1. Introduction

Chirality and associated circular dichroism (CD) are very intriguing properties of biomolecules. Chirality refers to the geometrical property that the original microscopic or macroscopic structure cannot be brought to congruence with its mirror image. Circular dichroism, defined as the difference in absorption of left circularly polarized (LCP) and right circularly polarized (RCP) light, is one of the most commonly used spectroscopic techniques for chirality studies. CD spectroscopy provides important structural information and is widely used for characterizing organic and biological molecules [1–25].

Chiral structures have been observed and analyzed by many researchers since 1970s [1–25]. In the last decade, various two- and three-dimensional chiral structures have been proposed and discussed [2–25]. Although the chiral optical response of three-dimensional plasmonic nano-structures is significantly enhanced, these nano-structures are difficult to fabricate compared to planar structures [4–9]. On the other side, it has been demonstrated that even handed quasi-planar and planar plasmonic structures show profound chiral interaction with circularly polarized light despite the fact that they are not truly chiral [10–18]. The optical excitation of the chiral localized surface plasmon resonances (LSPRs) generates chiral electric fields [25]. LSPR is an optical phenomena generated by a light wave trapped within conductive nanoparticles smaller than the wavelength of light [26, 27]. The phenomenon is a result of the interactions between the incident light and surface electrons in a conduction band. This interaction produces coherent localized plasmon oscillations with a resonant frequency that strongly depends on the composition, size, geometry, and dielectric environment [26, 27].

Electromagnetic fields with strong optical chirality are formed in the vicinity of chiral plasmonic structures, which strongly interact with chiral molecules [9, 19–21]. These electromagnetic fields might ultimately enable the detection of individual chiral molecules and their discrimination due to a significantly enhanced interaction of the molecules with the external light field mediated by the plasmonic nanostructure [22–24]. Planar structures have been proposed to obtain the strong circular dichroism and optical chirality for microwave [12], near-IR [3, 13–16], and visible [17, 18, 22] regimes, but there is no planar structure with strong circular dichroism and optical chirality in the literature for detecting of the individual chiral molecules in mid-IR regime.

In this paper, a windmill-shaped planar structure (WS-PS) array is proposed to obtain optical chirality for the mid-IR regime. Strong circular dichroism from WS-PS array is obtained numerically. The optical chirality and electric field distributions of WS-PS array are also determined by the Finite Difference Time Domain (FDTD) [28–31] method. FDTD method is a powerful method for solving Maxwell's equations in complex geometries. In addition, FDTD can obtain the frequency solution by exploiting Fourier transforms, thus a full range of useful quantities can be calculated, such as the complex Poynting vector and the transmission/reflection of light [28–31]. The dependence of spectral characteristics on the geometrical parameters of the WS-PS is also analyzed with FDTD method. The proposed WS-PS arrays may have potential for biosensing applications such as detection of Myoglobin, Bovine serum albumin, Cytochrome c, Lysozyme, Ovalbumin, α-Chymotrypsin, and Concanavalin A which have resonances in the mid-IR regime [32].

2. Circular dichroism of WS-PS arrays

Figure 1 shows the schematic of unit cell of the WS-PS. In Fig. 1(a), H illustrates the height of the structure, W indicates the center width of structure, and P shows the periodicity of the structures in the array. The WS-PS comprises two gold (Au) layers of thickness t separated by a magnesium fluoride (MgF₂) layer of thickness d as shown in Fig. 1(b). This structure is an example of the metal-dielectric-metal sandwich structures typically employed as planar structure [3]. The left-handed (LH) windmill-shaped structure with four-fold structural symmetry is placed on a CaF₂ substrate with refractive index of 1.42 [33]. The refractive index of MgF₂ is taken 1.38 [15]. In the simulations, the dielectric constant of gold (Au) is taken from [34].

 

Fig. 1 Schematics of proposed WS-PS. (a) Top view of the unit cell structure. (b) Perspective view of the unit cell structure.

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In this study, WS-PS arrays are modeled with a commercial FDTD package (Lumerical FDTD Solutions) for the numerical analysis. FDTD package uses a rectangular, Cartesian style mesh. It's important to understand that of the fundamental simulation quantities (material properties and geometrical information, electric and magnetic fields) are calculated at each mesh point. The package has a conformal mesh algorithm that involves forcing the mesh to be smaller near complex structures where the fields are changing very rapidly to obtain accurate results. In this study, a mesh size of 5 nm is also used to increase the numerical grid density around the sharp points. Periodic boundary conditions are used along x and y axes and perfectly matched layers are employed along + z axis, the direction of the illumination source. A normal incident plane wave from above is used to apply LCP and RCP excitation. As the incident light wave strikes the structure, it will be absorbed, reflected, and transmitted through the structure.

In order to characterize chiral structures, one normally examines the circular dichroism (CD) spectra. To calculate the CD of the left -handed WS-PS array, transmission and reflection spectra of the structure are obtained with FDTD method for H = 1600 nm, W = 100 nm, P = 1900 nm, t = 35 nm, and d = 35 nm. Absorption spectra of structure is computed by using the transmission and reflection results. Figures 2(a) and 2(b) depict the determined optical spectra for LCP and RCP excitations from above (forward illumination), respectively. It can be seen from Figs. 2(a) and 2(b) that there are three transmission resonances around the frequencies of 50 THz, 81 THz, and 111 THz. For resonance at 50 THz, the transmission dip is close to zero for both RCP (T_RCP) and LCP (T_LCP) waves, which means the structure exhibits same behavior for both RCP and LCP excitations at this resonance point and almost does not transmit any light. For resonance at 81 THz, the transmission dip for RCP wave is much deeper than that for LCP wave, which means the resonance for LCP wave is much stronger than RCP wave. While for resonance at 111 THz, the resonance for RCP wave is much stronger than LCP wave. Corresponding CD results of the left-handed and right-handed WS-PS arrays are calculated by using difference in absorption (CD = A_LCP - A_RCP) under LCP and RCP excitations (Fig. 2c). As can be seen from Fig. 2(c), the WS-PS arrays have two CD resonances at the frequencies of 81 THz (f₁) and 111 THz (f₂). The spectra for the right handed WS-PS array simply reveal a reversed sign of the CD as expected from symmetry [15, 22]. CD amplitudes of WS-PS arrays are slightly different for forward and backward illumination in Figs. 2(c) and 2(d). Therefore, proposed WS-PS array exhibits CD in the mid-IR regime. In addition, the sign of CD did not change under different illumination directions which means there is no polarization conversion in the WS-PS arrays [7].

 

Fig. 2 (a, b) Transmittance, reflection, and absorption spectra of left-handed WS-PS for (a) LCP and (b) RCP excitation. (c, d) Circular dichroism of left-handed (LH) and right-handed (RH) WS-PS arrays under (c) forward and (d) backward illumination. The corresponding parameters are H = 1600 nm, W = 100 nm, P = 1900 nm, t = 35 nm, and d = 35 nm.

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3. Chiroptical near-fields of WS-PS arrays

In order to understand the physical origin of the optical response of left-handed WS-PS arrays, the near-field distributions at the resonance peaks under RCP and LCP excitations for WS-PS arrays with H = 1600 nm, W = 100 nm, P = 1900 nm, t = 35 nm, and d = 35 nm are analyzed. Figures 3(a) and 3(b) show the electric field, |E|, distributions at the air-metal interface (top surface of the top gold layer) for RCP excitation at the f₁ and f₂ resonance points illustrated in Fig. 2(c), respectively. Similarly, Figs. 3(c) and 3(d) illustrate the electric field distributions for LCP excitation at the f₁ and f₂ resonance points, respectively. As can be seen from Fig. 3, the electric fields are concentrated on the sharp corners of the structure. Molecules in these corners may undergo a much stronger interaction with the electromagnetic field than those that lie well away from metallic particles. This means that the dielectric environment of the near surface region of the WS-PS can strongly influence the resonant frequencies. This phenomenon is the basis of the bio-sensing capabilities of chiral structures [22].

 

Fig. 3 Electric field distributions by the WS-PS illuminated with (a, b) RCP and (c, d) LCP at f₁ and f₂ resonance points. The corresponding parameters are H = 1600 nm, W = 100 nm, P = 1900 nm, t = 35 nm, and d = 35 nm.

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Local field enhancement (red points in Fig. 3) alone is not enough to account for the enhanced chiral response. Owing to the symmetry of the metallic structures in this case, plasmon oscillations in different branches are coupled together to generate chiral fields. To parameterize the local density of the chirality of an electromagnetic field, researchers have introduced the following time-even pseudo scalar, termed the optical chirality (C) [20]:

 

Fig. 4 Optical chirality, C, enhancement by the WS-PS illuminated with (a, b) RCP and (c, d) LCP at f₁ and f₂ resonance points (H = 1600 nm, W = 100 nm, P = 1900 nm, t = 35 nm, and d = 35 nm).

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Total optical chirality of the near fields generated by the structure at f₁ and f₂ resonance points under RCP and LCP excitations is also computed by summing the chirality over all points in the numerical grid. Total chirality values of near fields at f₁ and f₂ resonance points under RCP excitations are respectively 22822 and −3233. Total chirality values are −18372 and −5288 at f₁ and f₂ resonance points, respectively, under LCP excitations. It is observed that total chirality values are not zero for both RCP and LCP excitations, which means proposed WS-PS array has ability to distinguish the left and right handed molecules.

4. Tuning spectral response of the WS-PS arrays

To control the spectral response of the proposed WS-PS arrays, dependence of the spectral response on height, center width, periodicity of WS-PS and thicknesses of MgF₂ and Au is investigated. Influence of incident angle (θ) which is angle between a ray incident on a surface and normal is also explored.

Figure 5 depicts the correlation between CD and geometrical parameters of left-handed WS-PS arrays. Figure 5(a) illustrates the effect of height (H) variation while other parameters kept constant. It has been observed that the both resonance frequencies of the CD decrease with the increasing H. Amplitude of the CD at first resonance point decreases linearly with the increasing H while the amplitude of CD at second resonance point firstly increases, then decreases. Figure 5(b) shows the CD results for center width (W) variation. As the center width of the WS-PS increases, the resonance frequencies of the structure slightly increase and amplitude of CD decreases linearly. The dependence of CD spectra on the periodicity (P) is shown in Fig. 5(c) that resonance frequency of CD is not affected by periodicity while amplitude of CD changes slightly with periodicity. Figures 5(d) and 5(e) depict the dependence of the CD spectra on the thicknesses of MgF₂ and Au, respectively. As can be seen from Figs. 5(d) and 5(e), first resonance frequency and amplitude of CD increase with increasing thicknesses of MgF₂ and Au. But the amplitude of CD increases firstly, then decreases dramatically for second resonance point for both MgF₂ and Au. Third resonance frequency of CD is also appeared with increasing thicknesses of MgF₂ and Au. The effect of incident angle (θ) variation is illustrated in Fig. 5(f) which shows that the resonance frequency of CD is not affected by incident angle variation and the amplitude change is negligible with θ.

 

Fig. 5 Circular dichroism results of WS-PS arrays. (a) H-variation at fixed W = 100 nm, P = 1900 nm, d = 35 nm, t = 35 nm, and θ = 0°, (b) W-variation at fixed H = 1700 nm, P = 1900 nm, d = 35 nm, t = 35 nm, and θ = 0°, (c) P-variation at fixed H = 1700 nm, W = 100 nm, d = 35 nm, t = 35 nm, and θ = 0°, (d) d-variation at fixed H = 1700 nm, W = 100 nm, P = 1900 nm, t = 35 nm, and θ = 0°, (e) t-variation at fixed H = 1700 nm, W = 100 nm, P = 1900 nm, d = 35 nm, and θ = 0°, (f) θ-variation at fixed H = 1700 nm, W = 100 nm, P = 1900 nm, d = 35 nm, and t = 35 nm.

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Eventually, resonance frequencies of CD from WS-PS arrays are dependent on the geometrical parameters (H, W, d and t) of structure but the variation of periodicity (P) and the incident angle (θ) does not have any effect. Therefore, the resonance frequencies of CD from proposed WS-PS arrays can be easily tuned by changing H, W, d, and t parameters. Due to the resonance frequency variations with changing the geometrical dimensions of structure, the resonances in the CD spectra may be attributed to the excitation of LSPRs in the WS-PS arrays.

5. Conclusion

In conclusion, a WS-PS array to obtain optical chirality for the mid-IR regime is introduced for the first time. Strong CD from WS-PS array is determined numerically. The observations indicated that the circular dichroism characteristic of the proposed WS-PS arrays is dependent on the geometrical parameters of WS-PS arrays such as height, center width, and thicknesses of MgF₂ and Au. The resonance frequency of CD is not affected by incident angle and periodicity of structure. The chiroptical near-field response of WS-PS arrays is also investigated. The electric field and optical chirality enhancements of WS-PS arrays are determined by using the FDTD method. Electromagnetic fields with strong optical chirality can be formed in the near field of WS-PS arrays. Due to the enhanced near-field chiroptical response and tunable spectral behavior, WS-PS arrays may have potential for biosensing applications.