Al-Rubaiee et al. Journal of the European Optical Society-Rapid Publications Journal of the European Optical (2021) 17:11 https://doi.org/10.1186/s41476-021-00157-8 Society-Rapid Publications RESEARCH Open Access Metamaterials subwavelength terahertz resonant cavities M. Al-Rubaiee1,2* , A. H. Al-Janabi3, S. C. Fleming1 and A. Argyros1 Abstract One of the unique properties of metamaterials is the ability to manipulate electromagnetic waves at subwavelength scales, made possible by their structure on these scales. Here, rather than consider effective bulk properties, we consider the properties of microscopic features based on considering resonant unit cells. We used wire array metamaterials to form localized resonant cavities by changing the resonance frequency of one or more unit cells, surrounded by unchanged unit cells that do not support resonance for the propagating mode (i.e. forming a band gap). We validate our approach experimentally with electromagnetic waves in the terahertz range, demonstrating and characterizing subwavelength resonant cavities in this range. These resonant cavities can pave the way for ultra-compact subwavelength waveguides and other optical components. Keywords: Metamaterials, Subwavelength cavities, Resonator Introduction study metamaterials based on resonant unit cells [12, Wave propagation control is of fundamental interest in 14]. In photonic crystals, light can propagate in linear many areas of engineering and physics. One of the de- defects, typically comprised of removed unit cells [15, signs that has proven its efficiency in controlling electro- 16]. In wire array metamaterials, waveguiding and finite magnetic waves is the photonic crystal [1, 2]. This sub-wavelength resonators can be achieved by changing artificial media requires structures with dimensions the resonance frequency of one or more unit cells, sur- comparable to the wavelength (relatively large dimen- rounded by unchanged unit cells that do not support the sions) [3–5]. Metamaterials can control wave propaga- resonance for the propagating mode, thus forming a tion at deep subwavelength spatial scales potentially band gap (when measuring transmission through the enabling applications in nano-sensors directly on chip sample, there is a range of frequencies with low trans- [6–8]. They are usually metal-dielectric composites cap- mission which we refer to as bandgap, while the range of able of achieving unique electromagnetic properties not frequencies with high transmission we refer to as reson- encountered in natural materials [9–11]. This deep sub- ance) [17]. wavelength feature of metamaterials gives an advantage Here, we consider the case of defects in finite-size wire over photonic crystals in terms of wave manipulation [3, array metamaterials. The metamaterial consists of two- 12, 13]. Metamaterials have typically been studied for dimensional periodic arrays of wire segments, with each their effective bulk properties, such as negative refrac- wire perpendicular to the plane of the array, the wire tion [14–16]. However, for some properties it is neces- diameter d and spacing a being much smaller than the sary to go beyond this effective medium paradigm; in wavelength. The length of the wire segments L0 however this work a microscopic approach has been used to is not sub-wavelength: each wire segment supports reso- nances at frequencies for which an integer number of * Correspondence: [email protected] half-wavelengths corresponds to the wire’s length – the 1Institute of Photonics and Optical Science (IPOS), School of Physics, The Fabry-Perot resonances [18]. Changing the resonance University of Sydney, Sydney, NSW 2006, Australia 2Al-Karkh University of Science, Baghdad 10003, Iraq frequency can thus be achieved simply by changing the Full list of author information is available at the end of the article © The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Al-Rubaiee et al. Journal of the European Optical Society-Rapid Publications (2021) 17:11 Page 2 of 9 length of the wires, according to the following equation Zeonex has less loss than PMMA in the wavelength re- [12]: gion of interest. Several samples with different lengths, ranging from μ mc 430 to 275 m were prepared by cutting short sections f m ¼ ð1Þ from this fibre, then polishing the sample faces with pol- 2nL 0 ishing papers with a sequence of roughnesses of 3 μm, μ μ where c is the speed of light, m is an integer larger than 1 m and 0.3 m. This is to make them as regular and or equal to 1, n is the background refractive index. smooth as possible and to finely control the sample In this periodic array, a defect is introduced by having length. A microscope image of the face of the metama- one or several segments of different length ’ with resonant terial fiber, after sample preparation by polishing, is ′ shown in Fig. 1. frequencies f m. At the resonant frequencies of these wires, the fields can be strongly confined at the defect site. To characterize the behavior of this metamaterial we The other parameters, such as diameter and spacing, need to measure the spectral transmission of the sample do not play a major part in the resonance, although in the THz range to determine the resonance and band- these parameters give some control over the tradeoff be- gap frequencies. The transmission of the samples was tween quality factor and mode volume. By reducing the measured using a THz far field detector time domain diameter and spacing, the quality factor and mode vol- spectroscopy (TDS) system. This system comprised a ume of the defect mode will both increase. The defect Coherent MIRA Ti:Sapphire mode locked laser, operat- mode’s field is typically confined to a small area around ing at 800 nm, producing 180 fs pulses at 86 MHz repeti- the wire (S) given by eq. (2), where the wire diameter is tion rate with average power of approximately 600 mW limited to be larger than a few skin depths [14]: exciting THz antennas for source and detection. Gener- ally, the detection antenna was placed in the far field to determine overall spectral properties with good signal S ¼ð2aÞ2 ð2Þ strength. To measure spatial distributions with good precision, near field detection was also used. The sam- ples were attached to a metal disc with a single hole (the Methodology same size as the sample diameter) in the center to block Subwavelength cavities using metal wire array metama- unwanted signal during transmission measurement and terials were prepared and characterized as follows. Sub- allow only the signal that passed through the sample to wavelength resonators and waveguides, operating in the reach the detector. The transmission of two samples microwave region, made of an array of copper wires of (430 μm and 375 μm length) were measured using the relatively large dimensions have been demonstrated in THz far field system to identify the resonance and band- our previous work [19]. In the current work and in order gap frequencies of each wire array metamaterial sample to move to frequencies higher than microwave (i.e. THz (these length values are not especially significant; these or optical frequencies), the length of the wire array must samples were chosen because of their uniformity in term be much smaller, according to eq. (1) as well the wire of thinness and face polishing). The expected resonance diameter (d) which should preferably be maintained for the two samples, calculated using eq. (1), where n = within a/4 to a/8 [14]. Drawn metamaterial fibers 1.53 for Zeonex and m = 2, gives a resonance frequency, seemed practical to be used for preparing a wire array f, for the first sample of 0.455 THz, and 0.522 THz for on small dimensions; these drawn metamaterial fibers the second sample. The measured transmission consist of metal wires embedded, typically, in polymer. spectrum, along with resonance and bandgap frequency Metamaterial fibers, consisting of indium wires in regions, are shown in Fig. 2, for these sample lengths at PMMA and/or Zeonex, have been drawn with different m = 2 and show a good match with the frequencies cal- dimensions using the fiber drawing process. culated above. An appropriate metamaterial fiber was chosen from In order to demonstrate a subwavelength resonator samples fabricated for earlier work by fibre drawing [20]. using our samples, one or more wires need to be shorter It comprised a Zeonex host material incorporating mul- than the other wires of the sample to shift their reson- tiple indium wires. The overall diameter was 950 μm, ance frequencies to the bandgap side of the longer wires. without cladding, the wire spacing was 50 μm, the wire Etching was chosen as a practical method to shorten one diameter 22 μm, with total of around 450 wires. The or more wires. We chose hydrochloric acid, as it is read- choice of this metamaterial fiber was based on its di- ily available and used for metal etching, and importantly mensions and material. It is not too small for handling: it does not affect the polymer.