Error from Delay Drift in Terahertz Attenuated Total Reflection Spectroscopy
- 513 Downloads
In this article we discuss the influence of temporal stability on the value obtained for dielectric properties of materials measured by terahertz time-domain spectroscopy with particular emphasis on attenuated total reflection. The stability of three different terahertz attenuated total reflection spectroscopy systems is carefully characterized. The formalism for the complex refractive index extraction is presented and the effect of delay errors is calculated numerically. We found that good thermal stability of the terahertz system helps to minimize delay fluctuations and therefore the uncertainty of the resulting complex refractive index.
KeywordsAttenuated total reflection Delay shift Uncertainty Error
The field of terahertz spectroscopy has seen enormous progress over the last three decades, but very particularly over the last ten years . Among the most important advances is the establishment of the technique known as terahertz time-domain spectroscopy (THz-TDS) . Owing to its extraordinary signal to noise performance TDS is probably the most widely used and powerful spectroscopic technique for the far infrared band . TDS has opened the possibility to study a wealth of systems in the band between microwaves and infrared (30 GHz to 10 THz or 30 µm and 10 mm) that include crystalline solids [4, 5], liquids , gases  and many other systems [8, 9, 10]. Furthermore, enormous progress has been achieved in the development of filters , modulators  and other components for this spectral band.
Time-domain spectroscopy is based on the use of femtosecond near-infrared pulses to generate single cycle electromagnetic transients of radiation either by ultrafast charge separation [13, 14, 15], or by optical rectification in a non-linear crystal . Unlike in traditional optics where radiation is detected either by bolometric or photon-counting devices THz-TDS uses a fraction of the same femtosecond pulse mentioned earlier to gate a detector that is used to map the temporal waveform of the electric field. This makes TDS immune to thermal background noise. However, time-domain setups are not noise or uncertainty free, this has been discussed previously in the literature [17, 18].
A system of study that has attracted particular interest within the terahertz community is water. The strong interaction of water with terahertz radiation is caused by its collective dynamics [19, 20], which at its time, plays a key role in the way it interacts with proteins and other biomolecules . Therefore the study of proteins in aqueous solution using terahertz radiation is of enormous importance to understand their interaction and function [22, 23, 24, 25, 26, 27, 28]. Yet, these studies have proven challenging given that transmission of terahertz through water is relatively low. Therefore schemes to obtain the dielectric properties of water itself and aqueous solutions in reflection geometries have been proposed [29, 30]. Among those schemes, attenuated total reflection (ATR) is probably the most widely used [31, 32, 33, 34].
In this article we evaluate the effect of delay drift between the THz-generation and detector-gate pulses. These drift can cause significant errors for transmission spectroscopy of thin films , but very particularly for reflection spectroscopic techniques such as ATR. Therefore we discuss how these errors propagate through the data processing and their impact on the final refractive index and absorption coefficient measured by ATR. We, additionally, present experimental evidence that this technique is particularly susceptible to small fluctuations on the relative delay used in TDS setups. We also evaluate the magnitude of such fluctuations with three different TDS systems and conclude that the fluctuations in the mutual pulse delay are mostly related to temperature changes and not necessarily related to mechanical stage imperfections.
1 Fluctuations of ATR for Different Spectroscopy Systems
System A (Fiber setup): Is a THz-TDS (shown in Fig. 1a) setup based on an Er:Fiber laser which provides 90 fs pulses with a central wavelength of 1560 nm at a repetition rate of 100 MHz with an average power of ~80 mW. These pulses are divided inside the laser and coupled out using two fiber ports. After propagating through 6 m of fiber, the pulses of one of the arms are coupled out into free-space and delayed using a computer controlled mechanical stage. This beam is coupled back into a 1.05 m fiber that guides it to an LT-InGaAs/InAlAs stripline photoconductive emitter antenna with a gap between contacts of 25 µm biased by 20 V. The generated terahertz radiation is collimated and focused by a pair of polyethylene lenses, it subsequently propagates through a HR-FZ Silicon prism (as shown on Fig. 1a). Another pair of polyethylene lenses is used to collect and focus the transmitted THz radiation onto a photoconductive detector. The pulses from the second port of the laser are guided through 7.05 m of fiber onto a 10 µm dipole photoconductive detector fabricated on LT-InGaAs/InAlAs.
System B (Semi fiber setup): Is a THz-TDS (shown in Fig. 1b) based on the same laser as described in system A. In this system only one port of the laser was used supplying ~50 mW of average power. The laser is guided through 6 m of optical fiber. This beam is coupled out into the free space and using a polarizing beam splitter cube (1200–1600 nm) the laser pulses are divided into two parts. The first part is delayed using a computer controlled mechanical stage. This beam is coupled back into a 1.05 m fiber that guides it to an LT-InGaAs/InAlAs stripline photoconductive emitter antenna with a gap between contacts of 25 µm biased by 20 V. After generation the THz transients are collimated and focused by a pair of polyethylene lenses, subsequently the THz radiation propagates through a HR-FZ Silicon prism (as shown on Fig. 1b). Another pair of polyethylene lenses is used to collect and focus the transmitted THz radiation onto a photoconductive detector. The second part of the femtosecond pulses from the beam is guided through a 1.05 m of optical fiber onto a LT-InGaAs/InAlAs detector.
System C (Free space setup): Is a standard THz time-domain system is based on a Ti:Sapphire femtosecond laser which provides 70 fs pulses with a central wavelength of 780 nm at a repetition rate of 80 MHz with an average power of ~100 mW. The laser pulses are divided using a beam splitter. The first part is delayed using a computer controlled mechanical stage. This beam is used to excite a SI-GaAs stripline photoconductive emitter antenna with a gap between contacts of 10 µm biased by 20 V. The produced terahertz radiation is collimated and focused by a pair of off-axis parabolic mirrors. It subsequently propagates through a HR-FZ Silicon prism (as shown in Fig. 1c). Another pair of off-axis parabolic mirrors is used to collect and focus the transmitted THz radiation onto a photoconductive detector antenna. The second part of the laser is used to gate a 5 µm dipole photoconductive detector fabricated on LT-GaAs.
2 Delay Stability
From the previous measurements it is clear that the delay drift of the fiber system causes significant errors on the ATR measurements. In order to have a more quantitative feeling for the effect that the drift has on the measured refractive index and absorption coefficient we decided to model the effect of rigid shifts on the sample pulse with respect to de reference pulse. Before presenting such results, we would like to go through the formalism to extract the complex refractive index from the ATR measurements.
3 ATR Data Processing and Uncertainty
4 Final Remarks
The effect of fluctuations in the delay between the sample and reference pulses induced by delay drift of the system itself can have a very significant effect on ATR measurements. This is also true for measurements of dielectric properties by other forms of time-domain reflection spectroscopy and even for transmission spectroscopy in the case of thin samples. We found that the delay fluctuations are more significant in fiber coupled systems. We also found that the temperature stability of the laboratory is critical in order minimize these drifts.
The advantages of fiber coupled systems for “real-world” applications are well known. These systems are far more stable, robust and flexible, therefore the implementation of reflection or transmission (in the case of thin samples) time-domain spectroscopy based on systems of this kind will require further engineering in order to obtain accurate results. Users of these technologies are encouraged to perform a careful characterization of the delay drift of their systems in order to determine if the accuracy they can achieve is good enough for their particular application.
We gratefully acknowledge funding by the German Federal Ministry of Economics and Technology through the project 61308462 and CONACyT through grant number 131931. Amin Soltani achnowledges funding by the German Academic Exchange Service.
- 1.M Tonouchi. Cutting-edge terahertz technology. Nat. Photon., 1:97–105, 2007.Google Scholar
- 2.P U Jepsen, D G Cooke, and M Koch. Terahertz spectroscopy and imaging - modern techniques and applications. Laser Photon. Rev., 5:124–166, 2011.Google Scholar
- 3.C A Schmuttenmaer. Exploring dynamics in the far-infrared with terahertz spectroscopy. Chem. Rev., 104:1759–1779, 2004.Google Scholar
- 4.H Zhan, V Astley, M Hvasta, J A Deibel, D M Mittleman, and Y Lim. The metal-insulator transition in vo[sub 2] studied using terahertz apertureless near-field microscopy. Appl. Phys. Lett., 91:162110, 2007.Google Scholar
- 5.James Lloyd-Hughes and Tae-In Jeon. A review of the terahertz conductivity of bulk and nano-materials. Journal of Infrared, Millimeter, and Terahertz Waves, 33(9):871–925, 2012.Google Scholar
- 6.John F Federici. Review of moisture and liquid detection and mapping using terahertz imaging. Journal of Infrared, Millimeter, and Terahertz Waves, 33(2):97–126, 2012.Google Scholar
- 7.H W Hübers, S G Pavlov, H Richter, A D Semenov, L Mahler, A Tredicucci, H E Beere, and D A Ritchie. High-resolution gas phase spectroscopy with a distributed feedback terahertz quantum cascade laser. Appl. Phys. Lett., 89:061115, 2006.Google Scholar
- 8.Kaori Fukunaga, Yuichi Ogawa, Shin’ichiro Hayashi, and Iwao Hosako. Terahertz spectroscopy for art conservation. IEICE Electronics Express, 4(8):258–263, 2007.Google Scholar
- 9.R Gente, N Born, N Voß, W Sannemann, J Léon, M Koch, and E Castro-Camus. Determination of leaf water content from terahertz time-domain spectroscopic data. Journal of Infrared, Millimeter and Terahertz Waves, 34(3-4):316–323, 2013.Google Scholar
- 10.M Schwerdtfeger, E Castro-Camus, K Krügener, W Viöl, and M Koch. Beating the wavelength limit: three-dimensional imaging of buried subwavelength fractures in sculpture and construction materials by terahertz time-domain reflection spectroscopy. Applied Optics, 52(3):375–380, 2013.Google Scholar
- 11.N Vieweg, N Born, I Al-Naib, and M Koch. Electrically tunable terahertz notch filters. Journal of Infrared, Millimeter, and Terahertz Waves, 33(3):327–332, 2012.Google Scholar
- 12.Marco Rahm, Jiu-Sheng Li, and Willie J Padilla. Thz wave modulators: a brief review on different modulation techniques. Journal of Infrared, Millimeter, and Terahertz Waves, 34(1):1–27, 2013.Google Scholar
- 13.CW Berry, N Wang, MR Hashemi, M Unlu, and M Jarrahi. Significant performance enhancement in photoconductive terahertz optoelectronics by incorporating plasmonic contact electrodes. Nature communications, 4:1622, 2013.Google Scholar
- 14.M B Johnston, D M Whittaker, A Corchia, A G Davies, and E H Linfield. Simulation of terahertz generation at semiconductor surfaces. Phys. Rev. B, 65:165301, 2002.Google Scholar
- 15.G Klatt, F Hilser, W Qiao, M Beck, R Gebs, A Bartels, K Huska, U Lemmer, G Bastian, M B Johnston, M Fischer, J Faist, and T Dekorsy. Terahertz emission from lateral photo-Dember currents. Opt. Express, 18:4939–4947, 2010.Google Scholar
- 16.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, 1996.Google Scholar
- 17.L Duvillaret, F Garet, and J-L Coutaz. Influence of noise on the characterization of materials by terahertz time-domain spectroscopy. J. Opt. Soc. Am. B-Opt. Phys., 17:452–461, 2000.Google Scholar
- 18.W Withayachumnankul, B M Fischer, H Y Lin, and D Abbott. Uncertainty in terahertz time-domain spectroscopy measurement. J. Opt. Soc. Am. B-Opt. Phys., 25:1059–1072, 2008.Google Scholar
- 19.J Xu, K W Plaxco, and S J Allen. Absorption spectra of liquid water and aqueous buffers between 0.3 and 3.72 thz. J. Chem. Phys., 124:036101, 2006.Google Scholar
- 20.M Heyden, J A Sun, S Funkner, G Mathias, H Forbert, M Havenith, and D Marx. Dissecting the thz spectrum of liquid water from first principles via correlations in time and space. Proc. Natl. Acad. Sci. U. S. A., 107:12068–12073, 2010.Google Scholar
- 21.Benjamin Born and Martina Havenith. Terahertz dance of proteins and sugars with water. Journal of Infrared, Millimeter, and Terahertz Waves, 30(12):1245–1254, 2009.Google Scholar
- 22.J Xu, K W Plaxco, and S J Allen. Probing the collective vibrational dynamics of a protein in liquid water by terahertz absorption spectroscopy. Protein Sci., 15:1175–1181, 2006.Google Scholar
- 23.S Ebbinghaus, S J Kim, M Heyden, X Yu, U Heugen, M Gruebele, D M Leitner, and M Havenith. An extended dynamical hydration shell around proteins. Proc. Natl. Acad. Sci. U. S. A., 104:20749–20752, 2007.Google Scholar
- 24.U Heugen, G Schwaab, E Brundermann, M Heyden, X Yu, D M Leitner, and M Havenith. Solute-induced retardation of water dynamics probed directly by terahertz spectroscopy. Proc. Natl. Acad. Sci. U. S. A., 103:12301, 2006.Google Scholar
- 25.J Xu, K W Plaxco, and S J Allen. Collective dynamics of lysozyme in water: terahertz absorption spectroscopy and comparison with theory. J. Phys. Chem. B, 110:24255–24259, 2006.Google Scholar
- 26.Seung Joong Kim, Benjamin Born, Martina Havenith, and Martin Gruebele. Real-time detection of protein-water dynamics upon protein folding by terahertz absorption spectroscopy. Angewandte Chemie International Edition, 47(34):6486–6489, 2008.Google Scholar
- 27.E Castro-Camus and M B Johnston. Conformational changes of photoactive yellow protein monitored by terahertz spectroscopy. Chem. Phys. Lett., 455:289–292, 2008.Google Scholar
- 28.Robert J Falconer and Andrea G Markelz. Terahertz spectroscopic analysis of peptides and proteins. Journal of Infrared, Millimeter, and Terahertz Waves, 33(10):973–988, 2012.Google Scholar
- 29.C Ronne, L Thrane, P O Astrand, A Wallqvist, K V Mikkelsen, and S R Keiding. Investigation of the temperature dependence of dielectric relaxation in liquid water by thz reflection spectroscopy and molecular dynamics simulation. J. Chem. Phys., 107:5319, 1997.Google Scholar
- 30.L Thrane, RH Jacobsen, P Uhd Jepsen, and SR Keiding. Thz reflection spectroscopy of liquid water. Chemical Physics Letters, 240(4):330–333, 1995.Google Scholar
- 31.Atsushi Nakanishi, Yoichi Kawada, Takashi Yasuda, Koichiro Akiyama, and Hironori Takahashi. Terahertz time domain attenuated total reflection spectroscopy with an integrated prism system. Rev. Sci. Instrum., 83:033103, 2012.Google Scholar
- 32.Masaya Nagai, Hiroyuki Yada, Takashi Arikawa, and Koichiro Tanaka. Terahertz time-domain attenuated total reflection spectroscopy in water and biological solution. International journal of infrared and millimeter waves, 27(4):505–515, 2006.Google Scholar
- 33.Hideki Hirori, Kumiko Yamashita, Masaya Nagai, and Koichiro Tanaka. Attenuated total reflection spectroscopy in time domain using terahertz coherent pulses. Japanese journal of applied physics, 43:1287, 2004.Google Scholar
- 34.D Y K Ko and J R Sambles. Scattering matrix-method for propagation of radiation in stratified media - attenuated total reflection studies of liquid-crystals. J. Opt. Soc. Am. A-Opt. Image Sci. Vis., 5:1863–1866, 1988.Google Scholar
- 35.John F O’Hara, Withawat Withayachumnankul, and Ibraheem Al-Naib. A review on thin-film sensing with terahertz waves. Journal of Infrared, Millimeter, and Terahertz Waves, 33(3):245–291, 2012.Google Scholar