1. Introduction

Metamaterials acquire their properties from embedded subwavelength structures grouped together to exhibit the required values of permittivity and permeability in the desired frequency range, in order to manipulate electromagnetic (EM) waves [1–3]. The origin of electromagnetic metamaterial properties lies in the shape and size of periodic structures of a circuit, and the material that consists of those structures [4]. So far, the majority of metamaterials were based on ring resonator circuits, typically split ring resonators (SRRs) and asymmetric SRRs (ASRs), which can also be described as simple LC circuits [5,6]. It is known that the LC resonance frequency scales inversely with the lateral size of SRR structures, thus, with the decrease of the wavelength, high-resolution patterning using focused ion beam (FIB), electron beam (EB) and lithography methods [7–10] becomes more difficult.

While reaching limitations of the tuning of properties by the size and shape of structures, major attention has been brought to novel materials, including nonlinear media, which showed great potential for the control and enhancement of unique metamaterial phenomena [11–13]. The development of linear metamaterials was supported by a considerable number of available material response, which included the capability of implementing magnetic, electric, and electromagnetic properties. The implementation of the magnetic response in metamaterials brought various complex phenomena, especially when magnetic nonlinearity was included [14]. The EM coupling raised naturally for nonlinear materials, thus, nonlinear designs have to include a large set of nonlinear susceptibilities, which are negligible for conventional media [15–17]. For that reason, the development of nonlinear metamaterials can be advanced by the use of anisotropic materials, among which carbon nanotubes (CNTs) could play a significant role in future advancements. Unique structure [18,19] and nonlinear electric and optical properties [20–23], such as anisotropic electrical conductivity of horizontally aligned CNT forest [24], and anisotropic optical absorption of vertically-aligned CNTs [25,26] have great potential in the development of metamaterials.

CNTs act as nearly ideal one-dimensional nanorod antennas with very high aspect ratio geometry [27]. Furthermore, the behavior of a single-walled CNTs (SWNTs) under the EM radiation is similar to direct gap semiconductors with absorption spectra dominated by exciton lines [22,28]. In addition, Avouris et al.[29] confirmed that the nonlinear optical behavior of CNTs was related to a high third-order susceptibility with sub-picosecond recovery time [30,31], in which the source of the nonlinearities was an effect of the saturation of the resonant excitation lines. CNTs can absorb essentially entire spectrum of the EM radiation by both free carrier and excitonic absorption processes, which combined with very high mobilities of carriers, makes them perfect for broadband photonic and optoelectronic applications [32]. Also, as compared to other conventional nonlinear media, the advantage of CNTs lies in easy integration into optical fibers and waveguide environments, due to additional freedom provided by the manipulation of internal electronic structures for the engineering of optical and electrical properties. High shielding effectiveness accompanied by a high dielectric constant of SWNTs [33,34] can be tuned by control of growth parameters and post-processing operations, such as chemical treatment or a molecular functionalization [35], which is impossible for typically used materials.

Unique nonlinear properties and structure of CNTs were utilized for various promising applications, like light sources in nanoscale, photodetectors, photovoltaic devices, ultrafast lasers [36–40]. Also, the first attempts of combining metamaterial and photonic designs with CNTs were recently presented by some groups [41–43]. Butt et al. [27] showed photonic devices fabricated as the arrays of multi-walled CNTs (MWNTs) [44,45], while Hong et al.[35] studied terahertz metamaterials composed of CNT films with cut slits, to interact with the EM wave. The spray-coated CNT films prepared on Si₃N₄ ceramic metamaterials improved the total performance of the metamaterial composite in the EM field [22]. Despite interesting results obtained by those groups, in order to fully utilize nonlinear properties originated from the anisotropic behavior of CNT forest, metamaterial circuit designs combined with vertically-aligned high-density CNT forest seem to be a right direction towards the advancement of the development of various applications.

CNT metamaterials can be used for the improvement of plane dipole copper antennas by the transformation into metamaterial design, which results in a high enhancement of radiation power and matching properties [46]. In metamaterial antennas, the propagation of the EM wave stimulates a time-dependent spatially static field, which gives a constant value of the phase at any point of the antenna and allows for the improvement of directivity. The replacement of copper with oriented CNT forests with high absorption of incident light allows for the decrease of reflection losses and the increase of the efficiency of the antenna. Also, the advantage of CNTs over metallic materials in antenna applications include higher flexibility, weight saving, and higher reliability under harsh conditions. Except for antennas, CNT metamaterials can be used in optical rectennas and solar cells. The light irradiation excites electrons-hole pairs within carbon nanotubes and converts them to current flow. A further increase of the absorption of light in CNT metamaterials could increase the amount of generated current, thus, increase the efficiency of future devices, as more current could be generated from the same amount of irradiated light. Finally, in energy storage devices the use of CNT forest metamaterials could lead to increased absorption of the Vis-MIR radiation [47–49], and increase the generation of heat, which then could be used to store more energy [50]. With a proper design of the metamaterial circuit, the heat could also be transferred in the material, with minimal losses.

The purpose of this study is the investigation of properties and potential resonant effects in novel CNT forest metamaterials in the SRR geometry, under an unpolarized infrared (IR) light. The study includes the investigation of the influence of geometrical parameters of metamaterials composed of patterned vertically-aligned SWNT forest, on the total reflectance in the near-infrared (NIR) range. The study of the total reflectance was carried out to evaluate the reflection from CNT metamaterials, for suitability in future applications, such as the beforementioned antennas, heat, and energy storage devices, solar cells, and so on. The influence of the SRR shape, like the height h, the depth of the SRR dip d, and the gap size g of SRR was examined. The total reflectance of CNT metamaterials depends on the shape of designed structures, and by precise control of the geometry, change of the IR properties is expected. The study of the coupling effects originated from the structure of metamaterial resonators, rather than the CNT forest, was also conducted. Moreover, finite-difference-time-domain (FDTD) simulations of geometrical parameters of anisotropic CNT forest metamaterial structures were also carried out and the simulated reflectance, transmittance, and absorbance responses are discussed.

2. Experimental

CNT forest metamaterials were fabricated according to the following procedure: (a) deposition of thin AlO_x/Fe catalyst film, (b) FIB patterning of metamaterial circuits, followed by (c) FIB secondary etching process [7], continuously, without breaking the vacuum, and finally (d) the synthesis of CNT forest by a chemical vapor deposition (CVD) method.

The deposition of the catalyst film was conducted by radio frequency (RF) magnetron sputtering method on thermally grown 100-nm-thick silicon oxide film (th-SiO₂), coated on polished (Ra < 0.15 nm) p-type silicon (Si) substrates of ρ = 100 Ω⋅cm. Prior to the deposition, a vacuum chamber was evacuated to a base pressure of < 5.0×10⁻⁴ Pa, which was followed by the introduction of 25 sccm of argon (Ar) at a working pressure of 0.8 Pa. For the deposition of 30-nm-thick AlO_x buffer layer and 0.9-nm-thick Fe catalyst layer, Al₂O₃ and Fe targets were used, both of 99.99% purity and 2 inches diameter, mounted horizontally on the top of the chamber. The details of the sputtering process were described previously in [51].

The patterning of metamaterial designs in the catalyst film was carried out by the FEI QUANTA 3D 200i FIB system. Silicon samples were introduced into the vacuum chamber and the patterning of designed metamaterials was performed, using a Ga ion beam source at an acceleration voltage of 30 kV and a beam current of 30 pA. The FIB patterning was followed by the FIB secondary etching process, applied to the entire surface of the patterned area, to remove the redeposited material and clean the surface of substrates. Parameters of the FIB patterning and the influence of the FIB secondary etching process were presented in [7].

The growth of carbon nanotubes was carried out using a thermal catalytic CVD (CCVD) method on the patterned AlO_x/Fe catalyst. Prior to the growth, a quartz furnace (2 inches diameter) CVD chamber was evacuated to the base pressure of < 5.0×10⁻⁴ Pa. The evacuation was followed by the heating in a vacuum with a temperature ramping speed of 60°C/min until the process temperature of 730°C was reached. The annealing was carried out for 2.5 min in a hydrogen atmosphere at 29 Pa (65 sccm) and was followed by CNT synthesis in acetylene (15 sccm) and hydrogen (15 sccm) gaseous atmosphere at the pressure of 110 Pa. The growth time was precisely controlled and limited to a few seconds, to reduce the total height of CNT forest to single micrometers. The synthesis process was described in detail before in [52].

The geometry and quality of CNT forest metamaterials were investigated by a field emission scanning electron microscope (FE-SEM) JEOL JSM-5310. For structural and quality analysis of CNTs, a micro-Raman HORIBA JOBIN YVON HR-800 spectrometer was used, with a laser excitation line of 532.08 nm. Infrared reflectance and transmittance spectra of CNT metamaterial arrays were obtained using a Fourier Transform Infrared Spectroscopy (FT-IR) JASCO FT/IR 660 PLUS combined with an IR microscope JASCO IRTRON IRT-30 with an incident light perpendicular to the surface of the sample. The circular measurement area of a diameter of 28 µm was defined by an aperture in the light path of the IR microscope. Obtained spectra were measured in unpolarized incident light and normalized to the Si substrate.

A simulation of the geometry of CNT forest metamaterial circuits was conducted using the FDTD method in the Fujitsu Poynting for Optics software, assuming an anisotropic z-axis orientation of the CNT forest bulk media. In simulations, a polarized pulse source in the differential Gaussian waveform was used as an incident beam. The EM wave was calculated using a Drude model for anisotropic CNT bulk, and dielectric model for the SiO₂ insulator substrate, following insulating th-SiO₂ film (leakage current density below 0.1 nA/cm² at 1 MV/cm [53]) in the growth experiment. The role of the dielectric surface was to separate each of the resonator structures from each other, so there was no electrical conduction between them, but only the EM short-distance interactions. The complex relative permittivity of CNT material was obtained from the refractive index of SWNT film [54] at 2 µm wavelength and was defined as n = 1.35 + 0.2i at the frequency range of 1-200 THz. The refractive index of SiO₂ of n = 1.4524 at 2 µm wavelength, was obtained from [55].

3. Results and Discussion

3.1 Experiment

Figure 1(a) shows a schematic representation of an SRR structure with highlighted geometrical parameters of CNT forest metamaterials investigated in this study. The influence of the variation of the gap (split) size g, the dip depth d, and the height h of SRRs on the total IR reflectance was studied, and results were presented in following parts. Figure 1(b) shows a typical SEM image of a patterned SRR array on the AlO_x/Fe catalyst, before the growth of CNTs. Dark color represents an area with as-deposited pristine catalyst (SRR shape), while the catalyst film was removed by the FIB patterning from brighter areas. As mentioned in the previous section, the patterning step was combined with the FIB secondary etching process, developed for the sole purpose of the CNT forest metamaterial fabrication. Normally, a material sputtered during the FIB milling can partially redeposit on the pristine catalyst surface; thus, the secondary etching was introduced for the cleaning purpose. The removal of redeposited contamination, followed by roughness decrease and thinning of the Fe film allowed for high-quality patterning of the catalyst and the growth of high-density vertically-aligned CNT forest into SRR design (Fig. 1(c)) with the smallest linewidth below 200 nm [7].

 

Fig. 1. (a) Graphical illustration of investigated geometrical parameters of CNT forest metamaterials: height h, dip depth d, and gap size g. SEM images of (b) patterned AlO_x/Fe catalyst substrate and (c) a tilted view of CNT forest SRR metamaterial array.

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A detailed characterization of a pristine CNT forest for the fabrication of SRRs was presented in previous reports [51,52]. The density, alignment, diameter and optical properties of CNT forest were studied to increase the absorption of incident light; thus, optimized growth parameters were used in this study. To confirm the same type of CNTs, an additional analysis was carried out for presented CNT SRRs, using the micro-Raman analysis. The results (see Appendix A) showed a very high intensity of the RBM peaks, indicating the presence of SWNTs with an estimated diameter of 0.7–1.1 nm. High peak intensity ratio I_G/I_D of 8.03, 9.6, 10.87 and 9.24 for 2, 3, 4, and 5 s growth, respectively, indicated a high crystallinity and order of graphene sheets of CNTs in SRRs, confirmed also by a high intensity of the 2D band. The presence of the G^- peak around 1560 cm⁻¹ suggested that the majority of SWNTs in the patterns were of semiconducting type. The presence of M peak and iTOLA peak was also confirmed in the presented spectra. The M band was related to various effects related to the curvature of SWNTs, while the high-frequency iTOLA peak observation was associated with the dispersion of phonon branches in low defective graphite [56,57].

Figures 2(a)–2(e) show top and tilted side-view SEM images of fabricated CNT metamaterial arrays with a variation of the gap size g. As can be seen, high-quality patterns were obtained after the synthesis process of vertically-aligned CNTs and the investigation of the influence of the gap size g on the total IR reflectance was carried out. The size of individual SRRs was 2×2 µm, at the height of CNTs of about 4 µm. The variation of the gap size, from 0 µm (Fig. 2(a)) for a closed ring geometry to 1.2 µm (Fig. 2(e)) for SRRs, was precisely controlled during the FIB patterning. To reduce possible fluctuations of structure and properties, each array was fabricated on the same sample, within a small distance from each other, to allow the growth of SWNTs under identical conditions. Figures 2(f)–2(h) show the results of measurements of the total IR reflectance, transmittance, and calculated absorbance, respectively. According to Fig. 2(f), the highest value of the reflectance (53% for 4.5 µm wavelength) was observed for a closed ring (g = 0 µm), while for the array composed of SRR patterns with g = 0.6 µm, the value was reduced to 46% for the same wavelength. Generally, for most of the investigated range, the reflectance was reduced by 10–15%. SRR arrays with the g size of 0.3, 0.9, and 1.2 µm (Figs. 2(b) and 2(d)–2(e)) showed intermediate values of the reflectance. The transmittance in Fig. 2(g) followed a similar trend, with the highest values for the closed ring and the lowest ones for g = 0.6 µm. The highest values of total absorption were also obtained by the 0.6 µm gap size (Fig. 2(h)). In Fig. 2(f), the closed ring geometry showed the highest reflectance values, despite the highest absorption area among all patterns. Such results were associated with the absence of the gap in the ring and the absorption of light only in the CNT forest body. For SRR geometry the total absorption was additionally enhanced by the resonant effect of the introduced gap, in which under the external EM field, a self-induced current in SRRs led to the LC resonance. On the account of the unpolarized light source, only the resultant effect of the resonance was noted (decrease of reflectance), while the electric and magnetic resonant peaks were not observed.

 

Fig. 2. (a) – (e) Top view and angled SEM images of CNT SRR metamaterial arrays with the variation of the gap size of 0, 0.3, 0.6, 0.9, and 1.2 µm. (f) Reflectance, (g) transmittance, and (h) absorbance spectra of fabricated SRR patterns. Peaks related to absorption of H₂O and CO₂ in the CNT forest structure are assigned.

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Another important role during the tuning of the gap size was played by the height of CNT SRRs. With the decrease of the height from 4 µm to 0.75 µm, the difference between reflectance values, for different g, became larger. For CNT forest SRRs with reduced height, the gap size control has a larger influence on the reflectance than for taller CNTs, due to a change of the absorption in the body of CNTs, as the additional absorption of light can be easier achieved in shorter CNTs than tall ones (see Appendix B).

To observe strong resonances at wavelengths larger than the diameter of the structure [58,59], the resonator requires a gap in the ring. If this condition is met and a single, or multiple splits are added, the self-inductance and capacitance are generated, and the decrease of the resonant frequency can be observed, while the degree of a change depends on the shape of individual structures. For the investigated CNT SRRs (Figs. 2(f)–2(h)), larger g caused the decrease of the resonance intensity, which led to the overall decrease of the absorption. Due to the larger distance between planes of the capacitor in the SRR, a weaker resonance related to the magnetic part of the radiation occurred, resulting in a smaller reduction of the IR reflectance. These results led to the conclusion, that the resonant frequency of CNT SRR arrays can be tuned by the change of the gap size. In contrast, the reduction of the gap size resulted in the increase of the effective capacitance and thus the increase of the absorption was observed. In CNT metamaterials, SRRs with g = 0.6 µm showed higher absorption than structures with the 0.3-µm-wide gap. Presumably, existing defects of SRR geometry may have established a connection of the capacitor plates in some cases, which resulted in a closed ring-like behavior, reducing the absorbance. Consequently, more precise control of the fabrication is required to enhance the generation of larger capacitance and a further increase of the absorbance. This behavior was noted for the first time in CNT forest SRR arrays.

Figures 3(a)–3(d) show top-view SEM images of fabricated SRR arrays, in which the tuning of the dip size from 0 to 750 nm, was conducted. As in Fig. 2, to minimize the diversity of arrays, the CNT growth was carried out throughout the same experiment. The size of individual SRRs was 1×1 µm, at the height of CNTs of about 190 nm. Figure 3(e) shows measured total IR reflectance spectra of presented CNT metamaterials, and also for the comparison purpose, the reflectance of SRR arrays with d = 750 nm, prepared by the patterning of Au film.

 

Fig. 3. (a) – (d) SEM images of SRR patterns with different value of d parameter (0, 250, 500, and 750 nm) used for the tuning of the magnetic resonance. (e) FT-IR reflectance spectra of fabricated patterns. Peaks related to absorption of H₂O and CO₂ in the CNT forest structure are assigned.

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As shown in Fig. 3(e), similar to closed rings in Fig. 2, the square geometry of CNT arrays resulted in the highest measured reflectance, despite the highest absorption area, while the introduction of the dip in the square significantly decreased the reflectance for all the depths d = 250, 500, and 750 nm, even by 14% (from 60% to 52% for 4 µm wavelength). Due to the absence of the dip and the gap (Fig. 3(a)), which act as the inductance and capacitance, respectively, the generation of the LC resonance was impossible, resulting in the absorption of the radiation only in the bulk of CNT forest. On the other hand, the formation of the dip shape reduced the reflectance (increased absorption) and the results corresponded to the wave shift of the reflectance in the Ref. [60] observed by Enkrich for the dip size tuning in metallic SRRs. As shown in Fig. 3, even the smallest depth d = 250 nm caused a large reduction of the reflectance, leading to the conclusion, that even a small dip allowed for an electric coupling of the incident EM wave. Interestingly, also for the depths d = 500, and 750 nm, similar changes of the IR reflectance were noted. In polarized light, the variation of the dip size can be easily observed by the shift of magnetic resonance peaks [60]; however, in this study, the unpolarized light was used, thus, resonant peaks were not observed and only the overall effect of the dip depth variation could be seen through the change of the reflectance. As in Fig. 2, the height of the nanostructures also played an important role. Due to a small height of CNT SRRs (190 nm), the strength variation of the EM resonance, due to increased dip depth, was relatively small, allowing only for the compensation of absorption losses related to the further decrease of the absorption area. Presumably, with the increase of the height of CNTs, larger differences in the reflectance spectra would be observed between individual dip sizes.

For comparison, the SiO₂ normalized total IR reflectance of Au SRR arrays composed of 1${\times} $1 µm size structures with a height of 100 nm was also measured (Fig. 3(e)). For the dip size of 750 nm and identical geometry, the intensity of the total reflectance was increased about 4–5 times, as compared to the CNT arrays. Therefore, the usage of CNT metamaterials in applications, such as antennas, solar cells or energy storage, which require low reflectance and higher absorption of the medium, seems reasonable.

Figures 4(a)–4(d) show top-view SEM images of CNT SRR patterns (2×2 µm) with g = 1.2 µm. The growth time was precisely controlled to 2, 3, 4, and 5 s, which led to the height of SRRs of h = 0.19, 0.35, 0.75, and 2 µm, respectively. As anticipated, the height of CNT forest was increased with the growth time; however, due to the growth mechanisms of CNTs, in which the first phase of the formation of a CNT cap usually takes more time, the increase was nonlinear. For the growth time of 5 s (Fig. 4(d)), small defects of CNT SRRs were caused by the extended height of CNT forest, in which CNTs could not self-support each other anymore. In Fig. 4(e), a nonlinear decrease of the IR reflectance, usually between 25–30% for all wavelengths, was observed due to the increase of CNT forest height from 0.19 µm to 2 µm. This nonlinear behavior followed the exponential increase of the absorption coefficient with the increase of the height of the CNT forest.

 

Fig. 4. SEM images of CNT SRR patterns with the modification of the total height: (a) 190 nm, (b) 350 nm, (c) 750 nm, and (d) 2000nm. (e) Infrared reflectance spectra measured for SRR arrays. Peaks associated with the absorption of H₂O and CO₂ in CNTs were assigned.

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The dependence of the CNT height and the absorption of light was well studied [61–64]; however, the influence of the height of CNT forest SRRs was not investigated before. For the same type of CNTs, geometry, and spacing between individual SRRs, the height variation of CNT resonators seems to be the next primary reason behind changes in the total reflectance. Generally, for small incident angles, the interaction of light with CNT forest results in the reflection, absorption, and transmission of the radiation in the CNT bulk [65]. For taller CNTs, a distance of propagation of light in the forest is larger than for shorter CNTs, resulting in a higher number of absorption points, before the reflection from the bottom interface CNT-Si occurs. With the back reflection of light, the absorption of the radiation in the CNT forest body continues, and the reflectance is decreased further. Also in metamaterials, a further decrease of the reflectance of the EM radiation can be achieved by increasing the height of CNTs; however, because the self-supporting effect of neighbor CNTs also depends on the surface area of fabricated structures, a height-surface area ratio should be kept in the region, in which the crowding effect can still be utilized.

The increase of the CNT forest height could also affect the generation of resonances in SRRs by changing the surface area of capacitors, which presumably, could lead to the generation of stronger capacitance. In previous studies [66], we confirmed that the quality of walls in CNT SRRs, measured by the density and alignment of CNTs, played an important role in the control of the total reflectance. Within the region, in which the crowding effect allows for vertical alignment, without twisting and bending of SRRs, the strongest resonance should be observed. Naturally, smaller surface of capacitor plates for short height, as well as, twisting and bending of SRRs, would result in reduced capacitance, thus, weaker resonance.

While in Fig. 4, the change of the reflectance was mostly related to the height variation of CNT forests, in Fig. 2 and Fig. 3, the introduction of SRR features, such as the gap and the dip, was the main cause of the reflectance change. To understand the reasons behind the reduction of the reflectance in CNT forest SRRs, the structure-based model was proposed.

In both, metals and CNTs, a carrier transport by free electrons exists. In metals, carriers usually follow a random motion, rather than a straight path, and change their direction and velocity due to scattering in impurities, lattice, and surfaces, which results in a very short mean free path. On the other hand, due to the unique structure of CNTs, they exhibit ballistic electrical conduction along their axis, with mean free paths in the range of tenths of micrometers [67]. This important property affects the behavior of the bulk material under the light irradiation of the vertically-aligned CNT forest, allowing two possible ways of the energy absorption. Excluding the part of the light that does not directly interact with nanotubes, the energy can be dissipated in the structure in the form of heat, by increasing the vibration of the atoms in the lattice, like in most metals. The spare energy from the photons can also be transferred to material and utilized for the generation of new electrons from the structure of CNTs, resulting in the increased flow of current along nanotubes. Any electron flowing in nanotubes has a chance to excite and create new electrons and holes, which then are added to the current flow. Under favorable conditions, electrons can also transfer between nanotubes by the way of electron tunneling between nanotubes and by direct contact; however, without the external force, the flow and transfer of electrons are random and have a minor influence on the absorption. The described situation exists in any state of CNT forest, for every structure and geometry, which leads to the conclusion, that the reason behind the reduced reflectance in SRR, has its origin in the circuit shape, and its interaction with CNTs.

In solid metallic materials, the electric current in the SRR is induced by the electric field E of the incident light. Normally, the random motion of free electrons does not yield a net flow of carriers or a net current in the material, unless the external E field is applied. The distribution of the E field that penetrates the material is a function of depth, so the electric charge is mostly concentrated in the ‘top region’ of SRR. For that reason, metamaterials composed of metallic SRRs exhibit only absorption peaks at resonance frequencies, strictly controlled by the shape of resonator circuits. On the contrary, as mentioned before, the flow of the electrons along nanotubes allows for a homogenous distribution of the charge in the whole structure, not only in the top region. SRR self-inductance is caused by the flow of the electric current in the ring. This inductance gives rise to the capacitance due to enforced current flow and charge gathering in the gap. Under the external E field, SRR circuits composed of CNT forest behave in a similar way to metals, which means, that a current flow in the ring is also expected. This claim seems to have confirmation in the electric field distribution shown in Fig. 5. In Fig. 5(a), a closed ring geometry did not produce the LC resonance, showing only weak electric fields at walls perpendicular to the E field direction, while for the SRR (Fig. 5(b)), much stronger electric field was localized in the gap area, suggesting the electric charge accumulation, due to the asymmetry of SRR circuit. It was assumed, that the combination of induced current flow in CNT SRRs and vertically-aligned CNT forests can increase the absorption due to the following effects.

 

Fig. 5. Electric field distribution for (a) closed ring and (b) split ring resonator composed of CNT forest at 20 THz. (c) Schematic of the elctric current flow in the structure of the CNT SRR. Size of the simulated structures was 2×2 µm.

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First, the external E field leads to the self-induction of a directed current flow in CNT SRRs that allows accumulating the electric charge in the gap area, collecting electrons on one, and holes on the other side of the capacitor (Fig. 5(c)). Simultaneously, the number of carriers in the rest of the SRR reduces. As the light irradiation continues, this smaller saturation of carriers in the SRR circuit can cause further absorption of the energy by the increased generation of electron-hole pairs in individual CNTs. In metals, the generation of free electrons by light irradiation is negligible; thus, the increased light absorption could be achieved in the form of heat. This feature would explain why SRR circuits composed of CNTs showed reduced reflectance under light irradiation.

Another possible reason for the increased absorption in CNT SRRs is also related to the current flow induced by the E field. The LC resonance, which causes the flow of current, enhances the transport of the electron carriers between individual nanotubes in the forest, by both direct contact and tunneling effects. This enhanced transport of carriers may support the transfer of energy to nanotubes, which due to the structure of the CNT forest, were at the bottom of the forest, or completely separated from other nanotubes. This process would result in the increased absorption of the light in CNTs, which normally would receive only a minor part of the light energy. With the improved transport of charge in the CNT forest, the absorption of the energy in the structure becomes more homogenous, thus, the chance that the light will be transmitted or reflected from CNT forest decreases.

Under the irradiation of unpolarized light source, and due to the fact, that only one orientation of SRR arrays was fabricated, a preference towards one polarization existed, thus, only part of the component E field was used for the self-induction of electric current. This preferred orientation resulted in the observation of only minor or no absorption peaks in the CNT SRRs. Also, due to the absorption of light by excitonic and free-carrier absorption processes, and very high carrier mobilities, CNTs typically exhibit broadband absorption of the radiation, thus, even in the polarized light, absorption peaks might not be well defined. For that reason, in the next part, simulations of SRRs under polarized light were investigated.

3.2 Simulations of SRR circuits in polarized light

Figure 6 shows simulated reflectance, transmittance, and absorbance responses for the gap width modification from 0 to 1.2 µm (same as in the experiment Fig. 2). The electric field E of the incident beam was polarized linearly, so the E field was parallel to the gap, perpendicular to planes of the capacitor. Due to the applied polarization, the E field of the IR beam could couple to the capacitance and resonance peaks could be observed in simulated response spectra. Due to the absence of the gap in the closed ring geometry, primarily, single resonance could be observed at about 40 THz [59]. The opening of the gap resulted in two strong resonances, as the effective capacitance was generated. In Fig. 6 these resonances can be seen at approximately 12–17 THz, and 40 THz. The first resonant mode was related to the LC resonance of the CNT SRR and originated from the electric excitation of the magnetic resonance. An electric coupling of the external E field in the gap of SRR caused the excitation of the circular current between CNTs inside SRR structures [68]. The second peak was associated with the excitation of the dipole-like plasmons in the SRR pieces next to the gap. The third-order mode excited in the CNT SRR structure was related to the quality of the metamaterials, and formed around 60 THz, gradually changing shape with the increase of the gap size. Another resonant mode, observed approximately at 80 THz, appeared also for the closed ring geometry and increased its intensity up to the gap size of 0.6–0.9 µm, after which almost completely vanished, leaving a small trace in the simulated transmittance spectra at about 85 THz. It was assumed, that the evolution of the peak was related to the change of the first diffraction order into the SiO₂ substrate from an evanescent to a propagating one. Finally, in the range of 100–130 THz, a very broad peak without significant changes was observed in the same position and could possibly be associated with geometrical parameters of SRRs, such as total length of the coil and the ratio of height to width [58,59,69].

 

Fig. 6. Simulated reflectance, transmittance, and absorbance responses for CNT SRR metamaterial arrays in the dependence of the gap size, from 0 to 1.2 µm.

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In Fig. 6, the calculated absorbance response showed, that despite some minor fluctuations, the overall absorption of SRR arrays for the gap size of 0.3 and 0.6 µm was the highest, while the absorption of closed rings and the 1.2 µm-gap-width SRR was the lowest, which was in agreement with the results in Fig. 2. Also, excluding the resonant peaks, the total reflectance was also visibly reduced.

As shown in Fig. 6 for the closed ring geometry, a wide high reflectance peak was observed between 20-50 THz which also in the experiment (Fig. 2(f)) showed a large increase of the reflectance in the similar region between 30-45 THz. Then, for the 50-60 THz region, the simulated values of the reflectance had similar intensity, which was also observed as similar reflectance values in the experiment. For larger frequencies up to 100 THz, the intensity of reflectance and transmittance peaks changed dramatically, influencing the results, which is also visible in the experiment in Fig. 2. For both, the simulation and the experiment, the introduction of the gap caused an overall increase in the absorption for all of the SRRs, while the increase of the g, gradually reduced the absorption, from 0.3 µm to 1.2 µm.

It should be noted that the simulated responses and the experiment, despite many similarities described above, were also quite different in some parts. The variation between simulation and experiment potentially arose from the fact that the SRR circuit simulation was simplified to anisotropic medium with complex optical indices instead of the original CNT forest bulk material. More detailed simulation of SRRs composed of millions of nanotubes, including CNT-CNT interactions in macro scale, different alignment, chirality of nanotubes, etc. could possibly produce a more accurate image of the real material; however, at the same time, more computational power than the commercially available would be required. Also, potentially the polarization of the light in the simulation produced clearer resonance peaks in the response, which were not observed in the experiment.

Therefore, in conclusion, despite some deviation of the results, the simulation of the ideal anisotropic CNT medium were in relatively good agreement with the metamaterial effects observed in the actual experiment of the gap size modification.

Figure 7 shows simulated reflectance and transmittance responses for CNT SRRs, for the modification of the d size from 0 to 0.8 µm. The EM field with the k perpendicular to the SRR plane and the E field oriented parallel to the gap allowed for the excitation of the magnetic resonance. The asymmetry of resonators in the direction of the E field excited circular currents in CNT SRRs, resulting in the magnetic resonances at appropriate frequencies. In Fig. 7, for the square geometry (without dip), the simulated transmittance and reflectance showed generally one well-pronounced resonance at about 80–100 THz, possibly related to the excitation of the surface plasmons along the square surface parallel to the external E field. Additional peaks observed at 120–140 THz were associated with the higher-order excitation of the surface plasmons in the square shape. With the introduction of the dip in the square geometry, additional resonant peaks gradually appeared. The first resonant peak was observed at 60 THz for 0.2 µm dip depth and shifted to lower frequencies, down to about 30 THz for 0.8 µm depth. The increase of the dip size and the length of the SRR arms at the same time, resulted in the shift to lower frequencies (Fig. 7), due to the plasmon resonance of the single wire, in which the LC resonance was generated by the oscillating current in the SRR structure, due to the electric coupling in the gap. With the increase of the total length of the SRR wire, the ratio of the structure length to height also increased, resulting in the generation of a strong resonance shift toward lower frequencies. The decrease of the total length of the SRR wire, the shift of resonance peaks towards higher frequencies was observed. It should be noted, that the thickness of the wire, especially at the backside of the SRR structure, had a minor influence on the observed phenomena.

 

Fig. 7. Simulated reflectance, transmittance, and absorbance responses for CNT SRR metamaterial arrays in the dependence of the dip depth, from 0 to 0.8 µm.

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Similar behavior was observed for the second resonant peak, noted at 85 THz for 0.2 µm and shifted to about 70 THz for 0.8 µm. As a shift towards lower frequencies was observed, it was assumed that the second peak was originated from charge oscillation in the SRR structure, which excluded the plasmon origin of the peak. For the plasmon excited resonance, no change of the position of the peak would be observed. Third and fourth resonant modes were also observed at 100 and 110 THz, respectively, after the introduction of the dip into CNT structures. Finally, a broad resonance peak between 120–140 THz, which remained at the same position for all discussed geometries, was associated with a charge density oscillations in the arms of the SRR, perpendicular to the E field. The broad peak was less visible for the square geometry, as the plasmon was no longer excitable.

The observations of the simulated responses showed a significant decrease in the reflectance and a simultaneous smaller increase of the transmittance, which followed the increase of the d size (Fig. 7). The absorption of SRR arrays was also calculated showing an overall improvement of absorption for the SRR as compared to square shapes; however, due to numerous peaks of various intensity, a clear summary, which of the presented SRR structures had the highest absorption, was impossible. Additionally, a comparison with the experimental results in Fig. 3. showed that the initial values of the reflectance, which were visibly reduced with the introduction of the dip, were also observed in the simulation. In Fig. 7, for frequencies above 60 THz, the formation of resonance peaks of very low reflectance was observed, and while the difference between cases of different dip depth was relatively small, the initial translation from 0 to 0.2 µm gap and further was very significant. Therefore, also in the calculated absorption spectra, this large translation step was observed in the beforementioned frequency range.

As mentioned before, the reason behind the fluctuation of the results between the simulated response and the experiment had its origin in the simplification of the simulation and the incident light polarization. Resonance peaks in the simulation were easily studied due to the usage of a simplified anisotropic circuit in the polarized light, while the CNT bulk structure in the experiment was treated with the unpolarized light source.

Figure 8 shows simulated reflectance and transmittance responses for CNT SRRs with a height modification h = 0.19–2 µm, for the E field polarization parallel to the SRR gap. As can be seen, various peaks were observed in spectra, with the highest intensity at about 17, and 35 THz; however, as compared to previous simulations, no new peaks were noted, so the detailed analysis of resonance peaks was omitted. The change of the height was followed by the change of the SRR length-height ratio, resulting in the shift of resonance modes, which was described above, in the analysis of Fig. 7. Despite the shift change related to the SRR length-height ratio, also the increase of the area of capacitor plates was observed, resulting in the increase of the capacitance and the generation of stronger resonances. With the increase of the SRR height, a very significant decrease in the transmittance and also a variation of the reflectance were observed, which contributed to the increase of the absorption. Interestingly, similar to the reflectance change in Fig. 4, the increase of the absorption in Fig. 7, followed a similar nonlinear trend, which could confirm the experimental observations. Also, for the experiment (Fig. 4(e)), the shape of the reflectance curve translates from a relatively constant value (about 90%) for 0.19 µm height, to a broad peak between 50–120 THz, for 2 µm height. Interestingly, the formation of similar peaks in the simulation was observed in absorbance response and was originated from the change of the reflectance curve shape, due to the increased intensity of resonance peaks.

 

Fig. 8. Simulated reflectance, transmittance, and absorbance responses for CNT SRR metamaterial arrays in the dependence of the height, from 0.19 to 2 µm.

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4. Conclusions

The investigation of the total reflectance of patterned CNT forest metamaterials in the IR regime was presented. Results of fabrication of small size (linewidth ∼200 nm) CNT SRRs on the pre-deposited Fe catalyst were shown. The effect of the modification of the gap (split) size g, the dip depth d, and the height h was studied and showed considerable influence on the IR reflectance.

From the experiment under unpolarized light, it was concluded that:

Appendix A: CNT forest characterization

In this appendix, as shown in Fig. 9, we present the Raman spectra measured for pristine CNT forest grown according to previously optimized conditions, together with the results after the patterning of SRR structures, for various growth time.

 

Fig. 9. Growth time dependent Raman spectra of (a) as prepared CNT forest, and (b) patterned CNT forest.

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Appendix B: CNT SRR metamaterials composed of shorter CNTs

In this appendix we present the additional result of SRR metamaterials, fabricated from shorter CNT forest, to supplement the discussion of the gap size carried out in Fig. 2. As shown in Fig. 10, the decrease of the total height resulted in larger differences between the total reflectance results.

 

Fig. 10. (a) Top view SEM images of CNT SRR metamaterial arrays with the height of 2 µm, and the gap size of 0, 0.6, and 1.2 um. (b) Reflectance of fabricated patterns, and (c) values of reflectance for 2650 cm⁻¹ wavenumber.

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Funding

Japan Society for the Promotion of Science (17K06205, 24560050); joint research project of the Institute of Laser Engineering, Osaka University (2019B2-FURUTA). .

Acknowledgments

The authors would like to thank Mr. K. Kato and Mr. T. Phan for their support in FT-IR observations, and Mr. Hiroki Miyaji for experimental support.

Disclosures

The authors declare no conflicts of interest.

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