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Thin-wall cyclic olefin copolymer tube waveguide for broadband terahertz transmission
Optical Materials xxx (xxxx) xxx
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Thin-wall cyclic olefin copolymer tube waveguide for broadband terahertz transmission Yi Zhong, Guoxing Xie, Feng Mao, Jun Ding, Fangyu Yue, Shaoqiang Chen, Xuehui Lu **, Chengbin Jing *, Junhao Chu Engineering Research Center for Nanophotonics and Advanced Instrument of Ministry of Education; Key Laboratory of Polar Materials and Devices (Ministry of Education); The Extreme Optoelectromechanics Laboratory; Department of Materials; School of Physics and Electronic Science, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Terahertz transmission Polymer tube waveguide Dynamic coating method Terahertz time domain spectroscopy
A thin-wall cyclic olefin copolymer (COC) tube terahertz (THz) waveguide was proposed and fabricated for broadband terahertz transmission. A dynamic coating method was developed to prepare highly uniform COC tube waveguide samples with an inner diameter of 2.8 mm and three different wall thicknesses from 33.0 to 58.6 μm. The resonant frequencies and transmission bandwidths were measured by the THz time domain spectroscopy and proven to be adjustable by the wall thickness of the COC tube waveguides. The measured minimum losses of the waveguide sample with the wall thickness of 58.6 μm for the straight and bending transmissions are 0.10 dB/cm and 0.18 dB/cm at 1.05 THz, respectively.
1. Introduction The development of terahertz (THz) technology in emission, trans mission, and detection leads to a wide range of applications in communication, security, medical and spectroscopy [1]. It is of great importance to develop a reliable and applicable waveguide for the THz transmission. Great progress has been made on this research area and a variety of THz waveguides have been proposed, such as parallel plate waveguide [2], metal-wire waveguide [3], hollow metal waveguide [4], polymer tubes [5–12], metal/dielectric hollow glass waveguide [13,14], photonic crystal fibers [15–17] and metallic-grating hollow waveguide [18]. Among these different waveguides, the polymer tube waveguide composed of an air core and a dielectric layer is of particular interest because it features simple structure, low transmission loss and control lable transmission bandwidth. Commercial Teflon or PMMA tube waveguides [5,9] have been reported for low-loss THz wave trans mission. However, the main challenges for polymer waveguides in the THz range are narrow transmission bandwidth and material absorption that needs to be further reduced. Bao et al. [9] measured three poly methyl methacrylate (PMMA) tubes with the same air-core size (4 mm) and three different cladding thickness (1.29, 1.97 and 2.95 mm), and the measured losses were 0.05–0.5 cm 1 (0.22–2.2 dB/cm) in the 0.3–1 THz
range. Lu et al. [10] measured a Teflon pipe waveguide (with a core size of 9 mm and a cladding thickness of 0.5 mm) with a minimum loss of 0.004 cm 1 (0.02 dB/cm) at 0.42 THz. However, the transmission bandwidth is less than 0.2 THz. The narrow transmission bandwidth resulting from the polymer tube with a much thicker wall (greater than or equal to 200 μm) could hinder the applications of the waveguides [19, 20]. In addition, the transmission loss caused by material absorption needs to be further reduced. Recently, the cyclic olefin copolymer (COC) has been adopted for optical devices [21] and waveguides [22] in THz regime because of the low absorption (less than 0.3 cm 1 at 1 THz) and dispersion. It has been theoretically and experimentally demonstrated that COC is a promising THz material for THz waveguides [23,24]. The fabricated COC photonic crystal fiber with a diameter of 6 mm has a low-loss transmission bandwidth of about 0.2 THz [23]. However, the commercial COC tubes are not available for the simple COC tube waveguide, and the research on the fabrication of COC tube waveguides has not been reported yet. In this work, we proposed and fabricated a thin-wall COC tube waveguide. The experimental results demonstrated that the as-prepared waveguides with an inner diameter of 2.8 mm can exhibit the characteristics of broadband transmission (bandwidth is above 2.2 THz), low transmission loss (0.10 dB/cm) and bendability (bending angle 30� , bending radius
* Corresponding author. Department of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai, China. ** Corresponding author. E-mail addresses: [email protected] (X. Lu), [email protected] (C. Jing). https://doi.org/10.1016/j.optmat.2019.109490 Received 2 August 2019; Received in revised form 21 October 2019; Accepted 28 October 2019 0925-3467/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Yi Zhong, Optical Materials, https://doi.org/10.1016/j.optmat.2019.109490
Y. Zhong et al.
Optical Materials xxx (xxxx) xxx
40 cm).
strength of a tube waveguide structure with an excessively thin wall. To obtain a thin-wall COC tube THz waveguide, it is necessary to fabricate a COC tube with a thin and highly uniform tube wall along the waveguide direction. In previous research, the polymer thin-wall tube was fabricated by drawing a preform thick-wall tube to a thin-wall tube at the softening temperature [24,25]. Since preform thick-wall COC tube is not currently available, other fabrication methods should be devel oped in this work. According to the traditional dynamic coating method used for fabricating Ag/polymer coated hollow glass waveguide [26], a uniform polymer dielectric coating can be formed if the polymer solu tion flows through a glass tube at a constant rate aided by the peristaltic pump or vacuum pump. And the prepared dielectric layer could have a thickness of about 1–15 μm. However, such a wall thickness is not suf ficient to maintain mechanical strength of a polymer tube waveguide, and the wall thickness needs to be increased. In practice, the wall thickness of the tube sample can be predicted based on Eq. (2) [27].
Fig. 1(a) illustrates the structure and cross section of the proposed COC tube waveguide in this work. The waveguide consists of an air core with an inner diameter of D and a COC dielectric layer with a thickness of t. The refractive indexes for the air core and COC dielectric layer are n0 and n1, respectively. For tube waveguides, the resonant frequencies and theoretical bandwidth (the interval between two adjacent resonant frequencies) of the transmission windows can be calculated with the following relation [19]: mc fm ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi 2t n2 1
(1)
where m is the resonance order, c is the speed of light in free space, and t and n are the wall thickness and the refractive index of the tube wave guide, respectively. According to Eq. (1), to achieve broadband THz transmission, the wall thickness of the COC tube waveguide is consid erably crucial: the transmission bandwidth increases as the wall thick ness decreases. But in practice, there is a limitation for the decrease of the wall thickness, because it is very difficult to maintain mechanical
� t¼
aC 200
��
Vη γ
�12 =
2. Designs and experimental methods
(2)
where a is the bore radius of the substrate tube, C, η and γ are the concentration, the viscosity and the surface tension of the solution, respectively, and V is the flow speed of the coating solution. The wall thickness could be enhanced by increasing the concentration and vis cosity or the flow rate of the COC coating solution. In the traditional dynamic coating process, a polymer solution with low concentration and viscosity is used to build up a much thinner polymer coating inside hollow glass waveguide. To obtain a COC tube waveguide with a suffi ciently thick wall, a polymer solution with high concentration and vis cosity has to be used. However, it is hard to make such a solution flow throughout the glass tube at constant rate by peristaltic pump or vacuum pump. In this work, a fabrication procedure is developed to obtain a COC tube THz waveguide with an appropriate wall thickness and high uni formity. The experimental diagram is shown in Fig. 1(b). The COC so lution (C ¼ 15 wt%) was prepared by dissolving COC Granules in the chloroform. The COC solution was injected into a glass tube. A metal rod was placed inside the glass tube. The top end of the rod was wrapped with a corrosion-resistant elastomer and the other end was connected with a motor. As the motor ran at a constant speed, it pulled the metal rod going down. Accordingly, the COC solution inside the glass tube dropped (V ¼ 10 cm/min) and a uniform solution layer is adhered to the inner tube wall. The COC-coated glass tube sample was dried for 20 min by a dry air flow (flow rate 120 mL/min). The first COC tube waveguide (sample 1) with an enough mechanical strength was obtain after draw the dry COC layer out from the glass tube. The maximum length of the COC tube sample prepared using the process can reach up to 80 cm. With the same procedure, the flow speed V was reduced to 8 cm/min to prepare sample 2, and the concentrate C was reduced to 13 wt% to prepare sample 3. Theoretically, the thickness of COC layer can be further reduced by reducing the flow speed or the coating solution concentration. However, an excessively thin COC layer is fragile and it is hard to be drawn out from the glass tube. The proposed fabrication device can accurately control the flow speed of the coating solution V. Thus, COC tube waveguides with a highly uniform wall thickness are able to be prepared. Fig. 1(c) shows the picture of the first as-prepared COC tube waveguide (sample 1) with an inner diameter of 2.8 mm. In addition, a 5.7-mm-thick COC disk sample was fabricated using the COC raw material for the refractive index and absorption coefficient char acterizations on THz time-domain spectroscopy (THz-TDS). As shown in Fig. 1(d), the characterized refractive index n1 is around 1.525–1.530 and the absorption coefficient is 0.3–2.5 cm 1 within 0.2–3 THz range.
Fig. 1. (a) Structure and cross section of the COC tube waveguide. (b) Sche matic diagram of equipment used for fabricating the COC tube waveguide via dynamic coating method. (c) Digital picture for the prepared COC tube wave guide (sample 1). (d) The refractive index and absorption coefficient of COC materials measured on a disk sample with thickness of 5.7 mm.
3. Results and discussion The IR transmission spectra of the prepared COC tube waveguides 2
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(see Fig. 2) were recorded on Bruker 80 V FTIR spectrometer in order to estimate the thickness and uniformity of the tube waveguide samples. For each sample, a 14 cm long segment was cut off from a long tube sample for the IR spectrum analysis. The transmission spectra exhibit distinct interference fringes due to the film interference effect. Sample segments cut off from the top and bottom ends and the middle section of a 60-cm-long COC tube sample exhibit almost same interference fringes. This confirms that the COC tube samples prepared in current work have uniform wall thicknesses. The wall thickness can be estimated according to the wavenumbers between two adjacent peaks based on the following equation [28,29]: PN ~ nþ1 Vc ~ nÞ 1 ðV t ¼ n¼1 pffiffiffi2ffiffiffiffiffiffiffiffiffiffi (3) 2N n1 1
R is the reflection coefficient, which is related to the wavelength of the light, the material and the thickness of the dielectric layer, and the incident angle of the light. The calculated IR transmission spectra of COC tube waveguides with the thickness of 58.6 μm, 51.6 μm and 33.0 μm are plotted as the dash line in Fig. 2. It can be seen that the experimental and calculated IR spectra are approximately matched. To investigate the transmission window of the waveguide sample within the terahertz region, THz loss spectra of the COC tube wave guides (length 14 cm) were measured by THz-TDS as well. Fig. 3 shows the schematic of THz-TDS system for the measurement of COC tube waveguides. The femtosecond laser (Coherent Verdi G8) was used as a pump source, and the THz waves were obtained from a GaAs photo conductive antenna. THz pulse was coupled into the waveguide using a TPX lens (focal length 32 mm). The reference spectrum of the THz pulse was measured by adjusting the lenses to the confocal position. The frequency domain spectra can be obtained by Fast Fourier Transform (FFT) of the time domain spectra. Then the loss spectra of the waveguides can be calculated from the frequency domain spectra. Fig. 4 gives the attenuation spectra of the COC tube waveguide samples. The resonant frequencies of sample 1 and sample 2 are approximately 2.18 THz and 2.53 THz, respectively, which are close to the calculated resonant frequencies of 2.21 THz and 2.52 THz based on Eq. (1), respectively. The calculated resonant frequency of sample 3 is 3.93 THz that out of the range of spectra, thus, the resonant frequency cannot be seen on the attenuation spectra. The interval between two adjacent resonant frequencies is treated as the theoretical transmission band width, therefore, the transmission bandwidth for sample 1, 2, and 3 are 2.21 THz, 2.52 THz, 3.93 THz, respectively. As expected, as the wall thickness decreases, the resonant frequency and transmission band width increase. In fact, when the transmission frequency is close to the resonant frequency, the attenuation constant is too high for low-loss transmission. Therefore, the low-loss transmission window, controlling by wall thickness of tube waveguide, is more significant in practice. As the wall thickness increases, the low-loss transmission window moves toward the lower frequency region. In order to show a more reasonable bandwidth, or to observe a greater number of resonant frequencies in 0.5–3 THz range, the sample thickness needs to be increased to more than 100 μm. However, currently such a thick film cannot be prepared using our fabrication process. In fact, many researches have proved that the low-loss band is located in the antiresonant frequencies in thicker wall tube samples (thickness >100 μm) [6,9,19]. The theoretical trans mission loss of the COC tube waveguides is also calculated based on Eq. (4). As for the THz-TDS used in this work, the input THz beam has a divergence half angle of about 14� .The theoretical attenuation spectra of the tube samples are calculated and the results are shown in Fig. 4. As can be seen, the theoretical results show similar variation tendency to the measured spectra. The COC tube waveguide exhibits the character istic of broadband transmission. The dispersion of the COC polymer waveguide can be represented by the group velocity dispersion β2. It can be calculated based on the following formula [9,23]: � � �� β2 ¼ ν∂2 neff ∂ν2 þ 2∂neff ∂ν 2πc (5)
where N is the total number of fringes used for the calculation, ṽ is the centroid spectral wavenumber location of the Nth interference fringe. As seen in Fig. 2, the COC material absorption band in the wave number ranges from 5620 cm 1 to 6000 cm 1. The interference peaks are selected to avoid the absorption band and used to calculate the wall thickness according to Eq. (3). The wall thicknesses of tube samples 1, 2 and 3 reach about 58.6 μm, 51.6 μm and 33.0 μm, respectively, which indicates that the minimum thickness of the COC layer is about 33.0 μm. Then the theoretical transmission spectra of the COC tube waveguides were calculated by the ray model according to the geometric optics method [30–32]. The power of the incident beam is expressed as P0(θ), and the power of the output beam is P(z) after the beam passes through a waveguide of length z. P(z) can be calculated by: � Z θmax Z θmax PðzÞ ¼ P0 ðθÞexp½ 2αðθÞz�sin θdθ ¼ P0 ðθÞexp 0 0 � 1 RðθÞ z sin θdθ (4) 2acotθ where θ is the maximum incidence angle, α is loss constant of power, and
Fig. 2. Experimental and calculated IR spectra of the COC bulk material and prepared COC tube waveguides.
Fig. 3. Schematic of THz-TDS system for the measurement of COC tube waveguide. 3
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Fig. 4. Experimental loss spectra measured by THz-TDS and the calculated loss spectra of the COC tube waveguides.
where neff is the experimental effective index which can be calculated by the measured data from THz-TDS measurements, v is the frequency, c is the speed of light in free space. The dispersion of three COC tube waveguide samples was calculated. The results show that the dispersion |β2| is below 4 ps/THz/cm. It is worth mentioning that in the transmission spectrum measure ment of the waveguide by THz-TDS, the loss consists of transmission loss and coupling loss. The coupling loss is high owing to the large diver gence angle of the incident THz beams. Although the loss is relatively high, THz-TDS can still be used to observe the low-loss transmission window since it can provide a wide frequency range of THz radiations and transmission spectra measurement depends mainly on relative attenuation in unit of dB (that means the measurement can still be performed even under a higher loss condition). But as for the trans mission loss measurement at the frequency of interest, a more reason able loss value in unit of dB/cm can likely be obtained under low coupling loss condition. Therefore, the transmission loss of the COC tube sample was investigated on a VDI (Virginia Diodes, Inc.) THz source, which has a smaller divergence angle. The coupling loss is significantly reduced by focusing the THz beams and using the cut-back method in measurement. Although the maximum frequency of VDI THz source is 1.1 THz, the measured frequency range (0.75–1.1 THz) is in the low-loss band of the waveguides and the loss values are reasonable. Fig. 5(a) gives the experimental setup. The THz beam with a divergence half angle of about 6� was coupled into the COC tube waveguide which was fixed with two diaphragms. The output end of the waveguide was fixed with an adjusting diaphragm which can lateral movement to bend the waveguide, and the output power of THz beam was recorded by Golay Cell detector. Fig. 5(b) gives the measured straight transmission loss spectra. The
Fig. 5. (a) Experimental setup for measuring the transmission losses of the COC tube waveguides. (b) Experiment (straight transmission) and simulation loss spectra with the wall thickness of 58.6 μm, 51.6 μm and 33.0 μm. (c) Bending (30� ) transmission loss spectra with the wall thickness of 58.6 μm, 51.6 μm and 33.0 μm.
attenuation constant for sample 1, 2, and 3 are 0.10–0.26 dB/cm, 0.16–0.36 dB/cm, and 0.23–0.56 dB/cm within 0.75–1.1 THz range, respectively. As the wall thickness of the tube waveguides increases from 33.0 μm to 58.6 μm, the loss decreases. It is because the range of 0.75–1.1 THz is closer to the low-loss transmission window of the 58.6 μm wall thickness COC tube waveguide. The COC tube waveguide (t ¼ 33.0 μm) is unfavorable in this frequency range, even though it has the broadest transmission bandwidth. Therefore, the wall thickness should be adjusted according to the practical transmission frequency range. Considering that ray model is no longer applicable when the transmission wavelength is close to the inner diameter of waveguide [31], the commercial software COMSOL (COMSOL Multiphysics 5.3a) is used for the simulation of loss spectra (given in Fig. 5(b)). The funda mental transmission mode (HE11 mode) was considered in the simula tion. The simulated values is close to the experimental values, it proved that the dominant transmission mode is HE11 mode in the experiment. Compared with the simulated spectra, the experimental spectra are slightly shifted, which may result from the wall thickness variation of 4
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the COC tube waveguide. In Fig. 2, the measured interference peaks of sample 1 (t ¼ 58.6 μm) and sample 3 (t ¼ 33.0 μm) are not completely consistent with the calculated interference peaks, which confirms that there exists a slight fluctuation in the wall thickness from one end of the tube sample to the other end. Another unavoidable reason is that water vapor absorption leads to an increase in actual losses. To investigate the transmission behavior [10] of the tube sample under bending condition, the bending transmission loss is measured and the results are given in Fig. 5(c). The polarization of the input THz waves was perpendicular to the bending plane. When the bending angle of COC tube is 30� at a given bending radius of 40 cm, the attenuation constants for sample 1,2, and 3 are 0.18–0.31 dB/cm, 0.20–0.41 dB/cm, and 0.29–0.58 dB/cm within 0.75–1.1 THz range, respectively. The loss is not notably changed as the bending angle goes from 0� to 30� . This demonstrates the as-fabricated thin wall COC tube waveguide is bend able and can be a good candidate for hollow waveguide delivery of THz radiations. Compared with the reported transmission performances of Teflon or PMMA tube THz waveguides [9,10], the as-prepared COC tube wave guides have preferable performances of broadband and low transmission loss. The bandwidth (>2.2 THz) of COC tube waveguide is 10 times larger than the Teflon or PMMA tube waveguide (bandwidth < 0.2 THz). Besides, the COC tube waveguide (core size 2.8 mm) has a loss of 0.10 dB/cm, which is lower than the 4 mm core PMMA tube waveguide (0.22 dB/cm). Although the loss of COC waveguide is higher than the 9 mm core Teflon tube waveguide (0.02 dB/cm), the core size of the COC tube is three times smaller than the Teflon tube sample.
the work reported in this paper.
4. Conclusion
[16] [17]
Acknowledgments This work was supported by the National Natural Science Foundation of China, China (Grant Nos. 61775060, 61275100, 61761136006, and 61790583). The authors thank Xiaoqing Jia (Nanjing University) for assistance on the transmission measurement of samples with VDI THz source. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
In conclusion, we have successfully prepared the thin-wall COC tube waveguide for the THz transmission using a well controllable dynamic coating method. The IR transmission spectra confirm that the wall thickness of COC tube waveguide is of high uniformity. From the mea surement of THz-TDS, the broadband transmission window of the waveguides has been obtained. The bandwidth can be broadened by decreasing the wall thickness of COC tube waveguide, and the low-loss transmission window will be moved from higher frequency range to lower frequency range when the wall thickness increases. The straight and bending (30� ) transmission losses recorded on VDI systems reach 0.10–0.26 dB/cm and 0.18–0.31 dB/cm for sample 1, 0.16–0.36 dB/cm and 0.20–0.41 dB/cm for sample 2 and 0.23–0.56 dB/cm and 0.29–0.58 dB/cm for sample 3 within 0.75–1.1 THz range, respectively.
[18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
Declaration of competing interest
[28] [29]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence
[30] [31] [32]
5
M. Tonouchi, Nat. Photonics 1 (2007) 97–105. D.G. Cooke, P.U. Jepsen, Opt. Express 16 (2008) 15123–15129. N. Yudasari, J. Anthony, R. Leonhardt, Opt. Express 22 (2014) 26042–26054. K. Ito, T. Katagiri, Y. Matsuura, J. Opt. Soc. Am. B 34 (2017) 60–65. C.H. Lai, Y.C. Hsueh, H.W. Chen, Y. Huang, H. Chang, C.K. Sun, Opt. Lett. 34 (2009) 3457–3459. C.H. Lai, B. You, J.Y. Lu, T.A. Liu, J.L. Peng, C.K. Sun, H.C. Chang, Opt. Express 18 (2010) 309–322. M. Xiao, J. Liu, W. Zhang, J. Shen, Y. Huang, Opt. Express 21 (2013) 19808–19815. C.H. Lai, T. Chang, Y.S. Yeh, Opt. Express 22 (2014) 8460–8472. H. Bao, K. Nielsen, O. Bang, P.U. Jepsen, Sci. Rep. 5 (2015) 7620. J.T. Lu, Y.C. Hsueh, Y.R. Huang, Y.J. Hwang, C.K. Sun, Opt. Express 18 (2010) 26332–26338. B. You, J.Y. Lu, Opt. Express 24 (2016) 18013–18023. D. Yan, J. Li, Optik 180 (2019) 824–831. M. Navarro-Cía, M.S. Vitiello, C.M. Bledt, J.E. Melzer, J.A. Harrington, O. Mitrofanov, Opt. Express 21 (2013) 23748–23755. M. Navarro-Cía, J.E. Melzer, J.A. Harrington, O. Mitrofanov, J. Infrared Millim. Te. 36 (2015) 542–555. J. Yang, J.Y. Zhao, C. Gong, H.L. Tian, L. Sun, P. Chen, L. Lin, W.W. Liu, Opt. Express 24 (2016) 22454–22460. S. Li, Z. Dai, Z. Wang, P. Qi, Q. Su, X. Gao, W. Liu, Optik 176 (2019) 611–616. M.S. Islam, J. Sultana, M. Faisal, M.R. Islam, A. Dinovitser, B.W. Ng, D. Abbott, Opt. Mater. 79 (2018) 336–339. D.B. Tian, H.W. Zhang, Q.Y. Wen, Z.G. Wang, S. Li, Z.J. Chen, X.J. Guo, Appl. Phys. Lett. 97 (2010) 133502. E. Nguema, D. F�erachou, G. Humbert, J.L. Auguste, J.M. Blondy, Opt. Lett. 36 (2011) 1782–1784. C.H. Lai, Y.S. Yeh, C.A. Yeh, Y.K. Wang, Opt. Express 26 (2018) 6456–6465. F. Pavanello, F. Garet, M.B. Kuppam, E. Peytavit, Appl. Phys. Lett. 102 (2013) 111114. S. Atakaramians, A.V. Shahraam, M. Nagel, H.K. Rasmussen, O. Bang, T.M. Monro, D. Abbott, Appl. Phys. Lett. 98 (2011) 251110. K. Nielsen, H.K. Rasmussen, A.J.L. Adam, P.C.M. Planken, O. Bang, P.U. Jepsen, Opt. Express 17 (2009) 8592–8601. M.F. Xiao, J. Liu, W. Zhang, J.L. Shen, Y.D. Huang, Opt. Commun. 298 (2013) 101–105. S. Sato, T. Katagiri, Y. Matsuura, J. Opt. Soc. Am. B 29 (2012) 3006–3009. B. Bowden, J.A. Harrington, O. Mitrofanov, Opt. Lett. 32 (2007) 2945–2947. Y. Wang, A. Hongo, Y. Kato, T. Shimomura, D. Miura, M. Miyagi, Appl. Optics 36 (1997) 2886–2892. M. Miyagi, S. Kawakami, J. Light. Technol. 2 (1984) 116–126. J.E. Melzer, M. Navarrocía, O. Mitrofanov, J.A. Harrington, In Optical Fibers and Sensors for Medical Diagnostics and Treatment Applications XIV, 2014, p. 8938. M. Miyagi, J. Light. Technol. 3 (1985) 303–307. Y. Matsuura, M. Saito, M. Miyagi, A. Hongo, J. Opt. Soc. Am. 6 (1989) 423–427. C.M. Bledt, J.E. Melzer, J.A. Harrington, Appl. Opt. 52 (2013) 6703–6709.
Contents lists available at ScienceDirect
Optical Materials journal homepage: http://www.elsevier.com/locate/optmat
Thin-wall cyclic olefin copolymer tube waveguide for broadband terahertz transmission Yi Zhong, Guoxing Xie, Feng Mao, Jun Ding, Fangyu Yue, Shaoqiang Chen, Xuehui Lu **, Chengbin Jing *, Junhao Chu Engineering Research Center for Nanophotonics and Advanced Instrument of Ministry of Education; Key Laboratory of Polar Materials and Devices (Ministry of Education); The Extreme Optoelectromechanics Laboratory; Department of Materials; School of Physics and Electronic Science, East China Normal University, 500 Dongchuan Road, Shanghai 200241, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Terahertz transmission Polymer tube waveguide Dynamic coating method Terahertz time domain spectroscopy
A thin-wall cyclic olefin copolymer (COC) tube terahertz (THz) waveguide was proposed and fabricated for broadband terahertz transmission. A dynamic coating method was developed to prepare highly uniform COC tube waveguide samples with an inner diameter of 2.8 mm and three different wall thicknesses from 33.0 to 58.6 μm. The resonant frequencies and transmission bandwidths were measured by the THz time domain spectroscopy and proven to be adjustable by the wall thickness of the COC tube waveguides. The measured minimum losses of the waveguide sample with the wall thickness of 58.6 μm for the straight and bending transmissions are 0.10 dB/cm and 0.18 dB/cm at 1.05 THz, respectively.
1. Introduction The development of terahertz (THz) technology in emission, trans mission, and detection leads to a wide range of applications in communication, security, medical and spectroscopy [1]. It is of great importance to develop a reliable and applicable waveguide for the THz transmission. Great progress has been made on this research area and a variety of THz waveguides have been proposed, such as parallel plate waveguide [2], metal-wire waveguide [3], hollow metal waveguide [4], polymer tubes [5–12], metal/dielectric hollow glass waveguide [13,14], photonic crystal fibers [15–17] and metallic-grating hollow waveguide [18]. Among these different waveguides, the polymer tube waveguide composed of an air core and a dielectric layer is of particular interest because it features simple structure, low transmission loss and control lable transmission bandwidth. Commercial Teflon or PMMA tube waveguides [5,9] have been reported for low-loss THz wave trans mission. However, the main challenges for polymer waveguides in the THz range are narrow transmission bandwidth and material absorption that needs to be further reduced. Bao et al. [9] measured three poly methyl methacrylate (PMMA) tubes with the same air-core size (4 mm) and three different cladding thickness (1.29, 1.97 and 2.95 mm), and the measured losses were 0.05–0.5 cm 1 (0.22–2.2 dB/cm) in the 0.3–1 THz
range. Lu et al. [10] measured a Teflon pipe waveguide (with a core size of 9 mm and a cladding thickness of 0.5 mm) with a minimum loss of 0.004 cm 1 (0.02 dB/cm) at 0.42 THz. However, the transmission bandwidth is less than 0.2 THz. The narrow transmission bandwidth resulting from the polymer tube with a much thicker wall (greater than or equal to 200 μm) could hinder the applications of the waveguides [19, 20]. In addition, the transmission loss caused by material absorption needs to be further reduced. Recently, the cyclic olefin copolymer (COC) has been adopted for optical devices [21] and waveguides [22] in THz regime because of the low absorption (less than 0.3 cm 1 at 1 THz) and dispersion. It has been theoretically and experimentally demonstrated that COC is a promising THz material for THz waveguides [23,24]. The fabricated COC photonic crystal fiber with a diameter of 6 mm has a low-loss transmission bandwidth of about 0.2 THz [23]. However, the commercial COC tubes are not available for the simple COC tube waveguide, and the research on the fabrication of COC tube waveguides has not been reported yet. In this work, we proposed and fabricated a thin-wall COC tube waveguide. The experimental results demonstrated that the as-prepared waveguides with an inner diameter of 2.8 mm can exhibit the characteristics of broadband transmission (bandwidth is above 2.2 THz), low transmission loss (0.10 dB/cm) and bendability (bending angle 30� , bending radius
* Corresponding author. Department of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai, China. ** Corresponding author. E-mail addresses: [email protected] (X. Lu), [email protected] (C. Jing). https://doi.org/10.1016/j.optmat.2019.109490 Received 2 August 2019; Received in revised form 21 October 2019; Accepted 28 October 2019 0925-3467/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: Yi Zhong, Optical Materials, https://doi.org/10.1016/j.optmat.2019.109490
Y. Zhong et al.
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40 cm).
strength of a tube waveguide structure with an excessively thin wall. To obtain a thin-wall COC tube THz waveguide, it is necessary to fabricate a COC tube with a thin and highly uniform tube wall along the waveguide direction. In previous research, the polymer thin-wall tube was fabricated by drawing a preform thick-wall tube to a thin-wall tube at the softening temperature [24,25]. Since preform thick-wall COC tube is not currently available, other fabrication methods should be devel oped in this work. According to the traditional dynamic coating method used for fabricating Ag/polymer coated hollow glass waveguide [26], a uniform polymer dielectric coating can be formed if the polymer solu tion flows through a glass tube at a constant rate aided by the peristaltic pump or vacuum pump. And the prepared dielectric layer could have a thickness of about 1–15 μm. However, such a wall thickness is not suf ficient to maintain mechanical strength of a polymer tube waveguide, and the wall thickness needs to be increased. In practice, the wall thickness of the tube sample can be predicted based on Eq. (2) [27].
Fig. 1(a) illustrates the structure and cross section of the proposed COC tube waveguide in this work. The waveguide consists of an air core with an inner diameter of D and a COC dielectric layer with a thickness of t. The refractive indexes for the air core and COC dielectric layer are n0 and n1, respectively. For tube waveguides, the resonant frequencies and theoretical bandwidth (the interval between two adjacent resonant frequencies) of the transmission windows can be calculated with the following relation [19]: mc fm ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi 2t n2 1
(1)
where m is the resonance order, c is the speed of light in free space, and t and n are the wall thickness and the refractive index of the tube wave guide, respectively. According to Eq. (1), to achieve broadband THz transmission, the wall thickness of the COC tube waveguide is consid erably crucial: the transmission bandwidth increases as the wall thick ness decreases. But in practice, there is a limitation for the decrease of the wall thickness, because it is very difficult to maintain mechanical
� t¼
aC 200
��
Vη γ
�12 =
2. Designs and experimental methods
(2)
where a is the bore radius of the substrate tube, C, η and γ are the concentration, the viscosity and the surface tension of the solution, respectively, and V is the flow speed of the coating solution. The wall thickness could be enhanced by increasing the concentration and vis cosity or the flow rate of the COC coating solution. In the traditional dynamic coating process, a polymer solution with low concentration and viscosity is used to build up a much thinner polymer coating inside hollow glass waveguide. To obtain a COC tube waveguide with a suffi ciently thick wall, a polymer solution with high concentration and vis cosity has to be used. However, it is hard to make such a solution flow throughout the glass tube at constant rate by peristaltic pump or vacuum pump. In this work, a fabrication procedure is developed to obtain a COC tube THz waveguide with an appropriate wall thickness and high uni formity. The experimental diagram is shown in Fig. 1(b). The COC so lution (C ¼ 15 wt%) was prepared by dissolving COC Granules in the chloroform. The COC solution was injected into a glass tube. A metal rod was placed inside the glass tube. The top end of the rod was wrapped with a corrosion-resistant elastomer and the other end was connected with a motor. As the motor ran at a constant speed, it pulled the metal rod going down. Accordingly, the COC solution inside the glass tube dropped (V ¼ 10 cm/min) and a uniform solution layer is adhered to the inner tube wall. The COC-coated glass tube sample was dried for 20 min by a dry air flow (flow rate 120 mL/min). The first COC tube waveguide (sample 1) with an enough mechanical strength was obtain after draw the dry COC layer out from the glass tube. The maximum length of the COC tube sample prepared using the process can reach up to 80 cm. With the same procedure, the flow speed V was reduced to 8 cm/min to prepare sample 2, and the concentrate C was reduced to 13 wt% to prepare sample 3. Theoretically, the thickness of COC layer can be further reduced by reducing the flow speed or the coating solution concentration. However, an excessively thin COC layer is fragile and it is hard to be drawn out from the glass tube. The proposed fabrication device can accurately control the flow speed of the coating solution V. Thus, COC tube waveguides with a highly uniform wall thickness are able to be prepared. Fig. 1(c) shows the picture of the first as-prepared COC tube waveguide (sample 1) with an inner diameter of 2.8 mm. In addition, a 5.7-mm-thick COC disk sample was fabricated using the COC raw material for the refractive index and absorption coefficient char acterizations on THz time-domain spectroscopy (THz-TDS). As shown in Fig. 1(d), the characterized refractive index n1 is around 1.525–1.530 and the absorption coefficient is 0.3–2.5 cm 1 within 0.2–3 THz range.
Fig. 1. (a) Structure and cross section of the COC tube waveguide. (b) Sche matic diagram of equipment used for fabricating the COC tube waveguide via dynamic coating method. (c) Digital picture for the prepared COC tube wave guide (sample 1). (d) The refractive index and absorption coefficient of COC materials measured on a disk sample with thickness of 5.7 mm.
3. Results and discussion The IR transmission spectra of the prepared COC tube waveguides 2
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(see Fig. 2) were recorded on Bruker 80 V FTIR spectrometer in order to estimate the thickness and uniformity of the tube waveguide samples. For each sample, a 14 cm long segment was cut off from a long tube sample for the IR spectrum analysis. The transmission spectra exhibit distinct interference fringes due to the film interference effect. Sample segments cut off from the top and bottom ends and the middle section of a 60-cm-long COC tube sample exhibit almost same interference fringes. This confirms that the COC tube samples prepared in current work have uniform wall thicknesses. The wall thickness can be estimated according to the wavenumbers between two adjacent peaks based on the following equation [28,29]: PN ~ nþ1 Vc ~ nÞ 1 ðV t ¼ n¼1 pffiffiffi2ffiffiffiffiffiffiffiffiffiffi (3) 2N n1 1
R is the reflection coefficient, which is related to the wavelength of the light, the material and the thickness of the dielectric layer, and the incident angle of the light. The calculated IR transmission spectra of COC tube waveguides with the thickness of 58.6 μm, 51.6 μm and 33.0 μm are plotted as the dash line in Fig. 2. It can be seen that the experimental and calculated IR spectra are approximately matched. To investigate the transmission window of the waveguide sample within the terahertz region, THz loss spectra of the COC tube wave guides (length 14 cm) were measured by THz-TDS as well. Fig. 3 shows the schematic of THz-TDS system for the measurement of COC tube waveguides. The femtosecond laser (Coherent Verdi G8) was used as a pump source, and the THz waves were obtained from a GaAs photo conductive antenna. THz pulse was coupled into the waveguide using a TPX lens (focal length 32 mm). The reference spectrum of the THz pulse was measured by adjusting the lenses to the confocal position. The frequency domain spectra can be obtained by Fast Fourier Transform (FFT) of the time domain spectra. Then the loss spectra of the waveguides can be calculated from the frequency domain spectra. Fig. 4 gives the attenuation spectra of the COC tube waveguide samples. The resonant frequencies of sample 1 and sample 2 are approximately 2.18 THz and 2.53 THz, respectively, which are close to the calculated resonant frequencies of 2.21 THz and 2.52 THz based on Eq. (1), respectively. The calculated resonant frequency of sample 3 is 3.93 THz that out of the range of spectra, thus, the resonant frequency cannot be seen on the attenuation spectra. The interval between two adjacent resonant frequencies is treated as the theoretical transmission band width, therefore, the transmission bandwidth for sample 1, 2, and 3 are 2.21 THz, 2.52 THz, 3.93 THz, respectively. As expected, as the wall thickness decreases, the resonant frequency and transmission band width increase. In fact, when the transmission frequency is close to the resonant frequency, the attenuation constant is too high for low-loss transmission. Therefore, the low-loss transmission window, controlling by wall thickness of tube waveguide, is more significant in practice. As the wall thickness increases, the low-loss transmission window moves toward the lower frequency region. In order to show a more reasonable bandwidth, or to observe a greater number of resonant frequencies in 0.5–3 THz range, the sample thickness needs to be increased to more than 100 μm. However, currently such a thick film cannot be prepared using our fabrication process. In fact, many researches have proved that the low-loss band is located in the antiresonant frequencies in thicker wall tube samples (thickness >100 μm) [6,9,19]. The theoretical trans mission loss of the COC tube waveguides is also calculated based on Eq. (4). As for the THz-TDS used in this work, the input THz beam has a divergence half angle of about 14� .The theoretical attenuation spectra of the tube samples are calculated and the results are shown in Fig. 4. As can be seen, the theoretical results show similar variation tendency to the measured spectra. The COC tube waveguide exhibits the character istic of broadband transmission. The dispersion of the COC polymer waveguide can be represented by the group velocity dispersion β2. It can be calculated based on the following formula [9,23]: � � �� β2 ¼ ν∂2 neff ∂ν2 þ 2∂neff ∂ν 2πc (5)
where N is the total number of fringes used for the calculation, ṽ is the centroid spectral wavenumber location of the Nth interference fringe. As seen in Fig. 2, the COC material absorption band in the wave number ranges from 5620 cm 1 to 6000 cm 1. The interference peaks are selected to avoid the absorption band and used to calculate the wall thickness according to Eq. (3). The wall thicknesses of tube samples 1, 2 and 3 reach about 58.6 μm, 51.6 μm and 33.0 μm, respectively, which indicates that the minimum thickness of the COC layer is about 33.0 μm. Then the theoretical transmission spectra of the COC tube waveguides were calculated by the ray model according to the geometric optics method [30–32]. The power of the incident beam is expressed as P0(θ), and the power of the output beam is P(z) after the beam passes through a waveguide of length z. P(z) can be calculated by: � Z θmax Z θmax PðzÞ ¼ P0 ðθÞexp½ 2αðθÞz�sin θdθ ¼ P0 ðθÞexp 0 0 � 1 RðθÞ z sin θdθ (4) 2acotθ where θ is the maximum incidence angle, α is loss constant of power, and
Fig. 2. Experimental and calculated IR spectra of the COC bulk material and prepared COC tube waveguides.
Fig. 3. Schematic of THz-TDS system for the measurement of COC tube waveguide. 3
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Fig. 4. Experimental loss spectra measured by THz-TDS and the calculated loss spectra of the COC tube waveguides.
where neff is the experimental effective index which can be calculated by the measured data from THz-TDS measurements, v is the frequency, c is the speed of light in free space. The dispersion of three COC tube waveguide samples was calculated. The results show that the dispersion |β2| is below 4 ps/THz/cm. It is worth mentioning that in the transmission spectrum measure ment of the waveguide by THz-TDS, the loss consists of transmission loss and coupling loss. The coupling loss is high owing to the large diver gence angle of the incident THz beams. Although the loss is relatively high, THz-TDS can still be used to observe the low-loss transmission window since it can provide a wide frequency range of THz radiations and transmission spectra measurement depends mainly on relative attenuation in unit of dB (that means the measurement can still be performed even under a higher loss condition). But as for the trans mission loss measurement at the frequency of interest, a more reason able loss value in unit of dB/cm can likely be obtained under low coupling loss condition. Therefore, the transmission loss of the COC tube sample was investigated on a VDI (Virginia Diodes, Inc.) THz source, which has a smaller divergence angle. The coupling loss is significantly reduced by focusing the THz beams and using the cut-back method in measurement. Although the maximum frequency of VDI THz source is 1.1 THz, the measured frequency range (0.75–1.1 THz) is in the low-loss band of the waveguides and the loss values are reasonable. Fig. 5(a) gives the experimental setup. The THz beam with a divergence half angle of about 6� was coupled into the COC tube waveguide which was fixed with two diaphragms. The output end of the waveguide was fixed with an adjusting diaphragm which can lateral movement to bend the waveguide, and the output power of THz beam was recorded by Golay Cell detector. Fig. 5(b) gives the measured straight transmission loss spectra. The
Fig. 5. (a) Experimental setup for measuring the transmission losses of the COC tube waveguides. (b) Experiment (straight transmission) and simulation loss spectra with the wall thickness of 58.6 μm, 51.6 μm and 33.0 μm. (c) Bending (30� ) transmission loss spectra with the wall thickness of 58.6 μm, 51.6 μm and 33.0 μm.
attenuation constant for sample 1, 2, and 3 are 0.10–0.26 dB/cm, 0.16–0.36 dB/cm, and 0.23–0.56 dB/cm within 0.75–1.1 THz range, respectively. As the wall thickness of the tube waveguides increases from 33.0 μm to 58.6 μm, the loss decreases. It is because the range of 0.75–1.1 THz is closer to the low-loss transmission window of the 58.6 μm wall thickness COC tube waveguide. The COC tube waveguide (t ¼ 33.0 μm) is unfavorable in this frequency range, even though it has the broadest transmission bandwidth. Therefore, the wall thickness should be adjusted according to the practical transmission frequency range. Considering that ray model is no longer applicable when the transmission wavelength is close to the inner diameter of waveguide [31], the commercial software COMSOL (COMSOL Multiphysics 5.3a) is used for the simulation of loss spectra (given in Fig. 5(b)). The funda mental transmission mode (HE11 mode) was considered in the simula tion. The simulated values is close to the experimental values, it proved that the dominant transmission mode is HE11 mode in the experiment. Compared with the simulated spectra, the experimental spectra are slightly shifted, which may result from the wall thickness variation of 4
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the COC tube waveguide. In Fig. 2, the measured interference peaks of sample 1 (t ¼ 58.6 μm) and sample 3 (t ¼ 33.0 μm) are not completely consistent with the calculated interference peaks, which confirms that there exists a slight fluctuation in the wall thickness from one end of the tube sample to the other end. Another unavoidable reason is that water vapor absorption leads to an increase in actual losses. To investigate the transmission behavior [10] of the tube sample under bending condition, the bending transmission loss is measured and the results are given in Fig. 5(c). The polarization of the input THz waves was perpendicular to the bending plane. When the bending angle of COC tube is 30� at a given bending radius of 40 cm, the attenuation constants for sample 1,2, and 3 are 0.18–0.31 dB/cm, 0.20–0.41 dB/cm, and 0.29–0.58 dB/cm within 0.75–1.1 THz range, respectively. The loss is not notably changed as the bending angle goes from 0� to 30� . This demonstrates the as-fabricated thin wall COC tube waveguide is bend able and can be a good candidate for hollow waveguide delivery of THz radiations. Compared with the reported transmission performances of Teflon or PMMA tube THz waveguides [9,10], the as-prepared COC tube wave guides have preferable performances of broadband and low transmission loss. The bandwidth (>2.2 THz) of COC tube waveguide is 10 times larger than the Teflon or PMMA tube waveguide (bandwidth < 0.2 THz). Besides, the COC tube waveguide (core size 2.8 mm) has a loss of 0.10 dB/cm, which is lower than the 4 mm core PMMA tube waveguide (0.22 dB/cm). Although the loss of COC waveguide is higher than the 9 mm core Teflon tube waveguide (0.02 dB/cm), the core size of the COC tube is three times smaller than the Teflon tube sample.
the work reported in this paper.
4. Conclusion
[16] [17]
Acknowledgments This work was supported by the National Natural Science Foundation of China, China (Grant Nos. 61775060, 61275100, 61761136006, and 61790583). The authors thank Xiaoqing Jia (Nanjing University) for assistance on the transmission measurement of samples with VDI THz source. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
In conclusion, we have successfully prepared the thin-wall COC tube waveguide for the THz transmission using a well controllable dynamic coating method. The IR transmission spectra confirm that the wall thickness of COC tube waveguide is of high uniformity. From the mea surement of THz-TDS, the broadband transmission window of the waveguides has been obtained. The bandwidth can be broadened by decreasing the wall thickness of COC tube waveguide, and the low-loss transmission window will be moved from higher frequency range to lower frequency range when the wall thickness increases. The straight and bending (30� ) transmission losses recorded on VDI systems reach 0.10–0.26 dB/cm and 0.18–0.31 dB/cm for sample 1, 0.16–0.36 dB/cm and 0.20–0.41 dB/cm for sample 2 and 0.23–0.56 dB/cm and 0.29–0.58 dB/cm for sample 3 within 0.75–1.1 THz range, respectively.
[18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
Declaration of competing interest
[28] [29]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence
[30] [31] [32]
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M. Tonouchi, Nat. Photonics 1 (2007) 97–105. D.G. Cooke, P.U. Jepsen, Opt. Express 16 (2008) 15123–15129. N. Yudasari, J. Anthony, R. Leonhardt, Opt. Express 22 (2014) 26042–26054. K. Ito, T. Katagiri, Y. Matsuura, J. Opt. Soc. Am. B 34 (2017) 60–65. C.H. Lai, Y.C. Hsueh, H.W. Chen, Y. Huang, H. Chang, C.K. Sun, Opt. Lett. 34 (2009) 3457–3459. C.H. Lai, B. You, J.Y. Lu, T.A. Liu, J.L. Peng, C.K. Sun, H.C. Chang, Opt. Express 18 (2010) 309–322. M. Xiao, J. Liu, W. Zhang, J. Shen, Y. Huang, Opt. Express 21 (2013) 19808–19815. C.H. Lai, T. Chang, Y.S. Yeh, Opt. Express 22 (2014) 8460–8472. H. Bao, K. Nielsen, O. Bang, P.U. Jepsen, Sci. Rep. 5 (2015) 7620. J.T. Lu, Y.C. Hsueh, Y.R. Huang, Y.J. Hwang, C.K. Sun, Opt. Express 18 (2010) 26332–26338. B. You, J.Y. Lu, Opt. Express 24 (2016) 18013–18023. D. Yan, J. Li, Optik 180 (2019) 824–831. M. Navarro-Cía, M.S. Vitiello, C.M. Bledt, J.E. Melzer, J.A. Harrington, O. Mitrofanov, Opt. Express 21 (2013) 23748–23755. M. Navarro-Cía, J.E. Melzer, J.A. Harrington, O. Mitrofanov, J. Infrared Millim. Te. 36 (2015) 542–555. J. Yang, J.Y. Zhao, C. Gong, H.L. Tian, L. Sun, P. Chen, L. Lin, W.W. Liu, Opt. Express 24 (2016) 22454–22460. S. Li, Z. Dai, Z. Wang, P. Qi, Q. Su, X. Gao, W. Liu, Optik 176 (2019) 611–616. M.S. Islam, J. Sultana, M. Faisal, M.R. Islam, A. Dinovitser, B.W. Ng, D. Abbott, Opt. Mater. 79 (2018) 336–339. D.B. Tian, H.W. Zhang, Q.Y. Wen, Z.G. Wang, S. Li, Z.J. Chen, X.J. Guo, Appl. Phys. Lett. 97 (2010) 133502. E. Nguema, D. F�erachou, G. Humbert, J.L. Auguste, J.M. Blondy, Opt. Lett. 36 (2011) 1782–1784. C.H. Lai, Y.S. Yeh, C.A. Yeh, Y.K. Wang, Opt. Express 26 (2018) 6456–6465. F. Pavanello, F. Garet, M.B. Kuppam, E. Peytavit, Appl. Phys. Lett. 102 (2013) 111114. S. Atakaramians, A.V. Shahraam, M. Nagel, H.K. Rasmussen, O. Bang, T.M. Monro, D. Abbott, Appl. Phys. Lett. 98 (2011) 251110. K. Nielsen, H.K. Rasmussen, A.J.L. Adam, P.C.M. Planken, O. Bang, P.U. Jepsen, Opt. Express 17 (2009) 8592–8601. M.F. Xiao, J. Liu, W. Zhang, J.L. Shen, Y.D. Huang, Opt. Commun. 298 (2013) 101–105. S. Sato, T. Katagiri, Y. Matsuura, J. Opt. Soc. Am. B 29 (2012) 3006–3009. B. Bowden, J.A. Harrington, O. Mitrofanov, Opt. Lett. 32 (2007) 2945–2947. Y. Wang, A. Hongo, Y. Kato, T. Shimomura, D. Miura, M. Miyagi, Appl. Optics 36 (1997) 2886–2892. M. Miyagi, S. Kawakami, J. Light. Technol. 2 (1984) 116–126. J.E. Melzer, M. Navarrocía, O. Mitrofanov, J.A. Harrington, In Optical Fibers and Sensors for Medical Diagnostics and Treatment Applications XIV, 2014, p. 8938. M. Miyagi, J. Light. Technol. 3 (1985) 303–307. Y. Matsuura, M. Saito, M. Miyagi, A. Hongo, J. Opt. Soc. Am. 6 (1989) 423–427. C.M. Bledt, J.E. Melzer, J.A. Harrington, Appl. Opt. 52 (2013) 6703–6709.