Two-Dimensional Chiral Metasurfaces Obtained by Geometrically Simple Meta-atom Rotations

Two-dimensional chiral metasurfaces seem to contradict Lord Kelvin’s geometric definition of chirality since they can be made to coincide by performing rotational operations. Nevertheless, most planar chiral metasurface designs often use complex meta-atom shapes to create flat versions of three-dimensional helices, although the visual appearance does not improve their chiroptical response but complicates their optimization and fabrication due to the resulting large parameter space. Here we present one of the geometrically simplest two-dimensional chiral metasurface platforms consisting of achiral dielectric rods arranged in a square lattice. Chirality is created by rotating the individual meta-atoms, making their arrangement chiral and leading to chiroptical responses that are stronger or comparable to more complex designs. We show that resonances depending on the arrangement are robust against geometric variations and behave similarly in experiments and simulations. Finally, we explain the origin of chirality and behavior of our platform by simple considerations of the geometric asymmetry and gap size.


Materials & Solutions
All chemicals and solutions were used without further processing unless noted otherwise.Acetone (for HPLC, > 99.8 %), chromium etchant (standard), 2-propanol (IPA) (ACS reagent, > 99.8 %), were purchased from Sigma Aldrich.495 polymethacrylate (PMMA) A4, 950 PMMA A4 were purchased from Kayaku, Advanced Materials.950 PMMA A4 was mixed 1:1 with anisole to get 950 PMMA A2.E-Spacer 300Z was purchased from Showa Denko Europe GmbH.Anisole (for synthesis) was purchased from Merck.Microposit Remover 1165 was purchased from DUPONT.Methylisobutylketone (MIBK) was purchased by Technic.Glass substrates with 18 nm indium tin oxide (ITO) were purchased from Nanoscribe.The metasurface consists of rectangular rods that are inherently achiral and each meta-atom possesses C2 rotational symmetry as well as Mxy, Mxz, Myz mirror plane symmetries.To create a chiral metasurface, each meta-atom is rotated around its center with a rotation angle θ.In the achiral cases (θ = 0°, 45°) the Mxz and Myz mirror planes of each meta-atom coincide with the Mxz, Myz of the other meta-atoms in the arrangement.In the chiral cases (θ ≠ 0°, 45°) the Mxz, Myz mirror planes of each meta-atom do not coincide with the mirror planes of the other meta-atoms, so their arrangement is chiral.Chiral configurations are illustrated for two cases (θ = 15°, 30°), where the mirror planes of five individual meta-atoms are shown with different colors.
[5] Section 1 -Details on the electromagnetic simulations Simulations were performed using the commercially available finite-difference time-domain (FDTD) simulation package from Lumerical Inc.One unit cell was simulated using periodic boundary conditions in the xand yplane, while perfectly matched layers (PML) were used along the z-axis.Circularly polarized light was simulated with two sources of linearly polarized plane waves whose polarizations were perpendicular to each other and with a relative phase difference of 90° (RCP) or -90° (LCP).The plane waves were located 2.7 µm above the substrate and propagated in the z-direction.The dimensions of the meta-atoms were obtained from SEM and AFM measurements (Figure S2 and S3, respectively).The meta-atom was placed on a 75 µm thick glass (SiO2) substrate with an 18 nm thick ITO layer.A refined mesh with dimensions 540 x 540 x 300 nm 3 and a mesh size of 10 nm was placed around the meta-atom.The transmission was modeled with a 2D power monitor located 5 µm below the glass substrate.The location of the transmission monitor and the relatively large thickness of the glass substrate (75 µm) were necessary to properly take into account diffracted waves in the simulations.For a metasurface with a pitch of 540 nm on glass, the diffraction cutoff is about 810 nm.This means that, below 810 nm, these diffracted waves are trapped in the glass substrate, hence the monitor must be placed outside of the glass substrate to reflect the experimental conditions.
For co-and cross-polarization components in the simulation, we used a Transmission Monitor.This monitor can output complex vector field components in the plane of observation.To obtain the polarization components, we applied a Jones matrix for circular polarization to a vector of electric field and then used square of this quantity summed for all points of the plain in order to get the intensity of the field.This value was normalized to initial light source intensities.
[6] For all simulations, the spectral resolution was set to 2 nm.The dielectric constants of SiO2 were used directly from the Lumerical materials library. 1 Moerland and Hoogenbooms data were used for ITO. 2 The refractive indexes of the Si rods were taken from in-house white-light ellipsometry data. [7]

Section 2 -Details on the fabrication of the metasurfaces
Fabrication was performed similarly to other studies on chiral metasurfaces and has been reported before with minor changes in parameters. 3Glass substrates coated with 18 nm of ITO were purchased commercially from Nanoscribe and cut into smaller pieces using a glass cutter.Prior to amorphous silicon (a-Si) deposition, the glass substrates were cleaned by sonication in acetone and isopropanol for 3 min each, dried with N2, then treated with an oxygen plasma (Diener Femto, 100W, 20 mL/min; 3 min).Subsequently, 126 nm a-Si were deposited using plasma-enhanced chemical vapor deposition (PE-CVD) from Oxford Instruments (PlasmaPro 100).Deposition was performed for 8 min and 50 sec at 250 °C from silane (SiH4) with a flow of 500 sccm, a chamber pressure of 1000 mTorr and power of 10 W.
Electron beam lithography (EBL) was performed using a spin-coated PMMA bilayer as electronsenstive resist.The first layer (PMMA 495k A4) was spun at 5000 rpm for 1 min (acceleration 1000 rpm/sec) and baked on a hot plate at 170 °C for 3 min.The second layer (PMMA 950k A2) was spun with 3000 rpm for 1 min (acceleration 1000 rpm/sec) and also baked in the same way.
After PMMA, an e-spacer (electrification dissipating material) was spun at 2000 rpm for 1 min (acceleration: 1000 rpm/sec) to prevent charging during EBL.EBL was performed using an eLine Plus from Raith Nanofabrication with an acceleration voltage of 30 kV, an aperture of 20 μm, and a working distance of 10 mm.After EBL, the e-spacer was removed by rinsing the substrates in MilliQ-H2O and developed in a 3:1 mixture of isopropanol and methylisobutylketone (MIBK) for 55 sec.Finally, the samples were rinsed with isopropanol and dried with N2.
Next, 26 nm chromium were deposited using electron beam evaporation at a rate of 0.08 nm/sec at a pressure of ~10 -6 mbar.PMMA was then removed (lift-off) by immersing the samples in Microposit Remover 1165 for 17 hours.Mild sonication (80 kHz, 30 % Power) was applied for   [10]

Section 3 -Details on the optical setup
Optical characterization was performed following other studies on chiral metasurfaces reported previously (see also the setup figures in the Supporting Information). 4iefly, a custom-built transmission microscope was used on an optical table with a supercontinuum white light laser (SuperK Extreme from NKT Photonics) as the illumination source with a power of 5 % of the maximum value and a repition rate of 0.302 MHz.Horizontal (HP) or vertical (VP) linear polarization was generated using a broadband linear polarizer (LPVIS100 from ThorLabs, 550 -1500 nm) and circularly polarized light (CPL) was generated using a broadband quarter-wave plate (QWP, RAC4.4.20 from B-Halle, 500-900 nm).The QWP was located directly under the microscope objective (Olympus PLN, 10, NA = 0.25, which served as a condenser) to avoid reflections from mirrors, which can change the CPL purity degree of the illumination.
Light was condensed on the sample by the microscope objective and collected with a 60 objective (Nikon MRH08630, NA = 0.7).After alignment, the beam was slightly defocused to illuminate the entire metasurface (SEM images in Figure S2), and an aperture was used to select the light coming from the area occupied by the metasurface, minimizing the detection of any background illumination, that is, light which hasn't interacted with the metasurface.The light was then sent to a CCD camera or to a multimode fiber (ThorLabs M15L05, core size: 105 µm, NA = 0.22) connected to a grating spectrometer (Princeton Instruments, 300 g/mm grating period, blazed at 750 nm, 0.13 nm spectral resolution).
Cross-and co-polarized transmission measurements were performed by using a chiral analyzer consisting of a QWP (AQWP05-580 from Thorlabs, 350 -850 nm) and a linear polarizer (WP25M-UB from Thorlabs, 250 -4000 nm).The chiral analyzer was installed directly after the collection objective.90° rotation of the substrate (Schematic illustration on the left side).(b,e) Each set of measurements shows a distinct chiral signal, especially >900 nm, that reverses sign when the substrate is rotated by 90°, indicating elliptical polarization.(c,f) Average signal and standard deviation (std, shown as shaded area) from both measurements.All experimental spectra shown in the manuscript were recorded using this method.Section 5 -Excitation with linear polarization.
In an attempt to explain the origin of the observed chiral resonances, we simulated the transmission spectra of all metasurfaces illuminated with linearly polarized light.Circularly polarized light can be interpreted as two linear polarized waves with polarizations perpendicular to each other and having a phase difference of π/2 (LCP) or -π/2 (RCP).Thus, looking at linear polarizations allows us to decouple the interaction of the structure with CPL, which makes it easier to relate the resonances to the structure.For example for the achiral case with rotation angle of 0° some resonances only occur for one linear polarization, but not for the other.However, the influence of the phase difference between RCP and LCP light cannot be taken into account with this approach.
For all simulations, we used horizontal and vertical linear polarization, HP and VP, respectively, which remain in the same orientation during meta-atom rotation.First, we performed small parameter sweeps for the geometric dimensions of the achiral metasurface with rotation angle of 0° (Figure S7).Then, we simulated all metasurfaces with different rotation angles (Figure S8).
All resonances are labeled with numbers and symbols to facilitate the discussion.

Parameter sweeps:
We simulated the achiral sample with rotation angle of 0° and exclusively varied one parameter, i.e. length, width or pitch, while keeping the other parameters constant.The results are shown in Figure S7.Beginning with HP, we can see that resonances 1#, 2#, 3# 6# are exclusively shifting for variation of the structures, i.e. length and width, while they remain stable for pitch variation.
Resonance 4# is exclusively dependent on the pitch, while resonance 5# varies with both width and pitch.For VP, we can see that 7#, 8# are exclusively shifting for variation of the structure, i.e. length and width, while resonance 9#, 10# depend on all parameters and resonance 11# is exclusively depending on the pitch.Note: Resonance 10# varies in modulation strength for length       [22] Section 6 -Geometric asymmetry.
To characterize the geometric asymmetry, we calculated the geometric overlap of our meta-atoms with their mirror images for different rotation angles and analyzed at which rotation angles the geometric overlap of the structures is minimal, i.e., maximum asymmetry.A graphic representation can be found in Figure S12.We began with calculating the "normal" overlap of the structures (blue line in and schematic illustrations at the top of Figure S12).The structures are perfectly overlapping at 0° rotation angle, leading to a normalized geometric overlap 1.0.For positive and negative meta-atom rotations the overlap decreases and gets minimal for ±45°.Since chiral objects cannot be brought into coincidence by any lateral and translational operations, we performed the same calculation with a 90° rotation of one of the meta-atoms (red line in and schematic illustration at the bottom of Figures S12).At 90° rotation of one of the meta-atoms, the previous minimum geometric overlap at ±45° results in a perfect overlap, while the previous maximum at 0° becomes the minimum geometric overlap.The geometric asymmetry lies in between these two extremes and is illustrated as gray shadow in Figure S12, featuring a symmetric shape with the maximal geometric asymmetry at 22.5°.The values of the gap sizes are shown on the right y-axis, while the values of the geometric assymmetry are arbitrary.Their shape was taken from Figure S12 and was scaled that their minima (which corresponds to maximum geometric asymmetry) hits the spectra of transmission asymmetry in the graph to allow a better comparison.The values of the gap size have also been Materials & Solutions ...............................................................................................................................

Figure S1 :
Figure S1: Intuitive graphical representation explaining the chirality of the 2D chiral metasurface platform.The metasurface consists of rectangular rods that are inherently achiral and each meta-atom possesses C2 rotational symmetry as well as Mxy, Mxz, Myz mirror plane symmetries.To create a chiral metasurface, each meta-atom is rotated around its center with a rotation angle θ.In the achiral cases (θ = 0°, 45°) the Mxz and Myz mirror planes of each meta-atom coincide with the Mxz, Myz of the other meta-atoms in the arrangement.In the chiral cases (θ ≠ 0°, 45°) the Mxz, Myz mirror planes of each meta-atom do not coincide with the mirror planes of the other meta-atoms, so their arrangement is chiral.Chiral configurations are illustrated for two cases (θ = 15°, 30°), where the mirror planes of five individual meta-atoms are shown with different colors.
remove all PMMA-Cr residues.Reactive ion etching (RIE) was performed using a PlasmaPro100 from Oxford Instruments.RIE was performed with a mixture of 7 sccm Ar and 20 sccm Cl2 for 1 min and 12 sec with HF (high frequency) of 20 W and ICP (inductive coupled plasma) of 200 W at a pressure of 2 mTorr.Finally, the Cr was removed using a commercial Cr Etchant for 3 min.SEM images of the fabricated metasurfaces are shown in Figure S2.At least 10 meta-atoms were measured with the free software ImageJ to determine the lateral dimensions, i.e. length l, width w and pitch p.The height of the metasurfaces was determined with atomic force microscopy (AFM) (see Figure S3).

Figure S2 :
Figure S2: Scanning Electron Microscopy (SEM) images of the fabricated metasurfaces.(a) SEM images of the achiral metasurface with a rotation angle of 0° at different magnifications.The total size of all metasurfaces was 40 µm x 40 µm with 70 x 70 unit cells.(b) SEM images of all fabricated metasurfaces with different rotation angles from -45 ° to +45 ° in 5° steps.The scale bar is 200 nm.

Figure S5 :
Figure S5: Simulated transmission spectra for LCP and RCP illumination for all rotation angles.Simulated transmission spectra for rotation angles from 0 to -45° (a) and 0 to +45° (b).LCP illumination is shown as solid line, RCP as dotted line.The spectra have been offset for clarity.The light interaction is perfectly mirrored for the same clockwise and counterclockwise rotation.Experimental transmission spectra are shown in Figure S6.

Figure S6 :
Figure S6: Experimental transmission spectra for LCP and RCP illumination for all rotation angles.Experimental transmission spectra for rotation angles from 0 to -45° (a) and 0 to +45° (b).LCP illumination is shown as solid line, RCP as dotted line.The spectra have been offset for clarity.The light interaction is perfectly mirrored for the same clockwise and counterclockwise rotation.Simulated transmission spectra are shown in Figure S5.
(a) and width (b) variation, but does not experience any obvious shift in wavelength.SimilarlyResonance 8# varies for pitch variation, but only experiences a small shift in comparison to resonance 10# and 11#.

Figure S7 :
Figure S7: Parameter variation of the structures dimensions with horizontal and vertical linear polarization.Changes in the transmission spectra for the achiral sample with rotation angle of 0°.Top: Schematic illustration.Middle: illumination with horizontal linear polarization (HP).Bottom: illumination with vertical linear polarization (VP).(a) Increasing the rods length from 468 to 478 nm in 5 nm steps.(b) Increasing the rods width from 242 to 252 nm in 5 nm steps.(c) Increasing the pitch from 535 to 545 nm in 5 nm steps.The results are discussed in SI Section 5.

Figure
Figure S8: Simulated transmission spectra for horizontal and vertical linear polarisation.Horizontal and vertical linear polarisations, HP and VP, respectively are equal for positive and negative rotation angles.HP is shown at the top half of the figure and rotation angles are increasing downwards.VP is shown at the bottom half of the figure and rotation angles are increasing upwards.For ±45°, HP and VP are equal.Left: Simulated transmission spectra, the blue (red) arrows indicate the progression of peaks originating from the HP (VP) during the meta-atom rotation.Lighter blue (red) arrows indicate resonances, which are only barely visible.Right:Schemes illustrating the changes upon meta-atom rotation in respect to HP (in blue) and VP (in red).As example, for HP the width of the structure is increasing for HP (dark blue arrows), while the gap size decreases (light blue arrows) for rotations from 0 to 45°

Figure S9 :
Figure S9: Electric and magnetic near-field plots for the metasurfaces with rotation angle of 10° and 25° at their resonance wavelength.Electric (left) and magnetic (right) near field plots at resonance wavelength with rotation angles of 10° (a) and 25° (b) for LCP and RCP excitation.The electric and magnetic fields have been normalized the electric and magnetic field of the illumination source, E0 and H0, respectively.

Figure S10 :
Figure S10: Cross-and co-polarized transmission and transmission asymmetry.Cross-and co-polarized transmission was measured by employing a chiral analyzer to characterize the output polarization of the transmitted light, which allows to distinguish between the effects of 2D-and 3D-chirality, respectively.(a,b) Top: Experimental (solid line) and simulated (dotted line) cross-and co-polarized transmission.Bottom: Experimental (solid line) and simulated (dotted line) cross-and co-poralized transmission asymmetry.The main peak at 850 nm is mostly dominated by 2D chirality.

Figure S11 :
Figure S11: Gap sizes in the experimental realization.(a,b) SEM images at different magnifications showing the realized gap sizes.The measurement of 60 gaps resulted in an average gap size of (13.6 ± 3.1) nm.Only one out of the 60 gaps was bridged, which is visible at the top right (dashed white circle).

Figure S12 :
Figure S12: Asymmetry calculation of the metasurfaces with different rotation angles.Top: Graphic illustration of the geometric overlap of the metasurface with different rotation angles.The overlap is maximal for 0° and minimal for ± 45°, shown as blue line in the graph.Bottom: Graphic illustration of the geometric overlap with a 90° rotation of the meta-atoms.The overlap is maximal for ± 45° and minimal for 0°, shown as red line in the graph.For both, red and blue lines, the maximum overlap has been normalised to 1.0.The asymmetry is shown as black shaded area and is maximal for a rotation angle of 22.5°.

Figure S13 :
Figure S13: Comparison of the chiroptical response with the geometric assymetry and gap size for different meta-atom rotation angles and widths.a-c) Structures with decreasing width to decouple the geometric asymmetry from the gap size.Left: Schematic illustration.Right: Comparison of the peak transmission asymmetry T (black line) with the geometric asymmetry (blue line) and the gap size (red line) for different meta-atom rotation angles.The positive chiroptical response has been mirrored (dashed black line) for clarity.