Introduction
Terahertz time-domain spectroscopy(THz-TDS) is a method used for the measurement of the real and imaginaryparts of the complex index of refraction, complex dielectric constant,and complex conductivity of materials in the 0.1 to 10 THz frequencyband [1,2]. This method was invented and developedin the last two decades by researchers in the fields of optics andsemiconductor physics. Spectroscopy permits the measurement of theabsolute values of the real and imaginary parts of the complex indexof refraction with a well signal-to-noise ratio [3]. Based on measurements of the timedependence of the electric field of a short electromagnetic pulsetransmitted through a sample, the ratio of the Fourier transformsof measured data with and without the sample yields a complex spectroscopyof the sample in the frequency domain. The major advantages of thismethod are its high potential for material characterization and nondestructivetesting, which have been demonstrated for numerous applications, suchas the characterization of anisotropic crystal structures [4], characterization of diesel fueloil, biological macromolecules [5,6], biomedical and pharmaceuticalapplications [7,8], and the detection of hazardousor illicit substances [9,10]. Tourmaline, asan anisotropic and natural crystal, has had its optical constantscharacterized by terahertz frequency spectroscopy in previous research.One purpose of our work is the further application of THz technologyin geosciences, and in particular, research into mineral structure.
Tourmaline is a complex borosilicate,its crystal structure is a trigonal system and often has three orhexagonal columnar [11,12] shape. It has beenreported that tourmaline can be used for purifying the environmentand other applications related to the health of the human body [13]. As a special mineral, the characterizationof the dielectric and optical properties of tourmaline crystal inthe terahertz band is essential, as it can be used to guide tourmalinemodification, processing, and application development.
This paper reports on an experimentalstudy of the optical properties of tourmaline in the wide frequencyband of 0.3−2.2 THz (10−73 cm-1) using THz-TDS. The results presentedhere for the first time demonstrate how THz-TDS can be used to characterizethe dielectric properties of tourmaline. Furthermore, by using theoptical constants of tourmaline as a reference you can use THz-TDSto identify other crystals and minerals.
Experimental
The spectrometer used in the experimentconsisted of two parts, a typical transmission THz-TDS system fromDaheng New Epoch Technology Inc, and a mode-locked femtosecond Tisapphire laser. The Ti sapphire laser delivers 100 fs laser pulseswith 800 nm wavelength at a pulse repetition rate of 80 MHz. The THz-emitterwas a photoconductive antenna, and the THz-radiation pulses were detectedby electro-optic sampling using a ZnTe crystal and lock-in detectionas shown in Fig. 1. The polarization direction of the terahertz pulsewas horizontal. The spectrometer was purged with nitrogen gas. Measurementswere conducted at the air-conditioned temperature of the laboratory,equivalent to (22.0±1.0)°C.
Two samples with dimensions of 1mm × 10 mm × 10 mm were cut directly from one originalcrystal, which was black and mined from Brazil. As shown in Fig. 2,the cutting direction is perpendicular to the optical axis (C axis) for sample 1, while the cutting isalong the C axis for sample 2.During measurements, sample 1 and sample 2 were perpendicular to theTHz wave as shown in Fig. 3. Furthermore, different orientations ofsample 1 along the THz horizontal polarization direction were measured;the angles were 0°, 30°, 60°, 90°, and the initialangle was randomly defined. For sample 2, two different orientations,perpendicular and parallel to the polarization direction of the THzpulse, were measured.
Fig.3 Experimental schematic diagramof (a) sample 1 and (b) sample 2. The Z axis is the direction of propagation of the THz pulse, and the P axis is the polarization direction of theTHz pulse. When rotating the sample 1, the polarization directionof the THz pulse is always perpendicular to the C axis of tourmaline. For sample 2, the polarization directionof the THz pulse is perpendicular to the C axis of tourmaline. When sample 2 is rotated by 90°, the polarizationdirection of the THz pulse is parallel to the C axis |
Results and discussion
Using the physical model of THz opticalparameters [14,15], the frequency dependencies of the index of refractionand absorption coefficient were calculated from the time-domain THztransmission data. The absorption and the index of refraction versusfrequency, for sample 1, are shown in Fig. 4. The data was consideredaccurate only up to 1.8 THz. Above this frequency, the absorptionof the weak higher frequency components is so strong that the attenuated,transmitted spectral components became obscured by the detected systemnoise. The terahertz pulse vibration direction is vertical with respectto the C axis. Under this case,this pulse is an ordinary pulse. The dispersion of tourmaline in thisband can be characterized by the index of refraction and the frequency.Based on the ordinary ray refractive index of 2.717 at 1 THz, and2.737 at 1.8 THz, a quadratic relationship between the refractionindex and the frequency was found. These results indicate that thevariation of the refractive index with frequency is in agreement withthe normal dispersion relation.
There is a relationship between vibrationabsorption and the tourmaline structure. In this experiment, the structureperpendicular to the C axis canbe characterized by the absorption coefficient at different anglesas shown in Fig. 4(b). It can be seen that the absorption coefficientsbetween the 0° and 60° plots, as well as between the 30°and 60° plots, present similar values. This is consistent withthe triangular structure of the tourmaline.
According to the characteristicsof terahertz waves, as well as the position of the resonance energylevel of molecules, the transmission spectrum will exhibit absorptioncharacteristics. The reason for this resonance absorption is generallythe intermolecular rotation and vibration, weak molecular interactions,and the molecular group overall vibration mode [16].
For sample 2, the index of refractionand absorption versus frequency for the ordinary ray and extraordinaryray are presented in Fig. 5. The index of refractions for the ordinaryray and extraordinary ray were no = 2.677 and ne = 2.443 at 1 THz, respectively, and no = 2.702 and ne = 2.466 at 1.8THz, respectively. It should be noted that the dispersion for theextraordinary ray is the same as that for the ordinary ray. The indexof refraction between the extraordinary and ordinary ray at 1 and1.8 THz have almost the same difference values of approximately 0.23,which results in the birefringence of tourmaline being much more evidentin the terahertz band compared to the optical frequency band. Theresults in Fig. 5(a) are also fitted well by a simple quadratic dependence.
Here, two absorption coefficients αo and αe were defined; αo was definedas the absorption coefficient of terahertz vibration perpendicularto the tourmaline optical axis direction, while αe was defined as the absorptioncoefficient of terahertz vibration along the tourmaline optical axisdirection. In Fig. 5(b), the absorption of the extraordinary ray issignificantly less than that of the ordinary ray; data for the extraordinaryray was considered accurate up to 2 THz. Different absorption coefficientsin both directions of tourmaline demonstrate its dichroism. It showsthat THz-TDS has the potential to identify aspects of the tourmalinecrystal. Although the intensities of the absorption in different vibrationdirections were different, a similar tendency is presented. This suggeststhat it is feasible to characterize the tourmaline structure usingTHz-TDS technology.
To verify the above results for anothersample, sample 3 was prepared to determine the corresponding indexof refraction and absorption coefficient spectra. Sample 3 and sample2 were cut from the same crystal and both are parallel to the C axis. Results show that the index of refractionof sample 3 and sample 2 exhibit the same properties. The absorptioncoefficients of the two samples are compared in Fig. 6. The absorptioncoefficients of the two samples are consistent for terahertz pulsevibration along the C axis. Whenthe terahertz vibration direction is perpendicular to the C axis, there is a slight divergence in theabsorption coefficient. These results indicate that in the tourmalinestructure the terahertz absorption spectra of the three anionic groupsis more sensitive along the C axisthan in the vertical direction of the C axis.
Conclusions
In conclusion, the optical constantsof tourmaline between 0.3 and 2.2 THz have been measured by terahertztime-domain spectroscopy. The index of refraction and absorption coefficientof the tourmaline crystals in different directions were determined.The differences in the presentation of the tourmaline refractive indexand absorption spectra in different directions indicate that a methodfor analyzing the structure of tourmaline, as well as other crystalsand minerals, can be realized by the THz technology.