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  • Primer
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Terahertz time-domain spectroscopy

Nature Reviews Methods Primers volume 3, Article number: 48 (2023) Cite this article

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Abstract

The terahertz band of the electromagnetic spectrum was the least explored region of the spectrum prior to the introduction of the technique known as time-domain spectroscopy (TDS) in the late 1980s. Since its introduction, terahertz TDS has enabled the study of a plethora of physical, chemical and biological phenomena; from excitons and Cooper pairs in solids to the hydration dynamics of biomolecules. Terahertz techniques can be used to non-destructively analyse samples from diverse fields, such as art conservation and industrial quality control, whereas terahertz imaging can act as a sensitive hydration probe in biological tissue and other materials. This article focuses on TDS, a unique hybrid between microwave and optical technologies. By measuring the time-dependent electric field waveform, rather than the intensity of the electromagnetic wave, one directly accesses the spectral amplitude and phase of the electric field. As a result, both the refractive index and absorption coefficient (or the complex dielectric function) of a sample can be measured simultaneously. The technique is based on the generation and detection of single-cycle pulses of radiation, enabling measurements with sub-picosecond time resolution. This Primer summarizes the basics of such systems and gives a few illustrative application examples.

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Fig. 1: The electromagnetic spectrum highlighting the terahertz band.
Fig. 2: Simplified terahertz time-domain spectrometer.
Fig. 3: Terahertz time-domain signal processing I: basic processing steps.
Fig. 4: Terahertz time-domain signal processing II: eliminating multiple reflections.
Fig. 5: Terahertz birefringence of a liquid crystal.
Fig. 6: Intensity reflection spectrum of a one-dimensional photonic crystal composed of five layers.
Fig. 7: Terahertz imaging for the study of diabetic foot syndrome.

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References

  1. Tonouchi, M. Cutting-edge terahertz technology. Nat. Photonics 1, 97–105 (2007). This work is one of the most comprehensive overviews on the state of the art about sources and detectors.

    ADS  Google Scholar 

  2. Leitenstorfer, A. et al. The 2023 terahertz science and technology roadmap. J. Phys. D. Appl. Phys 56, 223001 (2023). This work presents the broadest overview of the field to date.

    ADS  Google Scholar 

  3. Smith, P. R., Auston, D. H. & Nuss, M. C. Subpicosecond photoconducting dipole antennas. IEEE J. Quantum Electron. 24, 255–260 (1988). This pioneering publication introduces TDS.

    ADS  Google Scholar 

  4. Fattinger, C. & Grischkowsky, D. Terahertz beams. Appl. Phys. Lett. 54, 490–492 (1989).

    ADS  Google Scholar 

  5. Hu, B. B. & Nuss, M. C. Imaging with terahertz waves. Opt. Lett. 20, 1716–1718 (1995). To our knowledge, this work is the first demonstration of time-domain imaging.

    ADS  Google Scholar 

  6. Chan, W. L., Deibel, J. & Mittleman, D. M. Imaging with terahertz radiation. Rep. Prog. Phys. 70, 1325–1379 (2007).

    ADS  Google Scholar 

  7. Zhang, X. C. & Auston, D. H. Optoelectronic measurement of semiconductor surfaces and interfaces with femtosecond optics. J. Appl. Phys. 71, 326–338 (1992).

    ADS  Google Scholar 

  8. Rudd, J. V., Zimdars, D. A. & Warmuth, M. W. in Commercial and Biomedical Applications of Ultrafast Lasers II Vol. 3934 (eds Neev, J. & Reed, M. K.) 27–35 (SPIE, 2000).

  9. Stübling, E. et al. A THz tomography system for arbitrarily shaped samples. J. Infrared Millim. Terahertz Waves 38, 1179–1182 (2017).

    Google Scholar 

  10. van Mechelen, J. L. M., Frank, A. & Maas, D. J. H. C. Thickness sensor for drying paints using THz spectroscopy. Opt. Express 29, 7514–7525 (2021).

    ADS  Google Scholar 

  11. Grischkowsky, D., Keiding, S., van Exter, M. & Fattinger, C. H. Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors. J. Opt. Soc. Am. B 7, 2006–2015 (1990).

    ADS  Google Scholar 

  12. Yasui, T., Saneyoshi, E. & Araki, T. Asynchronous optical sampling terahertz time-domain spectroscopy for ultrahigh spectral resolution and rapid data acquisition. Appl. Phys. Lett. 87, 061101 (2005).

    ADS  Google Scholar 

  13. Janke, C., Först, M., Nagel, M., Kurz, H. & Bartels, A. Asynchronous optical sampling for high-speed characterization of integrated resonant terahertz sensors. Opt. Lett. 30, 1405–1407 (2005).

    ADS  Google Scholar 

  14. Kim, Y. & Yee, D.-S. High-speed terahertz time-domain spectroscopy based on electronically controlled optical sampling. Opt. Lett. 35, 3715–3717 (2010).

    ADS  Google Scholar 

  15. Dietz, R. J. B. et al. All fiber-coupled THz-TDS system with kHz measurement rate based on electronically controlled optical sampling. Opt. Lett. 39, 6482–6485 (2014).

    ADS  Google Scholar 

  16. Wilk, R., Hochrein, T., Koch, M., Mei, M. & Holzwarth, R. OSCAT: novel technique for time-resolved experiments without moveable optical delay lines. J. Infrared Millim. Terahertz Waves 32, 596–602 (2011).

    Google Scholar 

  17. Jördens, C. et al. Micro-mirrors for a multifocus terahertz imaging system. J. Microw. Wirel. Technol. 2, 300–304 (2006).

    Google Scholar 

  18. Hunsche, S., Mittleman, D. M., Koch, M. & Nuss, M. C. New dimensions in T-ray imaging. IEICE Trans. Electron. E81-C, 269–276 (1998).

    Google Scholar 

  19. Beard, M. C., Turner, G. M. & Schmuttenmaer, C. A. Terahertz spectroscopy. J. Phys. Chem. B 106, 7146–7159 (2002). This work is probably the first widely used review in the field.

    Google Scholar 

  20. Kadlec, F., Kadlec, C., Kužel, P., Slavı́ček, P. & Jungwirth, P. Optical pump–terahertz probe spectroscopy of dyes in solutions: probing the dynamics of liquid solvent or solid precipitate? J. Chem. Phys. 120, 912–917 (2004).

    ADS  Google Scholar 

  21. Richter, C. & Schmuttenmaer, C. A. Exciton-like trap states limit electron mobility in TiO2 nanotubes. Nat. Nanotechnol. 5, 769–772 (2010).

    ADS  Google Scholar 

  22. Pizzuto, A. et al. Nonlocal time-resolved terahertz spectroscopy in the near field. ACS Photonics 8, 2904–2911 (2021).

    Google Scholar 

  23. Xiao, Z., Wang, J., Liu, X., Assaf, B. A. & Burghoff, D. Optical-pump terahertz-probe spectroscopy of the topological crystalline insulator Pb1–xSnxSe through the topological phase transition. ACS Photonics 9, 765–771 (2022).

    Google Scholar 

  24. Schmuttenmaer, C. A. Exploring dynamics in the far-infrared with terahertz spectroscopy. Chem. Rev. 104, 1759–1779 (2004).

    Google Scholar 

  25. Auston, D. H., Cheung, K. P. & Smith, P. R. Picosecond photoconducting Hertzian dipoles. Appl. Phys. Lett. 45, 284–286 (1984).

    ADS  Google Scholar 

  26. Wilk, R. et al. in Conf. Lasers and Electro-Optics (CLEO) https://doi.org/10.1109/CLEO.2007.4452856 (Optica, 2007).

  27. Dietz, R. J. B. et al. THz generation at 1.55 µm excitation: six-fold increase in THz conversion efficiency by separated photoconductive and trapping regions. Opt. Express 19, 25911–25917 (2011).

    ADS  Google Scholar 

  28. Globisch, B. et al. Iron doped InGaAs: competitive THz emitters and detectors fabricated from the same photoconductor. J. Appl. Phys. 121, 053102 (2017).

    ADS  Google Scholar 

  29. Jepsen, P. U., Jacobsen, R. H. & Keiding, S. R. Generation and detection of terahertz pulses from biased semiconductor antennas. J. Opt. Soc. Am. B 13, 2424–2436 (1996).

    ADS  Google Scholar 

  30. Van Rudd, J., Johnson, J. L. & Mittleman, D. M. Cross-polarized angular emission patterns from lens-coupled terahertz antennas. J. Opt. Soc. Am. B 18, 1524–1533 (2001).

    ADS  Google Scholar 

  31. Yang, K. H., Richards, P. L. & Shen, Y. R. Generation of far‐infrared radiation by picosecond light pulses in LiNbO3. Appl. Phys. Lett. 19, 320–323 (1971). This work introduces terahertz generation by optical rectification.

    ADS  Google Scholar 

  32. Wu, Q. & Zhang, X. C. Free‐space electro‐optic sampling of terahertz beams. Appl. Phys. Lett. 67, 3523–3525 (1995). This work introduces electro-optic sampling.

    ADS  Google Scholar 

  33. Wu, Q. & Zhang, X. C. Free-space electro-optics sampling of mid-infrared pulses. Appl. Phys. Lett. 71, 1285–1286 (1997).

    ADS  Google Scholar 

  34. Leitenstorfer, A., Hunsche, S., Shah, J., Nuss, M. C. & Knox, W. H. Detectors and sources for ultrabroadband electro-optic sampling: experiment and theory. Appl. Phys. Lett. 74, 1516–1518 (1999).

    ADS  Google Scholar 

  35. Castro-Camus, E. et al. Photoconductive response correction for detectors of terahertz radiation. J. Appl. Phys. 104, 053113 (2008).

    ADS  Google Scholar 

  36. Kužel, P., Němec, H., Kadlec, F. & Kadlec, C. Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy. Opt. Express 18, 15338–15348 (2010).

    ADS  Google Scholar 

  37. Hintzsche, H. et al. Terahertz radiation at 0.380 THz and 2.520 THz does not lead to DNA damage in skin cells in vitro. Radiat. Res. 179, 38–45 (2013).

    ADS  Google Scholar 

  38. Markelz, A. G. & Mittleman, D. M. Perspective on terahertz applications in bioscience and biotechnology. ACS Photonics 9, 1117–1126 (2022). This paper reviews biological applications.

    Google Scholar 

  39. Yeh, K.-L., Hoffmann, M. C., Hebling, J. & Nelson, K. A. Generation of 10 μJ ultrashort terahertz pulses by optical rectification. Appl. Phys. Lett. 90, 171121 (2007).

    ADS  Google Scholar 

  40. Hough, C. M. et al. Disassembly of microtubules by intense terahertz pulses. Biomed. Opt. Express 12, 5812–5828 (2021).

    Google Scholar 

  41. Vázquez-Cabo, J. et al. Windowing of THz time-domain spectroscopy signals: a study based on lactose. Opt. Commun. 366, 386–396 (2016).

    ADS  Google Scholar 

  42. Withayachumnankul, W. & Naftaly, M. Fundamentals of measurement in terahertz time-domain spectroscopy. J. Infrared Millim. Terahertz Waves 35, 610–637 (2014). This work is an excellent reference on the processing of time-domain signals.

    Google Scholar 

  43. Naftaly, M. & Dudley, R. Methodologies for determining the dynamic ranges and signal-to-noise ratios of terahertz time-domain spectrometers. Opt. Lett. 34, 1213–1215 (2009).

    ADS  Google Scholar 

  44. Duvillaret, L., Garet, F. & Coutaz, J.-L. Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy. Appl. Opt. 38, 409–415 (1999). This work is one of the first comprehensive methods for complex refractive index extraction with non-ideal samples.

    ADS  Google Scholar 

  45. Dorney, T. D., Baraniuk, R. G. & Mittleman, D. M. Material parameter estimation with terahertz time-domain spectroscopy. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 18, 1562–1571 (2001).

    ADS  Google Scholar 

  46. Pupeza, I., Wilk, R. & Koch, M. Highly accurate optical material parameter determination with THz time-domain spectroscopy. Opt. Express 15, 4335–4350 (2007).

    ADS  Google Scholar 

  47. Huang, S. et al. Improved sample characterization in terahertz reflection imaging and spectroscopy. Opt. Express 17, 3848–3854 (2009).

    ADS  Google Scholar 

  48. Pashkin, A., Kempa, M., Němec, H., Kadlec, F. & Kužel, P. Phase-sensitive time-domain terahertz reflection spectroscopy. Rev. Sci. Instrum. 74, 4711–4717 (2003).

    ADS  Google Scholar 

  49. Jepsen, P. U., Møller, U. & Merbold, H. Investigation of aqueous alcohol and sugar solutions with reflection terahertz time-domain spectroscopy. Opt. Express 15, 14717–14737 (2007).

    ADS  Google Scholar 

  50. Fan, S., Parrott, E. P. J., Ung, B. S. Y. & Pickwell-MacPherson, E. Calibration method to improve the accuracy of THz imaging and spectroscopy in reflection geometry. Photonics Res. 4, A29–A35 (2016).

    Google Scholar 

  51. Thrane, L., Jacobsen, R. H., Uhd Jepsen, P. & Keiding, S. R. THz reflection spectroscopy of liquid water. Chem. Phys. Lett. 240, 330–333 (1995).

    ADS  Google Scholar 

  52. Jepsen, P. U. & Fischer, B. M. Dynamic range in terahertz time-domain transmission and reflection spectroscopy. Opt. Lett. 30, 29–31 (2005).

    ADS  Google Scholar 

  53. Hirori, H., Yamashita, K., Nagai, M. & Tanaka, K. Attenuated total reflection spectroscopy in time domain using terahertz coherent pulses. Jpn J. Appl. Phys. 43, L1287 (2004).

    ADS  Google Scholar 

  54. Soltani, A. et al. Crystallization caught in the act with terahertz spectroscopy: non-classical pathway for l-(+)-tartaric acid. Chem. Eur. J. 23, 14128–14132 (2017).

    Google Scholar 

  55. Chen, X. & Pickwell-MacPherson, E. An introduction to terahertz time-domain spectroscopic ellipsometry. APL Photonics 7, 071101 (2022).

    ADS  Google Scholar 

  56. Astley, V., Reichel, K. S., Jones, J., Mendis, R. & Mittleman, D. M. Terahertz multichannel microfluidic sensor based on parallel-plate waveguide resonant cavities. Appl. Phys. Lett. 100, 231108 (2012).

    ADS  Google Scholar 

  57. Laman, N., Harsha, S. S., Grischkowsky, D. & Melinger, J. S. High-resolution waveguide THz spectroscopy of biological molecules. Biophys. J. 94, 1010–1020 (2008).

    Google Scholar 

  58. Jones, G. & Gordy, W. Submillimeter-wave spectra of HCl and HBr. Phys. Rev. 136, A1229–A1232 (1964).

    ADS  Google Scholar 

  59. Messer, J. K., De Lucia, F. C. & Helminger, P. Submillimeter spectroscopy of the major isotopes of water. J. Mol. Spectrosc. 105, 139–155 (1984).

    ADS  Google Scholar 

  60. Jepsen, P. U. & Clark, S. J. Precise ab-initio prediction of terahertz vibrational modes in crystalline systems. Chem. Phys. Lett. 442, 275–280 (2007).

    ADS  Google Scholar 

  61. Siegrist, K. et al. High-resolution terahertz spectroscopy of crystalline trialanine: extreme sensitivity to β-sheet structure and cocrystallized water. J. Am. Chem. Soc. 128, 5764–5775 (2006).

    Google Scholar 

  62. Ruggiero, M. T., Sibik, J., Orlando, R., Zeitler, J. A. & Korter, T. M. Measuring the elasticity of poly‐l‐proline helices with terahertz spectroscopy. Angew. Chem. Int. Ed. 55, 6877–6881 (2016).

    Google Scholar 

  63. Łuczyńska, K., Drużbicki, K., Runka, T., Pałka, N. & Węsicki, J. Vibrational response of felodipine in the THz domain: optical and neutron spectroscopy versus plane-wave DFT modeling. J. Infrared Millim. Terahertz Waves 41, 1301–1336 (2020).

    Google Scholar 

  64. Bawuah, P. & Zeitler, J. A. Advances in terahertz time-domain spectroscopy of pharmaceutical solids: a review. TrAC. Trends Anal. Chem. 139, 116272 (2021).

    Google Scholar 

  65. Allis, D. G., Fedor, A. M., Korter, T. M., Bjarnason, J. E. & Brown, E. R. Assignment of the lowest-lying THz absorption signatures in biotin and lactose monohydrate by solid-state density functional theory. Chem. Phys. Lett. 440, 203–209 (2007).

    ADS  Google Scholar 

  66. Ruggiero, M. T., Zhang, W., Bond, A. D., Mittleman, D. M. & Zeitler, J. A. Uncovering the connection between low-frequency dynamics and phase transformation phenomena in molecular solids. Phys. Rev. Lett. 120, 196002 (2018).

    ADS  Google Scholar 

  67. Ruggiero, M. T. Invited review: modern methods for accurately simulating the terahertz spectra of solids. J. Infrared Millim. Terahertz Waves 41, 491–528 (2020).

    Google Scholar 

  68. Zhang, W., Song, Z., Ruggiero, M. T. & Mittleman, D. M. Terahertz vibrational motions mediate gas uptake in organic clathrates. Cryst. Growth Des. 20, 5638–5643 (2020).

    Google Scholar 

  69. Banks, P. A. et al. Thermoelasticity in organic semiconductors determined with terahertz spectroscopy and quantum quasi-harmonic simulations. J. Mater. Chem. C. Mater 8, 10917–10925 (2020).

    Google Scholar 

  70. Schweicher, G. et al. Chasing the “Killer” phonon mode for the rational design of low-disorder, high-mobility molecular semiconductors. Adv. Mater. 31, 1902407 (2019).

    Google Scholar 

  71. van Exter, M. & Grischkowsky, D. Optical and electronic properties of doped silicon from 0.1 to 2 THz. Appl. Phys. Lett. 56, 1694–1696 (1990).

    ADS  Google Scholar 

  72. Huggard, P. G. et al. Drude conductivity of highly doped GaAs at terahertz frequencies. J. Appl. Phys. 87, 2382–2385 (2000).

    ADS  Google Scholar 

  73. Kaindl, R. A., Carnahan, M. A., Hägele, D., Lövenich, R. & Chemla, D. S. Ultrafast terahertz probes of transient conducting and insulating phases in an electron–hole gas. Nature 423, 734–738 (2003).

    ADS  Google Scholar 

  74. Stein, M. et al. Dynamics of charge-transfer excitons in type-II semiconductor heterostructures. Phys. Rev. B 97, 125306 (2018).

    ADS  Google Scholar 

  75. Bergren, M. R., Palomaki, P. K. B., Neale, N. R., Furtak, T. E. & Beard, M. C. Size-dependent exciton formation dynamics in colloidal silicon quantum dots. ACS Nano 10, 2316–2323 (2016).

    Google Scholar 

  76. Bellissent-Funel, M.-C. et al. Water determines the structure and dynamics of proteins. Chem. Rev. 116, 7673–7697 (2016).

    Google Scholar 

  77. Heugen, U. et al. Solute-induced retardation of water dynamics probed directly by terahertz spectroscopy. Proc. Natl Acad. Sci. USA 103, 12301–12306 (2006).

    ADS  Google Scholar 

  78. Markelz, A. G. Terahertz dielectric sensitivity to biomolecular structure and function. IEEE J. Sel. Top. Quantum Electron. 14, 180–190 (2008).

    ADS  Google Scholar 

  79. Niessen, K. A. et al. Protein and RNA dynamical fingerprinting. Nat. Commun. 10, 1026 (2019).

    ADS  Google Scholar 

  80. Mittleman, D. M., Cunningham, J., Nuss, M. C. & Geva, M. Noncontact semiconductor wafer characterization with the terahertz Hall effect. Appl. Phys. Lett. 71, 16–18 (1997).

    ADS  Google Scholar 

  81. Kanda, N., Konishi, K., Nemoto, N., Midorikawa, K. & Kuwata-Gonokami, M. Real-time broadband terahertz spectroscopic imaging by using a high-sensitivity terahertz camera. Sci. Rep. 7, 42540 (2017).

    ADS  Google Scholar 

  82. Chen, A. et al. Non-contact terahertz spectroscopic measurement of the intraocular pressure through corneal hydration mapping. Biomed. Opt. Express 12, 3438–3449 (2021).

    Google Scholar 

  83. Hernandez-Cardoso, G. G. et al. Terahertz imaging demonstrates its diagnostic potential and reveals a relationship between cutaneous dehydration and neuropathy for diabetic foot syndrome patients. Sci. Rep. 12, 3110 (2022).

    ADS  Google Scholar 

  84. Wilk, R., Pupeza, I., Cernat, R. & Koch, M. Highly accurate THz time-domain spectroscopy of multilayer structures. IEEE J. Sel. Top. Quantum Electron. 14, 392–398 (2008).

    ADS  Google Scholar 

  85. Vieweg, N., Shakfa, M. K., Scherger, B., Mikulics, M. & Koch, M. THz properties of nematic liquid crystals. J. Infrared Millim. Terahertz Waves 31, 1312–1320 (2010).

    Google Scholar 

  86. Jansen, C., Wietzke, S., Astley, V., Mittleman, D. M. & Koch, M. Mechanically flexible polymeric compound one-dimensional photonic crystals for terahertz frequencies. Appl. Phys. Lett. 96, 111108 (2010).

    ADS  Google Scholar 

  87. Lindley-Hatcher, H. et al. Real time THz imaging — opportunities and challenges for skin cancer detection. Appl. Phys. Lett. 118, 230501 (2021).

    ADS  Google Scholar 

  88. Hernandez-Cardoso, G. G. et al. Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept. Sci. Rep. 7, 42124 (2017).

    ADS  Google Scholar 

  89. Naftaly, M. in 2016 41st Int. Conf. Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) https://doi.org/10.1109/IRMMW-THz.2016.7758763 (IEEE, 2016).

  90. Naftaly, M., Clarke, R. G., Humphreys, D. A. & Ridler, N. M. Metrology state-of-the-art and challenges in broadband phase-sensitive terahertz measurements. Proc. IEEE 105, 1151–1165 (2017).

    Google Scholar 

  91. Jepsen, P. U. Phase retrieval in terahertz time-domain measurements: a “how to” tutorial. J. Infrared Millim. Terahertz Waves https://doi.org/10.1007/s10762-019-00578-0 (2019).

    Article  Google Scholar 

  92. Withayachumnankul, W., Fischer, B. M., Lin, H. & Abbott, D. Uncertainty in terahertz time-domain spectroscopy measurement. J. Opt. Soc. Am. B 25, 1059–1072 (2008).

    ADS  Google Scholar 

  93. Yang, F. et al. Uncertainty in terahertz time-domain spectroscopy measurement of liquids. J. Infrared Millim. Terahertz Waves 38, 229–247 (2017).

    Google Scholar 

  94. Méndez Aller, M., Abdul-Munaim, A., Watson, D. & Preu, S. Error sources and distinctness of materials parameters obtained by THz-time domain spectroscopy using an example of oxidized engine oil. Sensors 18, 2087 (2018).

    ADS  Google Scholar 

  95. Ornik, J. et al. Repeatability of material parameter extraction of liquids from transmission terahertz time-domain measurements. Opt. Express 28, 28178–28189 (2020).

    ADS  Google Scholar 

  96. Okada, K. et al. Scanning laser terahertz near-field reflection imaging system. Appl. Phys. Express 12, 122005 (2019).

    ADS  Google Scholar 

  97. Knoll, B. & Keilmann, F. Near-field probing of vibrational absorption for chemical microscopy. Nature 399, 134–137 (1999).

    ADS  Google Scholar 

  98. Zhan, H. et al. The metal-insulator transition in VO2 studied using terahertz apertureless near-field microscopy. Appl. Phys. Lett. 91, 162110 (2007).

    ADS  Google Scholar 

  99. Huber, A. J., Keilmann, F., Wittborn, J., Aizpurua, J. & Hillenbrand, R. Terahertz near-field nanoscopy of mobile carriers in single semiconductor nanodevices. Nano Lett. 8, 3766–3770 (2008).

    ADS  Google Scholar 

  100. Cocker, T. L., Peller, D., Yu, P., Repp, J. & Huber, R. Tracking the ultrafast motion of a single molecule by femtosecond orbital imaging. Nature 539, 263–267 (2016).

    ADS  Google Scholar 

  101. Dong, J., Wu, X., Locquet, A. & Citrin, D. S. Terahertz superresolution stratigraphic characterization of multilayered structures using sparse deconvolution. IEEE Trans. Terahertz Sci. Technol. 7, 260–267 (2017).

    ADS  Google Scholar 

  102. Ferguson, B., Wang, S., Gray, D., Abbot, D. & Zhang, X.-C. T-ray computed tomography. Opt. Lett. 27, 1312–1314 (2002).

    ADS  Google Scholar 

  103. Dorney, T. D. et al. Terahertz reflection imaging using Kirchhoff migration. Opt. Lett. 26, 1513–1515 (2001).

    ADS  Google Scholar 

  104. Withayachumnankul, W., Fischer, B. M. & Abbott, D. Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements. Proc. R. Soc. A Math. Phys. Eng. Sci. 464, 2435–2456 (2008).

    ADS  Google Scholar 

  105. Mikerov, M., Ornik, J. & Koch, M. Removing water vapor lines from THz-TDS data using neural networks. IEEE Trans. Terahertz Sci. Technol. 10, 397–403 (2020).

    ADS  Google Scholar 

  106. van Exter, M., Fattinger, C. H. & Grischkowsky, D. Terahertz time-domain spectroscopy of water vapor. Opt. Lett. 14, 1128–1130 (1989).

    ADS  Google Scholar 

  107. Klatt, G. et al. High-resolution terahertz spectrometer. IEEE J. Sel. Top. Quantum Electron. 17, 159–168 (2011).

    ADS  Google Scholar 

  108. Mickan, S. P., Xu, J., Munch, J., Zhang, X.-C. & Abbott, D. The limit of spectral resolution in THz time-domain spectroscopy. Photonics Des. Technol. Packag. 5277, 54–64 (2004).

    ADS  Google Scholar 

  109. Duling, I. & Zimdars, D. Terahertz imaging: revealing hidden defects. Nat. Photonics 3, 630–632 (2009).

    ADS  Google Scholar 

  110. Lambert, F. E. M. et al. Layer separation mapping and consolidation evaluation of a fifteenth century panel painting using terahertz time-domain imaging. Sci. Rep. 12, 21038 (2022).

    ADS  Google Scholar 

  111. Chen, X. et al. Terahertz (THz) biophotonics technology: instrumentation, techniques, and biomedical applications. Chem. Phys. Rev. 3, 011311 (2022).

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Material Sciences Center, Philipps-Universität Marburg, Marburg, Germany

    Martin Koch, Jan Ornik & Enrique Castro-Camus

  2. School of Engineering, Brown University, Providence, RI, USA

    Daniel M. Mittleman

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Contributions

Introduction (M.K.); Experimentation (E.C.-C.); Results (D.M.M. and J.O.); Applications (M.K. and E.C.-C.); Reproducibility and data deposition (J.O. and D.M.M.); Limitations and optimizations (D.M.M., E.C.-C. and J.O.); Outlook (M.K.); Overview of the Primer (all authors).

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Nature Reviews Methods Primers thanks Axel Zeitler, Young-Mi Bahk, Frederic Garet and Mona Jarrahi for their contribution to the peer review of this work.

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Birefringence

Electromagnetic radiation propagates in materials at a speed that is usually lower than the speed of light in vacuum, measured by the refractive index of the material. Some materials show not only one but two different speeds that depend on the polarization of the light. These materials are said to be birefringent. Birefringence is the difference of the two refractive indices.

Electromagnetic transients

Short pulses of electromagnetic radiation that contain only one or just very few cycles of oscillation.

Fabry–Perot effect

The interference effect of multiple reflections of a wave that appears in a layer of material.

Fourier transform

A mathematical operation that acts on a function f of a variable, such as time, and that finds its components F as a function of another variable, in this case the frequency. It is an operation that calculates how much of each frequency (the amplitude of the spectrum) is present in the original function f, and the relative delay of each frequency (the phase spectrum).

Windowing

An operation applied on a function f of a variable x that multiplies it by another function W also of the variable x. Usually the window function is 1 at certain value of x, typically corresponding to the maximum of f. The window either tends to zero at the ends of the domain or goes to zero within a smaller interval and remains at zero from those points onwards.

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Koch, M., Mittleman, D.M., Ornik, J. et al. Terahertz time-domain spectroscopy. Nat Rev Methods Primers 3, 48 (2023). https://doi.org/10.1038/s43586-023-00232-z

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