Fiber-Drawn Metamaterial for THz Waveguiding and Imaging
In this paper, we review the work of our group in fabricating metamaterials for terahertz (THz) applications by fiber drawing. We discuss the fabrication technique and the structures that can be obtained before focusing on two particular applications of terahertz metamaterials, i.e., waveguiding and sub-diffraction imaging. We show the experimental demonstration of THz radiation guidance through hollow core waveguides with metamaterial cladding, where substantial improvements were realized compared to conventional hollow core waveguides, such as reduction of size, greater flexibility, increased single-mode operating regime, and guiding due to magnetic and electric resonances. We also report recent and new experimental work on near- and far-field THz imaging using wire array metamaterials that are capable of resolving features as small as λ/28.
KeywordsMetamaterials Terahertz Waveguide Imaging Wire array Fiber drawing
Work at terahertz (THz) frequencies, loosely defined as 0.1 to 10 THz in frequency or 3 mm to 30 μm in wavelength, has been rapidly increasing due to the relatively recent availability of affordable and practical THz sources and detectors, bridging the so-called THz gap which had previously resulted in this part of the spectrum being under-utilized (see for example ). THz radiation is very attractive for numerous applications including short-range wireless communication, imaging, chemical and biological spectroscopy and sensing, material characterization, and security (see for example [2, 3, 4, 5]). The foremost challenge for exploiting THz radiation is the lack of materials offering a suitable THz electronic response. Metamaterials have sparked an exciting opportunity for manipulating THz waves beyond what is possible with natural materials [6, 7].
Metamaterials are man-made composites with structure on a sub-wavelength scale, where the arrangement of the sub-wavelength features defines the permittivity and permeability . Hence, metamaterials’ control over the permittivity and permeability can provide extraordinary functionalities not available with naturally occurring materials, such as cloaking, sub-diffraction imaging, and sub-wavelength confinement [9, 10, 11]. The ability to control radiation on scales comparable to or smaller than the wavelength makes metamaterials of particular interest in the THz region allowing a further boost to THz technology and development.
The fabrication of metamaterials is considered easier at microwave wavelengths, as the lattice constant is on the order of millimeters. However, at THz and shorter wavelengths, it becomes challenging as the dimensions become micro- and nano-scale. A decade ago, most THz metamaterials were limited to two-dimensional geometries (also known as metasurfaces) and fabricated using photolithography . Since then, new fabrication techniques such as stereolithography (3D printing) , inclined X-ray lithography, and project lithography [13, 14] or self-organization  have been proposed, enabling the manufacture of THz metamaterials. Over recent years, we have pioneered the use of fiber drawing to realize longitudinally invariant 3D metamaterials.
Fiber drawing of metamaterials, inspired from optical fiber drawing, is an efficient fabrication technique to realize THz metamaterials: it allows great control in scalability and has the potential for mass production because of the ease of manufacturing large quantities. Using this technique, we have successfully achieved the fabrication of arrays of two quintessential meta-atoms: wire arrays which give control over the permittivity, and split-ring-resonators—similar to LC circuits with a magnetic resonance—to tailor the permeability. Based on these two meta-atoms, the responses of THz metamaterials have been characterized, and corresponding novel devices, including hollow core waveguides for THz wave guidance and imaging probes for focusing and magnification, have been demonstrated. In this review, we focus on the fiber-drawn metamaterial-based THz waveguides and imaging applications we have recently demonstrated.
This review is organized as follows. In Sect. 2, we describe and discuss the fiber drawing method to fabricate THz metamaterials. Section 3 presents three kinds of THz waveguides with metamaterial cladding. In Sect. 4, we review and report new results on the subwavelength imaging technologies using straight and tapered wire-array metamaterials at THz frequencies. Finally, the conclusion and outlook are presented in Sect. 5.
2 Fiber Drawing of Metamaterials
Fiber drawing enables the fabrication of structures with a cross-sectional pattern that extends for very long lengths. The idea of using fiber drawing for metamaterials naturally emerged from the combination of well-developed techniques: stack-and-draw (or drill-and-draw) procedures routinely used in the production of photonic crystal fibers and the Taylor wire process. Photonic crystal fibers (or microstructured fibers) are optical fibers with guidance properties determined by air holes properly arranged in the fiber cross-section. They were first realized in fibers made of fused silica , and subsequently in polymer fibers . The Taylor wire process [18, 19] is a technique that was developed to fabricate glass-coated microwires. In this technique, a glass tube containing molten metal is drawn to reach the desired size. We have exploited a combination of the Taylor wire process with fiber-preform micro-structuring first pioneered by the University of Bath in a different context  to fabricate fibers with novel and extreme electromagnetic properties, e.g., indefinite media.
The fabrication process relies on the plastic deformation of a macroscopic reproduction of the desired structure. The initial structure in its macroscopic form is called a preform, and it can be created by stacking tubes, by drilling into bulk materials, by casting, by extrusion [17, 21], or by 3D printing . The preform is placed vertically in a furnace and heated above the glass transition temperature, where it can be deformed. Controlling the ratio between the velocity at which the preform is fed into the furnace and that at which it is pulled out, it is possible to control the size of the final product. Multiple drawing stages can be used when necessary. This process allows for easy scalability and mass production of the structures.
The standard host materials used are polymers, which have drawing temperatures between 150 and 200 °C including poly-methyl methacrylate (PMMA), Cyclic-Olefin polymer (Zeonex®), polycarbonate (PC), and polyurethane (PU). Some of these are very interesting at THz frequencies because of their material attenuation and dispersion, others because of their mechanical properties.
An alternative approach to realizing metamaterials with a magnetic response which makes use of fiber drawing but does not make use of the Taylor wire process is to sputter a spool of fully dielectric rods/fibers with metal and obtain ridge u-shaped metal structures [32, 33].
2.1 Tunable Metamaterials
Metamaterials fabricated by fiber drawing typically result in a rigid dielectric structure with fixed refractive index, making subsequent tuning of the electromagnetic properties difficult. Adding air holes to the structure could be a first solution to this problem, where tunability is achieved by filling the air holes with liquids of various refractive indices. However, few liquids have sufficiently low losses at THz frequencies. We instead explored the increased deformability air holes provide: applying lateral pressure deforms the structure (as well as the average refractive index). Despite the apparent advantages of this design, the polymer we used, PMMA, did not allow reversible tuning .
2.2 Towards the Infrared
3 Hollow Core Waveguides with Metamaterial Cladding
A key requirement to achieve compact THz devices is a strongly confining single mode and low loss waveguide. Several waveguide solutions based on technologies from both electronics and photonics have been proposed [37, 38, 39, 40, 41]; among these, hollow core waveguides are one of the best options for guiding THz radiation due to the very low material absorption of air. However, hollow core waveguides suffer from multimode operation as they have a core diameter larger than the operating wavelength to minimize reflection losses [42, 43, 44, 45, 46]. Metamaterials offer a new paradigm to reduce the number of modes due to their unusual optical properties [47, 48]. A theoretical investigation, aiming at lowering losses of large core IR fibers, by Yan and Mortensen, showed that wire-based metamaterials could provide guidance to transverse magnetic (TM) modes . Motivated by their work, we have developed a fully analytical model for modal analysis (the characteristic equation for guided modes and relevant mode existence condition) of hollow core waveguides with uniaxial metamaterial cladding [47, 48]. This study enables us to discover many other interesting and unusual properties of highly anisotropic metamaterial clad waveguides, such as various regimes of subwavelength confinement and guidance due to magnetic and electric resonances, which was also subsequently studied for solid core waveguides with metamaterial cladding . We also showed that waveguides with uniaxial anisotropic cladding can be used to create sub-wavelength dimension cavities . Here, we summarize our recent experimental demonstrations of THz hollow core waveguides with metamaterial cladding.
3.1 Hollow Core Flexible THz Waveguide with Wire Metamaterial Cladding
3.2 Hybrid Antiresonant Metamaterial Waveguides
A slightly different approach to exploiting the properties of an indefinite wire array cladding can be taken by combining an antiresonant guiding structure and a metamaterial cladding . Antiresonant structures allow guidance in a region with lower refractive index than the surrounding material when the surrounding material is sufficiently thin. Light can couple out only when constructive interference occurs within the thin layer . This guiding mechanism allows for broadband guidance in simple hollow structures. Recently, it was demonstrated that using a hypocycloidal core (achieved by a ring of capillaries) can greatly reduce the guiding loss of antiresonant structures . These structures have therefore been investigated in an attempt to achieve low loss guidance also for THz frequencies [57, 58], but it is very challenging to fabricate the thin core wall structures with the required accuracy.
As shown in the previous section, a ring of metal wires around the core allows guidance in a hollow core for a specific mode and for a certain bandwidth . The same concept could be scaled to a larger core structure allowing multiple modes that also has a reduced cladding thickness needed to achieve an antiresonant structure. In this structure, the electric field component of the modes along the propagation direction experiences confinement due to the metal wires, while the radial electric field component is confined by antiresonant guidance. The combination of both of these guiding mechanisms has the potential for low loss, broadband guidance. Since this is not the ideal antiresonant structure, both because of the achievable loss and because of the impractical condition of keeping the ring suspended in air, a tube lattice structure has been investigated.
The thin capillaries containing a large number of wires were fabricated. A cross-section of one of the capillaries is shown in the bottom inset of Fig. 8. In this particular sample, 40 metal wires of about 100 μm in diameter are embedded in a ⁓400 μm thick and 3 mm diameter capillary. Six of these capillaries, 10 cm in length, have been arranged to form a hybrid metamaterial antiresonant fiber (inset Fig. 8). Simulations of this fiber geometry indicate that the loss is expected to be as low as 0.3 dB/m, and characterization of this waveguide is currently being performed.
3.3 Air-Core Waveguides with Magnetic Resonator Cladding
There are two ways to excite the magnetic response of the SRR: a magnetic field H with a component parallel to the SRRs axis  or an electric field E with a component across the slot of the SRR [61, 62], as presented in Fig. 9b. In the vicinity of the resonance frequency, the effective permeability and magnetoelectric coupling have a maximum imaginary part and strong variation in the real part, leading to a strong impedance mismatch between air and the SRR array. As a result, when an SRR array is excited with a plane wave traveling orthogonally to the fiber axis, there will be a sharp drop in the transmittance at the resonance. The plasmonic response of the SRR array can be excited when the electric field E has a component parallel to the SRRs axis: due to the longitudinal invariance of the SRRs, in this orientation, the SRR array is equivalent to a wire array, exhibiting metallic behavior. For frequencies below the effective plasma frequency (a function of spacing and diameter of the “wires”), the array exhibits negative permittivity resulting in metallic reflection, while at higher frequencies, it effectively behaves as a dielectric. Directional invariance, along the length, results in spatial dispersion of the SRR array. Therefore, with increasing wave vector component along the axis of array, the dip due to resonant response and the plasma frequency both shift to higher values.
4 Sub-Diffraction Imaging
Wire metamaterials offer a new paradigm to beat the optical diffraction limit by converting evanescent waves to propagating waves of constant phase velocity . WMMs act as a sub-diffraction-limited endoscope in which the propagating waves carry sub-wavelength features from the object plane to an image plane at the opposite side of the medium. Employing fiber drawing techniques, we fabricated WMMs with straight, tapered, and prism shapes for THz frequencies. We experimentally demonstrated that our fabricated magnifying and non-magnifying hyperlenses can be used for focusing with resolution up to λ/28 in the near-field  and up to λ/13 in the far-field  at THz frequencies. Compared to other techniques proposed for THz sub-diffraction imaging, WMM hyperlenses enjoy relatively low losses: at the lower frequency end of the THz spectrum, our tapered hyperlens could focus light to sub-wavelength focal spots with no measurable loss increase compared to the loss of the dielectric.
In a second experiment, the tapered WMM was used in reflection, so that it serves a dual purpose: the THz signal is focused through the WMM onto the sample (increasing energy density), while the reflected beam is magnified through the WMM and directed to the far-field detector. The sample is then scanned in front of the hyperlens. This is comparable to scanning optical near-field microscopes, where the coupling from near-field, evanescent waves to far field is done using a sharp tip or apertures, but with a much increased coupling efficiency. This allows one to turn any THz far-field system into a near-field scanner, simply by adding the tapered WMM, with reasonably high signal-to-noise ratio (25 dB in this case).
5 Conclusion and Discussion
In summary, we have reviewed the most recent results in fiber-drawn metamaterials for THz applications, i.e., hollow core waveguides and hyperlenses for imaging and focusing. The fundamental elements in these devices were fiber-drawn wire arrays and split-ring resonators. This approach can be used to fabricate metamaterials which can be employed to manipulate both permittivity and permeability, using wire arrays and split-ring resonators, respectively. We have shown how this technique is appropriate for the entire THz spectrum. Moreover, this technique allows for the realization of metamaterials which, instead of having a fixed response, are tunable. Choice of materials appears to impose a practical lower limit to the size of the realized structures with polymers; however, a change of materials allows for further scaling extending the working frequency range of drawn metamaterials to the entire IR. The fundamental meta-atoms have been exploited for several applications. We elaborated on three different types of hollow core waveguides with metamaterial cladding: the wire metamaterial cladding enables flexibility and widening of the single-mode operating range for a wavelength sized core and, combined with antiresonant guidance, promises extremely low loss and broadband waveguides; parallel plates, made of split-ring resonators, providing electric and magnetic resonances, proved to confine THz radiation in a hollow core by various guiding mechanisms. Moreover, we reported experimental demonstration of WMM hyperlenses for near- and far-field THz imaging. The straight hyperlens was used to resolve features as small as λ/27, and the tapered hyperlens can focus/magnify features as small as λ/28.
The development of fiber-drawn metamaterials appears to have reached the level of maturity required for practical applications. Perfecting the drawing and expanding the portfolio of materials will allow the use of this technique for applications in a very broad spectral range (from microwaves to the near-IR). Moreover, it is possible to exploit the metal structure not only in passive devices (as waveguides and imaging devices) but also for active and tunable devices. Creating small structures for long wavelengths in a simple and effective way will hopefully make the THz frequency region seem closer to the shorter wavelength part of the spectrum than it feels like today.
The work was supported in part by Australian Research Council (ARC), Centre of Excellence scheme CUDOS (CE110001018), and ARC under the Discovery Early Career Project Award number DE140100614 and Discovery Project DP140104116. This work was performed in part at the Optofab node of the Australian National Fabrication Facility (ANFF), using NCIRS and NSW State Government funding. A.S. acknowledges support of the Eugen Lommel Stipend and Marie Sklodowska-Curie grant of the European Union’s Horizon 2020 research and innovation program (708860).
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