Surface plasmons have a fundamental role in the dynamics of photon–electron interactions and in optical metamaterials. Terahertz (THz) time-domain spectroscopy was used to characterize the complex dielectric constant, index of refraction, and conductivity of super-aligned, free-standing, multi-walled carbon nanotube films over the range 0.2-2.5 THz. These complex parameters were in excellent agreement with Maxwell-Garnett and Drude-Lorentz models. In addition, surface plasmon excitations in engineered, subwavelength, multi-walled carbon nanotube metasurfaces were examined. The observed surface plasmon resonances, reproduced by simulation, could be changed over the THz frequency range by altering the lattice constant of the arrays. The THz transmission was enhanced at the resonance peak. Overall, the results indicate potential applications for THz metasurfaces based on super-aligned, free-standing multi-walled carbon nanotubes.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Surface plasmon polaritons (SPPs) are surface electromagnetic waves originated from the resonance interaction between the free electrons of the conductor and the electromagnetic field of the light [1,2]. Renewed interest in SPPs comes from the patterned conductor on the micro/nanometer scale. SPPs-assisted resonant enhancement of THz transmission through subwavelength aperture arrays has been of great interest recently because of potential applications in imaging, sensing, and spectroscopy [3, 4]. Most subwavelength aperture arrays have been based on metallic or semiconductor films, although grapheme, carbon micro-fibers and single-walled carbon-nanotube (SWCNT) network films have been shown to enhance THz transmission [5–7]. Due to their unique mechanical, optical, and electrical properties, multi-walled carbon nanotubes (MWCNTs) have been very useful in a myriad of optical and electronic applications, and can carry high current densities along their axes. Large-area carbon nanotube films have been used as modulators, sensors, and displays because of their transparency, conductivity, and anisotropic properties [8, 9].
As a novel nanomaterial, the electrical conductivity, dielectric constant and transmission properties of CNT films have attracted much attention in order to explore the potential in the field of applications of THz waves, such as polarizers, electromagnetic interference shielding (EMI) [10, 11]. Li et al demonstrated SWCNTs-polymer composites can be used as EMI shielding materials, and concluded that the shielding efficiency of SWCNTs with larger DC conductivity was much larger than that of SWCNTs with small DC conductivity . Kim et al also verified that the shielding efficiency of MWCNTs-PMMA composites increased with DC conductivity . The transparent SWCNT-PET exhibited good shielding efficiency in the THz range . It is noted that the shielding efficiency of the film is strong correlated with the THz conductivity and the application of super-aligned MWCNTs as THz shielding materials has not been considered in detail. Therefore, it is necessary to research THz conductivity and transmission properties of aligned MWCNT films.
Here, THz time-domain spectroscopy was used to characterize the complex conductivity and dielectric response of a 5-μm-thick, super-aligned, free-standing MWCNT films in the absence of substrate effects. Compared with the transmission properties of unaligned MWCNTs film, super-aligned MWCNTs film exhibits an anisotropic transmission behavior. Also examined was resonantly enhanced transmission of THz waves through free-standing carbon nanotube metasurfaces perforated with two-dimensional (2D), periodic square aperture arrays. These arrays were fabricated in 10-mm × 10-mm areas of 5-μm-thick, free-standing MWCNT films. Three square aperture arrays were fabricated with different periods and the same aperture size.
2. Samples fabrication and experiments
Vertical, super-aligned MWCNT arrays were synthesized on a substrate by low-pressure chemical vapor deposition [15–17]. The important feature of the CNT arrays was that a continuous, 300-μm-thick, unidirectional sheet, composed of a thin layer of parallel-aligned MWCNTs, could be directly drawn out from the super-aligned MWCNT “forests.” CNTs in the film were horizontally aligned along the direction of the draw and were joined end-to-end by strong van der Waals forces. The MWCNT film thickness could be controlled by stacking several layers of sheets. In this way, a 5-μm-thick free-standing film consisting of 100 sheet layers was fabricated on a square polytetrafluoroethylene frame. Figure 1(a) shows a MWCNT film without a pattern. The MWCNTs were highly aligned. By using laser-machining, 2D square patterns with various periods were produced on the MWCNT films, as shown in the scanning electron microscope (SEM) images in the inset of Fig. 2(b). Figure 1 (c) shows the high-resolution TEM image of MWCNTs including 8 nested tubules.
For THz time-domain spectroscopy (CIP-TDS, Daheng New Epoch Technology Inc. Beijing, China), a GaAs emitter and a ZnTe detector were used. A mode-locked Ti: sapphire laser with an average power of 500 mW at 800 nm was used to generate the THz pulses. The transmitted pulses were detected by an electro-optic technique. The scanned delay time is 150ms and the spot size of THz focused beam is ~3mm in our experimental system. The system was enclosed in a box filled with dry nitrogen gas to reduce water vapor absorption.
3. Results and discussions
Figure 2 shows a THz input reference pulse incident on the sample. The THz output pulse (labeled by perpendicular or TM and parallel or TE polarizations) transmitted through the sample in Fig. 2 was normalized with respect to the THz input reference pulse. The reduced amplitude was due to absorption by the sample and to refection losses at the surface. The ratio of the peak of the TM pulse to that of the TE pulse was approximately 7:1 in Fig. 1 (a), and manifests the anisotropic character of the film. The anisotropic character of the film is decided by the unique structure of carbon nanotubes within film. As shown in Fig. 1, the length of CNT in axis is much large than that in radial direction. This anisotropic structure leads to the different electric and optical properties along or perpendicular to the tubes. Such a property of highly oriented CNTs can be used as a polarization analyzer for THz wave.
Frequency-domain spectra obtained through fast Fourier transformations of the time-domain signals in Fig. 2 contained phase and amplitude information at different frequencies. The ratio of the sample spectrum to the reference spectrum was used to determine the complex index of refraction vs. frequency. The detailed relationship between the complex dielectric constant, conductivity, and complex index of refraction was described previously .
There has been no recently reported analysis of the dielectric parameters for a single-layer, free-standing MWCNT film in the THz frequency range. Here, the complex dielectric constant, conductivity, and complex index of refraction of free-standing MWCNT films for TE and TM polarization were analyzed. As shown in Fig. 3, the index of refraction and conductivity decrease gradually with increasing frequency over the range 0.2–2.5 THz. The index of refraction in TE polarization case was larger than that in TM polarization case.
Since the index of refraction is dependent on phase retardation, the MWCNTs for TM polarization [shown in Fig. 3(d)] further affect the THz wavefront phase. The concentration of carbon nanotubes was sparse due to the relatively low volume density, and the network of crossed carbon nanotubes in the MWCNT thin films had both metallic and very minors semiconducting CNTs. The orientation of carbon nanotubes presented in both directions in the MWCNT films (even very minors along one direction, it still cannot be eliminated), and the MWCNT films were filled with air. It was difficult to measure the apparent density of the film. Therefore, to determine the electron and phonon parameters of the MWCNT films, the samples reported in this work have to be treated as composite material, the experimental results were fitted by combining the Maxwell-Garnet (MG) and Drude-Lorentz (DL) models as follows :
The fit for the real part of the permittivity was as good as that for the imaginary part [Figs. 3(b) and 3(e)]. The negative value of the real part indicated that the MWCNT films had a quasi-metallic behavior and a broad absorption spectra for direct transitions across the electronic energy gap . Table 1 lists the best-fit parameters for the data using MG theory combined with DL model. The fits are plotted in Fig. 3 as solid lines that agreed well with the experimental data points. In the fits, the plasmon frequency was ωp/2π = 4.78 THz for TE polarization, which was larger than that of semiconductors [21,22]. The damping rate γ was 0.03 THz for TE polarization, corresponding to collision times τ = 33.3 ps. Because ωp was proportional to , the MWCNTs had a higher carrier density n0 for the TE case, which was verified by the TE polarization conductivity in Fig. 3 (c). Since the lower signal-to-noise ratio of THz-TDS at lower frequencies, we provide the experimental results in the THz range from 0.25 THz to 2.5 THz. In fact, THz conductivity peak can be achieved by using our parameters in Table 1 at much lower frequencies.
In Table 1, the plasmon frequency was reduced to 1.83 THz for TM polarization case; thus, the carrier density was also reduced. The higher damping rate in TE polarization case indicated that there were many bonding electrons available. The effective collision length was estimated by l = νfτ μm, which was slightly smaller than the length of the MWCNTs in the super-aligned arrays (νf is the Fermi velocity of nanotubes) . Although the length of the MWCNTs was a few hundred micrometers in the films, the effective collision length of the nanotubes was determined by their cross-junction structure, which determined the collision time. Figure 1(b) revealed that the films had many aligned nanotube bundles. The larger bundles were produced from the arrays of longer nanotubes. In nanotube bundles, the large number of contacts between adjacent nanotubes provided extra electron transport paths and changed the effective collision length. Additionally, the effective DC conductivity σDC (σDC = ε0ωp2/γ) of the films at zero-frequency was approximately 2.65 × 103 S/cm and 5.85 × 102 S/cm for TE polarization and TM polarization, respectively, where ε0 is the vacuum permittivity. Correspondingly, the effective average carrier density (n0 = σDCmeγ/e2) in TE polarization and TM polarization was 2.86 × 1023 m−3 and 4.16 × 1022 m−3, respectively. We compared our THz conductivity to the reported results . We find that the DC conductivity of the anisotropic MWCNT films is between the homogenous MWCNTs film and the monolayer grapheme, but that the DC conductivity is much larger than that of grapheme-like layer .
It is the first time that we extract the optical parameters of highly aligned free-standing MWCNT films in the THz frequency range. Previous reported results are focused on the MWCNT films based on substrate. It is found that the plasmon frequency is lower than that of the MWCNT films based on silicon substrate . However, the difference between these two results is not necessarily conclusive since the CNTs have different surface morphology (including individual CNTs or a rope of CNTs). Especially, it is very difficult to control their structure and electrical character during each growth of CNTs.
The polarization-dependent properties of the MWCNTs sheets could be used as subwavelength plasmonic THz devices. Plasmon excitation in MWCNTs film aperture arrays could also be made by engineering the lattice constant. The MWCNT metasurfaces were patterned via laser-machining into 2D periodic arrays of subwavelength apertures. In Fig. 4(d), the area of the apertures was a × b μm2 and the lattice constant components were px and py in x and y axis direction, respectively. The three samples in Fig. 4 were patterned with identical aperture dimensions (a = b = 150 μm) and thickness, but different lattice constants.
Figure 5 plots THz transmission through three arrays with different lattice constants. In Fig. 5(a), excitation of the spoof surface plasmon mode at the MWCNT metasurface-air interface was observed when the THz polarization was parallel to the CNT axes. When the THz polarization was perpendicular to the CNT axes, the spoof surface plasmon mode resonance disappeared. Similar behavior was observed in the other samples [Figs. 5(b) and 5(c)]. The reason for such phenomenon is the unique electronic properties of CNTs due to the quantum confinement of electrons normal to the CNT axis. In the radial direction, electrons are confined by the monolayer thickness of the grapheme sheet and they can only propagate along the CNT axis under the case of this quantum confinement. Therefore, the spoof surface plasmon wave can be excited in TE polarization.
The resonance frequency fres shifted to lower energy with increasing lattice constant: 1.27, 1.0, and 0.83 THz for lattice constants of 200, 250, and 300 μm, respectively. Thus, excitation of the resonance spoof surface plasmon of these MWCNT metasurface could be adjusted by changing the lattice constant, enabling manipulation and control of THz waves. To understand the resonance characteristics of the THz surface plasmon, factors determining the resonance peaks were analyzed. According to the dispersion relations of surface Plasmon ) and the condition of the momentum conservation where, k0 is a free space wave-vector, ksp is the surface plasmon wave-vector, and Gx and Gy are the reciprocal lattice vectors with |Gx| = |Gy| = 2π/p, the resonance frequency is given by (), where m and n are integers, p is the lattice constant, c is the speed of light in vacuum, and εmet and εsub are the metal and substrate permittivities, respectively . Here, εsub = εair ≈1. However, the resonance peak did not follow the above expression, but instead was governed by ([m, n] = [ ± 1, ± 1]) and, more importantly, its transmittance increased. was the effective dielectric constant in the near-field apertures. This was the main result of this work: the prediction of accurate resonance peaks in a free-standing nanotube film. The resonance peaks in Fig. 5 for the three samples obey the latter expression. The first-order [ ± 1, ± 1] spoof surface plasmon mode was excited in the subwavelength free-standing MWCNTs sheet arrays. This differed from previous results for subwavelength MWCNTs sheet arrays supported on silicon substrates . The enhancement factor (EF) for the transmission of the resonance peaks can be defined as the ratio of the resonance peak amplitude transmission to the saturated transmission amplitude . Thus, EF = 1.83, 2.25, and 2.33 for the 200-μm, 250-μm, and 300-μm lattice constants, respectively.
Numerical simulations were performed by using the finite integral technique in CST Microwave Studio software. This method provides quantitative information on the spoof surface plasmon distributions in MWCNT arrays. In the simulation model, the MWCNT films have been considered as macro-scopic bulk material rather than nanotubes with specific shapes and orientations. The dielectric constants shown in Figs. 4(b) and 4(e) have been used in the simulation. Periodic boundary conditions were applied along x and y axes. Figures 5(d)-5(f) plot the simulated transmission spectra of MWCNT aperture arrays with varied lattice constants. Although the transmittance in the simulated results was slightly larger than what was observed, the simulation results adequately reproduced the experimentally observed spectra. This slight discrepancy did not affect the explanation of resonance transmission.
In order to show clear signature of spoof SPPs, the dispersion curve of spoof SPPs provided by the dispersion relation is shown Fig. 6. It is noted that the spoof SPPs mode is located beyond the light line and approaches the light line asymptotically at lower frequencies, which also indicates that the momentum mismatch problem has been overcome. The spoof SPPs has greater momentum than a free space photon of the same frequency, meanwhile, it has shorter wavelength.
Figure. 7(a) shows the surface current, E-field, and H-field distributions in a MWCNT sheet with a 200-μm lattice constant. The E-field distribution revealed a dipole nature and its localized properties. Figure. 7(a) also indicates that the field amplitude maxima were at two sides of the MWCNT sheet. The intensity of the E-field was much larger than the THz transmittance enhancement, which implied that the THz wave was highly concentrated on two sides of the square aperture, but only a small fraction of the THz wave was transmitted. The transmitted THz electromagnetic fields exhibited near-field effects from the array. Inset in Fig. 7(a) shows the shape of electric field of SPPs at the CNTs film/air boundary. As expected, a dome-like shape of the electric field has been observed. The dependence of transmission on the angle of incidence is shown in Fig. 7(b), where the transmission was mapped in response to obliquely incident THz waves for the 250-μm lattice constant. The transmission could be tuned for angles up to 65°. Beyond 40°, the transmission degraded rapidly, and the resonance frequency decreased with increasing incident angle.
Free-standing MWCNT films were fabricated and precise effective dielectric constants were determined over a broad THz range. Theoretical results obtained by combining the MG and DL models fit the experimental data. Surface plasmon resonances in the MWCNT films could be tailored in structure-engineered, subwavelength MWCNT square arrays, which represented the simplest of THz metasurfaces. These results demonstrated that aligned free-standing MWCNT films have potentially important and diverse applications in THz metamaterials. Their properties could be generalized to more sophisticated metasurfaces based on MWCNT films. It is anticipated that the resonances could become even stronger in square arrays in proportion to an increased conductivity in higher-quality, super-aligned, laser-trimmed MWCNT metasurfaces . Moreover, the transmission of the metasurface could be much higher than the current values by using densification.
National Natural Science Foundation of China (NSFC) (61201075, 61377036, 60971015).
The authors thank Dr. Yi Zhang (Daheng New Epoch Technology Inc. Beijing, China) for his kind support with the TDS measurement.
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