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A dielectric pipe waveguide is successfully demonstrated as a terahertz refractive index sensor for powder and liquid-vapor sensing. Without additional engineered structures, a simple pipe waveguide can act as a terahertz resonator based on anti-resonant reflecting guidance, forming multiple resonant transmission-dips. Loading various powders in the ring-cladding or inserting different vapors into the hollow core of the pipe waveguide leads to a significant shift of resonant frequency, and the spectral shift is related to the refractive-index change. The proven detection limit of molecular density could be reduced to 1.6nano-mole/mm3 and the highest sensitivity is demonstrated at around 22.2GHz/refractive-index-unit (RIU), which is comparable to the best THz molecular sensor [Appl. Phys. Lett. 95, 171113 (2009)].
©2012 Optical Society of America
1. Introduction
Minute material detection has attracted considerable attention in biochemistry and medicine, which require sensors capable of highly sensitive, label-free and noninvasive detections for bio-sensing. Terahertz (THz) electromagnetic waves, with a spectrum lying between the far infrared and microwave regions, have been extensively applied for noninvasive and label-free molecular detections because of their low photonic energy and multiple spectral features at this frequency range [1]. Generally, there are two sensing methods in THz range. The first, as in THz time-domain spectroscopy (THz-TDS) and Fourier transform infrared (FTIR) spectroscopy, measures the spectral lines of molecular resonances while the molecules are illuminated with broadband THz waves. This sensing strategy requests analytes in sufficient quantities or thicknesses to exhibit power or phase differences in the probing THz waves and is thus certainly inadequate to sense minute molecules [2]. The second method is based on the resonant properties or photonic band-gap effect of sensing devices [3]. The devices are quite sensitive to the refractive-index change of ambient media placed in the active sensing regions, such as micro-strip line resonators [4], metamaterial resonators [5], and waveguide resonant cavities [6]. These THz sensors permit the highly sensitive detection of the nanometer-thick molecular layer [5] and femto-mole DNA molecules [4]. However, the open and planar geometry of these devices are difficult to integrate with fluidic sensing, and a strictly engineered resonant structure or a photonic band-gap structure is required.
In the optical frequency range, a dielectric-ring-cladding hollow waveguide or a dielectric micro-tube waveguide has been theoretically demonstrated as compact and efficient biochemical sensors based on the built-in resonator in the cladding region [7]. The dielectric-ring cladding acts as a Fabry–Pérot (FP) etalon, and optical waves which satisfy the FP resonance condition will oscillate in and penetrate the ring cladding which becomes leaky to form multiple transmission dips [8]. Other optical waves are reflected by the cladding, which acts similarly to highly reflective FP mirrors, and are confined within the hollow core based on the anti-resonant reflecting optical waveguide (ARROW) mechanism [9]. The resonant frequency of ARROWs is highly sensitive to the geometrical parameters of the cladding layer and the waveguide’s hollow core [7]. Recently, THz waveguides based on ARROWs have been experimentally demonstrated for low-loss and broadband transmission of THz pulses [8], and for thin film sensing [10]. Various subwavelength-thick molecular layers adhered on the inner surface of the dielectric cladding are easily identified and the limit of thickness detection is obtained as λ/225 [10].
In this presentation, we experimentally demonstrate a refractive-index sensor using a simple dielectric pipe waveguide in THz frequency range. The THz pipe waveguides are demonstrated to be able to successfully identify various powders with different mixed concentrations and various vapors based on sensing slight changes of the refractive index in the cladding layer and hollow core of the pipe waveguide, respectively. All the detected powders and liquids may have the same appearances and are difficult to be recognized via naked eyes. The best sensitivity approved in the presentation approaches 22.2GHz/RIU for powder sensing and the detection limit of vapor molecules is reduced to 1.6nano-mole/mm3. The pipe-waveguide-based THz sensors present advantages in that they are easily acquired from ordinary plastic pipes or tubes with no need for any additional fabrication of resonant structures, and that the simultaneous confinement of the probed THz waves and fluids in the same channels results in the interaction lengths being sufficiently long. In addition, the THz pipe waveguide provides a sharp resonant line-width for highly-sensitive detection and it can be integrated with various biochips for molecular sensing due to the large evanescent fields of resonant waves leaked from the dielectric pipe walls; this cannot be achieved in metallic cavity type bio-sensors despite the use of the ultrahigh quality factor (or Q-factor) for sensing applications [6]. The dielectric-pipe-waveguide-based refractive index sensor could potentially be applied in micro-fluidic systems for bio-chemical detection and inspecting industrial pollutants.
2. Powder sensing with the cladding layer of a pipe waveguide
In the powder sensing experiment, we used a 15cm-long polypropylene (PP) pipe as a THz pipe waveguide with a composite ring-cladding and a hollow core with an inner diameter Din of 12.00mm. The composite ring-cladding consists of a 0.39mm-thick PP pipe-wall covered by a 0.55mm-thick adsorbent layer as the outer cladding. The cross section of the PP pipe waveguide sensor is illustrated in Fig. 1(a) . The adsorbent layer is made of polyvinylchloride (PVC) plastic sheet with triangular arrays of circular air holes, as illustrated in Fig. 1(b). The adsorbent layer’s porosity is determined by the hole dimension and the arrangement of the holes. As shown in Fig. 1(b), the air-hole diameter a in the PVC adsorber is 1.10mm. The separations between adjacent holes (b) and holes along the closest diagonal (c), are 1.40mm and 2.70mm, respectively. Even though the periodic hole-diameter matches THz wavelength, we do not observe any transmission dip related to the hole resonance in the transmission spectrum of the pipe waveguide. According to the aforementioned geometrical parameters of the PVC porous layer, the porosity of the adsorber is calculated at 50%. The porous structure of the adsorber could be filled with powder grains to replace the air space for sample loading. The estimated effective refractive index neff of the adsorber can be calculated from Eq. (1),
wherein ρ, nhole, and nPVC respectively represent the porosity of adsorber, and the refractive indices of both the hole-space and the PVC material. For a bare pipe without a sample loaded on the adsorber, ρ, nhole, and nPVC are, respectively, 50%, 1.00, and 1.63 [11] and the effective refractive index of the adsorber in this experiment could thus be calculated from Eq. (1) as 1.354. We used the waveguide based THz time-domain spectroscopy (THz-TDS) system [12] to measure the spectral properties of the PP pipe waveguides with and without analytes loaded in the adsorber layer. The pipe is put at the focus of parabolic mirror, EFL~80mm, and the spot diameter is around 3mm in 0.01~1THz, measured by knife-edge method for 1/e2 definition. The input THz spot is several times smaller than the hollow-core diameter of pipe waveguide, 12mm and 5.57mm separately for PP and glass pipes, in order to efficiently excite the waveguide modes. When the THz waves propagated output from a pipe, one 50mm-diameter plastic lens with focal length of 50mm collimates THz waves into a pair of parabolic mirrors for efficient detection by a photoconductive antenna. We have successfully measured multiple resonant dips in THz transmitted spectrum of the pipe waveguide by using the waveguide based THz-TDS, and the dip positions in the transmitted spectrum are corresponded to the peak positions in loss-constant spectrum measured by cutback method, where the spectral positions of loss peaks (i.e. transmission dips) match the theoretical frequencies of resonance modes in the pipe waveguide [12]. Although the transmission spectrum includes the frequency-dependent input/output coupling loss as well as the waveguide propagation loss, the resonant-dip positions are approved to be independent of the coupling conditions [12] and are absolutely determined by the geometrical parameters of the pipe waveguide [8,9, 12]. Therefore, the observed dips in normalized transmission spectrum are able to well define spectral positions of different resonant THz waves in a pipe waveguide. Based on the sensing scheme of dielectric pipes, inserting samples in the pipe-wall or hollow core introduces additional refractive index changes in the composite cladding or core region of the pipe waveguide and results in the spectral shifts of resonant dips.
Fig. 1 (a) Cross section of a PP-pipe-waveguide sensor with an inner diameter Din of 12mm. (b) Top view of the porous PVC adsorber. (c) Theoretical and measured normalized transmission power spectra of a PP-pipe waveguide, which include the 1st and 2nd-order resonant dips at 0.12~0.4THz. (Inset) Transverse THz modal power distributions at the 1st and 2nd-order resonant frequencies in the PP-pipe-waveguide. The cyan and orange regions respectively represent the PP pipe-wall and porous PVC adsorber, and the hollow core of the waveguide is located at positions of −6~6mm.
Figure 1(c) illustrates the measured and theoretical transmission power spectra of the PP-pipe-waveguide sensor without powders loaded on the adsorber, and they are individually normalized relative to the maximum value in each curve. The theoretical spectrum of Fig. 1(c) is calculated by the finite-difference time-domain (FDTD) method using Rsoft software without consideration of the frequency dependent emitted THz spectrum, and the calculation is based on the pipe’s geometrical parameters including the physical dimensions of the pipe waveguide as well as the refractive indices of the PP material (1.50 [13]), air space (1.0), and the adsorber (1.354). As shown in Fig. 1(c), the first order resonant dip of the bare pipe is measured at a frequency of 0.166THz and the dip position is consistent with the theoretical one considering the index of the adsorber as 1.354. However, the theoretical second-order resonant dip calculated at a frequency of 0.335THz is not very deep in the measured result due to the decreased visibility of high order interference, caused by the high attenuation of the secondary reflectance in the composite cladding [14]. In addition, the power transmission of the measured spectrum is obviously lower than the simulated one as shown in Fig. 1(c). It is because the less emission of THz waves below 0.2THz in our THz-TDS system, however, in theoretical simulation, the input THz power for each frequency is assumed to be constant. The inset of Fig. 1(c) shows the simulated transverse THz modal power distributions corresponding to the 1st and 2nd-order resonant-dip frequencies, obtained via FDTD simulation. We can see that the oscillation amplitudes of the THz power within the composite cladding (i.e. the cyan and orange regions) are greater than or very close to those in the hollow core and extend outside the cladding region, revealing heavy leakage at resonant frequencies. Comparing the modal power pattern at the 2nd-order resonant frequency (0.335THz) with that at the 1st-order resonant frequency (0.166THz) shows more THz power is confined within the hollow core of the pipe waveguide for the 2nd-order resonant wave, indicating that the propagation loss induced from FP resonance in the cladding for the 2nd-order resonant wave is not obvious. Thus the spectral depth of the 2nd-order resonant dip (at 0.335THz) is not deep enough to detect the index-variation of cladding region with sufficient sensitivity. Therefore, due to its sharp line-width, the 1st order resonant dip (at 0.166THz) is chosen for sensing powders in the cladding. Based on the FP criteria, the wavelength of THz waves resonated in the composite cladding could be calculated by Eq. (2),
where λm, d, m, ncld and ncor are, respectively, the mth-order resonant wavelengths, thicknesses of pipe walls, orders of the resonant modes, and effective refractive indices of both the composite cladding and core [9]. In other words, the phases in the composite cladding region must be integers of half-oscillations, i.e. mπ [9]. For m = 1, the phase of the 1st-order resonant mode in the composite cladding is π, as shown in the inset of Fig. 1(c). When ncld is increased, the effective optical path ( = ) [10] in the composite cladding region is also increased, resulting in an increased resonant wavelength to keep the π-phase in the cladding region. According to above formula, the red-shifted wavelength of the resonant wave is approximately proportional to the effective cladding index. Based on above concept, we could identify powders using the cladding structure of the PP-pipe-waveguide sensor.The powder-sensing experiment tested melamine (melamine, Nippon Bacterial Test Co., Ltd.), tryptophan (T8941 L-tryptophan, Sigma-Aldrich Inc.) and their mixtures. Both are white powders with a grain size of tens of micrometers and are similar in appearance. The powdered analytes were prepared in containers and a 15cm-long PP pipe with two sealed ends was completely inserted into the container to approximately full fill the porous adsorber with powders. The powder-adsorbed length of pipe waveguide should be 5cm at least to generate resonant modes and to form the obvious spectral dips. Loading powders in the adsorber causes the 1st-order resonant dip shift to low frequency range due to an increase of ncld, as illustrated in Fig. 2(a) . The measured 1st-order resonant frequency is shifted from 0.166THz to 0.163THz, while tryptophan powders are fully adsorbed in the porous PVC layer. Replacing the tryptophan with melamine results in a more obvious spectral shift from 0.166THz to 0.149THz. Based on the averaged spectral positions shown in Fig. 2(a), the effective refractive index neff of the outer cladding layer loaded with various powders could be obtained by FDTD. For example, for tryptophan and melamine powders, neff is respectively calculated as 1.373 and 1.489, indicating that melamine powder contributes a higher refractive index than that of tryptophan powder in the same adsorber. Figure 2(b) illustrates the simulated transmission spectrum of the pipe-waveguide sensor with different effective refractive indices neff of the outer cladding layer. We can see that raising the ratio of melamine powders would increase neff and result in a spectral redshift of the resonant-dip, as shown in Figs. 2(a) and 2(b). For 31.6%- and 66.7%-malamine-mixed powders, the resonant dips for the two mixed powders are respectively located at 0.160THz and 0.154THz, where the dip-shifts, relative to the dip position of the blank PP pipe, are increased with the mixed ratio of the melamine grains. Based on FDTD calculations, the corresponding effective refractive indices neff of the outer cladding layer for 31.6%- and 66.7%-melamine mixed powders are 1.390 and 1.444, respectively. The refractive indices of the powders could be derived from both Eq. (1) and from the outer waveguide-cladding indices neff indicated in Fig. 2(b).
Fig. 2 (a) Measured spectral positions of 1st-order resonant waves for different adsorbed powders in the outer cladding. (b) Simulated spectral positions of 1st-order resonant waves. (c) Dependence of the 1st-order resonant-dip frequency on refractive indices of melamine, tryptophan and their mixed powders measured by the PP-pipe-waveguide sensor. The indices of melamine and tryptophan powders are compared with the results measured by THz-TDS. (d) Transverse power distributions of the 1st-order resonant wave in the PP-pipe-waveguide sensor for different refractive indices of the outer cladding.
The frequency deviation (error bars on solid curves) of each data point in Fig. 2(a) are obtained by repeated spectral measurements of the powders-loaded pipe for five times, and range from +/−1GHz to +/−4GHz. Because the powdered shape of melamine is different from that of tryptophan, the adsorbing ability is decreased for the mixed powders compared with the pure powders. For each measurement, it is necessary to re-load the test powders on the porous adsorber, and the poor adsorbing ability makes the un-uniformity of powder loading which leads to the larger frequency deviation of spectral measurement. Therefore, the frequency deviations for the pure melamine and tryptophan powders are about +/−1~+/−2GHz, but are increased to +/−2~+/−4GHz for the mixed powders due to their poor adsorbing abilities on the porous cladding of the waveguide. For 31.6%-melamine mixed powder, a serious frequency uncertainty of approximately +/−4GHz exists in spectrum (green error bars in Fig. 2(a)), but the deviation is decreased to +/−2GHz for increasing the melamine concentration of 66.7% (blue error bars in Fig. 2(a)). It is because the adsorbing ability of melamine powders is higher than that of tryptophan powders and the frequency deviation is comparably low. The issue does not occur in recognizing pure powders and the frequency uncertainty is only contributed form system reliability, less than +/−2GHz.
Figure 2(c) shows the relation of the 1st-order resonant-dip frequency and refractive indices for the melamine, tryptophan and their mixed powders measured by the PP-pipe-waveguide sensor. The respective measured indices of the melamine and tryptophan powders are 1.76 and 1.10, which nearly match the values obtained by conventional THz-TDS. The respective refractive indices of 31.6%- and 66.7%-malamine mixed powders are 1.20 and 1.50 as recognized by the PP-pipe waveguide. From the sensing results shown in Fig. 2(c), the refractive indices of powders are almost inversely proportional to the dip frequencies and their error bars are estimated from the measured frequency deviations in Fig. 2(a). The average sensitivity of the PP-pipe sensor to sense powders is estimated at around 22.2GHz/RIU from the slope of the fitting line in Fig. 2(c), which is quite sensitive as the presented THz molecular sensors [6]. In Figs. 2(a) and 2(b), increasing the outer cladding index not only results in the redshift of the resonant wavelength, but also decreases THz transmission power at resonant-dip frequency.
This spectral behavior could be explained by the simulated modal power distributions of the pipe waveguide with different effective refractive indices of outer cladding, as illustrated in Fig. 2(d). This shows that the evanescent powers of resonant modes in the central part of the hollow-core are clearly reduced when the outer cladding indices are increased from 1.354 to 1.489. Thus, the transmitted power of the resonant dip in the low frequency range is absolutely lower than that in the high frequency range. Comparison the calculation with the measured results (Figs. 2(a) and 2(b), respectively), the measured power difference (i.e. the variation of dip depth) between adjacent spectral dips is more distinct than the calculated result because the additional absorbed or scattered powers from both the PVC sheet and the powder grains are not considered in the FDTD calculation.
Currently, THz powder sensing have been extensively applied to illicit drugs [15], explosive and hazard powders [16] via their finger-print THz spectra. The demonstrated THz pipe sensor is potentially able to distinguish various powders mentioned above within a finite THz bandwidth because the surrounding’s refractive index change can make a significant shift of resonant frequency. In the practical applications, the simple pipe waveguide not only enables to recognize the quantities and concentrations of the suspended powder pollutants, such as for industrial or environmental pollution detections, but also enables to noninvasively monitor the dynamical generations of compounds in chemical reactions, for example, ammonia gas interacts with hydrochloric acid producing particles of chloride ammonium.
3. Vapor sensing with the hollow core of the pipe waveguide
To demonstrate vapor sensing, the hollow core of a dielectric pipe is used to detect various volatile liquids that easily evaporate into atmosphere as vaporized molecules. In general, volatile liquids corrode certain plastic materials, making glass pipes more suitable than PP pipes for sensing vapors. We dropped and sealed a small amount of different liquids in the hollow core of glass-pipe waveguides to fill the hollow core with vaporized molecules where they interacted with THz waves. A 30cm-long-glass pipe, closed by two polyethylene (PE) caps at the ends, was used as a vapor sensor and characterized by means of THz-TDS. In Fig. 3 , the measured spectral resonant-dips of a blank glass pipe are well consistent with theoretical dips calculated by FDTD based on the dimensions of the glass pipe as well as the refractive indices of the air-core and glass material. The cross section of the glass-pipe sensor is shown in the inset of Fig. 3, where the inner core diameter Din and the thickness of pipe-wall are 5.57mm and 1.17mm, respectively. The refractive indices of the air-core and glass used in simulation are 1 and 2.6 [13], respectively. Figure 3 shows four resonant dips of the glass-pipe waveguide in the range of 0.2~0.5THz, located at frequencies of 0.201THz, 0.266THz, 0.326THz, 0.392THz and 0.452THz. According to Eq. (2), the resonant dip frequency changes with ncor, thus we could identify various vapors in the hollow core by detecting the spectral shifts of the resonant dips. The THz resonant waves in the hollow core must be sufficiently evanescent to realize a highly sensitive THz-pipe-waveguide sensor with analytes loaded in the hollow core because it assures sufficient interaction between the probed THz-resonant wave and the vaporized molecules. Based on the transverse power distributions of resonant waves in a PP-pipe waveguide (shown in the insets of Fig. 1(c) and Fig. 2(d)), the higher THz transmission power in the central part of hollow core is observed in the higher-order resonant-dip, i.e. the dips in the high frequency range. Therefore, the resonant dip at 0.452THz is suitable for probing vapors within the hollow core of the glass pipe because its resonance power is sufficient to interact with vapors for sensitive detection.
Fig. 3 Theoretical and measured transmission spectra of a glass-pipe waveguide. (Inset) Cross section of the glass-pipe-waveguide sensor.
In the vapor sensing experiment, 0.05c.c. each of water, hydrochloric acid (HCl), acetone and ammonia were separately dropped into the hollow core, with the evaporated vapors enclosed in the hollow core of the glass pipe. In Fig. 4(a) , the transmission dip at 0.452THzshifts toward the high frequency range when various vapors are loaded in the hollow core, and the spectral dip position is changed to 0.461THz, 0.465THz and 0.477THz, respectively, for the hydrochloric acid, acetone and ammonia vapors. With the measured spectral shifts shown in Fig. 4(a), FDTD can be used to calculate the corresponding effective refractive indices of the hollow core as 1.016, 1.035 and 1.102, respectively, for the vapors of hydrochloric acid, acetone and ammonia. In the vapor sensing experiment, the dip-frequency-shift only occurs in a resonance dip of 0.452THz but, unlike the simulated spectrum shown in Fig. 4(b), other resonance dips in the low-frequency range do not exhibit any spectral shift. The zero spectral-shift for the low-frequency-resonant dips results from the amounts of leaky resonance-waves in the hollow core being insufficient to sense the presence of vapor molecules. This again indicates that resonant waves for detecting vapors in the hollow core of a dielectric-pipe waveguide require high transmission powers to identify slight core-index variations contributed from low-density-gas vapors. This low sensitivity phenomenon is straightforward connected to all the anti-resonant frequencies located among the resonant frequencies, less than 0.52THz, without any significant spectral shift.
Fig. 4 (a) Different spectral dip-positions of the resonant wave at 0.452THz in measurement for different volatile liquids. (b) Calculated transmission spectrum of the resonant wave at 0.452THz for different effective-core-refractive indices. (c) Relationship of effective-core-refractive indices and the dip frequencies for different volatile liquids. (d) Relationship of dip-frequency-shift and the estimated vapor densities.
Figure 4(c) shows the relation between the spectral dip frequencies around 0.452THz and the effective core-indices of the glass-pipe waveguide infused with different vapors, where the error bar is around +/−1GHz from the system repeatability of spectral measurement. As shown in Fig. 4(c), the dip frequencies increase with the effective refractive indices of the core being filled by different vapors, and the increased effective refractive indices arise from the different vapor pressures of the volatile liquids in the sealed-hollow core, despite having the same liquid volume (0.05c.c.). In general, different volatile liquids have different saturated vapor pressures at normal atmospheric pressure and temperature, and they generate different quantities of vaporized molecules in the hollow core space. That is, the vapor pressures ofvolatile liquids are proportional to the quantities of vaporized molecules in the enclosed-pipe-core space, and the high density of the vapor molecules in the hollow core results in the large effective core-index, which would make the resonant dip of 0.452THz an apparent blueshift. Figure 4(c) plots the calculated effective core indices neff.cor and dip frequency positions for vapor molecules of hydrochloric acid, acetone and ammonia. The effective core index neff.cor is a function of dip frequency ν, and can be fit by neff.cor = 24-103ν + 114.9ν2. From the polynomial fit, any slight index variation could be estimated to identify the molecules which fully fill the core of the glass-pipe sensor. Nevertheless, the presence of 0.05c.c.-volume water in the pipe cannot contribute any spectral shift, corresponding to the effective refractive index of 1 in the core because, compared with the other strongly volatile liquids (i.e., hydrochloric acid, acetone and ammonia), the density of vaporized water molecules is quite low. Our sensing result, which the effective core-index is increased with the vapor pressure of volatile liquid, is reasonable because the vapor pressures of water, hydrochloric acid, acetone and ammonia at 1 atmosphere and 20°C are, respectively, around 17 [17], 38 [18], 202 [18] and 308 [17] mm-Hg. For qualitative analysis, the vaporized molecules discussed in this work are considered to be ideal gases and their densities in the enclosed pipe would be calculated based on ideal-gas law. Figure 4(d) shows the relationship between molecular density (ρ) and spectral dip-shift, Δν, relative to the resonant dip of 0.452THz, and the nonlinear trend is fit as Δν = 26.3-e-ρ/2.7, where the spectrum deviation is around +/−2GHz based on repeated measurements of frequency shifts. From Fig. 4(d), we can see that the blueshift relative to 0.452THz gradually saturates when the vapor density is increased over 10nano-mole/mm3, leading to a dramatic decrease in the sensitivity of the glass-pipe sensor. Based on the spectral resolution of 4GHz in the current experiment and the fit curve in Fig. 4(d), the minimum detectable molecular quantity would be around 7.8micromole in the glass pipe, corresponding to a molecular density of 1.6nano-mole/mm3.
4. Conclusion
We successfully demonstrate a THz-refractive-index sensor using dielectric pipe waveguides for powder and vapor sensing. Highly sensitive detection is achieved based on the built-in FP resonant structure in the dielectric pipe waveguides, without any additional manufacture of resonant structures, and the sensing performance is shown to be superior to that of available THz refractive index sensors. The sensitivity in the PP-pipe-waveguide sensor is demonstrated to be around 22.2GHz/RIU. Furthermore, a glass pipe is demonstrated for use in vapor sensing with a minimum detectable molecular density as low as 1.6nano-mole/mm3, lower than that obtainable through conventional THz spectroscopy for sensing such low-density analytes. The THz-pipe-waveguide sensors could potentially be used in fluid sensing applications, such as bio-chemical detection and inspecting pollutants in dielectric pipes.
Acknowledgment
This work was supported by the Advanced Optoelectronic Technology Center, National Cheng Kung University, under projects from the Ministry of Education and the National Science Council (NSC 98-2221-E-006-014-MY2 and NSC 100-2221-E-006 −174 -MY3) of Taiwan.
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