Open Access
Add to BibSonomy
Abstract
In this study, we demonstrate on-chip terahertz absorption spectroscopy using dielectric waveguide structures. The structures’ evanescent fields interact with the sample material surrounding the waveguide, enabling the absorption signature of the material to be captured. The ability of fabricated terahertz dielectric waveguide structures, based on the newly developed silicon-BCB-quartz platform, to capture the fingerprint of α-lactose powder (as an example material) at 532 GHz is examined. Enhancement of the spectroscopy sensitivity through techniques such as tapering the waveguide, confining the field in a slot dielectric waveguide, and increasing the interaction length using a spiral-shaped waveguide are investigated experimentally. The proposed on-chip spectroscopy structures outperform conventional and state-of-the-art approaches in terms of sensitivity and compactness.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) absorption spectroscopy is a powerful analytical chemistry tool which can detect the intermolecular vibrations in chemical and organic molecules (THz band is the frequency range commonly understood as 0.3 to 3 THz). The study of these intermolecular vibrations has shed light on the dynamics of large biomolecules [1–3]. Free-space absorption spectroscopy, the conventional approach employed for THz spectroscopy, has been used to characterize a wide range of materials [4–8]. This setup faces a few challenges. Due to the diffraction limit and the long wavelength of THz waves compared to infrared signals, a large amount of sample material is required. In addition, the interaction length between the THz waves and the sample under test is limited by the available amount of the sample material. Finally, the low signal-to-noise ratio in the free-space setup, primarily attributable to the low power of THz sources and water vapor absorption at these frequencies, means weak absorption signatures cannot be captured (It worth mentioning that the signal-to-noise ratio can be improved in an optimized free-space setup, and the water vapor absorption can be decreased through enclosing some parts of the setup and purging the medium using a dry gas). Several recent works have reported improved free-space setup sensitivity, achieved by exploiting the localized electric field in metasurface structures [9–12].
THz waveguides have been explored extensively for sensing and spectroscopy applications [13–19]. Waveguide-based THz spectroscopy, in which the THz signal passes through a waveguide while interacting with the sample, has many advantages over the free-space setup. Firstly, a smaller amount of sample is required. In a waveguide-based configuration, the waveguide modal field distribution (with sub-wavelength features) interacts with the sample; therefore, a sub-wavelength sample could interact with the entire mode power. Secondly, since the wave is propagating inside the waveguide, a better signal-to-noise ratio can be achieved. In the THz frequency range, several metallic waveguides have been used for waveguide-based absorption spectroscopy: single metal wire waveguides [13], microstrip line and coplanar waveguides [14,20–22], and parallel plate metallic waveguides [15,23]. Although these metallic waveguides reduce the amount of sample material required, their performance degrades rapidly as the frequency of operation increases. This is mainly due to the inherent losses of the metallic waveguides at THz frequencies.
Here, we propose and present theoretical and experimental results for a new THz absorption spectroscopy approach using THz dielectric waveguides. Although dielectric waveguides have been used extensively in infrared range of frequency for on-chip spectroscopy and sensing applications [24–30], these structures are not scalable to the THz range due to the technological challenges. Dielectric waveguides based on high-resistivity silicon (HR-Si) are a recently developed class of THz waveguides that are extremely low-loss, even at higher THz frequencies [31–41]. Due to this low-loss characteristic, a long waveguide could be used in the spectroscopy setup, which provides a long interaction length between the waveguide mode and the sample material, resulting in a highly-sensitive spectroscopy scheme compared to the other types of THz waveguides. In addition, given the availability of advanced fabrication facilities for the silicon-based devices, variant HR-Si structures could be created that further enhance the interaction between the THz wave and the sample material. Moreover, significant advancements over the past decade in integrating THz solid-state sources with HR-Si waveguides, makes dielectric waveguides promising candidates for fully integrated THz spectroscopy systems.
2. Silicon channel waveguide for $\alpha$-lactose fingerprint detection
To investigate our hypothesis that a dielectric waveguide could be used for THz absorption spectroscopy, we used silicon-BCB-quartz platform presented by authors in [33], a low-loss and easy-to-fabricate structure for THz compact systems (BCB stands for benzocyclobutene). A highly-sensitive SBQ-based sensor was designed, fabricated and used to measure the absorption of polycrystalline $\alpha$-lactose powder (obtained from Sigma-Aldrich Co.) experimentally demonstrating the new approach’s applicability to THz absorption spectroscopy. Lactose is an important disaccharide used in many food and pharmaceutical applications. $\alpha$-lactose (one of the lactose anomers) has an absorption fingerprint around 532 GHz [42,43]. Figure 1(a) shows the schematic of the SBQ THz sensor comprising a channel waveguide, a sample holder section in the middle (length of the sample holder is $L$ = 8 mm), and tapered channel waveguides at both ends. The structure was analyzed using finite element method simulation. As shown in Fig. 1(b), the evanescent fields of the waveguide’s fundamental mode extend out of the waveguide core region and interact with the material sample surrounding the waveguide. Fabrication of the device was performed using optical lithography and deep reactive-ion etching, an approach the authors have employed in [33].
The experimental setup is shown in Fig. 1(c), it includes frequency extender modules with rectangular metallic waveguide ports. The tapered SBQ channel waveguides are used as the transitions between the SBQ-channel-waveguide and the rectangular-waveguide ports. A digital weight with accuracy of 0.1 mg was used to have a consistent amount of sample powder in all measurements. We have used 20 mg of the sample powder consistently; however, obviously the amount of the sample powder can be decreased significantly through decreasing the width of the sample holder ($w$). The transmission signal through the SBQ waveguide when the sample holder is filled with $\alpha$-lactose powder is shown in Fig. 1(d). As shown in this figure, there is a drop in the signal around $532$ GHz, the well-known frequency signature of $\alpha$-lactose powder. This drop in the transmission signal is not only due to absorption by the sample material; it is also due to several mismatches between the rectangular waveguides and the SBQ waveguide, and reflections at the edges of the sample holder. In order to de-embed these mismatches for more accurate measurement of the absorption due to the loss in the sample material, a reference material was used. The reference material should be very low-loss at the frequency range of interest and should have a permittivity value close to that of the sample material ($\alpha$-lactose). Polyethylene has very low-loss in the THz range [44]. Very fine polyethylene powder (obtained from Micro Powders Inc.) was used as the reference material. The transmission signal through the SBQ waveguide with the sample holder filled with polyethylene powder is shown in Fig. 1(d). Using the measured transmission matrices for both the $\alpha$-lactose and polyethylene cases, the absorption values for the channel waveguide immersed in $\alpha$-lactose can be extracted.
Fig. 1. (a) Schematic of THz SBQ channel waveguide with sample holder [$w_{0}$ = 180 $\mu$m, $w$ = 5 mm, $L$ = 8 mm]. (b) Simulation results for electric field distribution over the channel waveguide cross section at 532 GHz, the dashed lines show the boundaries of silicon. (c) Measurement setup [(1) network analyzer, (2) and (3) frequency extender modules, (4) and (5) rectangular metallic waveguide ports, (6) SBQ waveguide with sample holder filled by material under test]. (d) Measured transmission signal for the two cases of sample holder filled by polyethylene and $\alpha$-lactose in arbitrary units.
2.1 Extracting the absorption
In the waveguide-based absorption spectroscopy, not all of the modal power interacts with the material sample. Since a part of the modal field is confined inside the waveguide, only the part of the field which is outside of the guiding region passes through the sample. For a waveguide immersed in a lossy material [45]:
in which, $P_{0}$ is the input power of the waveguide mode, $P$ is the output power, $\alpha _{WG}$ is the loss of the waveguide, $\alpha _{s}$ is the absorption coefficient of the lossy material surrounding the waveguide, $L$ is the length of the waveguide and lossy material, and $\Gamma$ is the interaction factor denoting the interaction between the waveguide mode and the lossy material.Suppose that the transmission matrices measured between the rectangular metallic waveguide ports for the $\alpha$-lactose and polyethylene cases are $\mathbf {T}$ and $\mathbf {T_{0}}$ respectively. Then:
in which, $\mathbf {T_{T}}$ is the transmission matrix from the rectangular metallic waveguide port to the SBQ waveguide mode (at the location of the beginning of the sample holder), and, $\mathbf {T_{R}}$ is the transmission matrix from the SBQ waveguide mode (at the location of the end the sample holder) to the other rectangular metallic waveguide port. For powders with the same real parts of permittivity, $\mathbf {T_{T}}$ and $\mathbf {T_{R}}$ would be the same. Then:Using Eq. (1):
3. Sensitivity enhancement through waveguide geometry modification
As presented in Eq. (1), increasing the multiplicand of the absorption coefficient of the lossy material surrounding the waveguide, which is $\Gamma L$, enhances the sensitivity to the losses in the material under test. The interaction factor ($\Gamma$) is a function of the waveguide geometry, and is formulated as [24–30,47,48]:
wherein, $v_{s}$ is the speed of light in the sample material medium, $v_{en}$ is the energy velocity of waveguide, and, $f$ is a factor called filling-factor given by:The cross section of the SBQ waveguide can be modified to enhance the interaction factor. For example, tapering the channel waveguide to a narrower width results in an increase of the evanescent portion of the mode in the cladding region. Also, by creating a slot region in the middle of the channel waveguide it becomes possible to confine the THz wave in the slot region for a stronger interaction with the sample material [41,49]. Both of these structures were analyzed, fabricated, and used for capturing the $\alpha$-lactose signature. Schematic of the tapered channel and slot waveguides, and the calculated distributions of the electric field over their cross sections (using finite element method simulations) are shown in Fig. 3(a)-(b) and (d)-(e) respectively. The interaction factor for the tapered channel waveguide was calculated versus its width and shown in Fig. 3(c). As shown in this figure, the interaction factor maximizes when the width of the waveguide is $w_{1}$ = 132 $\mu$m. However, a larger value ($w_{1}$ = 140 $\mu$m) was chosen for this dimension to have the cutoff frequency of the waveguide farther from the frequency band of operation (decreasing the width of the waveguide, increases its cutoff frequency). Similarly, the interaction factors for the slot waveguide were calculated versus the total width of the waveguide and the width of the slot region and are shown in Fig. 3(f) and (g), respectively. Although the interaction factor increases for smaller values for the slot width ($w_{s}$) as shown in Fig. 3(g), the chosen value for this dimension is 20 $\mu$m to make the loading of the powder sample easier. For the chosen dimensions, the interaction factors in the tapered channel and slot waveguides are about 2 and 3.8 times more than that in the channel waveguide, respectively. The tapered channel and slot waveguides were fabricated and used for capturing the $\alpha$-lactose signature. The absorption values for these structures were extracted from two sets of measurements (once immersed in $\alpha$-lactose powder and once immersed in polyethylene powder, as presented in Section 2.1), and are shown in Fig. 4. It can be seen that, the absorption values for these structures are stronger than those found for the SBQ channel waveguide by factors of 2.5 for the tapered waveguide and 3.7 for the slot waveguide. In the tapered waveguide, a larger portion of the waveguide mode power is in the cladding region [comparing Fig. 1(b) and Fig. 3(b)]; therefore, a stronger interaction between the THz waves and $\alpha$-lactose is expected. For the slot waveguide, due to the highly confined electric field in the slot region [considering Fig. 3(e)] an even stronger interaction is expected (as it was expected based on the calculated interaction factor for this waveguide). In Fig. 4, the plot for the tapered case is noisy for frequencies below 520 GHz. The cutoff frequency of the SBQ channel waveguide increases by narrowing its width; therefore, the signal for this structure is noisy for the lower end of the measurement frequency range as it is closer to the cutoff frequency of this structure.
Fig. 3. (a) Schematic of the tapered channel waveguide [$w_{1}$ = 140 $\mu$m, $L_{t}$ = 1 mm]. (b) Simulation results for electric field distribution over the tapered channel waveguide cross section at 532 GHz. (c) Interaction factor calculated for the tapered channel waveguide versus the waveguide width. (d) Schematic of the slot waveguide [$w_{s}$ = 20 $\mu$m, $w_{s}^\prime$ = 260 $\mu$m, $L_{t1}$ = 3 mm]. (e) Simulation results for electric field distribution over the slot waveguide cross section at 532 GHz. (f) and (g) show the interaction factors calculated for the slot waveguide versus total width of the waveguide and width of the slot region, respectively.
Besides modifying the waveguide cross section, the interaction between the THz waves and the sample material can also be enhanced through increasing the interaction length. A spiral-shaped SBQ waveguide was fabricated, as shown in Fig. 5(a) and (b). It provides a long interaction length (29.6 mm) in a compact structure. The absorption values for the spiral structure (extracted from two sets of measurements; once immersed in $\alpha$-lactose powder and once immersed in polyethylene powder) are shown in Fig. 5(c). The peak value of the absorption is significantly stronger than that measured by the SBQ channel waveguide (by a factor of 5.6), mainly due to the longer interaction length in the spiral-shaped waveguide.
Fig. 5. (a) Long spiral-shaped SBQ waveguide [$w^\prime$ = 5.54 mm, $L^\prime$= 15.1 mm, $R$ = 1 mm]. (b) Measurement setup. (c) Extracted absorption from the spiral-shaped waveguide measurements.
4. Comparison with the state-of-the-art approaches
All waveguide-based schemes, including the one proposed here, need significantly less amount of sample material compared to the conventional free-space setup. The $\alpha$-lactose signature captured by a microstrip line waveguide in [20] is very shallow; this is mainly due to the limited used interaction length (1 mm). Microstrip lines are highly lossy at THz frequencies. This property projects an upper limit for the length of the line, and consequently for the interaction length in the application of interest in [20]. Single metal wire is a low-loss type of THz waveguide and a long interaction length of this waveguide (e.g., 55 mm in [13]) can be used when extracting the $\alpha$-lactose signature. The absorption signature reported in [13] is less than 0.05 Np/mm. This is about half of the absorption signature measured using the proposed SBQ channel waveguide (0.8 Np for the waveguide length of $L$ = 8 mm; or 0.1 Np/mm), as shown in Fig. 2. Moreover, by capitalizing on the availability of advanced fabrication facilities for the silicon-based devices, it was possible to modify the geometry of the SBQ waveguide to enhance the strength of the captured fingerprint even further, as several variants were examined here. The absorption signature of $\alpha$-lactose captured in [13] is less than the signatures captured by the tapered and slot waveguides by factors of 5.6 and 7.2 respectively, as shown in Fig. 4. Similarly, the presented SBQ channel waveguide outperforms the metallic parallel plate waveguide presented in [23] and the Bragg waveguide presented in [50] in terms of the strength of the captured fingerprints.
5. Conclusions
In summary, it is clearly possible to use silicon-based waveguides for THz absorption spectroscopy. This type of THz waveguide shows extremely low-loss characteristics and a long interaction length between the THz waves and the sample material can be achieved. There is also the advantage of ease-of-fabrication for waveguide modification and the opportunity for further enhancement of the interaction between the THz waves and the sample material. It is important to mention that we have used $\alpha$-lactose as an example material; otherwise, the concept of the proposed spectroscopy scheme is applicable to any materials with absorption signatures in the THz band. Using the presented structures, fully integrated, compact, and sensitive THz spectroscopy systems are feasible.
Funding
Natural Sciences and Engineering Research Council of Canada; C-COM Satellite Systems Inc..
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. N. Nagai, R. Kumazawa, and R. Fukasawa, “Direct evidence of inter-molecular vibrations by THz spectroscopy,” Chem. Phys. Lett. 413(4-6), 495–500 (2005). [CrossRef]
2. P. F. Taday, I. V. Bradley, D. Arnone, and M. Pepper, “Using terahertz pulse spectroscopy to study the crystalline structure of a drug: A case study of the polymorphs of ranitidine hydrochloride,” J. Pharm. Sci. 92(4), 831–838 (2003). [CrossRef]
3. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]
4. Y. C. Shen, A. T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86(24), 241116 (2005). [CrossRef]
5. T. Tosaka, K. Fujii, K. Fukunaga, and A. Kasamatsu, “Development of complex relative permittivity measurement system based on free-space in 220-330 GHz range,” IEEE Trans. Terahertz Sci. Technol. 5, 1–8 (2014). [CrossRef]
6. J. Hammler, A. J. Gallant, and C. Balocco, “Free-space permittivity measurement at terahertz frequencies with a vector network analyzer,” IEEE Trans. Terahertz Sci. Technol. 6(6), 817–823 (2016). [CrossRef]
7. Y. Wang, Z. Zhao, J. Qin, H. Liu, A. Liu, and M. Xu, “Rapid in situ analysis of l-histidine and α-lactose in dietary supplements by fingerprint peaks using terahertz frequency-domain spectroscopy,” Talanta 208, 120469 (2020). [CrossRef]
8. G. Asai, D. Hata, S. Harada, T. Kasai, Y. Arashida, and I. Katayama, “High-throughput terahertz spectral line imaging using an echelon mirror,” Opt. Express 29(3), 3515–3523 (2021). [CrossRef]
9. R. Wang, Q. Wu, Y. Zhang, X. Xu, Q. Zhang, W. Zhao, B. Zhang, W. Cai, J. Yao, and J. Xu, “Enhanced on-chip terahertz sensing with hybrid metasurface/lithium niobate structures,” Appl. Phys. Lett. 114(12), 121102 (2019). [CrossRef]
10. B. Han, Z. Han, J. Qin, Y. Wang, and Z. Zhao, “A sensitive and selective terahertz sensor for the fingerprint detection of lactose,” Talanta 192, 1–5 (2019). [CrossRef]
11. J. Zhu, S. Jiang, Y. Xie, F. Li, L. Du, K. Meng, L. Zhu, and J. Zhou, “Enhancing terahertz molecular fingerprint detection by a dielectric metagrating,” Opt. Lett. 45(8), 2335–2338 (2020). [CrossRef]
12. J. Qin, W. Cheng, B. Han, Y. Du, Z. Han, and Z. Zhao, “Ultrasensitive detection of saccharides using terahertz sensor based on metallic nano-slits,” Sci. Rep. 10(1), 3712 (2020). [CrossRef]
13. M. Walther, M. R. Freeman, and F. A. Hegmann, “Metal-wire terahertz time-domain spectroscopy,” Appl. Phys. Lett. 87(26), 261107 (2005). [CrossRef]
14. T. Ohkubo, M. Onuma, J. Kitagawa, and Y. Kadoya, “Micro-strip-line-based sensing chips for characterization of polar liquids in terahertz regime,” Appl. Phys. Lett. 88(21), 212511 (2006). [CrossRef]
15. M. Theuer and J. S. Melinger, “High resolution waveguide terahertz time-domain spectroscopy,” J. Infrared, Millimeter, Terahertz Waves 32(11), 1267–1284 (2011). [CrossRef]
16. H. Amarloo, M. Neshat, and S. Safavi-Naeini, “Terahertz plasmonic-like waveguide for integrated sensing applications,” Electron. Lett. 49(13), 836–838 (2013). [CrossRef]
17. M. Islam, D. R. Chowdhury, A. Ahmad, and G. Kumar, “Terahertz plasmonic waveguide based thin film sensor,” J. Lightwave Technol. 35(23), 5215–5221 (2017). [CrossRef]
18. Z. Ma, S. M. Hanham, P. Arroyo Huidobro, Y. Gong, M. Hong, N. Klein, and S. A. Maier, “Terahertz particle-in-liquid sensing with spoof surface plasmon polariton waveguides,” APL Photonics 2(11), 116102 (2017). [CrossRef]
19. J. Sultana, M. S. Islam, K. Ahmed, A. Dinovitser, B. W.-H. Ng, and D. Abbott, “Terahertz detection of alcohol using a photonic crystal fiber sensor,” Appl. Opt. 57(10), 2426–2433 (2018). [CrossRef]
20. M. B. Byrne, J. Cunningham, K. Tych, A. D. Burnett, M. R. Stringer, C. D. Wood, L. Dazhang, M. Lachab, E. H. Linfield, and A. G. Davies, “Terahertz vibrational absorption spectroscopy using microstrip-line waveguides,” Appl. Phys. Lett. 93(18), 182904 (2008). [CrossRef]
21. M. Swithenbank, A. D. Burnett, C. Russell, L. H. Li, A. G. Davies, E. H. Linfield, J. E. Cunningham, and C. D. Wood, “On-chip terahertz-frequency measurements of liquids,” Anal. Chem. 89(15), 7981–7987 (2017). [CrossRef]
22. K. Yoshioka, N. Kumada, K. Muraki, and M. Hashisaka, “On-chip coherent frequency-domain THz spectroscopy for electrical transport,” Appl. Phys. Lett. 117(16), 161103 (2020). [CrossRef]
23. L. Hou, W. Shi, C. Dong, L. Yang, Y. Wang, H. Wang, Y. Hang, and F. Xue, “Probing trace lactose from aqueous solutions by terahertz time-domain spectroscopy,” Spectrochim. Acta, Part A 246, 119044 (2021). [CrossRef]
24. J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express 16(6), 4296–4301 (2008). [CrossRef]
25. W.-C. Lai, S. Chakravarty, X. Wang, C. Lin, and R. T. Chen, “On-chip methane sensing by near-IR absorption signatures in a photonic crystal slot waveguide,” Opt. Lett. 36(6), 984–986 (2011). [CrossRef]
26. L. Tombez, E. J. Zhang, J. S. Orcutt, S. Kamlapurkar, and W. M. J. Green, “Methane absorption spectroscopy on a silicon photonic chip,” Optica 4(11), 1322–1325 (2017). [CrossRef]
27. Z.-F. Wu, C.-T. Zheng, Z.-W. Liu, D. Yao, W.-X. Zheng, Y.-D. Wang, F. Wang, and D.-M. Zhang, “Investigation of a slow-light enhanced near-infrared absorption spectroscopic gas sensor, based on hollow-core photonic band-gap fiber,” Sensors 18(7), 2192 (2018). [CrossRef]
28. A. Gervais, P. Jean, W. Shi, and S. LaRochelle, “Design of slow-light subwavelength grating waveguides for enhanced on-chip methane sensing by absorption spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 25(3), 1–8 (2019). [CrossRef]
29. K. M. Yoo, J. Midkiff, A. Rostamian, C.-J. Chung, H. Dalir, and R. T. Chen, “InGaAs membrane waveguide: a promising platform for monolithic integrated mid-infrared optical gas sensor,” ACS Sens. 5(3), 861–869 (2020). [CrossRef]
30. M. Vlk, A. Datta, S. Alberti, H. D. Yallew, V. Mittal, G. S. Murugan, and J. Jágerská, “Extraordinary evanescent field confinement waveguide sensor for mid-infrared trace gas spectroscopy,” Light: Sci. Appl. 10(1), 26 (2021). [CrossRef]
31. N. Ranjkesh, M. Basha, A. Taeb, and S. Safavi-Naeini, “Silicon-on-glass dielectric waveguide—Part II: For THz applications,” IEEE Trans. Terahertz Sci. Technol. 5(2), 280–287 (2015). [CrossRef]
32. H. Amarloo and S. Safavi-Naeini, “Terahertz line defect waveguide based on silicon-on-glass technology,” IEEE Trans. Terahertz Sci. Technol. 7(4), 433–439 (2017). [CrossRef]
33. H. Amarloo, N. Ranjkesh, and S. A. Safavi-Naeini, “Terahertz silicon-BCB-quartz dielectric waveguide: an efficient platform for compact THz systems,” IEEE Trans. Terahertz Sci. Technol. 8(2), 201–208 (2018). [CrossRef]
34. N. Ranjkesh, H. Amarloo, S. Gigoyan, N. Ghafarian, M. A. Basha, and S. Safavi-Naeini, “1.1 THz u-silicon-on-glass (U-SOG) waveguide: A low-loss platform for THz high-density integrated circuits,” IEEE Trans. Terahertz Sci. Technol. 8(6), 702–709 (2018). [CrossRef]
35. N. Ranjkesh, S. Gigoyan, H. Amarloo, M. Basha, and S. Safavi-Naeini, “Broadband single-mode THz suspended silicon-on-glass waveguide,” IEEE Microw. Wireless Compon. Lett. 28(3), 185–187 (2018). [CrossRef]
36. W. Gao, X. Yu, M. Fujita, T. Nagatsuma, C. Fumeaux, and W. Withayachumnankul, “Effective-medium-cladded dielectric waveguides for terahertz waves,” Opt. Express 27(26), 38721–38734 (2019). [CrossRef]
37. E. Akiki, M. Verstuyft, B. Kuyken, B. Walter, M. Faucher, J.-F. Lampin, G. Ducournau, and M. Vanwolleghem, “High-Q THz photonic crystal cavity on a low-loss suspended silicon platform,” IEEE Trans. Terahertz Sci. Technol. 11(1), 42–53 (2021). [CrossRef]
38. W. Gao, W. S. Lee, X. Yu, M. Fujita, T. Nagatsuma, C. Fumeaux, and W. Withayachumnankul, “Characteristics of effective-medium-clad dielectric waveguides,” IEEE Trans. Terahertz Sci. Technol. 11, 1 (2020). [CrossRef]
39. D. Headland, W. Withayachumnankul, X. Yu, M. Fujita, and T. Nagatsuma, “Unclad microphotonics for terahertz waveguides and systems,” J. Lightwave Technol. 38, 1 (2020). [CrossRef]
40. H. Li, M. X. Low, R. T. Ako, M. Bhaskaran, S. Sriram, W. Withayachumnankul, B. T. Kuhlmey, and S. Atakaramians, “Broadband single-mode hybrid photonic crystal waveguides for terahertz integration on a chip,” Adv. Mater. Technol. 5(7), 2000117 (2020). [CrossRef]
41. H. Amarloo and S. Safavi-Naeini, “Terahertz slot dielectric waveguide implemented on the silicon-BCB-quartz platform,” IEEE Transactions on Terahertz Science and Technology, doi: 10.1109/TTHZ.2021.3049650 (2021).
42. E. R. Brown, J. E. Bjarnason, A. M. Fedor, and T. M. Korter, “On the strong and narrow absorption signature in lactose at 0.53 THz,” Appl. Phys. Lett. 90(6), 061908 (2007). [CrossRef]
43. S. Yamauchi, S. Hatakeyam, Y. Imai, and M. Tonouchi, “Terahertz time-domain spectroscopy to identify and evaluate anomer in lactose,” Am. J. Anal. Chem. 04(12), 756–762 (2013). [CrossRef]
44. Y.-S. Lee, Principles of terahertz science and technology (Springer, 2009).
45. A. Nitkowski, L. Chen, and M. Lipson, “Cavity-enhanced on-chip absorption spectroscopy using microring resonators,” Opt. Express 16(16), 11930–11936 (2008). [CrossRef]
46. M. D. Janezic and J. A. Jargon, “Complex permittivity determination from propagation constant measurements,” IEEE Microw. Guid. Wave Lett. 9(2), 76–78 (1999). [CrossRef]
47. N. A. Mortensen and S. Xiao, “Slow-light enhancement of beer-lambert-bouguer absorption,” Appl. Phys. Lett. 90(14), 141108 (2007). [CrossRef]
48. H. Amarloo and S. Safavi-Naeini, “Interaction between a waveguide mode and an absorptive medium,” arXiv preprint arXiv:2103.02120 (2021).
49. H. Amarloo and S. Safavi-Naeini, “Slot plasmonic waveguide based on doped-GaAs for terahertz deep-subwavelength applications,” J. Opt. Soc. Am. A 32(11), 2189–2194 (2015). [CrossRef]
50. J. Li, H. Qu, and J. Wang, “Photonic Bragg waveguide platform for multichannel resonant sensing applications in the THz range,” Biomed. Opt. Express 11(5), 2476–2489 (2020). [CrossRef]
