Circular dichroism of pseudo-two-dimensional metal nanostructures: Rotational symmetry and reciprocity

The geometrical feature of matter in which a mirror image is not superposable to its original geometry, known as chirality, is an important topic in the field of materials science.¹ The research field of chirality continues to expand, and its concept is essential in the natural sciences over a wide range of spatial scales, which span from elementary particle physics to atoms and molecules, nanomaterials, life science, and even astronomy.² The importance of chirality is not only limited to materials but also relevant in the studies of fields and phenomena typified by chiro-optical effects (optical activity in a broad sense) of materials: that is, optical phenomena arising from the differential response of materials to left- and right-circularly polarized light. Chiro-optical effects of three-dimensional chiral materials, such as optical rotation (OR) or circular dichroism (CD), have been widely utilized as indispensable methods to study the chirality of molecules and nanomaterials since the studies of Pasteur.^3–5 Researchers in the field of nanosciences have also recently shown interest in studies of chiro-optical effects. Following the establishment of a method for fabricating nanostructures using electron beam lithography, a number of studies of chiro-optical effects based on designed (pseudo-) two-dimensional chiral nanostructures, noble metal nanostructures in particular, have been reported.^6–8 A few techniques have also been developed to fabricate three-dimensional chiral metal nanoparticles through dry processes and wet chemical methods, and the chiro-optical effects for such materials have attracted the attention of researchers.^9,10 In addition, methods to construct chiral assemblies of nonchiral (achiral) nanoparticles (including multilayered electron beam lithography) and the chiro-optical effects for such assemblies have been reported.^11–15 In terms of observation and measurement methods, great advances have been made in experimental studies of nonlinear chiro-optical effects,¹⁶ chiro-optical microscopy,^17–19 and so forth. Consequently, unique chiro-optical effects that show different characteristics compared to conventional effects found for molecules have been observed and theoretical and simulation studies to interpret such effects have been pioneered.^20–32 

Regarding the chiro-optical effects of two-dimensional and pseudo-two-dimensional nanostructures, a number of studies focusing on plasmon resonances of metal nanostructures have been reported.^{6–8,16–19,33,34} A two-dimensional structure can be defined as chiral when the mirror image is not superposable to the original as far as it remains in the two-dimensional plane. Strong chiro-optical effects have been reported for two-dimensional gammadion-structured metal nanostructures with fourfold rotational symmetry.^6–8,20,35 For fish-scale two-dimensional chiral structures with twofold rotational symmetry, it has been argued that the observed chiro-optical effects have a different origin compared to those usually observed for a three-dimensional chiral matter.^33,34 Theoretically, based on the Lorentz reciprocity theorem, it is expected that two-dimensional chiral structures with one- or twofold rotational symmetry exhibit chiro-optical effects, while structures with threefold or higher rotational symmetry do not.^36–38 This theoretical prediction was confirmed with an electromagnetic simulation study.³⁵ However, pseudo-two-dimensional gammadion-type metal nanostructures with fourfold rotational symmetry fabricated using electron beam lithography exhibit strong chiro-optical effects. This behavior was attributed to the substrates used to fabricate the structures, which were considered to make the system three-dimensional.^8,35 Although experimental studies of pseudo-two-dimensional systems and theoretical discussions have provided a general trend for the chiro-optical characteristics, systematic measurements for pseudo-two-dimensional chiral nanostructures with varying rotational symmetry and a detailed discussion from a unified point of view are indispensable for understanding the basis of chiro-optical effects. In the present work, pseudo-two-dimensional chiral gold nanostructures with one-, two-, and fourfold rotational symmetry were fabricated using electron beam lithography, and the circular dichroism (CD) spectra for such structures were measured and analyzed. CD spectra measured with light incident onto the front side of the gold nanostructures (forward measurement) are compared with spectra obtained using light incident onto the back side of the substrate (backward measurement). To eliminate the optical effect of the substrate, spectral measurements were performed using an index matching liquid with the same refractive index as the substrate, which was filled into the front side of the nanostructures. We, thus, experimentally confirm that the difference in rotational symmetry of the nanostructure leads to completely different chiro-optical characteristics. We also obtain information for the origin of chiro-optical effects in pseudo-two-dimensional systems with fourfold rotational symmetry.

The pseudo-two-dimensional gold nanostructures were fabricated on glass substrates using electron beam lithography (using Elionix ELS-7500EX) and the lift-off method. The thickness of the gold nanostructure was set to 100 nm. A Ti adhesion layer (thickness of 2 nm) was deposited between the glass substrate and gold nanostructures. Scanning electron microscopy (SEM) images of the fabricated patterns were recorded using a field-emission SEM system (Hitachi High-Tech SU8010). The fabricated gold nanostructures are schematically shown in Figs. 1 and 2. The unit structures were arranged as square lattice arrays. The pitch of the unit cell was 570 nm. The arrays had an area size of 500 × 500 µm². The designed base length and width of each arm were 370 and 50 nm, respectively, while the arm widths for the obtained sample materials were wider: typically 80–110 nm.

The CD measurements were performed using a commercial CD spectrometer (JASCO J-1500CD). As the area of the gold nanostructures fabricated on the glass substrates was limited to 500 × 500 µm², the CD measurement area was restricted by setting a pinhole with a diameter of 0.5 mm in front of the sample. The optical measurement was performed with the incident light normal to the sample substrate. To suppress the unfavorable effect of the anisotropy of the sample in the substrate plane, the CD spectra were measured at 0°, 45°, 90°, and 135° of rotation in the plane, and then the obtained spectra were averaged. The CD spectra measured at 0°, 45°, 90°, and 135° of in-plane rotation are shown in the supplementary material (Fig. S5). The results show that the angle dependence is negligible within the experimental accuracy, for the fourfold symmetry samples. For the two- and onefold symmetry nanostructure arrays, small differences among the spectra obtained with the different in-plane rotational angles are found in the long-wavelength regions (where the anisotropy contribution becomes significant, see Sec. IV for details). However, the angle dependences are found to be sufficiently small compared with the entire CD spectra. Analysis based on the averaged CD spectra is reasonable, and the small angle dependence has little effect on the discussion of correlation between the symmetry and reciprocity of CD spectra. To be exact, the CD spectra obtained with a conventional CD spectrometer are those of extinction CD, which consist of contributions from scattering CD and absorption CD. The nanomaterials used in the present study are composed of unit structures with a size on the order of 100 nm. The optical extinction caused by materials of this size may include a significant contribution from scattering. Moreover, in the extinction CD measurement, a significant portion of the signal is considered to be due to the circularly polarized dissymmetry of the scattering light. Estimating the ratio between scattering and absorption for materials with a complex shape is not straightforward and needs detailed light scattering experiments or electromagnetic calculations. We do not conduct that in the present work, but discuss the relation of extinction CD, including both contributions of scattering and absorption, to materials symmetry.

For the gold nanostructures fabricated on glass substrates, the front side (surface side of the nanostructures) faced the air, while the back side (substrate side) faced the glass substrate, leading to different optical environments for each side. To examine the three-dimensional effects arising from such a structure, we used, for the gammadion-structure samples, a cell structure with index matching liquid filled into the front side of the samples (Fig. 3). The refractive index of the liquid was n = 1.52, which is close to that of the substrate (n = 1.523). In general, light scattering is sometimes reduced by index matching treatment, and this is likely the case in the system we adopted in this work. However, in the plasmonic systems adopted in the present study, the resonance wavelength drastically changes when the index matching liquid is introduced, and the primary effect observed is that of spectral changes resulting from it.

The extinction spectra for the samples were measured with the absorption spectrometry function of the CD spectrometer. Since the optical flux was restricted by a small pinhole in this measurement function, we could not obtain spectra with sufficient quality (in the CD measurement mode, much higher quality spectra were obtained because the signal fluctuation factor was partly compensated automatically). For this reason, we used the extinction spectra only for the purpose of confirming the existence of plasmon resonances in the measured wavelength range. Here, we do not analyze the details for plasmon modes based on the extinction spectra, and, instead, focus on the reciprocity of the CD spectra between forward and backward measurements. The extinction spectra are summarized in the supplementary material (Fig. S1) for reference.

Electromagnetic theory predicts the following concerning the chiro-optical effects of two-dimensional chiral structures measured with light incident normal to the plane.^37,38

1. A two-dimensional chiral material is chiro-optically inactive when the structure has threefold or higher rotational symmetry (C_n, n ≧ 3).

2. When the structure has two- or onefold rotational symmetry (C_n, n ≦ 2), it exhibits chiro-optical effects arising from the in-plane anisotropy. In this case, the chiro-optical signal measured with light incident on the back side (backward measurement) is inverted from that in which light is incident from the front side (forward measurement). (Hereafter, in this paper, we call this phenomenon “chiro-optical inversion.”)

If the front and back sides of the two-dimensional structure are not equivalent to each other (pseudo-two-dimensional structure), the system is not rigorously two-dimensional and behaves as a three-dimensional system. Typical examples include nanostructures fabricated on a substrate and structures with different material compositions or surface shapes on the front and back sides. In this case, the structure exhibits chiro-optical effects for the threefold or higher rotational symmetry cases too. In the following, we analyze and discuss the experimental results obtained based on the fundamental characteristics (1) and (2) mentioned above.

As a representative pseudo-two-dimensional system with fourfold rotational symmetry, CD spectra were measured for the gammadion-shaped gold nanostructure with forward (CD_f) and backward (CD_b) light illumination, as shown in Fig. 4. The gammadion structures were arranged in square lattice arrays. The average [(CD_f + CD_b)/2] and the difference [(CD_f − CD_b)/2] in the forward- and backward-measured spectra are also shown for the purpose of discussion below. In the right-handed gammadion, a negative CD peak is found at ∼700 nm, and positive peaks are found at ∼550 and ∼650 nm. For an ideal two-dimensional fourfold rotational symmetry structure, theory predicts no CD signal, as described in Subsection III A; the observed result is not consistent with this theoretical prediction. The fact that the CD signal is observed in this system indicates that the fabricated gold nanostructure does not possess an ideal two-dimensional fourfold rotational symmetry. There are two possible reasons (either one or both) for this result:³⁵ (a) The symmetry of the system is lowered from fourfold rotational symmetry, and (b) the system cannot be described as two-dimensional. If (a) is true, according to rule (2) mentioned in Subsection III A, the CD signals observed with forward and backward measurements should be inverted to each other (chiro-optical inversion). However, the CD spectra observed with the forward and backward measurements are very similar. The reciprocity of the CD spectra with respect to forward and backward measurements is, thus, proven to be valid almost completely. This indicates that the CD signals principally originate from the three-dimensional character of the system, rather than a lowering of the in-plane symmetry from the ideal fourfold rotational symmetry. If we examine the forward–backward difference in the CD spectra in detail, we find a small difference at a wavelength of ∼610 nm for the case when the index matching liquid is not used (this difference becomes very small when the index matching liquid is used). The origin for this behavior is not clear at this moment. A possible reason for this observation is that the symmetry of the system is lowered from the ideal fourfold rotational symmetry, which results in a difference in CD for forward and backward light incidence at this wavelength (i.e., chiro-optical inversion).

Under the measurement conditions, the front surface of the nanostructure faces the air and the back side faces the glass substrate, and the optical environments for the two faces are different. We cannot exclude the possibility that the observed reciprocity of the CD signals arises from this reason. Then, we next carried out CD measurements with the front side of the sample filled with index matching liquid to ensure that the optical environment of both faces is approximately the same. The results shown in Fig. 5 show that the CD spectra obtained with forward and backward measurements are in excellent agreement, and the reciprocity is almost perfect. The CD signals observed in the gammadion structure with fourfold rotational symmetry are therefore considered to arise from factors other than the existence of the substrate. A plausible origin is that the metal nanostructure is not ideally planar but has a three-dimensional shape, for example, having a rounded surface shape on the front side. The Ti adhesion layer between the glass substrate and gold nanostructures in the fabricated sample can contribute to the three-dimensional character of the structure. To examine this possibility, we need to measure the CD spectrum for a sample with a Ti coating deposited onto the top surface (the front side) of the gold nanostructure, filled with index matching liquid on the front side. We have fabricated such samples. However, we did not succeed in obtaining sufficiently reproducible and high-quality data. We, thus, do not discuss the details for these experiments here. The CD spectral data obtained for the Ti top-coated sample are shown in the supplementary material (Fig. S2) for the purpose of reference. The fabricated sample nanostructures show, at least semiquantitatively, that the reciprocity also holds in this case.

By removing some parts of the arms from the gammadion structure, italic f-, S-, and upright f-shaped pseudo-two-dimensional gold nanostructures were prepared. These nanostructures have two-, two-, and onefold in-plane rotational symmetry, respectively. The samples measured were arranged in square lattice arrays. The symmetry of the whole sample depends on the orientation of each unit nanostructure in the lattice, in addition to the symmetry of each unit structure. We first examine the CD spectra measured for the arrayed samples with the four unit structures on the square lattices arranged in a fourfold rotational (C₄) symmetry (Fig. 2, left half). In all of these spectra, the reciprocity between forward and backward measurements is observed to hold with a high degree of accuracy, as shown in Figs. 6–8 for the italic f-, S-, and upright f-shaped structures, respectively. These samples have fourfold rotational symmetry, as mentioned above, and, consequently, the symmetry is the same as that of gammadions. This is the reason why they exhibit reciprocity for the CD spectra. The origin of the CD signal is considered to be the difference in surface shape for the front- and back-side surfaces of the metal nanostructures.

Next, we investigate the CD spectra measured for the nanostructure arrays with a simple translational lattice (Fig. 2, right half), where the orientations of all the unit structures are the same. From these spectra, it is difficult to see that the reciprocity between forward and backward measurements holds, as shown in Figs. 9–11 for the italic f-, S-, and upright f-shaped structures, respectively.

For wavelengths shorter than 650 nm, the CD signals obtained with forward and backward measurements show similar tendencies but do not agree well with each other (the CD signals obtained for the S-shaped structure show relatively good agreement). In the longer wavelength region, the CD spectra obtained with forward and backward measurements are very different from each other. For instance, for the case of the italic f-shaped structures (Fig. 9), the CD signals obtained at 800 nm for the forward and backward measurements are almost completely inverted to each other for both the right- and left-handed structures. For the case of the S-shaped structures (Fig. 10), the CD spectral features in the forward and backward measurements are inverted to each other (i.e., chiro-optical inversion) over the entire wavelength region above 650 nm. Although the upright f-shaped structures do not exhibit a clear tendency compared with the italic f- and S-shaped structures, they still tend to show CD signals with opposite signs between the forward and backward measurements in the long-wavelength region for both the right- and left-handed structures. Such inverted CD spectral features are clearly observable from the large amplitudes of the difference spectra [(CD_f − CD_b)/2] shown in Figs. 9(C), 10(C), and 11(C). In particular, the inverted features are prominent in the S-shaped structures where nearly complete chiro-optical inversion is observed in the long-wavelength region and are consistent with the theoretically expected selection rule discussed as item (2) in Subsection III A. This result can be understood from the fact that the electromagnetic modes resonant in the long-wavelength (low frequency) region, among the plasmon resonances of the nanostructures, have large anisotropy, leading to the chiro-optical effect described as item (2) in Subsection III A arising from the in-plane modes with large anisotropy. [If the mode is in-plane isotropic, the symmetry of the mode is essentially threefold or higher (C_n, n ≧ 3).] The chiro-optical inversion is not evident in the short-wavelength region, probably because the anisotropy of the plasmon modes is small. The situation in this case is thus similar to that found for the gammadion structure, where the CD signal most likely originates from the three-dimensional character of the structure due to the surface-shape difference between the front and back sides of the metal nanostructures. As shown in the supplementary material (Fig. S3), chiro-optical inversion was found to exist across almost the whole visible wavelength region in other S-shaped gold nanostructure arrays with different detailed shapes and sizes.

When the incident optical field can be regarded as a spatially uniform plane wave, which ensures a satisfying dipole approximation, and nonlinear polarization is absent, the electric permittivity (or susceptibility) of a system with threefold or higher rotational symmetry is in-plane isotropic. The permittivity of a two- or onefold rotational symmetry system is in-plane anisotropic. From the analysis of the experimentally obtained CD spectra for pseudo-two-dimensional chiral gold nanostructures described above, the following results are demonstrated.

• Although two-dimensional gammadion structures with fourfold rotational symmetry are theoretically chiro-optically inactive, as the plasmon modes are in-plane isotropic, the real samples exhibit CD signals. This is interpreted as a consequence of the three-dimensional chiral character of the system due to the presence of different surface structures for the front and back sides of the metal nanostructures. Reciprocity for the forward and backward measurements was thus observed. In some wavelength regions, the reciprocity was found to be imperfect, which can be attributed to nonideal fourfold rotational symmetry.

• For the case of two- and onefold rotational symmetry structures, the reciprocity of CD signals did not hold. As the resonant modes of these structures are in-plane anisotropic, chiro-optical inversion can be anticipated theoretically. We indeed find that this is the case for some samples from the CD spectra measured in the long-wavelength region. In other wavelength regions, clear chiro-optical inversion is not observed. This is probably because the signal contribution from the three-dimensional chiral character dominates in real samples.

It is revealed that the chiro-optical behavior measured for pseudo-two-dimensional chiral gold nanostructures fabricated on glass substrates with electron beam lithography arises from three-dimensional chiral characteristics due to differences in surface shape between the front and back sides of such structures. The reciprocity of CD signals for the forward and backward measurements changes depending on the balance between the in-plane isotropic and anisotropic components of plasmon modes. When the isotropic component is dominant, it is found that nearly complete reciprocity holds. On the other hand, if the anisotropic component is dominant, the CD signal obtained with the backward measurement is almost completely inverted from that with the forward measurement. For the fourfold rotational symmetry gammadion structure, the in-plane isotropic component is found to be dominant in real samples, and reciprocity for the CD signals is observed. For chiral structures with two- and onefold rotational symmetry, both in-plane isotropic and anisotropic components contribute to the signal, and, hence, the extent of both the reciprocity and chiro-optical inversion changes depending on the wavelength of the incident light and the resonant modes. These findings will be valuable for a general understanding of the chiro-optical effects of artificial chiral nanostructures typified by pseudo-two-dimensional chiral systems.

See the supplementary material for the extinction spectra of fabricated samples, the CD spectral data for the gammadion-shaped gold nanostructures top-coated with Ti and filled with index matching liquid on the front surface, the CD data for S-shaped gold nanostructures with different dimensions compared to that discussed in the main text, and in-plane rotational angle dependences of CD spectra of the chiral gold nanostructure arrays.

This work was supported in part by Grants-in-Aid for Scientific Research (Grant Nos. JP16H06505, JP21H04641, JP21K18884, and JP22H05135 to H.O. and Grant Nos. JP17H02767 and JP23H00091 to Y.T.). We thank Professor Malcolm Kadodwala and Dr. Cameron Gilroy for fruitful discussions.

The authors have no conflicts to disclose.

Kensaku Endo: Data curation (lead); Methodology (equal); Visualization (lead). Shun Hashiyada: Data curation (supporting); Investigation (supporting); Methodology (equal); Writing – review & editing (supporting). Tetsuya Narushima: Data curation (supporting); Investigation (supporting). Yoshihiko Togawa: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Hiromi Okamoto: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.