Open Access
Add to BibSonomy
Abstract
We report on the fabrication and characterisation of a terahertz (THz) refractive index matching solution (TeraSol) based on barium titanate (BaTiO3) particles and benzocyclobutene (BCB). The high refractive index of BaTiO3 in the THz range makes this material ideal for tuning the effective refractive index of the solution over a wide range. Exploiting the effective medium approximation, we are able to determine the concentration of BaTiO3 particles necessary to obtain target refractive index values between n = 1.8 and n = 5, optimised to match those of substrates widely used in the THz. TeraSol can dramatically reduce the reflections from the substrate during measurements with THz time domain spectroscopy at cryogenic and room temperature. These properties make TeraSol an appealing material for anti-reflective coatings.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The terahertz (THz) regime is an important spectral region ranging from bio-medicine [1,2] and food technology [3] to security and telecommunications [4–7]. Recently, also several platforms for studying quantum phenomena have been developed in this frequency range [8–10]. Nowadays, the most efficient methods for THz generation and detection are photoconductive antennas (PCA) [11], electro-optic sampling [12,13] and quantum cascade lasers [14,15]. The THz regime started being explored only in the last 30 years due to the lack of sources and detectors, limiting materials and devices that could be exploited in this regime. Thus, new devices and materials have to be investigated in order to fill the so-called THz gap. Materials commonly used in the THz have refractive indices between n = 1.3 for polytetrafluoroethylene (PTFE) [16] and n = 6.5 for lithium niobate (LiNbO3) [17]. The difference in the refractive indices between materials with n ≫ 1 and air n = 1 generates reflections at the interfaces, lowering the efficiency of certain devices due to insertion and extraction losses. Thus, in measurements based on coherent detection, for example THz time-domain spectroscopy (THz-TDS), the resolution is limited by secondary reflections. Major works have suggested methods for eliminating the reflections, such as numerical [18,19] or with impedance matching [20] both in THz-TDS and THz imaging. Chen et al. [21] have also demonstrated a broadband antireflection coating based on micropyramid structures for silicon. Here, we suggest another option, the refractive index matching. In the optical regime, there is a plethora of research and methods for achieving effective refractive index matching and anti-reflection coating. These methods are usually based on particles, such as plastic, glass or synthetic rubbers [22–24] and have found various applications, mainly in photonics [25] and optical coupling [26]. In the THz regime there is a lack of such refractive index-matching approaches, and thus index matching has not yet been demonstrated. In this work we demonstrate an innovative solution for refractive index matching in the THz regime, with refractive indices in the range from n =1.8 to n =5. The presented THz refractive index Solution (TeraSol) consists of barium titanate BaTiO3 [27,28] and benzocyclobutene (BCB) allowing the refractive index to be tuned by changing the concentrations of the different constituents. In [29], Smith et al. successfully demonstrated, using micropowder materials, the tuning of the refractive index in the THz regime for the fabrication of optical components. By combining the properties of BaTiO3 and BCB TeraSol provides effective refractive index matching and is promising for use as anti-reflective coating. We characterised the optical properties of the components and the refractive index solutions in a THz-TDS. Using TeraSol as an intermediate layer between substrates, the echoes of the samples were effectively suppressed and etalon effects minimised at room and cryogenic temperatures.
2. Characterisation and fabrication of the samples
All samples presented in this work were measured using THz-TDS, illuminating a PCA with a Ti:sapphire laser with 71 fs pulse duration at 800 nm wavelength and 80 MHz repetition rate at an average power of 500 mW on the PCA. For the detection of the transmission through the samples we used electro-optic sampling with a 3 mm long ZnTe (110) crystal. The refractive indices were calculated from transmission measurements using the parameter extraction method suggested by Duvillaret et al. [30], where the optical parameters are derived without the Kramers-Kronig relations. For the refractive index characterisation of the TeraSol samples we used GaAs windows and metallic spacers in order to achieve specific thickness for the TeraSol samples of ∼400 μm as described in [31].
We fabricated and characterised refractive index matching solutions designed to match the refractive indices of three common substrate materials namely silicon (Si), gallium arsenide (GaAs) and sapphire. A summary of the refractive indices of these substrates at 0.4 THz as measured with THz-TDS [31] is presented in Table 1. The values are consistent with previously reported values [32]. Since these are the most commonly used materials in the THz regime we optimised the solution for refractive indices n =3.3 to 3.6. In order to achieve an efficient refractive index matching, a material with high refractive index in the THz is required. We used BaTiO3 particles because of the relatively high THz refractive index (n = 19 for bulk material and n ≈ 9.5 for thin films [33]) and because they are compatible with common fabrication techniques. In order to achieve a target effective refractive index of n = 3.5, we suspended the particles in a material with lower refractive index. BCB was selected because it is commonly used for thin film depositions and it has low absorption in the THz regime [34,35]. In addition, we used oleic acid as a surfactant in order to prevent aggregations between the particles. BaTiO3 powder, BCB and oleic acid are important for obtaining a homogeneous solution with the right refractive index even when deposited in thin layers.
Table 1. Refractive indices of frequently used substrates in the THz regime at 0.4 THz frequency.
For preparation we mixed BaTiO3, oleic acid, heptane and BCB. We used a commercially available BaTiO3 powder purchased from Sigma-Aldrich with BaTiO3 (IV), 99.995 % trace metals basis. Oleic acid ≥ 99 % was also purchased from Sigma-Aldrich. Previous works have suggested oleic acid in solution with heptane as a suitable surfactant for BaTiO3 [36]. The solution of BaTiO3, oleic acid and heptane was sonicated for 1 hour and afterwards the BCB was added. The solutions remained under the hood for the evaporation of the heptane since the boiling temperature of heptane is at 98.42 °C. The entire process was performed under hood and at 22 °C. For all the different TeraSol samples we used 0.1 ml BaTiO3 powder (with density 6.08 g/ml at 25 °C) and 0.1 ml of oleic acid. The volume of BCB was changed in order to obtain different concentrations and thus different refractive indices. To minimise the error in concentration and achieve better control of the volume we used positive displacement micropipettes during the process. The mean size value of the BaTiO3 particles was measured with Scanning Electron Microscopy (SEM) and estimated to be 421 nm with a standard deviation of 227 nm. In order to investigate any aggregations in the solution, an SEM image was taken of a TeraSol sample with f =30 % of BaTiO3 particles on a GaAs substrate. As can be seen in Fig. 1 there was very little aggregation between the particles, Fig. 1(a), and the size of the particles was uniform, Fig. 1(b).
Fig. 1 (a) Scanning electron microscope (SEM) picture of TeraSol on a GaAs substrate. (b) Histogram showing the distribution of BaTiO3 particle size from the SEM picture in (a).
To accurately determine the correct refractive index for our solutions and match the refractive indices of the desired THz materials, the effective medium approximation was used. With the concentration (f), volume/volume (v/v), the refractive indices of the BaTiO3 powder, the medium (oleic acid and BCB) and the solution, we could tune the concentration of the BaTiO3 powder such that the solution matches the refractive index of the desired material (e.g. GaAs). The effective medium approximation is described by [37]
where εBaTiO3 is the dielectric constant of the BaTiO3 powder, εeff is the effective dielectric constant of the suspension, εs is the dielectric constant of the medium (oleic acid and BCB).The refractive indices of oleic acid, as the surfactant, and BCB were also measured using the parameter extraction method. For oleic acid, the refractive index is noleic acid = 1.62 ± 0.02 and for BCB nBCB=1.65 ± 0.02 at 0.4 THz [38]. Using Eq.(1) [39], the measured refractive indices of different concentration of f of the BaTiO3 powder and the refractive indices of the medium (oleic acid and BCB) we estimated the real part of the refractive index of the BaTiO3 powder as nBaTiO3 = 5.9 ± 0.3 and the imaginary part as κBaTiO3 = 0.3 ± 0.1, from a linear fit. The error of the BaTiO3 powder complex refractive index measurement was calculated using the standard deviation.
3. Results
Various TeraSol samples with different concentrations of BaTiO3 powder were prepared for identifying its impact on the dielectric constant of TeraSol. We created five different solutions with concentrations f = 10 %, 20 %, 30 %, 35 % and 40 % BaTiO3 powder in solution with oleic acid and BCB. Since the refractive indices of BCB and oleic acid are similar (noleic acid = 1.62 and for BCB nBCB = 1.65), the different and higher refractive index for our experiments was the refractive index of BaTiO3 (the real part measured as nBaTiO3 = 5.9 and the imaginary part as κBaTiO3 = 0.3). For extracting the complex refractive index of the BaTiO3 powder, we used the effective medium approximation in different concentrations of TeraSol. We repeated the calculation for different concentrations of TeraSol, namely f = 10 %, 20 %, 30 %, 35 % and 40 %, giving an average value of nBaTiO3 = 5.9± 0.3 and κBaTiO3 = 0.3 ± 0.1. Fig. 2 (a) and (b) shows the real part and the imaginary part of the dielectric constant of TeraSol using the value of BaTiO3 powder as estimated from the Eq.(1), in comparison with the dielectric constant of TeraSol in different measured concentrations. Furthermore, the dielectric constants ε of the TeraSol samples were calculated from the refractive index measurements [31]. The imaginary and real parts of the dielectric constants were calculated as Re(ε) = n2 − κ2 and Im(ε) = 2nκ respectively, where n and κ are the real and the imaginary parts of the refractive index. We report in Fig. 2 the real and imaginary parts of the dielectric constant as a function of the concentration at frequency 0.4 THz. The dielectric constant of TeraSol increases linearly with the BaTiO3 and by varying the concentration of BaTiO3 powder the refractive index can be tuned from n = 1.8 to n = 5. We were able to reach f = 50 % before the particles start to aggregate. In addition, the errors (standard deviation) for the dielectric constants (real and imaginary parts) were calculated by estimating the error in the concentration to be δf = ±1 %, as shown in Fig. 2. In table 2 is a summary of the values of the real and imaginary part of the refractive index (n, κ) and the dielectric constant (Re(ε), Im(ε)) respectively of TeraSol with different concentrations of BaTiO3, namely f = 10 %, 20 %, 30 %, 35 % and 40 % at 0.4 THz frequency. The values of the refractive indices were estimated using a parameter extraction algorithm [30].
Fig. 2 (a) The data points show the real part of the dielectric constant of TeraSol with different concentrations of BaTiO3 powder, namely f = 10 %, 20 %, 30 %, 35 % and 40 % at frequency 0.4 THz, including errors. The lines represent the real part of the dielectric constant of TeraSol using the complex refractive index of BaTiO3 powder estimated from Eq.(1) (nBaTiO3 = 5.9 and κBaTiO3 = 0.3). (b) The imaginary part of the dielectric constant of TeraSol with different concentrations of BaTiO3.
Table 2. The values of the Real and Imaginary part of the Refractive Index (n, κ) and the Dielectric Constant (Re(ε), Im(ε)) of TeraSol with different Concentrations of BaTiO3 at frequency 0.4 THz.
When f ≥ 30 % the thickness varied by ±20 μm across the surface of the samples and these thickness fluctuations were therefore the dominant error in our measurements as we show in Fig. 2. In order to investigate the reproducibility of our samples, we made different solutions with the same concentration and we estimated the error in the refractive index of our process. The error in refractive index between two solutions of TeraSol (32 %) with the same concentration was estimated to be δn = ±0.1.
Furthermore, we used f = 30 % and f = 32 % of BaTiO3 and compared with other materials. As can be seen in Fig. 3(a), the refractive index of TeraSol (f = 30 %) was n30 % = 3.3 and the refractive index of TeraSol (f = 32 %) was n32 % = 3.7. However, the absorption of BaTiO3 is frequency dependent due to soft phonon modes [34] and is higher than the absorption of the substrates; thus the absorption of TeraSol is increasing with the concentration of BaTiO3, Fig. 3(b). Therefore, we show the refractive indices only up to 1.6 THz.
Fig. 3 (a) Refractive indices of TeraSol with two concentrations (f) of BaTiO3 (namely 30 % and 32 %) and of substrates GaAs, Si and Sapphire. Changing the concentration of BaTiO3 leads to different refractive indices that can be tuned in the range n = 1.7 to n = 5. (b) Absorption of TeraSol with two concentrations of BaTiO3 (namely 30 % and 32 %) and the substrates of GaAs, Si and sapphire.
The efficiency of TeraSol (30 %) as a refractive index matching solution was experimentally tested between two Si windows during THz-TDS measurements, Fig. 4. The thicknesses of the Si windows were 550 μm and they were one-side polished. For these experiments the two unpolished surfaces were in contact and three different measurements were performed. Firstly, we measured the signal of a single Si window and we were able to observe the first echo after 12 ps from the surface of the substrate, as shown in Fig. 4(a). In the spectrum, shown in Fig. 4(b), we could clearly see fringes appearing due to this first echo. The same experiment with two Si windows, shown in grey colour in Fig. 4, was performed and again the reflection from the first window was observed after 12 ps and the etalon effect can also be observed in the spectrum. As shown by the red colour in Fig. 4, with TeraSol applied as a thin layer of thickness d = 2 μm between the two Si windows the first reflection from the first window is minimised and the etalon effect on the spectrum was limited. Fig. 4 (green line) shows also the case when the refractive index of TeraSol is different from the refractive index of the substrate. The first reflection and the etalon effect on the spectrum are reduced but not as significantly as with the TeraSol with the same refractive index as the substrate. TeraSol was applied on the Si substrate with blade coating which was then attached to the other Si substrate, Fig. 4(a). Due to its high viscosity, TeraSol did not require further support for the attachment of samples during these measurements. The measured signal using two windows was the same in the range from 0.2 to 2.5 THz with and without TeraSol and no reduction of the signal or bandwidth was observed. Samples with TeraSol did not show any effect of degradation when they were measured after several days. In addition, after fabrication the TeraSol solutions could be applied as a thin film and showed the same performance for several months.
Fig. 4 (a) The signal of a single Si window, two Si windows and two Si windows with TeraSol between the two windows. With refractive index nTeraSol = 3.4 (red line) the suppression of the first reflection is more effective than with refractive index nTeraSol = 3.5 (green line). The effect of the first reflection is eliminated completely with nTeraSol = 3.4. (b) The absorption spectrum of the same samples.
The absolute amplitude reflectivity of the two windows with TeraSol is given by
where is the maximum signal of the echo of the sample, is the maximum signal of the main pulse of the sample and rsub is the reflectivity of a single window: where is the maximum signal of the echo of the substrate and is the maximum signal of the main pulse of the substrate. Using these relations we found an absolute amplitude reflectivity of rTeraSol = 2 %. We also repeated the same experiment for Si with low doping (n-doped with Phosphorus) and GaAs substrates and similar results for the absolute amplitude reflectivity were observed.TeraSol was also used at cryogenic temperatures (T = 4 K) as an index matching intermediate layer between two sapphire windows. In this experiment, sapphire was the substrate used for superconductor yttrium barium copper oxide (YBCO) films. High quality factor (Q) complementary split ring resonators were designed and fabricated in YBCO using the focused ion beam (FIB) technique [40]. The resonance frequency of the resonators was 0.38 THz, Fig. 5(b). The sapphire substrate with the YBCO film had a thickness of 500 μm and we attached another window with a thickness of 1000 μm using TeraSol for refractive index matching to increase the resolution of the measurement. For extracting the Fourier transform of the time domain measurement for observing a clear resonance the data needed to be trimmed before the first echo, Fig. 5(a), in order to avoid an etalon effect in the frequency spectrum, Fig. 5(b). The resolution of the measurements including the echo was 37.5 GHz, while cutting the data before the first echo reduced the frequency resolution to 62.6 GHz, Fig. 5(b). In addition, this clipping prohibits determining an accurate value of the Q factor for high-Q cavities. This resonance broadening arising from the setup limitation is evident in Fig. 5(b). Using TeraSol we could determine a quality factor of Q = 32 at zero magnetic field. However, using the above mentioned 1000 μm sapphire window with TeraSol, the spectral resolution of the measurement in the time domain is increased to be able to determine the Q factor of the cavity. Performing a damped sinusoidal fit to the time trace, which is thanks to the TeraSol long enough to do such fit as the first echo is suppressed, a quality factor of Q = 32 at zero magnetic field could be determined for the cavity, which is still below the resolution limited in the frequency domain.
Fig. 5 Normalised electric field amplitude and normalised spectrum of a single window of YBCO, with complementary split ring resonators with resonant frequency at 0.38 THz, on a sapphire substrate in comparison with the one of YBCO and two Sapphire windows with TeraSol in between. (a) The line with black (blue) colour represents the data without (with) the first echo in the grey area. The red line represents the data with TeraSol and additional 1000 μm of sapphire substrate. In addition, schematic representations of the samples are shown as insets. (b) Normalised frequency spectra. The difference in the spectra between the data with and without the echo is shown and compared with the data from the sample using TeraSol and 1000 μm of sapphire substrate.
4. Conclusion
In conclusion, we have demonstrated an effective refractive index matching solution for the THz regime. The components of the solution are BaTiO3 powder, BCB and oleic acid. The refractive index of TeraSol was measured and can be freely varied between n = 1.8 and n = 5 by adjusting the concentration of BaTiO3. We have shown that TeraSol, when applied as a thin film, does not affect the signal nor the bandwidth even if the absorption of BaTiO3 is significant for THz frequencies. We suggest the use of TeraSol for refractive index matching to substrates commonly used in THz science and technology, namely Si, GaAs and sapphire, as TeraSol can be used very effectively for the elimination of reflections in THz-TDS measurements. The high absorption of TeraSol in combination with readily accessible applications can be used to achieve absorptive boundary conditions in multiple THz devices. We also suggest other materials with high refractive index and lower absorption than BaTiO3, such as LiNbO3, for efficient THz refractive index matching. TeraSol has very low absolute amplitude reflectivity in the range of 0.2 THz to 2.5 THz when used as a thin film and can therefore find applications in THz optics and photonics.
Funding
European Research Council (ERC) Advanced Grant Quantum Metamaterials in the Ultra Strong Coupling Regime (MUSiC) with the ERC (340975); Swiss National Science Foundation (SNF) with National Centre of Competence in Research Quantum Science and Technology (NCCR QSIT).
Acknowledgments
We would like to acknowledge ScopeM (Scientific Center for Optical and Electron Microscopy) at ETH Zürich, for the SEM pictures. The authors would like to thank Shima Rajabali for fruitful discussions and Philipp Täschler for additional measurements.
References
1. Q. Sun, Y. He, K. Liu, S. Fan, E. P. Parrott, and E. Pickwell-MacPherson, “Recent advances in terahertz technology for biomedical applications,” Quant. Imag. Med. Surg. 7, 345 (2017). [CrossRef]
2. B. Fischer, M. Walther, and P. U. Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Biol. 47, 3807 (2002). [CrossRef] [PubMed]
3. C. Jansen, S. Wietzke, O. Peters, M. Scheller, N. Vieweg, M. Salhi, N. Krumbholz, C. Jördens, T. Hochrein, and M. Koch, “Terahertz imaging: applications and perspectives,” Appl. Opt. 49, E48–E57 (2010). [CrossRef] [PubMed]
4. Y. Salamin, B. Baeuerle, W. Heni, F. C. Abrecht, A. Josten, Y. Fedoryshyn, C. Haffner, R. Bonjour, T. Watanabe, M. Burla, et al., “Microwave plasmonic mixer in a transparent fibre–wireless link,” Nat. Photon. 12, 749 (2018). [CrossRef]
5. I.-C. Benea-Chelmus, T. Zhu, F. F. Settembrini, C. Bonzon, E. Mavrona, D. L. Elder, W. Heni, J. Leuthold, L. R. Dalton, and J. Faist, “Three-dimensional phase modulator at telecom wavelength acting as a terahertz detector with an electro-optic bandwidth of 1.25 terahertz,” ACS Photon. 5, 1398–1403 (2018). [CrossRef]
6. T. Kürner and S. Priebe, “Towards THz Communications - Status in Research, Standardization and Regulation,” J. Infra. Millim. THz Waves 35, 53–62 (2014). [CrossRef]
7. T. Nagatsuma, G. Ducournau, and C. C. Renaud, “Advances in terahertz communications accelerated by photonics,” Nat. Photon. 10, 371 (2016). [CrossRef]
8. G. Scalari, C. Maissen, D. Turčinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial,” Science 335, 1323–1326 (2012). [CrossRef] [PubMed]
9. G. Günter, A. A. Anappara, J. Hees, A. Sell, G. Biasiol, L. Sorba, S. De Liberato, C. Ciuti, A. Tredicucci, A. Leitenstorfer, et al., “Sub-cycle switch-on of ultrastrong light–matter interaction,” Nature 458, 178 (2009). [CrossRef]
10. Q. Zhang, M. Lou, X. Li, J. L. Reno, W. Pan, J. D. Watson, M. J. Manfra, and J. Kono, “Collective non-perturbative coupling of 2D electrons with high-quality-factor terahertz cavity photons,” Nat. Phys. 12, 1005 (2016). [CrossRef]
11. Y. C. Shen, P. C. Upadhya, H. E. Beere, E. H. Linfield, A. G. Davies, I. S. Gregory, C. Baker, W. R. Tribe, and M. J. Evans, “Generation and detection of ultrabroadband terahertz radiation using photoconductive emitters and receivers,” Appl. Phys. Lett. 85, 164–166 (2004). [CrossRef]
12. Q. Wu, M. Litz, and X. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924–2926 (1996). [CrossRef]
13. A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321–2323 (1996). [CrossRef]
14. S. Dhillon, M. Vitiello, E. Linfield, A. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. Williams, et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50, 043001 (2017). [CrossRef]
15. M. S. Vitiello, G. Scalari, B. Williams, and P. D. Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23, 5167–5182 (2015). [CrossRef] [PubMed]
16. F. D’Angelo, Z. Mics, M. Bonn, and D. Turchinovich, “Ultra-broadband THz time-domain spectroscopy of common polymers using THz air photonics,” Opt. Express 22, 12475–12485 (2014). [CrossRef]
17. X. Wu, C. Zhou, W. R. Huang, F. Ahr, and F. X. Kärtner, “Temperature dependent refractive index and absorption coefficient of congruent lithium niobate crystals in the terahertz range,” Opt. Express 23, 29729–29737 (2015). [CrossRef] [PubMed]
18. M. Naftaly and R. Miles, “A method for removing etalon oscillations from THz time-domain spectra,” Opt. Commun. 280, 291–295 (2007). [CrossRef]
19. H. Park, J.-H. Son, and C.-B. Ahn, “Enhancement of terahertz reflection tomographic imaging by interference cancellation between layers,” Opt. Express 24, 7028–7036 (2016). [CrossRef] [PubMed]
20. J. Kröll, J. Darmo, and K. Unterrainer, “Metallic wave-impedance matching layers for broadband terahertz optical systems,” Opt. Express 15, 6552–6560 (2007). [CrossRef] [PubMed]
21. Y. W. Chen, P. Y. Han, and X.-C. Zhang, “Tunable broadband antireflection structures for silicon at terahertz frequency,” Appl. Phys. Lett. 94, 041106 (2009). [CrossRef]
22. S. Wiederseiner, N. Andreini, G. Epely-Chauvin, and C. Ancey, “Refractive-index and density matching in concentrated particle suspensions: a review,” Exp. Fluids 50, 1183–1206 (2011). [CrossRef]
23. R. Budwig, “Refractive index matching methods for liquid flow investigations,” Exp. Fluids 17, 350–355 (1994). [CrossRef]
24. J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, “Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection,” Nat. Photon. 1, 176 (2007). [CrossRef]
25. L. S. Hung, C. W. Tang, M. G. Mason, P. Raychaudhuri, and J. Madathil, “Application of an ultrathin LiF/Al bilayer in organic surface-emitting diodes,” Appl. Phys. Lett. 78, 544–546 (2001). [CrossRef]
26. J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996). [CrossRef] [PubMed]
27. J. Hlinka, T. Ostapchuk, D. Nuzhnyy, J. Petzelt, P. Kuzel, C. Kadlec, P. Vanek, I. Ponomareva, and L. Bellaiche, “Coexistence of the Phonon and Relaxation Soft Modes in the Terahertz Dielectric Response of Tetragonal BaTiO3,” Phys. Rev. Lett. 101, 167402 (2008). [CrossRef]
28. S. Wada, H. Yasuno, T. Hoshina, H. Kakemoto, Y. Kameshima, and T. Tsurumi, “Size dependence of THz region dielectric properties for barium titanate fine particles,” J. Electroceramics 21, 198–201 (2008). [CrossRef]
29. B. Scherger, M. Scheller, C. Jansen, M. Koch, and K. Wiesauer, “Terahertz lenses made by compression molding of micropowders,” Appl. Opt. 50, 2256–2262 (2011). [CrossRef] [PubMed]
30. L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996). [CrossRef]
31. E. Mavrona, U. Chodorow, M. E. Barnes, J. Parka, N. Palka, S. Saitzek, J.-F. Blach, V. Apostolopoulos, and M. Kaczmarek, “Refractive indices and birefringence of hybrid liquid crystal - nanoparticles composite materials in the terahertz region,” AIP Adv. 5, 077143 (2015). [CrossRef]
32. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990). [CrossRef]
33. M. Misra, K. Kotani, T. Kiwa, I. Kawayama, H. Murakami, and M. Tonouchi, “THz time domain spectroscopy of pulsed laser deposited BaTiO3 thin films,” Appl. Surf. Sci. 237, 421–426 (2004). [CrossRef]
34. H. Zhang, L. A. Dunbar, G. Scalari, R. Houdré, and J. Faist, “Terahertz photonic crystal quantum cascade lasers,” Opt. Express 15, 16818–16827 (2007). [CrossRef] [PubMed]
35. L. Bosco, C. Bonzon, K. Ohtani, M. Justen, M. Beck, and J. Faist, “A patch-array antenna single-mode low electrical dissipation continuous wave terahertz quantum cascade laser,” Appl. Phys. Lett. 109, 201103 (2016). [CrossRef]
36. O. Kurochkin, E. Mavrona, V. Apostolopoulos, J.-F. Blach, J.-F. Henninot, M. Kaczmarek, S. Saitzek, M. Sokolova, and Y. Reznikov, “Electrically charged dispersions of ferroelectric nanoparticles,” Appl. Phys. Lett. 106, 043111 (2015). [CrossRef]
37. O. Levy and D. Stroud, “Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers,” Phys. Rev. B 56, 8035–8046 (1997). [CrossRef]
38. Z. Han, S. Ohno, Y. Tokizane, K. Nawata, T. Notake, Y. Takida, and H. Minamide, “Thin terahertz-wave phase shifter by flexible film metamaterial with high transmission,” Opt. Express 25, 31186–31196 (2017). [CrossRef] [PubMed]
39. M. Scheller, S. Wietzke, C. Jansen, and M. Koch, “Modelling heterogeneous dielectric mixtures in the terahertz regime: a quasi-static effective medium theory,” J. Phys. D: Appl. Phys. 42, 065415 (2009). [CrossRef]
40. J. Keller, G. Scalari, F. Appugliese, E. Mavrona, S. Rajabali, M. J. Süess, M. Beck, and J. Faist, “High Tc Superconducting THz Metamaterial for Ultrastrong Coupling in a Magnetic Field,” ACS Photon. 5, 3977–3983 (2018). [CrossRef]
