Chiral media, which can exist in nature in two mirror-superimposable forms (e.g., left- and right-handed quartz crystals), are optically active; i.e., they can rotate the polarization plane of a propagating light wave clockwise or counterclockwise depending on the sense of chirality. In solids, optical activity is scaled as $\mathit{a/}\lambda$ [1], where $a$ is the crystal lattice parameter and $\lambda$ is the light wavelength, and thus the effect is usually very weak. However, recent advances in nanotechnology have facilitated creation of artificial chiral structures that are often referred to as chiral metamaterials exhibiting a significant optical rotatory power [2–13]. In particular, chiral metamaterials possessing a strong optical activity open unique opportunities for a negative refraction [14–17], angular momentum conversion [18], and active polarization control, such as a terahertz polarization modulator [19,20] and an emitter of circularly polarized light [21].

In order to design chiral metamaterials with enhanced rotatory power, it is important to identify the wavelength at which strong optical activity is observed. Planar chiral metamaterials usually consist of arrayed nanoentities, such as rosettes [2–7,16], crosses [8,17], and U-shapes [10] that are isolated from one another. In these structures the resonant enhancement of the optical response is associated with localized Mie-type resonances of an individual nanoentity and the coupling between them. Because the shape of the individual nanoentities in chiral metamaterials is usually complicated, the analysis of their optical properties and identification of the resonances requires numerical calculations [4–10,17].

In periodic arrays of metal nanoparticles, propagating surface plasmon modes supported by interparticle coupling play an important role in determining the optical properties. Previously, by studying the dependence of resonance effects on the incident angle, we demonstrated the enhancement of optical activity using surface plasmon modes supported by interparticle coupling in two-dimensional (2D) arrays of chiral gammadion nanoparticles [22]. Moreover, we demonstrated that the propagating surface modes significantly enhance the optical activity in metallic and dielectric chiral structures [12,22–24]. In these cases, the observed resonances are well matched to the resonances predicted by the empty-lattice approximation [25,26]. However, the relation between periodicity of chiral structure and the optical activity resonance still remains unclear.

The simplest structure that can support this type of propagating surface plasmon mode is a metal ribbon. Correspondingly, a planar structure consisting of metallic ribbons deformed in a chiral manner offers a new design concept for chiral metamaterials. In addition, the investigation of optical properties of planar chiral networks is also of fundamental importance. This is because the domination of propagation modes allows the description of the optical properties of a chiral network by drawing an analogy with the nearly free electron model in solid state physics. Thus, chiral networks emerge as counterparts of the planar arrays of chiral nanoentities with optical properties that can be described in the tight-binding model framework.

In this Letter we investigate the phenomenon of optical activity in planar, chiral metal networks. By measuring the dependence of the polarization state of the transmitted light on the periodicity of the structures at normal incidence, it was confirmed experimentally that the enhanced polarization rotation occurs at the wavelength of the surface plasmon resonance predicted by the empty-lattice approximation.

Figure 1 shows the fabricated chiral structures with a left and right sense of twist, designed to possess a fourfold rotational symmetry axis along the substrate normal. These samples were fabricated using electron beam lithography and reactive ion-etching processes. The metal film on a fused silica substrate consists of a 2 nm thin titanium adhesion layer and a 23 nm thick gold layer. A 10 nm thick over etching layer is under the titanium layer. The structures were manufactured with periods of 600 and 800 nm to investigate the dependence of the spectra on periodicity.

 

Fig. 1. Scanning electron microscope images of the metal chiral nanostructures. Gray areas correspond to the gold thin film. (a) Left twisted, 600 nm period; (b) right twisted, 600 nm period; (c) left twisted, 800 nm period; and (d) right twisted, 800 nm period.

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Measurements were performed using polarization modulation with a tungsten lamp as the light source, as described in [22]. The transmission, polarization rotation, and ellipticity spectra were measured at normal incidence for zeroth-order transmitted light.

Nonideal focusing of the electron beam resulted in a slight nonequivalence of the $X$ and $Y$ axes of the manufactured nanostructures. In order to distinguish between the polarization effects originating from the chirality and the linear birefringence originating from the imperfection of the manufacturing process, measurements were performed at several inplane angles by rotating the sample [22]. At normal incidence, the polarization rotation $\mathrm{\Delta }$ and the ellipticity $H$ of the transmitted beam, as a function of the sample azimuth angle $\phi$, can be described by [2,3]:

The spectra of transmission, chirality-induced polarization rotation $\theta$, and the ellipticity $\eta$ for the 600 and 800 nm period chiral metal structures with opposite senses of twist are presented in Fig. 2. One can observe from Figs. 2(a) and 2(e) that transmission is nearly independent of the sense of twist over the entire spectral range although there are minor deviations due to imperfection in fabrication. One can also readily see from Figs. 2(b), 2(c), 2(f), and 2(g) that, over the entire spectral range, both $\theta$ and $\eta$ have opposite signs for the structures with left and right senses of twist. In addition, we confirmed that the $\theta$ and $\eta$ spectra satisfy the Kramers–Kronig relation. Wavelength dependence of the polarization rotation $\theta$ remains the same regardless of whether the light is incident from the metal [red line in Fig. 2(b)] or the substrate [Fig. 2(d)] side of the sample. That is, the observed polarization effect is due to the optical activity originating from the three-dimensional (3D) chirality of the metal network. As it was discussed in our previous papers [3,12], the 3D chirality of the sample is due to the presence of the dielectric substrate. The achieved polarization azimuth rotation is approximately 0.2°. The corresponding specific rotary power is comparable to that observed in our previous study [3], and the rotation angle can be increased by optimizing the thickness of the metal layer [24]. In the case of the 600 nm period samples, as shown in Figs. 2(a) and 2(b), resonances at 620 and 870 nm occur in both the transmission and polarization rotation spectra. One can observe from Figs. 2(e) and 2(f) that in the 800 nm period samples, resonances at 800 and 1150 nm occur. These experimental findings indicate that both the transmission and optical activity resonances have the same origin.

 

Fig. 2. (a),(e) Transmission, (b),(f) polarization azimuth rotation $\theta$, and (c),(g) ellipticity $\eta$ spectra for metal chiral structures with a 600 nm period (a)–(c) and a 800 nm period (e)–(g). The red and blue lines refer to the results obtained with the left- and right-twisted gammadions, respectively. (d) Polarization rotation spectrum with the opposite incidence to the left-twisted sample with a 600 nm period (see the text). In the top of the both graphs, the black thin lines correspond to the value of the left-hand side of Eq. (2), $N=m_x^2+m_y^2$. The blue and red thin lines are the dispersion-relation curves for the air–metal and metal–substrate interfaces, respectively, which correspond to the value of the right-hand side of Eq. (2). The circles indicate the wavelengths of the surface plasmon resonance.

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In the framework of the empty-lattice approximation, the surface-plasmon resonance condition of a metal thin film with periodic structures is given by

To check the validity of the experimental data, numerical simulations of the polarization effect were performed by using the reformulated Fourier modal method for crossed gratings with fourfold-rotational symmetry [27]. The parameters of the chiral metal network were taken from the scanning electron microscope and atomic force microscope images of the fabricated samples.

The wavelength dependencies of the refractive indices of gold and titanium were obtained from ellipsometry measurements. It can be seen in Fig. 3 that the calculated transmission and polarization spectra at normal incidence reproduce the measured spectra presented in Fig. 2, both qualitatively and quantitatively. Such a correspondence between the calculated and measured spectra becomes possible due to the drastic improvement (in comparison with [3]) of the fabrication quality.

 

Fig. 3. Calculated transmission, polarization rotation ($\theta$), and ellipticity ($\eta$) spectra of the left-twisted samples with a period of 600 nm at normal incidence. The experimental data are also shown for comparison.

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In conclusion, we have fabricated and characterized chiral metal networks composed of metal ribbons. We clearly observed, using samples with different periods at normal incidence, the optical activity of these chiral structures and demonstrated that resonant enhancement of the optical activity is associated with the surface plasmon resonance. A numerical simulation of the polarization effect reproduced the results of the experiment satisfactorily. The relative simplicity of the structures and the strong polarization effect observed open new prospects for the design of novel polarization modulation devices.