Abstract
Spatial dispersion effect of aligned carbon nanotubes (CNTs) in the terahertz (THz) region has significance for both theoretical and applied consideration due to the unique intrinsically anisotropic physical properties of CNTs. Herein, we report the angular dependent reflection of p-polarized THz wave from vertically aligned multi-walled CNT arrays in both experiment and theory. The spectra indicate that the reflection depends on the film thickness of vertically aligned CNTs, the incident angle, and the frequency. The calculation model is based on the spatial dispersion effect of aligned CNTs and performed with effective impedance method and the Maxwell-Garnett approximation. The results fit well with the experiment when the thickness of CNT film is thin, which reveals a coherent superposition mechanism of the CNT surface reflection and CNTs/Si interface reflection. For thick CNT films, the CNTs/Si interface response determines the reflection at small incident angles, while the CNTs surface effect dominates at large incident angles. This work investigates the spatial dispersion effect of vertically aligned CNT arrays in the THz region, and paves a way for potential anisotropic THz applications based on CNTs with oblique incidence requirements.
Highlights
THz wave region locates at the “gap” between the microwave region and the infrared region with broad prospect of applications[21]
Such as the spatial dispersion effect[22], which has been proposed to be found in wire media[23], is possible to be observed in aligned carbon nanotubes (CNTs) in THz region
Aligned CNT arrays with different thicknesses are synthesized on high-resistance silicon (HR-Si) by a floating catalytic chemical vapor deposition (CVD) method
Summary
Morphology characterization of the CNT samples with SEM and TEM. CNT arrays with different thickness are grown on HR-Si substrates by floating catalytic CVD as described in the Methods part. In order to reveal the underline mechanisms, Fourier transformation of the THz pulses from 1 to 9 ps in time domain have been performed, and the resulting frequency-dependent THz relative amplitude reflection spectra are shown in Fig. 5 with elevated incident angles 15°, 30°, 45°, 60° and 70°. When the incident angle becomes larger than 60°, sample thickness and frequency dependent reflection enhancement will appear. When the thickness is large enough such as CNT4 and CNT5, the reflection spectra seem to be flat in frequency domain These oblique incidence dependent reflection phenomena is originated from the anisotropic THz dielectric functions of CNT arrays. Because the experimental results have eliminated the internal reflections from the HR-Si substrate (as described in the time-domain data), the effective impedance of CNTs/HR-Si system can be written as[36]:
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