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Abstract
Terahertz (THz) radiation excites electronic and optical modes of many materials, and controlling interaction of these materials with THz pulses provides a fascinating avenue to achieve unprecedented functionalities in return. Here, woodpile-structured rare-earth orthoferrite metamaterials built with 3-D direct ink writing technology are proposed and experimentally demonstrated. Polarization-independent THz refraction and switching of resonances by varying the number of layers in the structure, as well as the structural parameters and specimen support angle are achieved. Such all-rare-earth-orthoferrite dielectric metamaterials are easy to fabricate and can be very promising in developing efficient and low cost THz functional metadevices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) radiation occupies a large portion of the electromagnetic spectrum between the infrared and the microwave range [1, 2], and incorporates advantages of these two bands, such as penetration of dielectric materials and nonpolar liquids [3–5]. Metamaterials are artificial electromagnetic media structured on a subwavelength scale [6, 7]. They are created by designing atom-like units to achieve unprecedented functionalities, which are difficult to obtain in naturally occurring materials [8–10]. In return, the optical modes of these materials provide a fascinating way to control THz waves [6, 11, 12]. Conventionally, metamaterials are composed of noble metals [13–15]. Localized surface plasmon resonance offers a range of exotic electromagnetic responses [16, 17], and provides metamaterials with an effective way to manipulate light [12, 18–20]. However, the subsequent conversion in matter of absorbed light into heat limits the use of plasmonic metamaterials [21, 22]. A different approach to the problem, based on all-dielectric unit cells, is emerging [6, 23, 24]. The use of all-dielectric media could alleviate absorption losses while allowing similar properties [25]. With a large dielectric constant and a small dielectric loss, at a subwavelength scale, artificial dielectric structures support strong electric and magnetic resonances, known as Mie type resonances, through internal excited polarization charges and circular displacement currents [25–27]. Structural parameters and composition support the desired effective permittivity and permeability, and become important factors in the control of light [28]. Recent work has revealed that important attributes of metal-based metamaterials, such as artificial electric and magnetic responses [29–31] and negative refraction [32], can also be achieved in all-dielectric systems, leading to an attractive alternative to lossy plasmonic metamaterials [33, 34]. At present, multifarious functionalities, such as optical magnetism [35], perfect reflectors [36], and optical vortexing [37], as well as active photoswitching [38], have been demonstrated in silicon-based metamaterials [39, 40]. However, broader applications of silicon are challenging in the THz or higher frequency ranges because of high costs and multi-step fabrication.
In this article, rare-earth orthoferrite metamaterials are proposed and experimentally demonstrated. Rare-earth orthoferrites show outstanding optoelectronic properties [41, 42], Magnon and electromagnon [43–45] and spin reorientation [46], as well as a high dielectric index and a low loss [47–49]. TbFeO3 is a suitable candidate for this study, as it has a stable magnetic structure over a broad temperature range [50, 51]. A more flexible and less costly processing method, 3-D direct ink writing technology, is introduced for the creation of woodpile-structured metamaterials. Polarization-independent THz refraction and switching of resonances are achieved.
2. Experimental Section
2.1 Sample Fabrication
TbFeO3 inks were first prepared by making a stable suspension in a deionized water solution of PVA. Analytical grade Tb4O7 (Founde Star Science and Technology, Beijing, PR China) and Fe2O3 (Aladdin, Shanghai, PR China) were selected as raw materials for preparation of the TbFeO3 ink. According to the stoichiometric compositions of the reactants, 33.33 mol% Tb4O7 and 66.67 mol% Fe2O3 powders were ball-milled in alcohol for 24 h, dried at 70 °C for longer than 12 h, and calcined at 1050 °C for 3 h. Pre-sintered TbFeO3 powders were added to the water solution of PVA. During each addition, the suspension was placed in a paint shaker for 20 min to ensure thorough mixing. The TbFeO3 ink was then loaded into a 5 cm3 syringe (EFD Inc., USA) and extruded from a glass nozzle on a double-sided polished sapphire wafer to form directly written samples.
An Adventure 3-D-LB-Printer (Shenzhen Adventuretech Co.,Ltd., China), a 3-D direct ink writing technology, is introduced for the creation of woodpile-structured metamaterials. Figures 1(a)–1(d) illustrate the direct 3-D writing procedure of a woodpile-structured metamaterial with four layers on a sapphire wafer. A layer-by-layer building process is used: a nozzle writes each layer in the x–y plane and is lifted in the z direction to allow each new layer to be written. The process of direct writing has been described previously [52].
After the direct writing process, the samples were dried in a drying oven for 24 h. Then the as-constructed samples were sintered in a muffle furnace using a solid-state reaction sintering method. During the sintering process, the temperature was increased to 600 °C at a rate of 3 °C/min and maintained at 600 °C for 4 h. Next, the temperature was raised to 1487 °C at a rate of 3 °C/min and maintained at 1487 °C for another 4 h. Finally, the TbFeO3 ceramics were prepared. The processes of drying and sintering were both under ambient conditions.
2.2 Terahertz Spectra Experiments
A Z3 THz time-domain spectrometer system (Zomega Terahertz Corp., USA) was used to characterize woodpile-structured metamaterials. This spectrometer system was equipped with a mode-locked Ti:sapphire laser source (Spectra Physics, USA) with a central wavelength of 780 nm and a pulse duration of 100 fs. The light from the mode-locked laser source passed through a beam splitter and was split into a pumping beam and a probing beam. A photoconductive antenna (low-temperature-grown GaAs) was excited by the pumping light to generate THz radiation. After free space propagation, the probing laser pulse arrived directly at an electro-optical crystal (ZnTe), and the THz radiation transmitted through the sample was detected by this crystal. The woodpile-structured dielectric metamaterial samples were placed in the THz radiation path to measure their THz transmittance. A time-delay mirror was moved by an electric motor to produce the required temporal delay between the THz pulse and probing light. The entire system was filled with high-purity (99.999%) nitrogen. Frequency-domain spectra corresponding to the time-domain spectra were obtained using a fast Fourier transform method. The modulation frequency and lock-in time constant were 21 kHz and 300 ms, respectively.
3. Results and Discussion
We characterized and analyzed the THz waveforms of TbFeO3 ceramics using a THz time-domain spectrometer (Zomega Terahertz Corp., USA). The ferromagnetic and antiferromagnetic frequencies of the bulk TbFeO3 were 0.35 and 0.54 THz, respectively (Fig. 2(a)). The dielectric constant ε and extinction coefficient κ were calculated using previously described methods to precisely determine the optical constants in THz time-domain spectroscopy [53, 54]. Equation (1-3) detailed the process of calculation.
Where n is the refractive index, D is the thickness, ϕ is the phase difference between the reference and signal spectra, and t is the transmittance. In this study, the values of ε and κ were 21 and 0.525, respectively. Incidentally, the dielectric constant of our TbFeO3 ceramic is less than that of a TbFeO3 single crystal. We believe that this is caused by the difference in the compactness and crystallinity between the ceramic and the single crystal. Furthermore, we studied the magnetic behaviors of the TbFeO3 ceramics under a changing applied magnetic field. We determined the values of the magnetic parameters by analyzing the magnetizing curve shown in Fig. 2(b). The saturation magnetization Ms, remnant magnetization Mr and coercivity Hc were 7 T, 0.78 A·m2/kg and 2.1 T respectively.
Fig. 2 THz and magnetic behaviors of TbFeO3 ceramic. (a) THz transmission spectrum of TbFeO3 ceramic. Ferromagnetic and antiferromagnetic resonances, of 0.35 and 0.54 THz, respectively, are excited. The inset shows a perovskite crystal structure. (b) Magnetizing curve: the saturation magnetization Ms, remnant magnetization Mr, and coercivity Hc are 7 T, 0.78 A·m2/kg, and 2.1 T, respectively.
Figure 3(a) shows side and top views of a woodpile-structured metamaterial, which exhibits face-centered-cubic symmetry. The structural parameters (rod diameter d and rod spacing p), and the number of layers could have an impact on the THz behavior of the metamaterial. Equally importantly, the relative orientation between the meta-atoms and incident THz pulses could change the distribution of incident THz fields on metamaterials. Thus, we created woodpile-structured metamaterials with four layers and eight layers, and varied the rod spacing p from 150 to 200 µm. In addition, THz behaviors at various specimen support angles θ were studied. Composite TbFeO3 and PVA inks (TbFeO3, 95 wt.%) were developed. Figure 3(b) shows the defined specimen support angle θ, which describes the relative orientation between the meta-atoms and the incident THz pulses. During rotation of metamaterials, the positions where the top layer is parallel or perpendicular to the THz magnetic field are defined as 0° and 90°, respectively. We collected the time-domain spectra of a woodpile-structured dielectric metamaterial with four layers for values of θ ranging from 0° to 180°. The rod diameter was 70 µm and the rod spacing was 150 µm. Figure 4(a) shows the signal spectra for angles of 0°, 30°, 60°, and 90°. Compared with the reference spectrum (Ref.), both the main and the second peaks experienced a significant time delay and an obvious amplitude decrease. Figures 4(b)–4(c) show the evolution of THz time-domain spectra as a function of θ. A 2-D view of the evolution of the main peaks is shown in Fig. 4(b). When θ was changed from 0° to 90°, the main peaks experienced a decrease in transmitted intensity, and a gradual increase in time delay. When θ was further increased from 90 to 180°, the opposite tendency was observed: increased transmitted intensity and decreased time delay. Figure 4(c) shows a 2-D view of the changes in the second peaks as a function of θ. These second peaks show declining transmitted intensity and an increasing time delay, as θ was rotated from 0° to 45°. However, the transmission increased and the time delay decreased as θ was varied from 45° to 90°. These trends repeated as θ was increased from 90° to 180°. Moreover, the changes were much more obvious, and the second peaks split into two peaks when the specimen support angles were ≈45° and ≈135°.
Fig. 3 Woodpile-structured metamaterial with four layers. (a) Side and top views. Rod diameter and rod spacing are marked d and p. (b) Specimen support angle. The relative orientation between the meta-atom and the incident THz pulses is marked as a specimen support angle θ.
Fig. 4 THz time-domain spectra of woodpile-structured metamaterial with four layers. (a) Detected signal spectra for θ = 0°, 30°, 60°, and 90°. The reference spectrum (Ref.) is collected without any sample. (b)–(c) Evolution of THz time-domain spectra as a function of θ. (b) A 2-D view of the main peaks. (c) A 2-D view of the second peaks. The rod diameter d and rod spacing p are 70 µm and 150 µm, respectively.
We investigated the THz behaviors of woodpile-structured metamaterials with different structural parameters, different numbers of layers, and different specimen support angles. Broadband and multifrequency THz transmission is shown in Fig. 5. Figure 5(a) displays THz resonances at 0° under three different conditions. In the four-layer samples, the THz resonances for a rod spacing p = 200 µm underwent a whole redshift compared with the resonances for a rod spacing p = 150 µm. The metamaterials with eight layers held partially similar resonances to the metamaterials with four layers. Moreover, new low-frequency resonances were observed for the eight-layer sample. Figures 5(c)–5(d) illustrate the evolution of these THz resonances with increasing specimen support angles. New resonances appeared and a few resonances disappeared during the rotation. Polarization-independent switching of resonances is shown in Fig. 6(a). According to Fermat’s principle [11, 55], the refractions are caused by the woodpile-structured dielectric metamaterials, as shown in Fig. 6(b). This refraction causes the switching of resonances and the evolution of resonances as a function of θ [56, 57].
Fig. 5 THz resonances of woodpile-structure. (a) Resonances with varied structural parameters at θ = 0°. (b)–(d) Evolution of THz resonances as a function of θ. (b) Four layers with d = 70 µm and p = 150 µm. (c) Four layers with d = 65 µm and p = 200 µm. (d) Eight layers with d = 65 µm and p = 150 µm.
Figure 7 shows simulated and measured transmission spectra of the woodpile-structured metamaterial at θ = 0°. The experimental results are in good agreement with the simulation. According to dielectric resonant theory, the magnetic and electric dipoles contribute to the resonances in dielectric metamaterials [25, 27, 28, 58]. The varied distributions of the incident THz fields result from the relatively changed position between the THz fields and the metamaterial. Therefore, resonances evolve as a function of specimen support angle. The rod diameter d and rod spacing p in our simulation and experiment are 70 µm and 150 µm, respectively. The dielectric constant ε, tangent of the loss angle (tan δ), and saturation magnetization Ms in our simulation are obtained from the numerical results given in Eq. (1-3) and Fig. 1. They are 21, 0.025, and 7 T, respectively. Commercially available software CST MICROWAVE STUDIO was used.
Fig. 7 Simulated (red line) and measured (black line) transmission spectra of woodpile-structured dielectric metamaterial with four layers. The specimen support angle is zero. Structural parameters for the simulation and experiment are d = 70 µm and p = 150 µm.
In the microwave range, there are suitable media, such as barium strontium titanate, to build metamaterials which can effectively control electromagnetic waves. However, such medium-material-based metamaterials have no strong responses in the THz electromagnetic range. Materials structuring metamaterials with a high electric constant are especially important. Frequency shift of transmission dips and emergence of new transmission dips were reported by applying a changed magnetic field [59, 60]. Magnetic tunability will make rare-earth orthoferrite metamaterials more attractive to researchers. Moreover, silicon and its alloy are challenging due to the high cost and multistep fabrication. Hence, this work offers an efficient and low cost THz metamaterials.
4. Conclusion
In this article, woodpile-structured rare-earth orthoferrite metamaterials are presented. A 3-D direct ink writing technology is introduced to create these metamaterials. The experimental results agree well with the simulation. Polarization-independent THz refraction and switching of resonances are achieved by varying the structural parameters and the specimen support angle θ. Refraction causes switching of resonances and the evolution of resonances as a function of θ. The proposed method is versatile and could enable various complex all-rare-earth-orthoferrite optical elements. At the same time, such dielectric metamaterials are easy to fabricate in THz range with low cost, making them very promising in developing efficient and low cost THz metamaterials.
Funding
National Key Research and Development Program of China under grant 2017YFB0406300; National Natural Science Foundation of China under grant 51788104, 51532004; The Science and Technology Plan of Guangdong province under grant 2014B090907002, 2017B090907004; The Science and Technology Plan of Shenzhen City under grant JCYJ20160301154309393.
Disclosures
The authors declare that there are no conflicts of interest related to this article
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