A terahertz (THz) tube waveguide with grating structure has been designed, fabricated and characterized as a microstructure waveguide sensor. The resonance and polarization properties of this microstructured tube have been experimentally and theoretically investigated, which indicates that the grating etched on the tube surface has a remarkable modulation effect on the tube resonance and polarization dependence for THz waves. Moreover, a real-time quantitative sensing has been realized based on this tube waveguide in the THz time-domain spectroscopy system. Compared with the bare tube without grating, the grating structure strongly enhances the interaction between THz evanescent field on the tube surface and analytes, improving the sensitivity. This microstructured PMMA THz tube reveals a high sensitivity of 50GHz/μl and precision of larger than 0.125μl with a good linear relationship for THz sensing applications.
© 2015 Optical Society of America
In recent years, terahertz (THz) sensing of chemical and biomedical compositions have revealed attractive potentials by using the recently developed terahertz time-domain spectroscopy (THz-TDS) [1–3 ], and considerable researches for THz sensors have been demonstrated in this field. For examples, planar metamaterials [4, 5 ], metal hole array , and microfluidic chip  have been used to detect biomaterials  or gas materials  on the surface of these on-chip devices. Recently, some THz metasurfaces have revealed very high sensitivity with a large resonant Q factor [10–12 ]. However, a crucial limitation based on these planar structures is not compatible with the dynamical online process or quantitative monitoring [13, 14 ]. Several waveguide-based resonant sensors have been demonstrated in the THz range, including the THz parallel-plate waveguide [15, 16 ], photonic crystal waveguide [17, 18 ] and THz fiber-based sensors [19, 20 ]. A fiber-based resonant sensor is required to simultaneously confine waves and analytes in the fiber’s hollow core or in the holes of the cladding region for fluid sensing. The fiber-based resonant sensor not only has an increased interacting length between light and analytes for highly sensitive detection, but also its flexible structure has advantages in the remote sensing.
THz dielectric tube waveguide consist of a large air-core and a thin dielectric layer, and its guiding mechanism is that of an anti-resonant reflection (ARR) with a leaky nature, so tube waveguide has a series of evenly spaced resonances with a large leakage loss, and the low loss THz wave transmission can be achieved nearby ARR frequency ranges. Lai et al. verified the ARR transmission properties , bending transmission and loss characteristics  of tube in theory and experiment. Bao et al. also investigated the broadband THz transmission property of tube and proved its low loss and low dispersion for THz transmission . Due to the resonances in THz tube waveguide, it can be seen as a resonator, which causes a series of resonant dips more sensitive to outside environment as the resonant modes extending outside the cladding significantly. You et al. reported the dielectric film thickness measuring  and powder refractive index sensing by using the tube waveguide . However, due to its smooth geometry of the tube wall and inefficient sensing mechanism of evanescent wave modulation on the tube surface, the sensitivity of the THz tube waveguide is still limited and not suitable for sensing, especially in quantitative detection.
One solution is to introduce the microstructure into the tube. Artificial electromagnetic microstructure shows very strong localized characteristics of the electromagnetic field to enhance the interaction between THz waves and analytes, which can significantly improve the detection sensitivity, and reduce the volume and quantity of analytes to realize high sensitive sensing. Zhou et al. wrote the Bragg gratings on the solid-core polymer fiber, and the result shows the enhanced resonance  and excellent filtering function  due to the bandgap of the periodic structures. A resonant THz sensor for paper quality monitoring by using THz fiber Bragg gratings was also demonstrated by Yan et al. . However, the transmission and resonance characters of THz tube waveguide with subwavelength grating structure have not been reported yet. Therefore, in this work, we fabricated grating structures on the surface of the PMMA tube waveguide, and investigated the transmission, resonance and the polarization characteristics of this waveguide theoretically and experimentally, which indicated that the grating structure can effectively modulate the resonance and polarization of the tube. Moreover, the real-time quantitative sensing was realized with a high sensitivity by using this grating tube in the THz-TDS system.
2. Device fabrication and experiment system
Our tube waveguide is composed of PMMA. The THz absorption coefficient of PMMA is lower than 0.2cm−1 below 1.5THz, and its refractive index is about 1.6 in the THz regime. The tube has a length of 55 mm, an outer diameter of 8 mm and a wall thickness of 1 mm as shown in Fig. 1(a) . The grating structure was etched on the outer surface of the tube by a 10.6μm CO2 Laser (Han’s Laser CO2-H10) writing system, by using point to point writing method with an average power of 0.6 W and repetition frequency of 5 kHz. As shown in Figs. 1(a) and 1(b), the tube surface is etched into the air grooves and PMMA ridges with 100 periods. The groove width is 220μm, the etching depth is 30μm, and the effective etching length around the tube is 1.66mm. Thus, the volume of one air groove is 0.22 × 0.03 × 1.66mm3 = 0.011μl, and the total groove volume on the waveguide surface is 0.011μl × 100 = 1.1μl. The ridge width is 80μm, so the period of this microstructure is 300μm and the whole length of the microstructure on the tube surface is 300μm × 100 = 30mm. Only one side of tube has the grating structures and another half of tube surface is smooth, as shown in Figs. 1(a) and 1(c).
Our experiments were performed on a self-built four parabolic mirrors THz-TDS system at room temperature with the humidity of less than 5% [28, 29 ]. THz pulses were generated by a low-temperature grown GaAs photoconductive antenna of 50 μm slit. The excitation source was a 75fs 800nm Ti: Sapphire laser. A (110) ZnTe crystal was used for detection. The working frequency range of this system was 0.1-3.5THz, and its signal to noise ratio (SNR) was over 50dB at 1THz. The measuring time step was 0.04ps in this experiment. The input port of tube waveguide was fixed at one focal point of the THz-TDS system by two tunable stops, and the output port was fixed at another focal point as shown in Fig. 1(a). THz waves were normally coupled into the tube, and the polarization direction of the incident waves was along z axis as shown in Fig. 1(a). The tube can be axially rotated along y direction in the stops. We define that 0° is along the polarization direction of THz waves as the grating faces up along z direction, and 90° faces x direction.
3. Experiments on resonance and polarization
We measured the grating tube with 0° and 90° to the THz wave polarization direction by the THz-TDS system, and also tested the same tube without the grating structure as a comparison and air signal without tube as a reference. As shown in Fig. 2(a) , all the time domain signals of the tube waveguides can be divided into two parts: the first pulse cycle is the signal straightly transmitting through air hole of the tube without any delay or dispersions compared to the air reference signal, and the grating structure has no influence on this pulse; the second pulse cycle is delayed to 3.84ps behind the first cycle, which originates that the THz waves transmit through and resonate in the dielectric layer of the tube as shown in Fig. 1(c), resulting a large group delay and dispersion occur. Apparently, the grating structure on the surface of dielectric layer strongly impacts on transmission and resonance of the second pulse cycle because this pulse transmits through the dielectric layer. Therefore, there is a delay of 0.4 ps between the tube without grating and with 0° grating in their second pulse cycle.
It is known that the interference of the above two pulse cycles will form a series of evenly spaced resonances in the frequency domain. In theory, this is a typical double-beam interference model. The resonance valley in the transmission spectrum can be obtained when the difference in single-pass transit time of the pulse propagating in air and the pulse guided by the waveguide approaches λ/2 or odd integer multiples, which can be expressed as:Fig. 1(c), where d = 1mm is the tube thickness. neff is the effective refractive index of the grating tube with or without filling liquid. According to Eq. (1), the interval between two adjacent resonant frequencies can be obtained as follows:
The experimental transmission spectra (in dB) follows = , where and are the amplitude spectra of the samples and air reference obtained by Fourier transform of the time domain pulses, and the experimental results are shown in Figs. 2(b) and 3(a) . The resonances with a bandwidth of 50 GHz are located at 0.34 THz, 0.61 THz, 0.89 THz, 1.14 THz, and 1.41 THz in the tube without grating as shown in Fig. 2(b). There is an equal frequency space of 0.27THz between these resonance frequencies. As seen from the time domain again, the optical path of this time difference can be expressed asEq. (3). If we bring this neff into Eq. (2), the ∆f = 260GHz can be obtained. It is very close to the experiment result of 270GHz because we should consider that ∆t is difficult to be accurately determined due to the dispersion delay of the second pulse. In fact, each frequency corresponds to a different neff due to the waveguide dispersion. By using experimental measurement, neff can be accurately calculated by Eq. (1) and resonance frequency fm in Fig. 2(b), but neff can be only approximately obtained by Eq. (3) and pulse delay time ∆t in Fig. 2(a). It can be seen as an average neff.
Compared to the grating tube, the tube without grating has a redshift of approximate 50 GHz at each resonance frequency point, which illustrates the modulation effect of the grating structure on the resonance frequencies of the tube waveguide. It should be noticed that there is a delay of 0.4 ps between the tube without grating and with 0° grating in Fig. 2(a). According to Eq. (3), in fact, ∆t = + 1ps corresponds to ∆neff = + 0.15, so the neff of waveguide without groove equals 1.576 + 0.06 = 1.636, which is also very close to the material refractive index of PMMA (i.e. about 1.6). The reason for the redshift of resonance point is that the grating structure reduces neff with the periodic air grooves, so the resonance frequency fm becomes smaller by Eq. (1). Therefore, both in time domain and frequency domain, the experimental results are in good agreement with the theoretical predictions.
The Q factor of the second resonance reaches 13, which is twice than that of the tube without grating. Among these resonances, the second and third ones have a higher Q factor than the others’, so in the following discussion, we focus on these two resonant frequencies.
Furthermore, Fig. 3 indicates the polarization dependence of this grating tube with 0°, 45°, and 90°. This polarization dependence originates from the grating structure only written on one side of the tube surface. As shown in Fig. 3, the grating tube with 0° has a largest frequency shift compared with the tube without grating. This result illustrates the maximum modulation effect of the grating on the resonance occurs when the polarization direction of incident THz waves is parallel with the grating surface direction. When the polarization direction is orthogonal to the grating surface, this modulation tends to be eliminated. The asymmetry geometry in the waveguide leads to the polarization dependence in the resonance.
In order to do further analysis, we numerally modeled and simulated this tube waveguide by the finite-different time-domain (FDTD) method. The simulation spectra are shown in Fig. 3(b), and they primarily fit with the experiment results in Fig. 3(a). Figures 4(a)-4(c) show the simulations of electric field distributions in the cross section of the grating tube (0°) at 0.65THz, 0.8THz, and 0.95THz, respectively. The resonance and leaky modes with a large loss are clearly shown at 0.65THz in Fig. 4(a) and 0.95THz in Fig. 4(c), and a guiding mode without radiation loss is located at 0.8THz in Fig. 4(c), which coincide with the transmission spectra in Fig. 3.
4. Sensing experiments and discussions
Sensing experiments were performed based on this grating tube. Firstly, the refractive index and absorption coefficient of ethanol in the THz regime were measured by the THz-TDS system as shown in Fig. 5 . Its refractive index decreases from 1.7 to 1.5 in the range of 0.2-1.4THz, and the absorption coefficient increases from 10 to 90 cm−1. This sensing experiment can be modeled as the ethanol layer with different thickness in the grating grooves as shown in Fig. 1(c). Because the optical properties of ethanol are different with that of air in the THz regime, so filling the ethanol in the grating groove can induce the changes of the resonance due to the different neff described by Eq. (1), and thus the quantity change of ethanol in the grating can also lead to the shift in resonance frequency. We used a precision dropper to drop 1.5μl of ethanol on the surface of the tube under an optical microscope carefully, ensuring that every groove was fully filled with ethanol and there was still a small amount of ethanol remaining on the unstructured parts of the tube. We have measured the THz transmission spectra series after dropping the ethanol for the different delay time T d, and the results are shown in Fig. 6 . For the second resonance shown in Fig. 6(a), with the time delay increasing, the resonance dip is located at 0.605THz (T d = 0s), and gradually moves to a higher frequency. After T d = 250s, the spectrum returns to the original one without liquid before dropping, of which resonance is located at 0.66THz. For the third resonance shown in Fig. 6(b), with the time delay increasing, the resonance dip at 0.895THz also gradually moves to a higher frequency, and finally tends to 0.95THz. The reason for this dynamic change can be interpreted by the volatilization of ethanol because the amount of liquid on the grating tube exposed in the air will be reduced as time passed by. The experimental results indicate that the amount decline of the liquid is reflected in the spectral changes at the different delay time T d.
It is notable that a good linear relation between the amount of ethanol and the delay time is shown in Fig. 7 , and the slope of the line indicates the decline rate of the ethanol on the grating tube due to the volatilization. We can calculate this frequency shift rate of 0.183GHz·s−1 for the second and third resonances in Fig. 7. As this sensing method relies on a change in neff of the waveguide, the minimum neff change which can be detected is determined by the time solution of the THz-TDS system. In this experiment, the time solution is 0.04ps, so the minimum neff = 0.006 based on the calculation in Section.3. According to the geometry of the grating tube described in Section.2, the total volume of analyte in the grooves is 1.1μl, so we can obtain the sensitivity of this grating tube sensor is 55GHz/ 1.1μl = 50GHz/μl. We define ‘sensing precision’ to describe the minimum amount of the analyte liquid distinguished by this sensing method, which is mainly determined by both the spectral resolution of THz-TDS system and sensitivity of this waveguide sensor. In our experiment, the spectral resolution is 6.25GHz, so the minimum amount is 6.25GHz/50GHz/µl = 0.125µl. Other liquids, such as water, acetone and petroleum ether, can be also well performed with the same sensitivity and accuracy by this sensing method based on the same principle.Therefore, the grating tube can be used as a sensitive sensor for real-time quantitative sensing.
To compare with the sensitivity of the grating tube sensor, we have also performed the sensing experiment based on the tube without grating. We doped the same amount of ethanol on the surface of the tube and repeated the previous experiments. Because only 1.5μl ethanol was dropped on the tube surface, surface tension and viscous force can ensure that ethanol does not flow away from the round surface. The whole dropping process is observed and done under an optical microscope, so we can carefully control the distribution of ethanol and the sensing volume the same as in the microstructured case. The results are shown in Fig. 8 . It can be seen that there are only very slight changes of resonances in the transmission spectra when the ethanol is attached on the surface of the tube without grating. Apparently, the bare tube is insensitive to the materials on its surface so that it cannot be used as a sensor. It indicates that the grating structure strongly enhances the sensitivity to the analytes on the tube, of which reason is that the evanescent wave on the outer surface is modulated by the grating structure, and the interaction between the evanescent wave and analytes are enhanced by the periodic grooves and ridges structure, so that the performance of grating tube is much better than that of the bare tube.
In conclusion, we designed and fabricated a PMMA grating tube as a microstructure waveguide sensor. The resonance and polarization characteristics of this grating tube have been experimentally and theoretically investigated, and it indicates that the grating etched on the tube surface has a remarkable modulation effect on the tube resonance and polarization dependence. Moreover, the real-time quantitative sensing has been realized based on this grating tube in the THz-TDS system. Compared with the bare tube without grating, the grating structure strongly enhances the interaction between THz evanescent field on the tube surface and analytes and thus improves the sensitivity. This grating tube reveals a high sensitivity of 50GHz/μl and precision of larger than 0.125μl with a good linear relationship. Compared with the developed optical sensing technology, the THz waveguide sensor is a novel sensing method based on THz-TDS technology with many advantages, such as very high signal to noise ratio, broad frequency range, and nondestructive non-contact real-time detection. Due to the huge different electromagnetic properties between the THz waves and optical waves, this THz sensing technology can be used to supplement the optical sensing technology on special occasions in the future.
This work was supported by the National Basic Research Program of China (Grant 2014CB339800), the National Natural Science Foundation of China (Grant 61171027, Grant 61505088), Natural Science Foundation of Tianjin (Grant 15JCQNJC02100), the National High Technology Research and Development Program of China (Grant 2011AA010205), and the Science and Technology Program of Tianjin (Grant 13RCGFGX01127).
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