Simultaneous broadband and high circular dichroism with two-dimensional all-dielectric chiral metasurface

2.1 Structure and simulated performance of proposed chiral metasurface

Figure 1A and B shows the schematic of the proposed broadband 2D all-dielectric chiral metasurface. The proposed chiral metasurface is formed by an array of the unit cell of split cross amorphous silicon (a-Si) ribs (i.e., first-order chiral structure) with a trapezoid-shaped a-Si wings (i.e., second-order chiral structure or sub-chiral structure) on a SiO₂ substrate, as depicted in Figure 1C. The period of the unit cell along the X- and Y-axis is P _x , and P _y , respectively, and the height of the a-Si ribs is h. The first-order chirality of the structure arises from the center (E) split of the two trapezoids from the center (O) of the unit cell (O is the origin of the unit cell) with a distance of Δx, and the second-order chirality (sub-chirality) of the structure is from chiral trapezoids with a width of l ₁ in the y-direction and a length of w connecting to the central bar with a width of l ₂, as shown in Figure 1D. The definition of Δx and Δw ₁, Δw ₂ is shown in Figure 1D, where Δx = x _E – x _O , Δw ₁ = x _B – x _A , Δw ₂ = x _C – x _D , where x _E , x _O , x _A , x _B , x _C , and x _D are the X-axis coordinates of points E, O, A, B, C, and D, respectively, and E is the midpoint of the lower base of the upper trapezoid ABCD. The two trapezoids are assumed to be the same (to simplify the structure) and are symmetric about the origin of the unit cell (O), in which a 2-fold rotation (C ₂) symmetry of the unit cell (i.e., rotational symmetry about the origin) is formed. It is noted that positive or negative signs of Δx and Δw ₁, Δw ₂ will generate different chiral responses of the structure, in which the sign of Δx will determine the sign of the first-order chirality of the structure while the sign of Δw ₁, Δw ₂ will determine the second-order chirality of the structure. In the following, the structure is assumed to be the first-order “left-handed” or “right-handed” chiral structure when Δx is positive or negative, respectively, and the second-order “left-handed” or “right-handed” chiral structure when Δw ₁ and Δw ₂ are positive or negative, respectively. The selective coupling of the first- and second-order chirality leads to an enhanced CD and PER over a broadband range simultaneously.

Figure 1:

Schematics of a left-handed 2D broadband all-dielectric chiral metasurface. (A, B) Schematics of the chiral responses to LCP and RCP incidences, respectively. (C) Perspective view of a unit cell with chiral a-Si nanopattern on a SiO₂ substrate. (D) Top view of the unit cell.

Figure 1A and B shows a left-handed circularly polarized (LCP) incidence impinging onto a first-order left-handed chiral metasurface (i.e., Δx is positive), from which a high-efficiency transmission can be obtained with a converted cross circular polarization, i.e., right-handed circularly polarized (RCP). In contrast, when an RCP incidence impinges onto the same metasurface (i.e., the incident circular polarization state is opposed to the helicity of the structure), a high reflection will be obtained with RCP state. It should be noted that the definition of LCP or RCP light is, respectively, anticlockwise or clockwise direction viewed against the direction of light propagation, which is the positive Z-axis in transmission or negative Z-axis in reflection. The performance of the proposed broadband chiral metasurface was characterized using the finite difference time domain method (FDTD) (Lumerical Finite Difference IDE, Canada). CD and PER in transmission are defined as:

where T _LCP, T _RCP represent the transmission of LCP and RCP light. In the calculation, the dielectric properties of a-Si given by Palik [38] are adopted and the refractive index of SiO₂ is assumed to be 1.44. The two orthogonal circular polarization states can be described by the Jones matrix: λ ⃗ LCP = 1 2 ( 1 , i ) , λ ⃗ RCP = 1 2 ( 1 , − i ) .

Figure 2 gives the results of two types of proposed chiral metasurface, in which one structure (labeled as HER, high extinction ratio) shows a very high PER of greater than 20 dB (up to 35 dB) and a high mean CD of greater than 0.9 (up to 0.993) in the wavelength range of 1.39–1.61 μm, as shown in Figure 2A and B, and the other (labeled as UBB, ultrabroadband compared to HER) shows a high extinction ratio of greater than 12 dB (up to 32 dB) and a high mean CD of greater than 0.8 (up to 0.990) in wavelength range of 1.35–1.72 μm, as presented in Figure 2E and F. The corresponding structural parameters for the HER structure are P _x = 947 nm, P _y = 895 nm, h = 350 nm, w = 330 nm, l ₁ = 273 nm, l ₂ = 174 nm, Δw ₁ = 111 nm, Δw ₂ = 93 nm, Δx = 105 nm, and P _x = 934 nm, P _y = 900 nm, h = 350 nm, w = 363 nm, l ₁ = 257 nm, l ₂ = 165 nm, Δw ₁ = 129 nm, Δw ₂ = 58 nm, Δx = 100 nm for the UBB structure. These optimal parameters are obtained with a particle swarm optimization algorithm in which different target functions are assumed for HER and UBB structures. The details of the optimization and calculation process are given in Figure S1 in Supplementary Material. It is noticed that Δx, Δw ₁, and Δw ₂ are all positive for both HER and UBB structures. Figure 2C and D shows the LCP and RCP components in the transmission and reflection optical fields with both LCP and RCP incidences for the HER structure. It is seen from Figure 2C that the HER structure transmits nearly 100 % of the incident LCP light propagating along +Z direction and converts most of the LCP incidence into RCP transmission (t _LR), while highly reflects the RCP incidence light and retains its handedness in the reflection (r _RR), as shown in Figure 2D. Similar to HER, structure UBB highly transmits the incident LCP light propagating along +Z direction and converts most of the LCP incidence into RCP transmission (t _LR), while highly reflects the RCP incidence light and retains its handedness in the reflection (r _RR) over a broader band than that of HER as shown in Figure 2G and H. This giant optical chiral response is distinct from that of 3D chiral structures [8, 9, 12] in terms of conversion efficiency of the cross polarization, which is consistent with that observed in C ₂ rotation symmetric structures [32, 39] in contrast to structures with 4-fold (C ₄) [31] or 3-fold (C ₃) rotation symmetry. These results exhibit the possibility of simultaneous broadband, high CD, and high PER with a relatively simple 2D all-dielectric structure, which is comparable to those working at narrow band [30, 32, 39, 40] or single wavelength [41, 42], and superior to all those working in the broadband, to the best of our knowledge.

Figure 2:

Simulated performance of the proposed 2D chiral nanostructures. (A, E) Transmission spectra of the HER and UBB structure under LCP and RCP illumination. (B, F) The corresponding PER and CD spectra of A, E. (C, G) Transmission coefficient spectra of LCP and RCP components under LCP or RCP incidences for HER and UBB structure. (D, H) Reflection coefficient spectra of LCP and RCP components under LCP or RCP incidences for HER and UBB structure. t _ij denotes the transmittance of “i” input and “j” output. r _ij denotes the reflectance of “i” input and “j” output. The subscripts “L” and “R” represent the LCP and RCP components, respectively.

2.2 Interaction of the first- and second-order chirality

The simultaneous broadband, high CD, and high PER with a simple 2D all-dielectric structure can be understood by the constructive coupling between the first- and second-order of chiral structures. Figure 3A shows the CD resulting from the first-order chiral structure by replacing the trapezoid in the HER structure with a rectangle (i.e., Δw ₁ = Δw ₂ = Δw = 0 nm so that second-order chiral structure disappears) while keeping other structural parameters the same as those in Figure 2A. Strong optical chiral responses over a broad wavelength range (1.35–1.75 μm) can be observed when the relative position of the upper and lower rectangles, Δx, is tuned, in which opposite CD responses that correspond to the left-handed and right-handed structures are observed for positive and negative Δx, respectively. The effect of the second-order chiral structure, i.e., the chiral trapezoid wing is also investigated by assuming Δw ₁ = Δw ₂ = Δw and keeping w and l ₁ the same as those in the HER structure, Figure 3B. The period in the Y-axis direction becomes half of that of the HER structure considering the fact that only one trapezoid is used while the period in the X-axis direction remains unchanged. It is seen that the nano parallelogram also exhibits a chiral response in 1.35–1.55 μm wavelength range, as shown in Figure 3B, although it is a bit smaller than that of the first-order chiral structure, Figure 3A. In Figure 3B, it is not surprising that no CD can be observed when Δw is zero because of the disappearance of the chirality of the rectangular structure. A positive CD is obtained when Δw is positive, i.e., a left-handed second-order chiral structure as defined above while a negative CD is obtained when Δw is negative, i.e., a right-handed second-order chiral structure.

Figure 3:

Interaction between the first-order and second-order of chiral structures. (A) CD spectra of the first-order chiral structure as a function of Δx. (B) CD spectra of the second-order chiral structure (parallelogram) as a function of Δw. (C) Overall CD spectra when a first-order left-handed chiral structure with Δx = 105 nm interacts with a second-order chiral structure with different Δw. (D) Overall CD spectra when a first-order right-handed chiral structure with Δx = −105 nm interacts with a second-order chiral structure with different Δw. Other structural parameters are the same as those in the left-handed HER structure in Figure 2A.

Figure 3C and D demonstrates the interaction of the first- and second-order chiral structures with different chirality, in which Figure 3C is of left-handed first-order chiral structure, i.e., Δx > 0 (Δx = 105 nm, the same as that in the HER structure in Figure 2A) while the second-order chirality changes with different signs of Δw of the chiral parallelogram, and Figure 3D is of right-handed first-order chiral structure, i.e., Δx < 0 (Δx = −105 nm is assumed) while the second-order chirality changes with different signs of Δw of the chiral parallelogram. It is seen from both Figure 3C and D that the same chirality of a first-order chiral structure and a second-order chiral structure, i.e., Δx and Δw have the same signs (either positive or negative), will significantly enhance the CD on the working band, and opposite chirality between a first-order chiral structure and a second-order chiral structure, i.e., Δx and Δw have opposite signs, will diminish significantly the CD on the band. The optimal coupling is achieved when Δw = 100 nm and Δx = 105 nm in Figure 3C with a maximum near-unity positive CD (solid red line) and Δw = −100 nm and Δx = −105 nm in Figure 3D with a maximum negative CD (dashed red line). Therefore, the constructive coupling between the first- and second-order chirality of the structure renders the solid physics basis for the superior CD performance of the proposed 2D chiral structure.

2.3 Multipole decomposition of the chiral optical fields

The underlying physical mechanism for the simultaneous broadband and high CD can also be understood semi-quantitatively with multipole decomposition analysis of the electric field generated from the chiral structure under both LCP or RCP illuminations. The near electric field generated by the chiral structure can be decomposed of multipole moment, in which the first four multipoles are electric dipole moment (ED, labeled with p), magnetic dipole moment (MD, labeled with m), electric quadrupole moment (EQ, labeled with Q ̂ e , which is a tensor) and magnetic quadrupole moment (MQ, labeled with and Q ̂ m , a tensor), respectively. The far-field transmission or reflection can then be calculated by the contribution from the scattering fields of these multiple components. Detailed information regarding the multipole calculation is given in Equations S2–S5 in Supplementary Material. It is noted that higher order multipoles are not considered because of the negligible contributions (about two orders of magnitude lower than the first four multipoles), as can be seen in Figure S2 in Supplementary Material. To show how these scattered fields of the multipoles contribute to the broadband CD exhibited by the HER metasurface, the backward scattering field, i.e., the reflection electric field, from the first four multipole components is examined [43]:

where v _d , k _d are the speed and wave number of light propagation in the surroundings (air), respectively, and F _i (⋅) (i = 1, … 8) represents the scattered vectorial optical fields from the multipole i, with phase φ _i = arg(F _i (⋅)). The intensity of the far field of reflection can thus be calculated by ( | E x s c | 2 + | E y s c | 2 ), in which vectorial superposition of the components (F _i (⋅)) from the multipoles is employed.

Figure 4A–E gives the plots of amplitude and phase of these individual components, F _i (⋅) and their interaction process under LCP incidence. The detailed calculation formulas are given in Equations S2–S5 in Supplementary Material. The interaction among the components F _i (⋅) (i = 1–4) in E x s c or F _i (⋅) (i = 5–8) in E y s c can be understood by interference of these components, as illustrated in Figure 4A. In E x s c (or E y s c ) (Figure 4A), the interferometric field of F ₁ + F ₄ (or F ₅ + F ₇) and F ₂ + F ₃ (or F ₆ + F ₈) are essentially out of phase, i.e., the phase difference between F ₁ + F ₄ (or F ₅ + F ₇) and F ₂ + F ₃ (or F ₆ + F ₈) is nearly 180°, which results in destructive interference, and the total interferometric field of the four multipoles is supressed (as indicated with black arrow line in Figure 4A). The detailed amplitudes and phases of the interference process are given in Figure 4B and C, in which the amplitude and phase of the first-stage interference, F ₁ + F ₄ and F ₂ + F ₃, are plotted with a solid green and a blue line, respectively, in Figure 4B and C. The amplitude after the second-stage interference between the fields F ₁ + F ₄ and F ₂ + F ₃ is plotted with a solid black line in Figure 4B. It is seen that the overall amplitude of E x s c (solid black line) after the 2-stage interference becomes low and flat within the whole wavelength band of interest (grey shaded area) although the amplitudes of F ₁ + F ₄ and F ₂ + F ₃ before the 2nd-stage interference are relatively high. The destructive interference that occurred in the 2nd-stage interference is clearly supported by the broad and flat phase difference of 180° between the fields of F ₁ + F ₄ and F ₂ + F ₃ in Figure 4C, solid black line. A similar two-stage interference process can also be observed among the four components, F _i (⋅) (i = 5–8) in E y s c , as depicted in Figure 4D and E, in which a low and flat amplitude within the interested wavelength band can also be obtained (solid black line in Figure 4D) due to the destructive interference originating from −180° phase difference between F ₅ + F ₇ and F ₆ + F ₈ (solid black line in Figure 4E). The intensity of the far field of reflection can thus be calculated by ( | E x s c | 2 + | E y s c | 2 ), which will result in low reflection in the case of LCP incidence. This is well consistent with that observed in Figure 2D in which reflection coefficients of both components (r _LL and r _LR) are low in the case of LCP incidence. Similarly, the interference process among the multipoles of the HER structure under RCP incidence can be also implemented. The detailed results and figures are given in Figure S3 in Supplementary Material. In contrast to the LCP incidence, a strong reflective field can be obtained for RCP incidence due to the constructive interference, as detailed in Figure S3. The different reflection behaviors between LCP and RCP incidences lead to a substantial difference in the reflectivity of the HER device, thereby giving rise to a large and broadband CD. For the UBB structure, the same interference process can be observed at a wider bandwidth as shown in Figures S5 and S6. The results of scattering CD spectrum based on the above semi-quantitative multipole model for HER and UBB are given in Figures S4 and S7 (Supplementary Material), respectively, which is in agreement with that demonstrated in Figure 2D and H.

Figure 4:

Vectorial field interference of multipoles in the reflection of HER structure under LCP incidence. (A) Illustration of the incident and reflection with HER metasurface and the multipolar interference processes in reflection field under LCP incidence. The vectorial superposition process of the x-component ( E x s c ) and y-component ( E y s c ) of the four multipoles (F ₁–F ₄ and F ₅–F ₈) are given in the complex plane, respectively. (B, D) Amplitudes of the four components of E x s c and E y s c , respectively, as well as the amplitudes formed by the first-stage and second-stage interference. (C, E) The corresponding phases of different components of E x s c and E y s c , and those after the first-stage and second-stage interference.

The cutoff behavior of the chiral response in the proposed lossless all-dielectric 2D chiral structure can also be well predicted with the multipoles. Figure 5A and B shows the scattered power ( C sca i , i = p, m, Q ̂ e , and Q ̂ m , which are given in Equations S7–S10 in Supplementary Material) of ED, MD, EQ, and MQ under LCP and RCP incidences, respectively. The parameters of the HER structure are used in which the height of the structure is h = 350 nm. It is seen that MD resonances are excited by both LCP and RCP incidences on the HER structure at wavelengths of 1.73 μm and 1.74 μm, respectively, as indicated by ‘o’ and ‘*’ in Figure 5A and B. Further examination of the MD resonances at different heights (h) of the proposed structure shows that the MD resonant wavelength at different heights of the structure forms the cutoff boundary of the chiral response of the proposed 2D chiral structure. Figure 5C and D gives the CD maps versus incident wavelength and the height of the HER and UBB structures (calculated directly with FDTD), respectively, in which symbols ‘o’ and ‘*’ denote the resonance wavelengths of the MD at the corresponding height (calculated with the multipole model as that in Figure 5A and B) under LCP and RCP incidences, respectively. A cutoff boundary of the chiral response in both the CD maps of HER and UBB is observed. Beyond the boundary (i.e., in the region of wavelength longer than the cutoff wavelength), the metasurface exhibits essentially no CD response (<0.1), as shown in the green area on the right side of Figure 5C and D. Remarkably, this boundary aligns excellently with the height-dependent trajectory of the wavelength of the MD resonance excited under both LCP and RCP incidence. Therefore, it is inferred that a cutoff wavelength of the chiral response exists in this type of 2D chiral structure and the cutoff wavelength can be predicted by the MD resonances. This is important in the designing of 2D chiral metasurfaces in which the cutoff wavelength and the corresponding structural dimensions can be pre-identified. The physical mechanism under the observation can be explained with Rosenfeld criterion [31]. For metasurfaces to achieve an optical chiral response, magnetic and electric dipole moments (p or m) must couple each other, following the Rosenfeld criterion p⋅m ≠ 0. When the wavelength of incident light is longer than the MD resonance wavelength, no in-plane magnetic dipole forms and therefore, no chiral response occurs. In contrast, when the incident wavelength is shorter than MD resonance wavelength, both the in-plane magnetic dipole and higher-order multipoles are excited, which allows the Rosenfeld criterion satisfied and subsequently the circular dichroism generated. Hence, the MD resonance directly determines the long-wavelength band edge of the CD spectrum.

Figure 5:

The cutoff behavior of chiral response of the proposed 2D all-dielectric chiral metasurface. Scattering power of individual multipole components in HER structure excited by (A) LCP and (B) RCP incidence. CD maps versus incident wavelength and height of structure of (C) HER structure and (D) UBB structure. Symbols “o” and “*” on the map denote the resonant wavelengths of the MD at the corresponding structure height for LCP and RCP incidence, respectively.

2.4 Measured performance of the fabricated chiral metasurfaces

The scanning electron micrographs (SEM) of the fabricated HER and UBB chiral structure arrays are shown in Figure 6A–C, in which Figure 6A and B is the top views of the HER and UBB structure, respectively, and Figure 6C is a typical cross-section of HER structure. It is seen that the dimensions of the fabricated structures are all in excellent agreement with the designed ones (Figure 2) with a deviation of ±20 nm. Figure 6D–G gives the measured transmittance and PER and their comparison with the theoretical results (solid lines) for the HER and UBB chiral structures, respectively. The measurement setup is given in Figure S8 in Supplementary Material. It is seen that the experimental results are all in good agreement with the simulated results. For the HER structure, Figure 6D and E, the measured average CD in 1.39–1.61 μm is about 0.9, and the average PER in this band is greater than 15 dB, up to 19.7 dB (about 93). For the UBB structure, Figure 6F and G, the measured average CD in 1.35–1.65 μm band is about 0.8, and the measured average PER in this band is greater than 13 dB, up to 17.5 dB (about 56). In order to further verify the polarization characteristics of the transmitted field, a linear polarizer between the CCD detector and the objective lens (O) is added to the measurement setup in Figure S8 (Supplementary Material), and the transmission is measured when rotating the added linear polarizer for HER structure. The measured transmissions and their comparison with the theoretical results at three different wavelengths (1.50 μm, 1.55 μm, and 1.60 μm) are given in a polar coordinate in Figure 6H. It is seen that the experimental and simulation results are all in good agreement at different wavelengths, in which a high ellipticity in the transmission in the wavelength range of 1.50–1.60 μm can be observed due to the high cross-polarization conversion rate of the device, as witnessed in Figure 2C. Compared with recent advances (detailed comparison is given in Table S1 in the Supplementary Material), our proposed structure can simultaneously have a high CD and PER over a broadband wavelength range, which has great potential applications in various polarimetric imaging and detections.

Figure 6:

Experimental measurement results. (A) SEM images of the HER. (B) SEM images of the UBB. (C) Typical SEM image of the cross section of the HER. (D) Experimental transmission spectra of HER structure under LCP and RCP illumination. (E) Corresponding PER spectra of HER. (F) Experimental transmission spectra of UBB structure under LCP and RCP illumination. (G) Corresponding PER spectra of UBB. (H) Polarization state of transmitted light after a rotated linear polarizer under LCP incidence onto HER structure at different wavelengths. The distance from the point in the polar coordinate to the origin represents the normalized amplitude.

To showcase the exceptional performance of proposed chiral structures using a limited number of meta-atoms, we further fabricated a chiral pattern as depicted in Figure 7A, in which the interior and exterior of the letters “CD” comprise enantiomeric counterparts (i.e., opposite chirality) of HER structure, respectively. Figure 7A shows the SEM image of the fabricated “CD” letters composed of two opposite chiral enantiomers inside and outside of the letters, and the corresponding chiral enantiomers are shown on the right side of Figure 7A. The transmissions of the fabricated “CD” pattern under LCP and RCP incidences are shown in Figure 7B in the wavelength range from 1.30 μm to 1.70 μm. In the experiment, to suppress the spatial coherence of the incident beam, a rotating glass diffuser was inserted between the linear polarizer and the attenuator in Figure S8 (Supplementary Material). Remarkably, under LCP illumination within the wide wavelength range of 1.40–1.60 μm, bright letters appear vividly on the dark background continuously, while the letters appear dark on the bright background under RCP illumination. When the incident wavelength deviates from the designed band, the contrast between the background and letters diminishes, as shown in Figure 7B. Especially, contrast reverse phenomenon of the “CD” pattern can be observed at the wavelength of 1.30 μm, which is well consistent with the theoretical prediction shown in Figure 2A as well as the experimental results in Figure 6D. It is noted that the letters’ line width measures around 10 μm, which holds great potential for spin-encoded imaging applications.

Figure 7:

Experimental transmission of the fabricated pattern composed of opposite enantiomers upon circularly polarized illumination. (A) SEM images of the fabricated pattern composed of two opposite chiral enantiomers. The interior and exterior of the letters “CD” are composed of enantiomers of HER, respectively. (B) Experimental images of the transmission of the pattern under the illumination of LCP and RCP at different wavelengths.