Circular dichroism spectroscopy has found many applications in biology over decades already [1,2]. More recently, it has also been proposed for infrared and terahertz frequencies [3,4]. In contrast to visible frequencies, however, conventional waveplates are often not readily available or limited in bandwidth and quality in these regimes. While small in amplitude in natural materials, chiro-optical effects like circular dichroism or optical activity are orders of magnitude larger in chiral metamaterials, for which many different designs have been introduced over the past decade for visible, infrared, terahertz, or microwave frequencies [5,6].

Chiral metamaterials based on metal helices allow for circular dichroism with unprecedented bandwidths while at the same time maintaining large extinction ratios. These attributes make them suitable for operation as scalable circular polarizers [7]. Tapered helices have been introduced to further enlarge extinction ratio and bandwidth [8]. Other applications for helical metamaterials include chiral near-field sensors or efficient circular-polarization converters [9,10].

While bandwidth and extinction ratio of previous helical metamaterial designs are encouraging, the overall performance has been limited by circular-polarization conversions: the end of the helix wire in each unit cell together with the helix axis defines a direction in space that breaks the rotational symmetry and introduces linear birefringence, thus causing nonzero off-diagonal elements of the Jones matrices. It has been shown theoretically that these conversions can be fully eliminated by intertwining three or four helices within each unit cell of a hexagonal or square lattice, respectively [11–16]. The principle of operation is, however, fundamentally different, as the undesired polarization can no longer be simply reflected but has to be absorbed. The cost for eliminating the polarization conversions is, therefore, a lower extinction ratio, which can be recovered by increasing the number of pitches [15].

Direct laser writing (DLW) is a versatile tool to fabricate almost arbitrary three-dimensional polymer structures with sub-micron resolution. Combining DLW in positive-tone photoresists with electro-chemical deposition of gold yielded the first gold-helix metamaterials with excellent metal quality for operation at mid-infrared frequencies—to date a benchmark for metamaterials as broadband circular polarizers [7]. The resolution of DLW is, however, limited by diffraction [17]. The resolution in positive-tone photoresists is often even worse, as it is limited by the chemistry of the resist rather than by optics. Thus, more complex helical metamaterials, e.g., based on $N=3$ intertwined helices, are out of reach for conventional DLW. Other techniques such as DNA-based self-assembly or glancing-angle deposition (GLAD) are inherently not suitable for $N$-helical designs, but have been successfully employed for dispersed helical nanostructures [18,19]. A promising candidate for making three-dimensional metallic structures is focused-ion-beam-induced deposition (FIBID). Indeed, $N$-helical metamaterials have been fabricated using FIBID, however, with small filling fractions and at rather large lattice constants [20].

In this Letter, we employ stimulated-emission depletion (STED)-inspired direct laser writing (STED-DLW). The overall fabrication process is depicted schematically in Figs. 1(a)–1(c). In a first step, a polymer template is written on a conductive, yet transparent indium-tin-oxide (ITO) covered glass substrate using a home-built STED-DLW setup described in Ref. [17]. Similar to Ref. [10], a polymer shell of the desired helical structure is created within each unit cell. Furthermore, a polymer floor is written in between the helices to avoid gold deposition in these areas. After development in the commercial developer mr-Dev 600, the polymer templates are directly transferred to isopropyl alcohol, to water, and finally to the gold electrolyte without intermediate drying. This minimizes damage due to capillary forces and ensures the presence of gold electrolyte in the small template voids. A scanning electron micrograph of a super-critically dried polymer template is shown in Fig. 1(d). After electro-chemical gold deposition similar to [10], the polymer cast is removed by oxygen-plasma etching, yielding the final gold structures depicted in Fig. 1(e). The footprint of each array is $60\mathrm{\mu m}\times 60\mathrm{\mu m}$. By simply closing off the polymer shell for two of the three helices within each unit cell, we have also fabricated arrays of single helices on the same substrate, allowing for a direct comparison between single and triple helices with identical geometrical parameters [see Fig. 1(f)].

 

Fig. 1. Our fabrication process is depicted schematically in (a)–(c). (a) First, a hollow polymer cast is made by STED-inspired direct laser writing. (b) The voids of the polymer template are filled with gold, using electro-chemical deposition. (c) Finally, the polymer template is removed in an oxygen plasma. (d) and (e) show scanning electron micrographs of the polymer cast and the final gold structures, respectively. (f) For comparison, arrays of single helices have been fabricated on the same substrate and employing the same fabrication process. (g) Scanning electron micrograph of single helices as previously fabricated by conventional direct laser writing in a positive-tone resist [7]. Scale bars in (d)–(g) are identical.

Download Full Size | PDF

A scanning electron micrograph of an array of single helices previously fabricated via conventional direct laser writing in a positive-tone resist is shown in Fig. 1(g) (taken from Ref. [7]). The direct comparison shows how much the axial resolution has been improved. This aspect is crucial for $N$-helix metamaterials.

Despite silanization of the ITO-covered substrates and high writing powers for the polymer floor, some residual gold with a thickness of approximately 50 nm is still deposited between the helices. This residual gold would lead to scattering and absorption of the incoming light and, therefore, to lowered transmission for both circular polarizations. To enhance the optical performance after oxygen-plasma etching, the samples are first exposed to a carbon-dioxide atmosphere, then immersed into ethanol to minimize capillary forces, and finally wet-etched in a commercially available aqueous gold etchant (MicroChemicals TechniEtch ACI2, diluted 1:9) for 400 s. After rinsing in water, the samples are dried super-critically. This procedure removes the residual gold almost entirely and, furthermore, leads to a slight decrease of the wire radius of the helices. The structural quality of the helices is not affected though.

The theoretical basis for $N$-helix metamaterials has been discussed in detail in previous publications for the cases of $N=3$ and $N=4$ [13,15]. Single-helix metamaterials break the rotational symmetry, which in turn leads to linear birefringence and circular polarization conversions. By intertwining $N=3$ or 4 helices within one unit cell, one recovers discrete rotational symmetry. If, furthermore, the translational lattice is also invariant under rotations of $\mathrm{\Phi }=\frac{360°}{N}$, the Jones transmission and reflection matrices must commute with the corresponding rotation matrix $R_{\mathrm{\Phi }}$. In circular polarization basis this yields

 

Fig. 2. Numerically calculated spectra for a metamaterial with $N=3$ and 2 axial pitches. The polarization-conserving transmittances and the polarization conversions are depicted by solid and dashed lines, respectively. The incoming circular polarization is color-coded. As expected, the circular polarization conversions are strictly zero. Over a large bandwidth from below 20 to 75 THz, strong circular dichroism is found.

Download Full Size | PDF

In order to measure reflectance and transmittance spectra on our fabricated structures, we use a Fourier-transform spectrometer (Tensor 27, Bruker Optik GmbH). A combination of a commercially available linear wire-grid polarizer (Thorlabs GmbH) and a custom-built superachromatic ${\mathrm{MgF}}_2$-based quarter-wave plate (B. Halle Nachfl. GmbH) is used to achieve circularly polarized incident light. The same combination in reverse order is used to discriminate between the two circular polarizations after transmission or reflection. Light impinges from the air side onto the helices. To approach normal incidence, the sample has been tilted, and an off-centered small aperture is used, reducing the full opening angle of the cassegrain objective to approximately 5 deg. All spectra in transmission are referenced to the polarization-conserving transmittance of the bare ITO substrate. All spectra in reflection are referenced to the normal reflectance, i.e., $R_{\mathrm{R}\mathrm{L}}$ or $R_{\mathrm{L}\mathrm{R}}$, of a silver mirror.

The transmittance and conversion spectra of the $N=3$ helix metamaterial [see Fig. 1(e)] are shown in Fig. 3(a), together with the corresponding numerical calculations. The spectra are depicted for frequencies from 46 to 80 THz. For lower frequencies, the supporting glass substrate becomes opaque. For higher frequencies, diffracted orders other than the zeroth orders occur. The normal transmittances, i.e., the squared moduli of the diagonal elements of the Jones transmission matrix, are in good overall agreement with the numerical calculations. A small peak at approximately 70 THz is due to vibrational absorption of atmospheric carbon dioxide. Other deviations can possibly be assigned to fabrication imperfections. Circular polarization conversions are below 2% throughout most of the operation band, which is less than the crossed polarizations measured on a bare ITO substrate (dashed gray line) and which can thus be assigned to polarization errors of the charcterization optics. In the case of single helices [see Fig. 1(f)], i.e., $N=1$ in Fig. 3(b), a broad operation bandwith and high extinction ratio is observed—as expected. Furthermore, throughout the operation band, the conversions are above the crossed polarizations of the bare ITO substrate and follow the trends of the numerical calculations.

 

Fig. 3. (a) Calculated (see Fig. 2) and measured spectra of the Jones transmission matrix for $N=3$ helix metamaterials. Polarizations are color-coded as in Fig. 2. In the bottom right panel, the measured crossed polarizations of the bare ITO substrate are depicted as a gray dashed line, indicating measurement artifacts due to polarization errors of the employed characterization optics. (b) Spectra as in (a), but for an array of single helices ($N=1$).

Download Full Size | PDF

The elimination of the polarization conversions becomes even more striking when inspecting the reflectance spectra, which are depicted in Fig. 4. Again, the top row shows the numerical calculations and experimental data for the case of $N=3$ helices. The squared moduli of the off-diagonal elements of the Jones reflection matrix, i.e., $R_{\mathrm{L}\mathrm{L}}$ or $R_{\mathrm{R}\mathrm{R}}$, are expected to be zero from theory, which is well supported by the experimental data. Due to reciprocity arguments, the diagonal elements, i.e., $R_{\mathrm{R}\mathrm{L}}$ or $R_{\mathrm{L}\mathrm{R}}$, are expected to be equal, which is also well represented by the experimental data [15]. As there are no diffracted orders other than the zeroth orders, this observation emphasizes once again that the difference in transmissions as observed in Fig. 3(a) is solely due to a difference in absorption.

 

Fig. 4. Reflection spectra in analogy to Fig. 3, again for (a) $N=3$ and (b) $N=1$. Note that the ordinary reflectances are $R_{\mathrm{R}\mathrm{L}}$ and $R_{\mathrm{L}\mathrm{R}}$, while the conversions are denoted by $R_{\mathrm{L}\mathrm{L}}$ and $R_{\mathrm{R}\mathrm{R}}$, as the orientation of the wave vector is flipped upon reflection. The small wiggles in the top-right panel are due to Fabry–Perot reflections in the glass substrate.

Download Full Size | PDF

This behavior is fundamentally different in the case of single helices, for which the spectra are depicted in Fig. 4(b). The two diagonal elements of the Jones reflection matrix are equal due to reciprocity. The experimental data show only small differences, which we assign to the finite opening angle of the objective lens and to fabrication imperfections. More importantly, however, the conversion from LCP to LCP, experimentally reaches values of approximately 80% over a large bandwidth, in good agreement with theory.

In conclusion, we have fabricated and characterized $N$-helix metamaterials for operation at mid-infrared frequencies. STED-inspired laser lithography combined with elecrochemical deposition and subsequent wet-etching yields structural quality and complexity out of reach for conventional DLW in positive-tone photoresists [7]. For the first time, we have measured all entries of the Jones transmission and reflection matrices. The measured spectra demonstrate that $N$-helical metamaterials do not only exhibit broadband circular dichroism, but also fully eliminate circular polarization conversions in reflection and in transmission. Despite bandwidths of up to 2 octaves and the absence of circular polarization conversions, however, a drawback of $N$-helix metamaterials is their small extinction ratio per axial pitch compared to single-helix metamaterials. In the future, dip-in depletion optical lithography might lead to a larger number of helix pitches and, thus, to competitive extinction ratios as well [22].