Concentration-Based Measurement Studies of L-Tryptophan Using Terahertz Time-Domain Spectroscopy (THz-TDS) ¨ zer,a,* Seher Go¨k,b Hakan Altan,a Feride Severcanb Zeynep O a b
Department of Physics, Middle East Technical University, 06800 Cankaya Ankara, Turkey Department of Biology, Middle East Technical University, 06800 Cankaya Ankara, Turkey
L-Tryptophan
is an extremely important amino acid for a variety of biological functions in living organisms. In this study we were able to measure changes in the concentration of L-tryptophan when incorporated into pellets with polyethylene as a host. The changes were measured both through the characteristic absorption bands of the C11 and C12 bonds in the low terahertz frequency range and using changes in the refractive index where pellets with higher concentrations of L-tryptophan showed higher refractive indices. The volumetric concentration of L-tryptophan in the polyethylene pellet was accurately determined with a simple model that explains the contribution to the complex refractive index for the resultant sample due to the two constituent materials. These measurements show that terahertz time-domain techniques can be applied to detect variation in concentration of certain amino acids rapidly by examining the relative phase delay and amplitude change of the terahertz transients. Index Headings: Terahertz time-domain spectroscopy; THz-TDS; L-tryptophan; CRI model; Biological screening.
INTRODUCTION The frequency range for terahertz (THz) waves is between the microwave and far-infrared regions of the electromagnetic spectrum. In the late 1980s, with the work of a few research groups, THz time-domain spectroscopy (THz-TDS) was developed, and now it has gained remarkable importance for several application areas.1 Its time-resolved nature and high signal-to-noise ratio are the main reasons that researchers today prefer THz-TDS for material characterization studies. In this regard, the characterization of organic, namely biological, samples is one of the important applications of THzTDS.2,3 Most of the vibrational modes in biological systems have low frequencies that lie in the mid-infrared to farinfrared part of the electromagnetic spectrum. Typically, these modes are infrared active and can be detected using a variety of measurement techniques, such as Fourier transform infrared (FT-IR) spectroscopy. FT-IR spectroscopy systems are not only limited in the lowfrequency range (to frequencies above 0.5 THz), they are also difficult to implement in studying the changes in refractive index of the investigated samples as opposed to the case with phase sensitive measurement techniques used in THz-TDS. The THz-TDS technique is especially important for studying samples in the 0.1–3.0 Received 28 May 2013; accepted 19 September 2013. * Author to whom correspondence should be sent. E-mail: zeynep.
[email protected] DOI: 10.1366/13-07165
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THz (3–100 cm1) region. Furthermore, THz-TDS typically uses sub 200 fs laser pulses, which enables higher signal-to-noise ratio as compared with low-energy photon detectors, used for conventional FT-IR spectroscopy.4 Within this low-frequency range, amino acids, building blocks of proteins, are highly sensitive to THz waves. Amino acids have been studied extensively, and complete THz fingerprint spectra have been gathered for many varieties. These findings can be applied in the identification of amino acid types and determination of structural isomers.5 For example, a previous study about the structural isomers a and b alanine revealed that they tend to show distinctly different spectra, although they have minor structural differences.6 L-Tryptophan (L-Trp) (Fig. 1) is an essential amino acid for humans, which means that it cannot be synthesized in the organisms’ body, and instead must be supplied externally for the biosynthesis of proteins and the proper maintenance of the many metabolic pathways. L-Tryptophan is the precursor of serotonin, a neuromediator that is closely related to stress response, sleep, mood, and appetite regulation.7–9 In addition, in different studies on malignant diseases, such as hematological neoplasias,10 adult T-cell leukemia,11 gastrointestinal cancer,12 and colorectal cancer,13 increased tryptophan degradation was observed. Throughout these studies it is important to keep in mind that amino acid structure and properties are in direct relationship with protein structure and properties. LTryptophan is rarely found in vegetables, so it is added to commercial food products and to some pharmaceuticals as a dietary supplement. Therefore sensitive, rapid, and less expensive L-Trp detection techniques are gaining increasing interest. For quantitative L-Trp detection, various techniques (spectrophotometry, chemiluminescence, electroanalytical methods, gas chromatography, high-performance liquid chromatography)14–18 have been developed. THz-TDS is a new technique that could help detection of these materials, especially in nonprepared samples, i.e., when the material is in a host or is out in the open. While THz measurements should be performed for different hosts that L-Trp can be found in, during routine measurements in the laboratory, typically the samples are mixed with a THz transparent host such as polyethylene and pressed into a pellet. During these measurements, in order to obtain the absorption spectrum of the sample, the spectrum of the pure host pellet is compared with that of a sample of interest within the host. The usefulness of this technique was shown in previous studies for different organic materials, comprising amino acids, proteins, sugars, nucleobases, and polypeptides.19–22
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FIG. 1. Representation of the L-tryptophan amino acid showing the relative bonds. The carbon bonds as depicted are associated with torsional vibrational modes seen in the low-frequency THz range.8,9
In this work, the differences between the refractive indices and power absorptions of pure L-tryptophan and L-tryptophan–polyethylene mixtures with different ratios are investigated using THz-TDS. We find that while we can measure the known absorption features in the lower part of the THz spectrum, we also see differences in the refractive index that allow us to rapidly identify different concentrations using a simple model that analyzes the relative volumetric concentration of the host and added material. The paper is organized as follows: the following section provides details of the experimental setup, sample preparation, and theoretical background of the experiment. The section after that gives information about the results of the experiment and the evaluation of these results. Finally, the last section summarizes the work and discusses future plans.
MATERIALS AND METHODS Tryptophan pellets were prepared by mixing the tryptophan and spectrophotometric grade high-density polyethylene (PE) powders. Polyethylene was purchased from Sigma-Aldrich (St. Louis, MO; No. 434 272) and stored at room temperature. L-tryptophan was purchased from Sigma-Aldrich (St. Louis, MO; No. T-8659) and used without any further chemical processing. Dry tryptophan powder was homogenized and mixed with PE in an agate mortar to reduce the solid particle size distribution, and then pellets were prepared via applying 1500 psi pressure for 10 min. By weight, 10 and 25% tryptophan containing PE pellets have 0.42 and 0.43 mm thicknesses, respectively, and were both prepared under the same conditions. For a negative-pure polyethylene and positive-pure tryptophan control sample, pellet tablets were pressed with a result of 0.49 and 0.71 mm thicknesses, respectively. Since strong water absorption bands in the 1 to 3 THz spectral range mask the absorption of amino acids, the system was purged with dry nitrogen at 300 K.8 The system that was used for THz-TDS is given in Fig. 2 schematically. The Ti:Al2O3 mode-lock laser output with an average power of 200 mW, repetition rate of 75 MHz, and pulse width of 17 fs is sent to a beam splitter that has a 95:5 transmission ratio. This beam splitter divides the beam in two arms: a generation arm and a detection arm. The generation arm starts with the lens for focusing the beam on the antenna, which is directly connected to a function generator with a square wave
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FIG. 2. Schematic representation of THz-TDS system: the part from generation to detection of THz radiation is enclosed in a Plexiglas chamber purged with dry air and nitrogen gas.
bias of 610 V at 1 kHz. After the generation of a THz wave with the help of the antenna, an off-axis parabolic mirror collimates the wave and the lens (TPX lens, D ¼ 50 mm, F no. 2) and focuses the THz wave onto the sample. After the sample, the second lens, the same type as the first lens, transmits the wave to the other off-axis parabolic mirror, where it focuses onto the detector crystal. In the detection arm after the attenuation filter, the beam is sent to a translational stage that enables the detection of the THz waveform through the sample. The next part of the detection arm is a lens that focuses the beam onto the ZnTe detector crystal for electro-optic detection. For detection of the THz pulse, the most important factor is that the path length of the beams traveled in both arms, and they have to be equal. After the ZnTe crystal there is a quarter-wave plate for polarization control, a Wollaston prism for dividing the beam into two separate polarization states, and finally a balanced photodetector. During the measurement, data acquisition and instrument control are done with the help of a computer and LabView software. The entire system is enclosed in a box that is purged with nitrogen gas. After the measurements of reference scans (without any sample) and sample scans (negative/positive control and positive pellets), the time-dependent data are converted to the frequency domain using the fast Fourier transform algorithm. Amplitude, time delay, and width of the pulse are the parameters extracted from the timedomain data, and transmittance, phase, and absorbance are some parameters extracted from the frequency domain.23–25 The refractive index can be calculated from both time-domain and frequency-domain data. Equation 1 explains the relation of time shift and refractive index, while frequency-dependent values of the refractive index can be obtained from Eq. 3. Time shift also can be expressed in frequency domain as shown in Eq. 2. When we substitute Eq. 2 into Eq. 1, the frequency-dependent refractive index formula, as indicated in Eq. 3, can be
obtained. Additionally, the power absorption coefficient for the sample is obtained by analyzing the transmission for varying thicknesses assuming the measurements are performed in the linear absorption regime (Eq. 4).26 n ¼ 1 þ c3
Dt ¼
Dt d
Du 2pv
n¼1þ
ð1Þ
ð2Þ Du 3 c 2pv 3 d
1 a ¼ lnðTÞ d
ð3Þ
ð4Þ
Here, n is the refractive index, c is the speed of light, Dt is the time shift, d is thickness, Du is the phase shift, t is frequency, a is the absorption coefficient, and T is transmittance. Loss through the sample is governed by absorption, reflection, and transmission, assuming that scattering processes are negligent. In the pellets that were prepared, the polyethylene and L-Trp powders had grain sizes much less than the wavelength of the investigating THz beam; thus, the measurements were done in the Raleigh scattering regime (l particle size), and since the wavelengths are large, loss due to scattering can be safely neglected. However, the loss due to reflection from the interfaces of the sample and the reference environment may have to be considered, !2 ! 1 ðn þ 1Þ2 a ¼ ln T ð5Þ d 4n where n is the refractive index of the sample, and the refractive index of air is 1.26 In our study, the pellets had a refractive index close to 1.5; thus, losses due to reflection from both interfaces of the sample were negligible compared with the loss through the sample and could be safely ignored.
RESULTS AND DISCUSSION Terahertz time-domain scans of the samples are given in Fig. 3. The increased ratio of tryptophan in polyethylene causes a proportional shift in the time domain. The THz waveform scans are sensitive enough to see a shift in the polyethylene þ 10%/25% tryptophan mixtures and pure polyethylene samples in terms of shifts in time domain with respect to the reference scans, which were taken without the sample in the sample holder. The sample holder was a metal aperture to hold the pellets vertically in place, large enough to transmit the full spectrum of the THz pulse profile, which limited the sample size to about 1 cm in diameter. As can be seen in Fig. 3, within the limit of the resolution of our scans, which was about 0.03 ps, these shifts were 0.67, 0.67, 0.74, and 1.94 ps for pure polyethylene, polyethylene þ10% tryptophan, polyethylene þ25% tryptophan, and pure tryptophan, respectively. Although there is not any remarkable difference between polyethylene þ 10%
FIG. 3. THz pulse transmission through the prepared/L-tryptophan mixture pellets.
tryptophan and pure polyethylene samples in terms of shifts in the time domain, there was a notable shift for the polyethylene þ 25% tryptophan sample with respect to the pure polyethylene sample. Also, the peak-to-peak amplitudes of the THz pulse decreased with respect to the percentage of tryptophan, and these differences were valid even for low percentage polyethylene mixture L-Trp pellets. Compared with changes in refractive index, these amplitude changes were more evident. The peakto-peak amplitudes decreased from 561.2 lV for the reference to 542.5, 521.9, 506.7, and 404.7 lV for pure polyethylene, polyethylene þ10% tryptophan, polyethylene þ25% tryptophan, and pure tryptophan, respectively. Understanding the relative content of L-Trp in any medium is an important parameter to assess during analysis of its interactions with various biological and nonbiological environments. To clarify the percentage dependent changes, we analyzed both the refractive index–based and absorbance-based changes as measured with the THz pulse measurements using the complex refractive index model (CRI).27 Various models exist to understand the behavior of a material in a host medium; CRI is a model that refers to a linear relation between the volumetric contents and refractive indices of mixing materials.27 Equation 6 relates the change in the refractive index of the host medium based on the volumetric concentration of the added material (x), n ¼ fx nx þ ð1 fx Þnh
ð6Þ
where n is the complex refractive index of mixture, fx is the volumetric fraction of added material (x), nx is the complex refractive index of added material (x), and nh is the complex refractive index of host.27 To understand the applicability to our measurements, the frequency-dependent refractive indices for the various pellets were calculated (Fig. 4). Significant differences in refractive indices between samples were observed in proportion with the tryptophan content. Pure tryptophan gave the highest index, with the approximate value of 1.84. The value of the frequencydependent refractive indices changed between 1.42 and 1.84 relative to the tryptophan content. With the CRI
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FIG. 4. Refractive indices for the various pellets using the time-domain data and equations given in the text.
analysis technique, the refractive index can be deduced directly from the data. Calculations of actual volumetric concentration and volumetric fractions were performed using the mass and density values that were procured from the sample data sheets; these values were 0.95 g/ml for polyethylene and 0.902 g/ml for tryptophan. For our samples the volumetric fractions (x) of tryptophan and
FIG. 5.
98
polyethylene are 0.095 and 0.905 for the sample with 10% tryptophan and 0.208 and 0.792 for the sample with 25% tryptophan, respectively. Due to the relatively flat response of the refractive index across the THz spectrum, the data were analyzed at a frequency of 1 THz. At 1 THz, refractive index values of 1.48 and 1.54 for 10 and 25% of tryptophan samples were measured, respectively. The shifts in time domain and the thicknesses of samples were substituted in to Eq. 1, and the refractive index values of 1.41, 1.48, 1.52, and 1.84 were calculated for pure polyethylene, polyethylene þ 10% tryptophan, polyethylene þ 25% tryptophan, and pure tryptophan, respectively. Also, using the CRI model and the measured refractive index values for the pure samples, refractive index values of 1.45 for the 10% and 1.50 for the 25% mixture were calculated. The reason for the slight difference between experimental and calculated results can be due to the methods used in the production of the pellets, in that there could be a nonlinear varying concentration of the tryptophan throughout the thickness of the sample. While the refractive index changes are dependent on the sample thickness, which needs to be known in advance, the absorbance depends only on the transmission. Figure 5a shows the calculated absorption coefficient depicting the characteristic tryptophan peaks in the frequencies of 1.42 and 1.82 THz in the 0–2 THz frequency region, as can be seen for the pure tryptophan pellet.
Power absorption coefficient between (a) 0.1–2 THz (b) 1.2–1.6 THz, and (c) 1.7–1.9 THz for the prepared pellets.
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TABLE I. Summary of the volumetric concentration calculations with CRI model. 10% Tryptophan by weight
Actual volumetric concentration % Volumetric concentration from real refractive index 63% Volumetric concentration from power absorption coefficient 65% Volumetric concentration from change in time-domain pulse amplitude 61%
The observed peak in the frequency of 1.42 THz has been attributed to the torsional motion of C11 and C12 in the tryptophan molecule, while the peak on 1.82 THz is associated with the ring torsions of C1–C9.9 The results given are consistent with the previous findings in the literature, where Alfano et al. reported these mentioned torsional vibrations at 1.44 and 1.84 THz, respectively.9 The absorption features are shown in closer view in Fig. 5b and 5c, demonstrating that it could be possible to observe the same peaks with a low percentage of tryptophan concentration in PE pellets. Using the peak absorption coefficients at 1.42 THz, we can use the CRI model for obtaining the volumetric concentration. Absorption coefficients of tryptophan, polyethylene, 10% tryptophan sample, and 25% tryptophan sample are 100.5, 3.02, 10.97, and 19.2, respectively. The results of the analysis with 10 and 25% tryptophan samples are 0.082 and 0.918, 0.166 and 0.834 volumetric indices for tryptophan and polyethylene. While the relative change in the power absorption coefficient also gave precise values for the volumetric concentration of the tryptophan content using the CRI model, as was the case with the refractive index results, both methods require the sample thickness to be known in advance for accurate analysis. Since the absorbance is related directly to the transmission through the sample without knowledge of the sample thickness, the transmission of the THz pulse peak amplitude was also analyzed with respect to the CRI model. Using the measurements as given in Fig. 3, the change of the peak amplitude can be related to volumetric concentrations that were obtained with CRI model. A summary of these volumetric concentration calculations with the CRI model is given in Table 1. These measurements show that varying concentration differences of tryptophan in a specific sample environment can be detected with precision using THz-TDS. Furthermore, the data show that relative concentrations can be deduced without prior knowledge of the dimensions of the sample. This opens up an opportunity for the use of THz-TDS in the screening and diagnosis of cancer and pathological disease as a new technique.
CONCLUSION Use of THz-TDS concentration-dependent changes of in a dry polyethylene environment was analyzed in order to gain a better understanding of the detection capability of this technique when applied to an investigation of the biophysical parameters of biological molecules. It was shown that refractive index changes and changes in relative strength of absorption features in the frequency domain could be used as significant L-Trp
25% Tryptophan by weight
Tryptophan
Polyethylene
Tryptophan
Polyethylene
9.5 13.5 8.2 14.4
90.5 86.5 91.8 85.6
20.8 29.7 16.6 25.8
79.2 70.3 83.4 74.2
signs for concentration-dependent monitoring with knowledge of the prepared sample dimensions. With the CRI model, the volumetric concentration-dependent changes in refractive index were monitored at 1 THz, while the power absorption coefficient changes were analyzed specifically for the characteristic tryptophan torsional vibrational mode measured at 1.42 THz. These measurements show that the CRI model is sufficient in explaining the concentration-dependent changes in these optical parameters. The CRI model was also applied to the relative change in the peak amplitude transmission for the THz pulse through various prepared pellet samples. The results show that accurate analysis of the relative volumetric concentration of L-Trp can be determined by analyzing this change without prior knowledge of sample thickness. This technique allows for rapid measurement of the relative concentration of the added material in the host. Implications of this study are that it could be useful in practical applications of THz-TDS for diagnosis and screening of biological molecules. Especially in current studies investigating the role of tryptophan in cell functionality, this new technique can open up an opportunity for the use of THz-TDS in screening and diagnosis of cancer and pathological diseases. 1. M.C. Beard, G.M. Turner, C.A. Schmuttenmaer. ‘‘Terahertz Spectroscopy’’. J. Phys. Chem. B. 2002. 106(29): 7146-7159. 2. B. Ferguson, X.C. Zhang. ‘‘Materials for Terahertz Science and Technology’’. Nat. Mater. 2002. 1(1): 26-33. 3. P.Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, X..C. Zhang. ‘‘A Direct Comparison Between Terahertz Time-Domain Spectroscopy and Far-Infrared Fourier Transform Spectroscopy’’. J. Appl. Phys. 2001. 89(4): 2357-2359. 4. M. van Exter, D.R. Grischkowsky. ‘‘Characterization of an Optoelectronic Terahertz Beam System’’. IEEE Trans. Microwave Theory Tech. 1990. 38(11): 1684-1691. 5. B. Jin, C. Zhang, P. Wu, S. Liu. ‘‘Recent Progress of Terahertz Spectroscopy on Medicine and Biology in China’’. Terahertz Sci. Technol. 2010. 3(4): 192-200. 6. Y. Zheng, Y. Li, W. Wang. ‘‘THz Time Domain Spectrum of bAlanine’’. Acta Chim. Sin. 2007. 65(1): 72-76. 7. S. Russo, I.P. Kema, R. Fokkema, J.C. Boon, P.H.B. Willemse, E.G.E. de Vries, J.A. den Boer, J. Korf. ‘‘Tryptophan as a Link Between Psychopathology and Somatic States’’. Psychosom. Med. 2003. 65(4): 665-671. 8. J.M. Chalmers, G. Dent. ‘‘Vibrational Spectroscopic Methods in Pharmaceutical Solid-State Characterization’’. In: R. Hilfiker, editor. Polymorphism: in the Pharmaceutical Industry. Weinheim, Germany: Wiley-VCH, 2006. Pp. 95-138. 9. B. Yu, F. Zeng, Y. Yang, Q. Xing, A. Chechin, X. Xin, I. Zeylikovich, R.R. Alfano. ‘‘Torsional Vibrational Modes of Tryptophan Studied by Terahertz Time-Domain Spectroscopy’’. Biophys. J. 2004. 86(3): 1649-1654. 10. A. Lewenhaupt, P. Ekman, P. Eneroth, A. Eriksson, B. Nilsson, L. Nordstrom. ‘‘Serum Levels of Neopterin as Related to the Prognosis of Human Prostatic Carcinoma’’. Eur. Urol. 1986. 12(6): 422-425.
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11. A.L. Mellor, D.H. Munn. ‘‘Tryptophan Catabolism and Regulation of Adaptive Immunity’’. J. Immunol. 2003. 170(12): 5809-5813. 12. D.H. Munn, M. Zhou, J.T. Attwood, I. Bondarev, S.J. Conway, B. Marshall, C. Brown, A.L. Mellor. ‘‘Prevention of Allogeneic Fetal Rejection by Tryptophan Catabolism’’. Science. 1998. 281(5380): 1191-1193. 13. D.H. Munn, M.D. Sharma, D. Hou, B. Baban, J.R. Lee, S.J. Antonia, J.L. Messina, P. Chandler, P.A. Koni, A.L. Mellor. ‘‘Expression of Indoleamine 2,3-Dioxygenase by Plasmacytoid Dendritic Cells in Tumor-Draining Lymph Nodes’’. J. Clin. Invest. 2004. 114(2): 280290. 14. D.J. Fletouris, N.A. Botsoglou, G.E. Papageorgiou, A.J. Mantis. ‘‘Rapid Determination of Tryptophan in Intact Proteins by Derivative Spectrophotometry’’. J. AOAC Int. 1993. 76(6): 1168-1173. 15. A.A. Alwarthan. ‘‘Chemiluminescent Determination of Tryptophan in a Flow Injection System’’. Anal. Chim. Acta. 1995. 317(1.3): 233– 237. 16. A. Babaei, M. Zendehdel, B. Khalilzadeh, A. Taheri. ‘‘Simultaneous Determination of Tryptophan, Uric Acid and Ascorbic Acid at Iron(III) Doped Zeolite Modified Carbon Paste Electrode’’. Colloids Surf., B. 2008. 66(2): 226-232. 17. V. Fabian, M. Pinter-Szakacs, I. Molna´r-Perl. ‘‘Gas Chromatography of Tryptophan Together with Other Amino Acids in Hydrochloric Acid Hydrolysates’’. J. Chromatogr. 1990. 520: 193-199. 18. C. Delgado-Andrade, J.A. Rufia´n-Henares, S. Jime´nez-Pe´rez, F.J. Morales. ‘‘Tryptophan Determination in Milk-Based Ingredients and Dried Sport Supplements by Liquid Chromatography with Fluorescence Detection’’. Food Chem. 2006. 98(3): 580-585.
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19. K. Yamamoto, K. Tominaga, H. Sasakawa, A. Tamura, H. Murakami, H. Ohtake, N. Sarukura. ‘‘Terahertz Time-Domain Spectroscopy of Amino Acids and Polypeptides’’. Biophys. J. 2005. 89(3): L22-L24. 20. S.E. Whitmire, D. Wolpert, A.G. Markelz, J.R. Hillebrecht, J. Galan, R.R. Birge. ‘‘Protein Flexibility and Conformational State: A Comparison of Collective Vibrational Modes of Wild-Type and D96N Bacteriorhodopsin’’. Biophys. J. 2003. 85(2): 1269-1277. 21. H..B. Liu, X..C. Zhang. ‘‘Dehydration Kinetics of D-glucose Monohydrate Studies Using THz Time-Domain Spectroscopy’’. Chem. Phys. Lett. 2006. 429(1.3): 229-233. 22. B.M. Fischer, M. Walther, P.U. Jepsen. ‘‘Far-Infrared Vibrational Modes of DNA Components Studied by Terahertz Time-Domain Spectroscopy’’. Phys. Med. Biol. 2002. 47(21): 3807-3814. 23. A.J. Fitzgerald, E. Berry, N.N. Zinovev, G.C. Walker, M.A. Smith, J.M. Chamberlain. ‘‘An Introduction to Medical Imaging with Coherent Terahertz Frequency Radiation’’. Phys. Med. Biol. 2002. 47(7): R67-R84. 24. E. Pickwell, V.P. Wallace. ‘‘Biomedical Applications of Terahertz Technology’’. J. Phys. D: Appl. Phys. 2006. 39(17): R301-R310. 25. M. Schirmer, M. Fujio, M. Minami, J. Miura, T. Araki, T. Yasui. ‘‘Biomedical Applications of a Real-Time Terahertz Color Scanner’’. Biomed. Opt. Express. 2010. 1(2): 354-366. 26. P.U. Jepsen, B.M. Fischer. ‘‘Dynamic Range in Terahertz TimeDomain Transmission and Reflection Spectroscopy’’. Opt. Lett. 2005. 30(1): 29-31. 27. M. Scheller, C. Jansen, M. Koch. ‘‘Applications of Effective Medium Theories in the Terahertz Regime’’. In: K.Y. Kim, editor. Recent Optical and Photonic Technologies. Rijeka, Croatia: InTech, 2010. Chap. 12. doi: 10.5772/6915: 231–250.
