1. Introduction

Metamaterials are artificial materials that can be used to manipulate electromagnetic waves in extraordinary ways through their exotic properties, which depend on their geometry rather than their composition. These properties can be used, for instance, for backward propagation, for achieving reverse Doppler and Cerenkov effects, or negative refraction [1]. Since their theoretical [2] and experimental demonstration [3], metamaterials have attracted intensive research interest in recent years because of their potential applications, for example, in imaging below the diffraction-limit [4–6], cloaking [7,8], slow light [9], and sensing [10].

The extraordinary electromagnetic properties of a metamaterial derive from the ability to engineer its “meta-atoms” to provide desired values of electric permittivity ε (manipulating the electric response), and magnetic permeability μ (manipulating the magnetic response) of the medium. Naturally occurring materials have a restricted range of responses, in particular the range of magnetic permeabilities of naturally occurring materials is close to the free space value for all but low frequencies. However, artificial magnetically-active materials can be made using arrays of split ring resonators (SRRs) [2]. The SRR is a circular ring of metal with a gap, for example, either one of the rings in Fig. 1(a) . Such a SRR has an inductance and capacitance (Cg in Fig. 1(a)), and acts as an LC resonator circuit which can be excited by an oscillating electromagnetic field. Near the LC resonance, the currents induce a strong magnetic dipole response, so that an array of SRRs can have an effective relative permeability differing substantially from unity [2].

 

Fig. 1 (a) An ideal double split ring showing capacitance between and within each ring, Cs and Cg, respectively. (b) Cross-section of preform; PMMA rods were inserted into the gap of each ring to maintain these gaps during drawing. (c) First drawing stage from 4 mm to 700 μm outer diameter. (d) Second drawing stage from 700 μm to 100 μm resonator diameter. A sleeve was added between the first and second draws. NB: Fragments of indium seen in the microscope image in (d) result from cleaving the fiber and are at the cleaved endface only.

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The capacitance of the meta-atom can be significantly increased by having a double split ring arrangement as shown in Fig. 1(a) [2]. A double split ring resonator (DSRR) consists of two concentric split rings of conducting material. In this case the gap between them, rather than the gap in the individual rings, is predominantly responsible for the enhanced capacitanceCs which, along with the increased inductance, makes the structure resonant at longer wavelengths compared to a single SRR of the same diameter [11]. As a consequence, for a given resonant wavelength the meta-atoms are smaller, and the material is closer to behaving as a homogeneous material that can be characterized by effective permittivity and permeability tensors, with minimal spatial dispersion and diminished scattering losses. This reduced size also has important technological implications for realizing devices. The use of DSRRs also minimizes direct electric excitation of the magnetic resonance by having two gaps with opposing induced electric dipole moments, reducing magneto-electric coupling.

The fabrication of SRRs for short wavelengths has mostly depended on costly techniques like electron-beam lithography, nano-imprint lithography, focused-ion beam milling, and direct laser writing. Low cost techniques like inkjet [12,13] and laser printing are changing this trend, at least for longer wavelengths such as the THz spectrum. Recently, fiber drawing has emerged as a potential technique to mass produce functional structures [14], including SRRs [15,16]. The process starts with a macroscopic cylindrical object called a preform, which is heated and drawn into fiber. If the preform consists of more than one material, with different optical and electrical properties, it will produce composite multi-material fibers; a well-known example is the Taylor wire process [17]. This technique has realized fibers with a metallic component which have demonstrated plasmonic resonances [18], metallic mode confinement [19], dielectric mirror fibers [20], and metal-insulator-semiconductor optoelectronic fibers [21]. Previously, metamaterial fibers for THz frequencies were fabricated based on techniques developed for microstructured polymer optical fibers [22], demonstrating wire metamaterials with a tailored effective permittivity [23], and fibers with a magnetic response in the THz using single SRRs [15]. In the latter work, the smallest SRR arrays achieved were about 100 μm in diameter with 100 μm spacing between resonators; this was obtained by re-drawing resonator fibers within a high aspect ratio rectangular slab. The high aspect ratio was necessary to obtain single layers of closely packed SRRs, but made it difficult to preserve the exact transverse geometry of the resonators. Using the same technique with more complex meta-atom geometries such as DSRR is thus challenging.

In the present work we demonstrate a different approach, relying on etching. Drawing is performed in two stages that maintain the circular symmetry of the fiber, thus minimising deformations. This results in a single DSRR at the center of a fiber with a thick jacket. This jacket is then removed by selective chemical etching allowing the fibers to be stacked in close proximity to obtain a homogenous medium made of an array of DSRRs. Finally, we experimentally characterize the transmittance of such arrays at THz frequencies, finding good agreement with numerical simulations.

2. Fabrication and sample preparation

Figure 1(b) shows a top-view schematic of the DSRR fiber preform, which was assembled as follows. A 1 mm thick indium foil was rolled around a polymethylmethacrylate (PMMA) tube along with a solid thin PMMA rod to create the split in the ring. This was inserted into a second PMMA tube, around which a second indium foil was rolled. This structure was inserted into a polycarbonate (PC) jacket to form the preform with an outer diameter of 15 mm. The preform was consolidated by stretching under vacuum to remove trapped air, to an outer diameter of 4 mm (step not shown), at temperatures of 185-195 °C and tensions of 400-500 g. The preform was then drawn down in two steps, at all times maintaining a circular cross section to minimize instabilities due to asymmetry.

In the first drawing step, shown in Fig. 1(c), the 4 mm preform was drawn to fiber with a diameter of approximately 700 μm at 180-190 °C and 100-200 g tension. The second stage, Fig. 1(d), involved sleeving the 700 μm DSRR in a thick jacket of polymer, such that the outer diameter was 9 mm. Two such structures were made, one in which the polymer used for the jacket was PMMA [24], and the other which used Zeonex 480R, a cyclo-olefin polymer with low absorption in the THz [25]. The resulting structures were further drawn to approximately 1.3 mm outer diameter as shown in Fig. 2(a) , at 170-180 °C with 100-200 g tension, such that the final resonators had a diameter of approximately 100 μm. It was found that low temperature, and thus high viscosity and high tension draws were required to minimize distortions. The thick jacket ensured the fiber had enough strength to withstand this tension. However, by the end of this draw the fiber diameter was still approximately 1.3 mm, which is larger than half the intended resonant wavelength, meaning the DSRR could not be assembled into a sub-wavelength array behaving like homogeneous metamaterial.

 

Fig. 2 Fiber cross-section after the second stage draw shown in Fig. 1(d), showing (a) a fiber prior to etching, (b) a close-up in which the different materials can be seen, and (c) a Zeonex-jacket fiber after etching. The images in (a) and (b) are illuminated from below making the metal appear black, whilst in (c) illumination is from above and the metal appears white.

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Chemical etching was used to reduce the thickness of the jacket. For PMMA a solution of acetone (80%, by volume), methyl isobutyl ketone (MIBK) (10%) and water (10%) was prepared [26]. At room temperature this solution removes the PMMA at a rate of 150 μm per hour (reducing the fiber diameter by 300 μm per hour) with a very low PMMA surface roughness. The etching of the PMMA jacket was stopped when the fibers reached a diameter of about 200 μm, to prevent damage through over-etching.

Fibers made with a Zeonex jacket were etched using cyclohexane, which readily dissolves Zeonex but leaves the PMMA and PC forming the inner and outer layers of the resonators unaffected. The fibers were etched to a diameter of approximately 100 μm, down to the PC layer. At room temperature Zeonex dissolved at a rate of 350 μm per hour with very good surface quality. Images of these fibers before and after etching are shown in Fig. 2. Zeonex was found to be a more suitable material for the outer jacket due to the faster etching rate, and the fact that cyclohexane does not affect the PMMA or PC in the DSRR. The latter meant that the etching did not need to be closely monitored, as over-etching was not possible.

Sections of each fiber were then manually assembled into two arrays (one with fibers made with a PMMA jacket, one with fibers made with a Zeonex jacket) one fiber thick and 25 fibers wide with approximately 300 μm center-center spacing between adjacent fibers, for characterization using spectroscopy. The final arrays were 7 × 7 mm in size.

3. Characterization

The transmittance of the DSRR arrays was characterized using a THz time-domain spectroscopy system based on photoconductive antennas pumped by a mode-locked Ti:Sapphire laser. The electric field of the radiation is recorded in the time domain, from which a power spectrum is obtained through a Fourier Transform. The measurements were taken with the magnetic field parallel to the fibers, as shown in Fig. 3(b) . The arrays were placed near the focus of a slowly converging THz beam (beam diameter of 3-4 mm) and the transmission was recorded. The arrays were placed in a 7 × 7 mm aperture, and measurements were normalized with respect to the transmittance of an identical, empty aperture. Figure 3(a) shows the measured transmission through a resonator array assembled from fibers made using a PMMA jacket. A clear transmission dip associated with the magnetic resonance is observed at 0.244 ± 0.005 THz (error reflects the frequency intervals of the discrete Fourier Transform).

 

Fig. 3 (a) Experimentally measured (red) and simulated (blue) transmittance for a resonator array assembled from fibers drawn with a PMMA jacket. Simulations for an array of perfectly shaped resonators is also shown (dashed curve). (b) Orientation of the fields and resonators in the experiments and simulations: the incident magnetic field is directed along the fibers. (c) Simulated magnetic fields for the fiber used in (a) at resonance (0.24 THz).

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For the numerical simulation, an optical microscope image of a resonator from the above array was imported into the finite element solver COMSOL 4.a [27]. The appropriate dispersive optical properties for all materials were included [24,28], and the transmittance was obtained via the scattering matrix parameter S₂₁ for a resonator array using periodic boundary conditions. The transmittance as a function of frequency is shown in Fig. 3(a), and is in good agreement with the measured transmittance – the position of the resonances agree to within the resolution of experimental spectrum. The differences in width and depth are attributed to the use of a converging beam in the experiment, compared to a collimated beam in the simulation; hence the experimental results represent the average resonance observed over a small range of incidence angles [29]. Uneven spacing between resonators due to the manual stacking and slight variations in cross-sectional shape along the fiber are also expected to contribute to the broader, shallower observed resonance. A resonator array assembled from fibers made using a Zeonex jacket was also characterized and modeled using identical methods, and a resonance near 0.25 THz was again observed, with a shallower depth of approximately 2 dB. Good agreement was found between the measurements and simulations, both in terms of the frequency and depth of the resonance in this case also. The different transmittance between the two samples (PMMA and Zeonex jacket) was attributed to differences in the shape of the resonators. Finally, a density plot of the component of the magnetic field parallel to the fibers for the PMMA-jacket resonator is shown at resonance (0.24 THz) in Fig. 3(c). The magnetic field inside the resonator is of opposite sign compared to the incident field, confirming the transmission dips are due to a magnetic resonance.

To assess the impact of the imperfections noted in the fabricated resonators, an array of comparable ‘perfect’ resonators also with 300 μm spacing between resonators was modeled and the results shown in Fig. 3(a). The perfect resonator array has a narrower resonance and at lower frequency of 0.144 THz, although this value is sensitive to the exact parameters chosen for this perfect case, particularly the thickness of dielectric between the individual resonators. The depth of the resonance is only moderately affected by the resonator shape, and is more strongly dependent on the spacing between resonators. For example, the depth reduces by approximately 2 dB when the spacing between resonators is increased by 100μm.

It is worth noting that only the μ_zz component (parallel to the fiber axis) is resonant, with the transverse components being in essence unity. The permittivity tensor is also highly anisotropic, with ε_zz being negative at the frequencies of interest (as an array of large metallic wires [16,30]), and the transverse components being close to the permittivity of the polymer. Furthermore the longitudinal component of both μ and ε depend on angle of incidence with respect to the fiber axis, because of the longitudinal invariance of the DSRR [29,30]. In particular the frequency of the magnetic resonance increases with angle of incidence [29].

4. Conclusion and discussion

We have demonstrated that fiber drawing techniques – which are intrinsically scalable to high throughput production – can be used to draw metamaterials with intricate meta-atoms, and have produced double split ring resonator fibers. We characterized arrays of DSRR fibers, demonstrating a magnetic resonance at approximately 0.25 THz, in good agreement with simulations. The resonances observed for the DSRRs here occur at a wavelength to resonator diameter ratio λ/d ≈14 (1.25 mm/90 μm). This is compared to the single SRRs of [16], with resonances corresponding to λ/d ≈8, and to those of [23] with λ/d ≈7. The DSRRs here are thus smaller relative to the operating wavelength, meaning metamaterials assembled with such resonators will be closer to a homogeneous medium described by effective permittivity and permeability tensors. This is of particular importance for the assembly of different metamaterials to get combined electric and magnetic response, for example by combining DSRR fibers with wire array fibers to obtain “woven” negative index material. Small resonator sizes are also important to achieve smooth gradients of effective electromagnetic properties such as those required for transform optics, and for the assembly of sub wavelength waveguides, where resonators have to be smaller than the core itself [31].