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Materials and Design 93 (2016) 423–430

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Materials and Design journal homepage: www.elsevier.com/locate/matdes

3D printed anisotropic dielectric composite with meta-material features D.V. Isakov a,⁎, Q. Lei a, F. Castles a, C.J. Stevens b, C.R.M. Grovenor a, P.S. Grant a a b

University of Oxford, Department of Materials, Parks Road, Oxford OX1 3PH, United Kingdom University of Oxford, Department of Engineering Science, Parks Road, Oxford OX1 3PJ, United Kingdom

a r t i c l e

i n f o

Article history: Received 11 November 2015 Received in revised form 29 December 2015 Accepted 31 December 2015 Available online 5 January 2016 Keywords: Additive manufacturing Fusion deposition Dielectric composites Metamaterials

a b s t r a c t This paper presents all-dielectric materials used to 3D print coupons with spatially varying dielectric permittivity and possessing high dielectric anisotropy. The coupons were directly printed through a dual-ﬁlament fused deposition modelling technique utilizing bespoke feedstock ﬁlament comprised a polymer-based micro-ceramic composite with controlled permittivity and loss. By designing the arrangement of both high and low permittivity ﬁlament materials in the printed coupons, the microwave operating frequency and magnitude of Mie-type resonances could be manipulated to provide metamaterial-like characteristics. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

1. Introduction Signiﬁcant progress has been made in the past two decades in the development and commercialization of additive manufacturing (AM) processes such as stereolithography, selective laser sintering, solid ground curing [1–4]. Recent generations of low-cost and ofﬁcefriendly additive manufacture printers now provide the potential to access mass-markets and to broaden additive manufacture concepts from being expensive and exclusive technologies to those that are easy-touse and affordable. AM processes are now used increasingly in research and in small lot manufacture to build engineering components having complex geometrical shape, high material yield and reduced lead times [5–11]. AM is also used for biomedical applications such as bone scaffolds, replacement tissues, organs and biodegradable templates [12–14]. In terms of AM using polymers as the feedstock material, thermoplastic have been investigated and applied extensively [5,7,15]. Furthermore, polymer composites containing a disperse minority fraction of inorganic powders materials may be processed and thus provide a broad range of thermo-physical, functional and mechanical properties. For example, wax-based feedstock ﬁlament with added piezoelectric lead zirconate titanate ceramic powder has been used to fabricate functional piezoelectric devices [16,17]. Multiple feedstocks containing lead magnesium niobate and silver-palladium have been used as to manufacture green components to be used as piezoelectric transducers [18], and parafﬁn-based thermoplastic feedstock with stainless steel and zirconia powder have also used for AM of green metal-ceramic components [19,20]. Structured aluminium/alumina composite materials ⁎ Corresponding author. E-mail address: [email protected] (D.V. Isakov).

with graded properties and good bonding between the metal and the ceramic phases have been produced by AM followed by sintering, incorporating fused silica in polypropylene [21]. Metal/polymer composites combining iron particles in a nylon matrix [22] or an acrylonitrile butadiene styrene (ABS) matrix [23] have been developed to improve the mechanical properties of rapid tooling. Comparatively high dielectric permittivity alumina particulate has been loaded into a wax fugitive binder for the fabrication of photonic crystal structures by AM, followed by burn-out of the wax [24]. This rapidly growing body of work on printable materials suggests that AM offers the possibility to control the properties of fabricated components by tailoring local composition and microstructure. This gives rise to a versatile development of AM for fabrication of metamaterials [7–10]—electromagnetic materials with engineered subwavelength structures designed to exhibit strong coupling with the electric and magnetic components of an incident electromagnetic wave. The focus of this paper is to consider the application of AM for the fabrication new electromagnetic materials, that after further development, could be used to realize various artiﬁcial phenomena such as cloaking [25–27], photonic bandgap crystals [28], left-handed metamaterials [29,30], and novel microwave circuits and antennas [31]. The most common materials approach to producing artiﬁcial electromagnetic properties (such as negative index of refraction) required by theoretical designs (such as those arising from spatial transformations [32]) has involved metallic split ring resonators or other metalcontaining sub-wavelength elements [26,33]. While many aspects of theory and design can be conﬁrmed using these types of structures, which are generally considered lossy, narrowband and present challenges for implementation in practical systems. Alternatively, high dielectric rods arranged in a much lower permittivity matrix can be used as resonator elements [29,34], giving weaker interactions with

http://dx.doi.org/10.1016/j.matdes.2015.12.176 0264-1275/© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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applied ﬁelds but with potential for lower loss. As it will be shown below, because these structures can be readily achieved by AM, the resonator approach based on dielectric arrays rather than metallic-based resonators may offer some further ﬂexibility in practical implementation, for example in geometric arrangements to produce graded index materials operating at microwave frequencies. This work demonstrates the feasibility of using bespoke polymerbased feedstock composite in AM to produce dielectric resonator structures, with strong anisotropy matching the ‘Wiener bounds’ [35,36] description of property anisotropy in layered composite systems. Our printed structures comprise a thin coupon (d b λ, where d is the coupon thickness and λ is the wavelength of incident microwave radiation, in the range from 12 to 18 GHz) within which there alternating layers, or ‘stripes’, of relatively low (polymer only) and high (polymer plus inorganic particles) dielectric constant materials. These striped coupons can be produced in a single operation directly from a CAD ﬁle using the AM process termed fused deposition modelling (FDM). Our implementation of FDM used two continuous thermoplastic based ﬁlaments as feedstock, one comprising polymer only, and the other the same polymer but with a high fraction of high permittivity inorganic microparticles. The ﬁlaments were melted in the print head and then extruded onto the forming coupon by the print head moving in the xy-plane according to the CAD ﬁle. The as-manufactured coupon had high density without the need for any post-deposition processing (such as sintering, machining, etching), and there was apparently good adhesion between polymer and composite regions, although as with all AM structures, a low fraction (b1 vol%) of internal micro-voids may persist [37]. The response of the coupons in different geometric orientations to incident microwave radiation across a range of frequencies showed, in accordance with effective medium theory and Weiner bounds, artiﬁcial dielectric anisotropy with a birefringence Δϵ of 1.15, along with geometry-dependent Mie-type resonance effects, characteristic of metamaterial-like behaviour. 2. Experimental A dual-extrusion FDM-type 3D printer (Makerbot Replicator 2) was used for the direct fabrication of rectangular coupons of polymer-based materials. The FMD process of building a solid object involves heating of the fed ﬁlament and squeezing it out layer-by-layer through a tiny nozzle (0.4 mm inner diameter) onto a heated surface, via a computer controlled three-axis positioning system (with a spatial resolution of approximately 100 μm in z-axis and 11 μm in x and y). The thermal energy imparted to the moving ﬁlament by the print head heater is partially conducted to the previously deposited underlying layer and the adjacent extruded ﬁlament on contact, and provided a molecular-scale diffusion bonding process at the interface between the extruded ﬁlament and pre-deposited material, resulting in good structural integrity [5]. As a result of the layer-by-layer approach, the printed objects most readily take the form of laminates, with stacked layers each containing lengths of contiguous extruded ﬁlament. To print coupons comprising relatively low and high permittivity striped regions, two types of ﬁlament (loaded onto two extruder heads) were used simultaneously; commercially supplied acrylonitrile butadiene styrene (ABS) or polypropylene (PP) was used for the low dielectric permittivity regions, while high dielectric permittivity regions used a mixed inorganic ceramic powder-polymer composite. The above mentioned polymers were chosen as the polymer matrix because they are standard materials for desktop 3D printers. Additionally, the boundary of the two printed (low-, and high-permittivity) layers must provide good adhesion between them. The high-permittivity ﬁlaments were fabricated as follows. Firstly, ABS pellets and the ceramic powder (various types, see later) were mixed in the target volume ratio (up to 30 vol% ceramic) and then stirred in acetone until there was total dissolution of the ABS. The resulting viscous suspension was spread out uniformly on trays in a fume cupboard and the acetone fully evaporated.

The dried mixed powder-binder feedstock was milled mechanically in a high speed grinder and resulting granules melted in a single-screw hot extruder to produce many metres of continuous composite ﬁlament of 1.7–1.8 mm diameter [38]. Micro-particles of different perovskite oxides such as BaTiO3 (Sigma-Aldrich), CaTiO3 (Alfa Aesar) and Ba0.64Sr0.36TiO3 (Trans-Tech), all with powder diameters b3μm, were added to the polymer matrices, providing a range of permittivities and losses, as described later. The dielectric properties of as-printed materials, with no layering or anisotropic design, was carefully characterized before resonating structures were designed, using a split-post dielectric resonator (SPDR, QWED) technique [39] and a Rohde&Schwarz ZNB20 vector network analyser. The resonator is designed for a nominal 15 GHz frequency and the actual measurements were taken at a frequency close to the nominal. The SPDR technique allows the determination of complex permittivity with greater sensitivity than transmission-reﬂection methods, albeit at a single frequency, and provides more reliable measurements in low loss (tanδ b 0.05) materials. Using the dielectric properties of each type of printed material, the commercial Comsol Multiphysics RF module, which is a ﬂexible implementation of the ﬁnite element method, was used to model the wave propagation in layered or striped coupons and to suggest the relative dimensions of each stripe to achieve the desired performance. A 3D model of the coupons, with predeﬁned material properties (for each type of material) observed experimentally, was constructed and the electromagnetic ﬁeld distribution together with complex scattering parameters were computed. Guided by the model-based design, 16 × 8 × 2 mm coupons were printed suitable for insertion following edge polishing into a Ku-band waveguide for characterization of dielectric properties using the VNA and the transmission/reﬂection line (TRL) technique. The TRL technique involved measuring the two port complex scattering reﬂected (S11) and transmitted (S21) parameters in the frequency range from 12 to 18 GHz so that the relative complex permittivity ϵr and permeability μr could then be obtained using the widely employed Nicholson–Ross–Weir (NRW) extraction method [40]. The printed coupons were also characterized using a single split ring resonator probe moving in an xy-plane above the coupon with 0.25 mm step resolution. The probe comprised a split ring (formed from a 5 mm section of 22 mm diameter copper tube of wall thickness 1 mm) ﬁxed between near ﬁeld coupled transmitting and receiving ports connected to a VNA. The resulting resonant frequency of this split copper ring arrangement depends on the ring geometry and capacity of the air gap in the region of the split in the ring [41]. If a material with dielectric permittivity greater than air is placed close (b0.5 mm) to the gap in the resonator ring, the ring resonant frequency shifts lower as a monotonic function of dielectric constant being probed and therefore the method can be used as a spatially sensitive surface dielectric probe. The measured permittivity from this technique differs from the bulk value and is best-suited to indicate relative changes in permittivity only, but offers a quick and convenient way to assess spatial variations in near-surface properties. A JEOL JSM-840 scanning electron microscope (SEM) operating at 15 kV was used to examine the structure of the printed samples. Thermogravimetric analysis of the ﬁlament feedstocks in which the polymer fraction was fully volatized at high temperature to measure the remaining weight fraction of inorganic particulates in the ﬁlaments was performed using a PerkinElmer PYRIS Diamond differential scanning calorimeter. 3. Results and discussion 3.1. Material characterization Fig. 1a shows typical examples of 3D printed structures consisting of arrays of alternating low (ABS only) and high (ABS + micro-particles) permittivity stripes aligned either vertically or horizontally. The chess-

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Fig. 1. a) Various printed coupons for dielectric characterization comprising stripes or other arrangements of relatively low (ABS only) and high (dielectric ceramic/ABS composite) permittivity materials; b) and c) are experimental measurements of the spatial distribution of the resonant frequencies of the split ring probe (qualitatively representing the local dielectric permittivity) in the 8-column (4 ﬁlled, 4 unﬁlled) and 4-row (2 ﬁlled, 2 unﬁlled) printed slabs estimated by the surface resonance probe technique.

board lattice is also shown to demonstrate the capability of the AM process to provide a huge range of possibilities for inter-leaved low and high permittivity materials. Fig. 1b and c show the measured spatial distribution of the resonant frequencies according to the split ring probe (qualitatively related to the local, effective dielectric permittivity) in the 8-column (4 ﬁlled, 4 unﬁlled) and 4-row (2 ﬁlled, 2 unﬁlled) coupons respectively. The surface probe showed good sensitivity to the different printed regions and suggested that the resulting spatial distribution of permittivity was qualitatively as intended. Identical coupons comprising only the unﬁlled polymer (hereafter associated with low permittivity, ϵl) or ﬁlled polymer + ceramic particulates (high permittivity, ϵh) were also printed to obtain the values for reference permittivities needed in the Comsol model. For successful 3D printing (without blocking, extruded ﬁlament breakage, merging of printed layers, etc.), the composite ﬁlament must have the appropriate balance of stiffness, toughness (essentially for robust handling and feeding), surface ﬁnish, small variance in diameter, dispersion and adhesion properties, which in practice provided an upper limit to how much inorganic particulate could be added [23]. Table 1 shows the experimentally measured dielectric properties of various as-printed materials. The particulate volume fractions in Table 1 were determined by thermogravimetric analysis. The maximum loading of fraction micro-particulate that could be printed reproducibly was approximately 30 vol%. The measured dielectric permittivities and loss for composites with BaTiO3, Ba0.64Sr0.36TiO3 and CaTiO3 are in good agreement with data published for polymer-ceramic composites of 0–3 connectivity [42–44]. Any slight differences might be associated with the different grades of polymers used for fabrication of the composites. Additionally, a small fraction of entrapped air/voids, that might arise as the ﬁlament is printed [45,46] can result in reduction of the effective dielectric permittivity. The detailed study on microwave dielectric characterization of Table 1 Printed materials and their estimated and measured dielectric permittivity and losses at 15 GHz (ABS — acrylonitrile butadiene styrene, PP — polypropylene). Material

Particulate vol. fraction

ϵr

tanδ

ABS + BaTiO3 ABS + Ba0.64Sr0.36TiO3 PP + CaTiO3 ABS PP

0.27 0.30 0.27

7.0 6.7 5.0 2.65 2.25

3.42 ×10−2 3.68 ×10−2 5.10 ×10−3 4.80 ×10−3 2.65 ×10−4

3D-printed high dielectric ceramic-polymer composites can be found in [38]. Fig. 2a and b show scanning electron microscope (SEM) images of the boundary between a printed layer of ABS only and an ABS + 30 vol.% Ba0.64Sr0.36TiO3 composite layer, indicating some micro-voiding in the polymer matrix. SEM micrographs show also that printed ABS + 30 vol.% Ba0.64Sr0.36TiO3 composite possess an acceptably dense microstructure and ﬁller particles (b 2 μm) distributed reasonably uniformly throughout the polymer matrix. 3.2. Anisotropy of dielectric permittivity An effective medium theory approach may be applied to two component composites to describe the maximum ϵmax and minimum ϵmin effective permittivity that might be expected from a system comprising relatively low ϵl and high ϵh permittivity components, which are known as ‘Wiener bounds’ (or absolute bounds) [47]: ϵ max ¼ f ϵh þ ð1−f Þϵl

ð1Þ

ϵh ϵl f ϵl þ ð1−f Þϵh

ð2Þ

ϵmin ¼

where f is the fraction of the high permittivity component. If the mixing procedure arranges each of the two components in preferred, clustered orientations then since the resulting macroscopic dielectric response is dependent on the vector direction of the exciting ﬁeld with respect to this arrangement, dielectric anisotropy can be achieved [36]. Noting that Eqs. (1) and (2) are length-scale independent, the fraction f can be taken as the overall fraction of the relatively high permittivity (ABS + ﬁller) composite material. Therefore, the overall dielectric response of the printed coupons in Fig. 1 (ignoring any resonance effects for the time being and noting as previously that d b λ) should show dielectric anisotropy as an electric ﬁeld is applied parallel or perpendicular to the orientation of the stripes, limited by the Wiener bounds. Note also that Eqs. (1) and (2) are equivalent in form to those describing conductance and capacitance connected in parallel and in series, respectively. Fig. 3a shows a plot of ϵmax and ϵmin from Eqs. (1) and (2) as a function of volume fraction f of the high permittivity composite with ϵl = 2.65 (corresponding to printed ABS only from experiment, Table 1) and ϵh = 7.0 (ABS + 27 vol% BaTiO3, Table 1). Fig. 3b shows the

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Fig. 2. SEM images of printed ABS + 30 vol.% ﬁlled Ba0.64Sr0.36TiO3: a) boundary between ABS and BST/ABS layers; b) distribution of the Ba0.64Sr0.36TiO3 particles throughout the ABS polymer matrix in BST/ABS composite layer.

measured dielectric permittivity as a function of frequency for the printed, striped coupons with an overall fraction of high permittivity stripes of 50 vol% and with the incident electric ﬁeld of the impinging microwaves either parallel (ϵ∥) or perpendicular (ϵ⊥) to the long direction of the stripes. The dielectric permittivity of the ABS only ϵl and ABS + 27 vol% BaTiO3 ϵh (again from Table 1) is also shown. Initially ignoring the inﬂexion in ϵ⊥, both ϵ∥ and ϵ⊥ were relatively stable over the frequency range at 4.8 and 3.65 respectively, and in very good agreement with the predictions of Eqs. (1) and (2) shown in Fig. 3a. Overall, the printed coupon showed the anisotropy of dielectric permittivity with high birefringence Δϵ = 1.15. Returning to Fig. 3b, the plot of ϵ⊥ showed a perturbation in the effective permittivity at 15.9 GHz. A similar effect was seen in all printed materials with alternate low and high permittivity number of layers (equivalent to periods) in the case of 2, 3 and 4 high permittivity stripes (per coupon height). The amplitude of this perturbation became less pronounced as the width of the high permittivity stripe decreased. These perturbations are now described in terms of resonance effects induced by the strip-like geometry. 3.3. Mie-type resonance Simple dielectric resonators possessing simultaneously negative effective permittivity and permeability have been reported recently for the case of regular arrays of high dielectric rods or cubes dispersed in

a lower permittivity matrix [29,34,48]. Such an effect is based on Mie resonance (the theory of the Mie scattering can be found elsewhere [49]). Brieﬂy, when the relative permittivity of the resonator is high with respect to the embedding medium, an internal subwavelength resonance is set up with a large displacement current (JD ∝ δE/δt, where E is electric ﬁeld, and t is time). The azimuthal component of the displacement current is greatly enhanced at the ﬁrst Mie resonance resulting in a large induced magnetic ﬁeld. As functions of the permittivity, multiple modes can be excited within the dielectric resonator. These electric and magnetic dipole resonances act as artiﬁcial ‘atoms’ which form the basis of all-dielectric metamaterials. In a material made up of a collection of resonant domains, their combined scattering response can provide a material with almost arbitrary values of effective permittivity and permeability. Drawing on this array of dielectric rods resonator concept, the printed alternating stripe structure presented here can now be considered as a periodic array of rectangular-shaped dielectric resonators. Fig. 4a shows simulations of the complex transmittance and reﬂectance parameters as a function of frequency for a coupon containing 4 high permittivity stripes with ϵh = 7.0 + 0.007i, interleaved between matrix stripes with ϵl = 2.6 + 0.003i. All simulations had the same geometric arrangements of the propagated wave and sample as used in our experiments: the wave propagated normally to the coupon with the electric ﬁeld vector oriented perpendicular to the stripes and the magnetic ﬁeld oriented parallel to the stripes. Within the 12–20 GHz frequency

Fig. 3. a) Wiener upper (ϵmax,) and lower (ϵmin) bounds as a function of volume fraction f of the high-permittivity composite for compounds with ϵl =2.65 and ϵh =7.0, corresponding to the ABS and BaTiO3 + ABS coupons. b) Measured real parts of the effective dielectric permittivities ϵ∥ and ϵ⊥ corresponding to the striped coupons with an overall fraction of high permittivity stripes of 50 vol% and with the incident electric ﬁeld of the impinging microwaves either parallel or perpendicular to the long direction of the stripes respectively.

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Fig. 4. a) Calculated complex scattering parameters for a 4-row coupon with alternating ϵl =2.6+0.003i and ϵh =7.0+0.007i dielectric constants; b) the corresponding extracted real and (c) imaginary parts of permittivity and permeability.

range, the simulations suggested two resonances at 15.19 GHz and 19.54 GHz. Using the standard NRW retrieval method [40], from the simulated reﬂectance and transmittance data the resulting effective real (ϵ') and imaginary (ϵ″) parts of the permittivity, and real (μ') and imaginary (μ″) parts of permeability as a function of frequency are shown in Fig. 4b (real parts) and c (imaginary parts, respectively).

These simulations showed qualitatively similar behaviour in ϵ' as seen in the experiments. To understand the Mie-modes leading to resonance, the computed spatial distribution of electric and magnetic ﬁelds around the resonance frequencies were simulated using the ﬁnite element method. Fig. 5 shows simulated distributions of electric and magnetic ﬁelds inside the

Fig. 5. a) Distribution of the electric and magnetic and ﬁelds in the slab with spatially varied dielectric permittivity near ﬁrst (a, b) and second (c, d) Mie resonances. The wave was normally incident on the slab along the z-axis with E∥x and H∥y.

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Fig. 6. The experimental reﬂection and transmission parameters as a function of frequency obtained for two different printed polymer coupons; a) with four high permittivity stripes, and b) with six high permittivity stripes. The solid lines are computer simulations for the coupons using ϵl =2.65+0.012i and ϵh =7.0+0.23i for the low and high permittivity striped regions respectively.

coupon having the same dielectric properties as a real 3D printed sample at the ﬁrst (Fig. 5a and b) and second (Fig. 5c and d) resonances. The ﬁeld distributions were relatively complex due to the multiple discrete boundaries between regions of high and low permittivity. Fig. 5a shows that in the vicinity of the ﬁrst resonance at 15.19 GHz, the circular component of electric ﬁeld (shown as concentric curves in y-plane) resulted in a comparatively strong magnetic ﬁeld (Fig. 5b). At the second resonance, the strong linearly polarized displacement currents (also seen as contour curves in y-plane, Fig. 5c resulted in enhancement of the azimuthal magnetic ﬁeld (Fig. 5d). Therefore, the resonances can be associated with ﬁrst TE11 mode and second TE12 mode of the Mie-resonances (magnetic and electric, respectively) [50,51]. According to the Mie theory, the resonant dielectric particle at the ﬁrst resonant mode is equivalent to a magnetic dipole, in which artiﬁcial polarization and resonance frequency are controlled by the particle geometry and its permittivity [29]. Consequently, the resonance frequency of the designed coupons can be governed by the size (period) of the high permittivity stripes. This was demonstrated experimentally using two different printed polymer coupons with four and six permittivity stripes. Fig. 6 shows the experimentally measured reﬂectance and transmittance coefﬁcients for these two coupons again with the stripes oriented perpendicular to the electric ﬁeld polarization (i.e. in the same orientation as shown in Figs. 4 and 5). Fig. 6 also shows simulations of the identical structures, in both cases showing good agreement with

experiment. These plots conﬁrm that the resonance behaviour was geometry-dependent, with the resonant frequencies and dips in transmission and reﬂection parameters governed by the width (or period) of the stripes. While the resonant frequency increased slightly with the number of stripes, the sharp changes in S-parameters around the resonant frequency were reduced. To explore resonant behaviour further, Fig. 7a and b shows simulations of the transmission S21 parameter and absorption A = 1 - R - T, where T is the transmission coefﬁcient and R is the reﬂection coefﬁcient, behaviour of coupons with different periods (number of layers). The resonance effect swiftly diminished for periods N6 per coupon (i.e. reducing stripe width) probably because of the fading of the multiple scattering of the waves within the close boundaries of the neighbouring dielectric rods. As previously described, the Mie-like resonance behaviour can also be tuned by changing the permittivity of the dielectric units themselves, because the frequency of the resonance modes is proportional to πc=ðω pﬃﬃﬃ ϵÞ [29,51]. In order to conﬁrm this, and recognizing that the permittivity of ferroelectric titanates is strongly temperature sensitive, Fig. 8 shows the measured scattering parameters as a function of temperature for a coupon again comprising alternate ABS + 27 vol% BaTiO3/ABS stripes. A peak in the dielectric permittivity of BaTiO3 occurs in the vicinity of the ferroelectric-paraelectric phase transition (~ 110 °C in bulk

Fig. 7. a) Simulations as a function of frequency for (a) the transmittance and (b) the relative absorption of the printed striped coupons, with increasing number (reducing thickness) of stripes.

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Fig. 8. Variation in transmittance with frequency of a printed coupon comprising alternating stripes of ABS and BaTiO3/ABS as a function of temperature.

BaTiO3 [52]), and Fig. 8 shows a reduction in the resonance frequency with increasing temperature from 20 °C to 105 °C. This redshift of approximately 300 MHz in S21 dip corresponded to an increase in the static dielectric permittivity of the high permittivity stripes of Δϵ = 0.4. There was also a reduction in the magnitude of the S21 amplitude at resonance with increasing temperature that was due to the corresponding strong rise in dielectric loss in BaTiO3 as the phase transition was approached. While losses in the BaTiO3 containing regions increased with temperature, damping out the resonant behaviour, the overall Mie-type resonance effect was governed by the dielectric loss of both the composite and polymer only regions. Fig. 9a shows a simulation of the predicted overall effective dielectric permittivity of a printed 2-period striped coupon as a function of frequency for high permittivity regions of ϵ'h = 7.0 but with different assumed low loss values. Fig. 9a shows that according to simulations (where permittivity is derived from the simulated reﬂectance and transmittance coefﬁcients using the NRW method), near-zero or negative permittivity i.e. metamaterial-like behaviour may be induced if losses could be restricted to tanδ≤ 5 ×10-5. To explore this possibility experimentally, the relatively high loss ABS polymer was replaced by lower loss polypropylene (ϵl = 2.25 + 0.0006i, Table 1) and BaTiO3 was replaced by CaTiO3 that has a very low loss of tanδ ≈ 3 × 10-4 [53]. Fig. 9b shows similar simulated data to the Fig. 9a, but also with experimental measurements of permittivity in a 2period printed PP and CaTiO3/PP composite coupon in which the

composite regions had ϵh = 5 + 0.025i (Table 1). Although less pronounced than shown in the simulation because of manufacturing imperfections such as retained air/voids, the relatively simple high permittivity, low loss striped arrangement similarly showed strong resonance, and the onset of metamaterial-like character.

4. Summary The ability to fabricate new feedstock materials for 3D printing in pursuit of practical all-dielectric artiﬁcial materials has been presented, together with simulations and experimental results on preliminary demonstrator structures. We show that 3D printed all-dielectric structures offer a convenient method to move towards the manufacturing of structures with metamaterial electromagnetic properties and tunable operational frequencies. The designed structures consisting of oriented dielectric stripes with alternating dielectric permittivity possessed well-deﬁned artiﬁcial anisotropy of effective permittivity, and a Mietype resonance. This resonance frequency could be controlled by making use of the degrees of design freedom facilitated by 3D printing, such as the periodicity of the different units, their relative permittivities and dielectric losses. Finally, the results show the potential for near-zero or less than unity values of effective permittivity and reveals the great potential for using fused-deposition 3D printing in manufacturing novel electromagnetic devices.

Fig. 9. Effect of the dielectric loss on the amplitude of Mie-type resonance. a) Computer simulation of the effective dielectric permittivity in a 2-period striped structure with alternating ϵl = 2.65 + 0.003i and ϵh = 7.0 + 7.0 * tan δ permittivities. b) The experimental extracted permittivity in a 2-period striped structure of PP + CaTiO3/PP composite (solid curve) and simulation (dotted curve), using ϵl =2.25+0.0006i and ϵh =5+0.025i.

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