⇦Chinese Physics Letters, 2019, Vol. 36, No. 12, Article code 124205 Terahertz Lens Fabricated by Natural Dolomite * Si-Bo Hao (郝思博), Zi-Li Zhang (张自力)**, Yuan-Yuan Ma (马媛媛), Meng-Yu Chen (陈梦宇), Yang Liu (刘阳), Hao-Chong Huang (黄昊翀), Zhi-Yuan Zheng (郑志远)** Affiliations School of Science, China University of Geosciences, Beijing 100083 Received 29 July 2019, online 25 November 2019 *Supported by the National Natural Science Foundation of China under Grant No 61805214, and the Fundamental Research Funds for the Central Universities under Grant No 2652017142.
**Corresponding author. Email: zlzhang@cugb.edu.cn; zhyzheng@cugb.edu.cn Citation Text: Hao S B, Zhang Z L, Ma Y Y, Chen M Y and Liu Y et al 2019 Chin. Phys. Lett. 36 124205    Abstract Optical operations have served as the basis of spectroscopy and imaging in terahertz regimes for a long time. Available lenses are practical tools for modulations. We fabricate a kind of biconvex lens from the natural dolomite cluster. The lens works well at 0.1 THz based on the relatively high refractive index and low absorption coefficients. Compared with the lens fabricated by a dolomite stone, such a lens can focus dispersive terahertz beam efficiently in terahertz imaging systems, which indicates that natural minerals hold promising applications in terahertz optics. DOI:10.1088/0256-307X/36/12/124205 PACS:42.25.Bs, 41.85.Ew, 81.05.-t, 42.79.-e, 42.79.Bh © 2019 Chinese Physics Society Article Text Recently, interest in the terahertz frequency range (from 0.1 to 10 THz) has arisen in sensing, imaging and spectroscopy.[1–4] One of the important aspects of extending the applications of terahertz waves is that manipulating terahertz waves depends on but is not limited to wave plates, gratings and waveguides.[5–8] Among these optical devices, the lens is a fundamental component that allows us to focus and collimate terahertz beams. In a terahertz system, commercial lenses are fabricated with popular polymers, such as polymethylpentene (TPX), polytetrafluoroethylene (PTFE) and high-density polyethylene (HDPE). However, the dielectric losses for these materials increase quadratically with the frequency in this band.[9] Meanwhile, the process to manufacture a lens with a long focal length and a high thickness is automatic and costly due to the low refractive indices. For example, the indices of PTFE and HDPE are 1.45 and 1.58, respectively.[10] To overcome these challenges, some natural minerals have rather uniform and high refractive indices of about 2 to 3, and have low absorption losses in the terahertz frequency range, which could be deemed as flexible alternatives to fabricate lenses with shorter focal lengths and thinner thicknesses. Moreover, due to the feature of being easily accessible and economical, natural minerals are attractive for terahertz optical applications. In this Letter, two kinds of biconvex terahertz lenses made from dolomite stone and its cluster crystal are designed, fabricated, and characterized. Terahertz time-domain spectroscopy (THz-TDS) measurement is first used to determine the optical properties of the refraction index and absorption coefficients. In light of these results, dolomite lenses are designed and fabricated. Then, the focusing performances of these two lenses are characterized using a plane-scanning imaging system. It is suggested that the mineral optical components are of desirable exploitations in the terahertz range.
cpl-36-12-124205-fig1.png
Fig. 1. Frequency-dependent refractive index and absorption coefficients of dolomite cluster and dolomite stone. The circle and the triangle represent the extracted refractive index and absorption coefficients of dolomite cluster and dolomite stone, respectively.
The dolomite stone and its cluster crystal are both original minerals mined from Zhejiang Linan, of which the main constitutes determined by x-ray fluorescence (XRF) are summarized in Table 1. According to these results and the results of previous studies, minerals composed of SiO$_{2}$, CaO and MgO basically exhibit the balance of less absorption while highly refractive to the terahertz wave.[11,12] To decide the optical parameters of the above two minerals, pellets with diameter of 13 mm and thickness of 1.4 mm were tested by THz-TDS. The detailed THz-TDS experimental configuration was depicted previously.[13] The sample cell with and without dolomite pellets was measured under the transmission pattern to obtain the sample and reference data, respectively. By performing the fast Fourier transformation (FFT) and comparing the reference and sample data, the frequency-dependent absorption coefficients and refractive index can be calculated as shown in Fig. 1. Compared with that of dolomite cluster-crystal, a little higher refractive indices of dolomite stone spans the spectral range from 0.2 THz to 1.4 THz, while fewer impurities of cluster crystal contribute to the absorption loss decreasing around twice from 19.4 cm$^{-1} $ to 9.3 cm$^{-1} $ at 1.0 THz.
Table 1. Percentages of the main constituents of natural dolomite.
Compound Percent composition (%)
CaO 68.49
MgO 20.01
SiO$_{2}$ 9.44
Others 2.06
To pick out the candidate, the design of two kinds of lenses was implemented using the lens maker's formula given as follow: $$ f=(n-1)^{-1}\Big(\frac{1}{R_1}-\frac{1}{R_2}\Big)^{-1},~~ \tag {1} $$ where $f$ is the focal length, $R_{1}$ and $R_{2}$ are the radiuses of curvature and $n$ is the refractive index. Subsequently, two kinds of lenses with the same diameter of 40 mm were fabricated (Fig. 2(a)) by following the conventional lens-making procedure. In brief, the dolomite blocks were shaped into cubes by cutting the side with a grinding machine. Both faces of the lens were then ground into typical lens shapes with the same spherical curvature radius of $R = 62$ mm and polished. Figure 2(b) shows the beam tracing diagram of the lens. The thickness of the lens at the center, $t_{\rm c}$, is 4.6 mm, and $t_{\rm e}$ at the edge is measured to be 1.2 mm. According to Eq. (1), the theoretical focal length of the designed lens is about 31 mm.
cpl-36-12-124205-fig2.png
Fig. 2. Display of biconvex lenses (a) and beam tracing diagram of the lens (b).
A plane-scanning measurement was conducted to detect the intensity distribution of the terahertz beam focused by mineral lenses. An avalanche diode (TeraSense Inc) delivers a 100 GHz Gaussian beam used as the wave source. The beam was collimated by a spherical lens, then directed to our mineral lenses and captured by the pyroelectric camera (12.8 mm $\times$ 12.8 mm imager, 160 pixels $\times$ 160 pixels) mounted on a motorized $X$–$Y$ translation stage to obtain the intensity distribution as shown in Fig. 3. The cluster-crystal lens (Fig. 3(b)) is capable of focusing the terahertz beam better than the stone lens (Fig. 3(a)) at almost the same focal point. Also, with the full width at half maximum (FWHM) of about 3.1 mm, the radial intensity distribution of cluster-crystal lens (Fig. 3(d)) shows better Gaussian-fitting profiles than Fig. 3(c), which is in accordance with Figs. 3(a) and 3(b). Consequently, cluster crystal of dolomite is more available in fabricating lenses.
cpl-36-12-124205-fig3.png
Fig. 3. Gaussian beam intensity images of the stone lens (a) and the cluster-crystal lens (b) at the focal point. The corresponding Gaussian fitting curves and the measured radial intensity distribution of the stone lens (c) and the cluster-crystal lens (d).
cpl-36-12-124205-fig4.png
Fig. 4. Two-dimensional beam intensity images of the cluster-crystal lens obtained at five different positions (a) and the axial maximum intensity distribution along the propagation distance (b).
To further investigate the variances of the focal spot size along the propagation direction, two-dimensional beam profiles of the cluster-crystal lens at specific positions are shown in Fig. 4(a). By varying the distance between the detector and the surface of the lens, five specific positions along the axial direction are chosen in steps of 5 mm over a range from 21 to 41 mm due to the short focal length. It can be seen that the spot size reaches its maximum value at the distance of 31 mm, which suggests that the spot energy is the most concentrated at this place. Moreover, axial intensity distributions are analyzed in Fig. 4(b). The maximum values of intensities are depicted as the red line. As can be seen, the Gaussian beam has the maximum intensity at the distance of 31 mm. This indicates that the measured focus length is equal to the theoretical design values. In summary, two kinds of dolomite lenses are designed, fabricated and characterized to be applied in terahertz beam focusing. Depending on the low absorption coefficients (5–10 cm$^{-1})$ and high refractive indices (2.0), lens of cluster-crystal dolomite has more distinct performance when collimating terahertz beams than its counterpart. The desirable focus properties (FWHM of 3.1 mm) are obtained using such a lens. It also has a series of obvious advantages, such as being inexpensive, a shorter focal length (31 mm), and a thinner thickness (4.6 mm). One could easily expand similar natural minerals over other optical components. It is believed that this work may help to open a research area aimed at using natural minerals to build novel terahertz units. References Temperature-Dependent Dielectric Characterization of Magneto-Optical Tb 3 Sc 2 Al 3 O 12 Crystal Investigated by Terahertz Time-Domain SpectroscopyTerahertz Three-Dimensional Imaging Based on Computed Tomography with Photonics-Based Noise SourceQuantitative Analysis for Monitoring Formulation of Lubricating Oil Using Terahertz Time-Domain Transmission SpectroscopyContinuous-wave terahertz high-resolution imaging via synthetic hologram extrapolation method using pyroelectric detector3D Printed Terahertz Diffraction Gratings And LensesHigh quality terahertz glass wave plates3D printed dielectric rectangular waveguides, splitters and couplers for 120 GHzPorous fibers: a novel approach to low loss THz waveguidesPlanar Porous Components for Low‐Loss Terahertz OpticsBroadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materialsCharacterizations of the Calamine tablets by terahertz time-domain spectroscopyCharacterization of the terahertz frequency optical constants of montmorilloniteInsights into the water status in hydrous minerals using terahertz time-domain spectroscopy
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