation and Exchange Programme (2019KW-027); Natural Science Basic Research Program of Shaanxi Province (2019JQ-862, 2019JQ-864); Shaanxi Provincial Research Plan for Young Scientific and Technological New Stars (2019KJXX-058); Natural Science Foundation of Shaanxi Provincial Department of Education (19JK0797); National Natural Science Foundation of China (12004303, 62005213).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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Figures (7)

Fig. 1.
Fig. 1. Schematic of ASMG array and parameters definition.
Fig. 2.
Fig. 2. (a) The absorption spectra of ASM alone, GRs alone, and L-ASMG; (b) ICD spectra of ASM alone, GRs alone, L-ASMG, and R-ASMG.
Fig. 3.
Fig. 3. The magnetic field distributions (color distributions) of L-ASMG excited by LCP and RCP lights at two resonant frequencies.
Fig. 4.
Fig. 4. The ICD spectra of L-ASMG with different (a) Px, (b) Py, (c) D, and (d) tSiO2.
Fig. 5.
Fig. 5. ICD spectra of L-ASMG with different parameters of the Si nanorods: (a) l, (b) w, (c) h, and (d) $\theta$ .
Fig. 6.
Fig. 6. ICD spectra of L-ASMG with different parameters of the GRs: (a) ${E_{fa}}$ , (b) ${E_{fb}}$ , (c) wG, and (d) Mx.
Fig. 7.
Fig. 7. (a) CD spectra of the different mixtures including achiral water, right-handed chiral molecular solution, left-handed chiral molecular solution, L-ASMG, and R-ASMG; (b) the CD enhancement factor f of chiral molecules.

Equations (6)

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σ ( ω ) = 2 i e 2 k B T π 2 ( ω + i τ 1 ) ln [ 2 cosh ( E f 2 k B T ) ] + e 2 4 { 1 2 + 1 π arctan ( ω 2 E f 2 k B T ) i 2 π ln [ ( ω + 2 E f ) 2 ( ω 2 E f ) 2 + ( 2 k B T ) 2 ] ,
ε = ε b γ ( 1 ω ω 0 + i Γ 1 ω + ω 0 + i Γ )
κ = β ( 1 ω + ω 0 + i Γ + 1 ω ω 0 + i Γ ) ,
f S P P s = c i 2 + j 2 P ε d + ε m ( f ) ε d ε m ( f ) .
f S P P s  -  x = c P x 1 ε ¯ d ,
ε ¯ d = ε S i O 2 V S i O 2 + ε S i 2 V S i + ε a i r ( V total V S i O 2 2 V S i ) V total = 1.45 2 P x P y 5 u m + 3.7 2 2 15 u m 5 u m 5 u m + 1 2 ( P x P y 45 u m P x P y 5 u m 2 15 u m 5 u m 5 u m ) P x P y 45 u m 1 .33 .
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