Efficient Optimization Approach for Accurate Parameter Extraction With Terahertz Time-Domain Spectroscopy
Abstract
We propose a novel optimization algorithm for the extraction of material complex refractive index in the terahertz (THz) frequency range. The algorithm is applied for materials with arbitrary frequency dependence. We utilize dispersive dielectric models for accurate parameter extraction of a sample of unknown thickness. This approach allows for simultaneously estimating the parameters and fitting them to one of the dispersive models of the materials in the THz frequency range. Our approach has been successfully illustrated through a number of examples with different dispersive models. The examples include the characterization of doped semiconductors used in surface plasmon plaritons in the THz regime. They also include characterizing carbon nanotubes.
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Refractive indices retrieved by these techniques can be fit using models such as the Drude-Lorentz model to extract further information about the material.
“For this purpose, the refractive indices are fit using models such as the Drude-Lorentz model [18, 25].”
From THz-TDS Time-Trace Analysis for the Extraction of Material and Metamaterial Parameters (2019) · cites this paper as [18]
Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601 · see citing works
Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors
Grischkowsky, D., Keiding, S., van Exter, M., & Fattinger, C. (1990) · Journal of the Optical Society of America B · doi:10.1364/josab.7.002006 · Cited by 2,239 · see citing works
Sequential quadratic programming
Boggs, P. T., & Tolle, J. W. (1995) · Acta Numerica · doi:10.1017/s0962492900002518 · Cited by 1,858 · see citing works
A reliable method for extraction of material parameters in terahertz time-domain spectroscopy
Duvillaret, L., Garet, F., & Coutaz, J.-L. (1996) · IEEE Journal of Selected Topics in Quantum Electronics · doi:10.1109/2944.571775 · Cited by 994 · see citing works
Sensing with Terahertz Radiation
Mittleman, D. M. (2003) · Springer series in optical sciences/SPringer series in optical sciences · doi:10.1007/978-3-540-45601-8 · Cited by 837 · see citing works
Material parameter estimation with terahertz time-domain spectroscopy
Dorney, T. D., Baraniuk, R. G., & Mittleman, D. M. (2001) · Journal of the Optical Society of America A · doi:10.1364/josaa.18.001562 · Cited by 807 · see citing works
Theory of Dielectrics: Dielectric Constant and Dielectric Loss
Fröhlich, H. (1958) · Medical Entomology and Zoology · Cited by 550 · see citing works
Duvillaret, L., Garet, F., & Coutaz, J.-L. (1999) · Applied Optics · doi:10.1364/ao.38.000409 · Cited by 505 · see citing works
Highly accurate optical material parameter determination with THz time-domain spectroscopy
Pupeza, I., Wilk, R., & Koch, M. (2007) · Optics Express · doi:10.1364/oe.15.004335 · Cited by 351 · see citing works
Optical and electronic properties of doped silicon from 0.1 to 2 THz
van Exter, M., & Grischkowsky, D. (1990) · Applied Physics Letters · doi:10.1063/1.103120 · Cited by 306 · see citing works
Uncertainty in terahertz time-domain spectroscopy measurement
Withayachumnankul, W., Fischer, B. M., Lin, H., & Abbott, D. (2008) · Journal of the Optical Society of America B · doi:10.1364/josab.25.001059 · Cited by 181 · cited 1× · see citing works
“The noise strength is 5 . The noisy transfer function of the sample is shown in Fig. 3. The reference sample thickness is set to 10.0 m. Although the mechanical uncertainty in the sample thickness is around 1% [ 17 ], we utilize a large uncertainty in the sample thickness (10%) to illustrate that our algorithm works f…”
MethodInfluentialWithayachumnankul, W., Png, G. M., Yin, X., Atakaramians, S., Jones, I., Lin, H., Ung, B. S. Y., Balakrishnan, J., Ng, B. W.-H., Ferguson, B., et al. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2007.900325 · Cited by 179 · see citing works
Influence of noise on the characterization of materials by terahertz time-domain spectroscopy
Duvillaret, L., Garet, F., & Coutaz, J.-L. (2000) · Journal of the Optical Society of America B · doi:10.1364/josab.17.000452 · Cited by 151 · see citing works
Terahertz time-domain spectroscopy of biological tissues
Nazarov, M. M., Shkurinov, A. P., Kuleshov, E. A., & Tuchin, V. V. (2008) · Quantum Electronics · doi:10.1070/qe2008v038n07abeh013851 · Cited by 128 · see citing works
Terahertz spectroscopy of naphthalene, α-naphthol, β-naphthol, biphenyl and anthracene
Han, J., Xu, H. L., Zhu, Z., Yu, X., & Li, W. (2004) · Chemical Physics Letters · doi:10.1016/j.cplett.2004.05.094 · Cited by 34 · see citing works
Kong, B. D., Sokolov, V. N., Kim, K. W., & Trew, R. J. (2008) · Journal of Applied Physics · doi:10.1063/1.2840063 · Cited by 11 · see citing works
Terahertz spectroscopy of naphthalene, alpha-naphthol, beta-naphthol, biphenyl and anthracene
Han, J., Hu, X., Zhu, Z., Yu, X., & Li, W. (2004) · Cited by 5 · see citing works
The calculation of dielectric dispersive models in THz range with GA
Zhu, W., Li, C., Zhang, G., & Fang, G. (2007) · Microwave and Optical Technology Letters · doi:10.1002/mop.22776 · Cited by 4 · see citing works
Optical properties of carbon materials in THz region
Chen, X., Ma, M., Ji, T., Wu, S., & Zhu, Z. (2007) · International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) · doi:10.1109/icimw.2007.4516625 · Cited by 2 · see citing works
Flagged first, then by citations
Cited by
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THz-TDS Time-Trace Analysis for the Extraction of Material and Metamaterial Parameters
Peretti, R., Mitryukovskiy, S., Froberger, K., Mebarki, M. A., Eliet, S., Vanwolleghem, M., & Lampin, J.-F. (2019) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2018.2889227 · Cited by 78 · see citing works
Model-Based Material Parameter Estimation for Terahertz Reflection Spectroscopy
Kniffin, G. P., & Zurk, L. M. (2012) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2011.2181921 · Cited by 46 · see citing works
Windowing of THz time-domain spectroscopy signals: A study based on lactose
Vázquez-Cabo, J., Chamorro-Posada, P., Fraile-Peláez, F. J., Rubiños-López, Ó., López-Santos, J. M., & Martín-Ramos, P. (2016) · Optics Communications · doi:10.1016/j.optcom.2015.12.069 · Cited by 42 · see citing works
Cassar, Q., Chopard, A., Fauquet, F., Guillet, J.-P., Pan, M., Perraud, J.-B., & Mounaix, P. (2019) · IEEE Transactions on Terahertz Science and Technology · doi:10.1109/tthz.2019.2937208 · Cited by 24 · see citing works
Krimi, S., Klier, J., Herrmann, M., Jonuscheit, J., & Beigang, R. (2013) · International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) · doi:10.1109/irmmw-thz.2013.6665871 · Cited by 22 · see citing works
Zhang, L., Fan, Y.-X., Liu, H., Xu, L., Xue, J.-L., & Tao, Z.-Y. (2017) · Journal of Lightwave Technology · doi:10.1109/jlt.2017.2707554 · Cited by 21 · see citing works
Alves-Lima, D. F., Li, X., Coulson, B., Nesling, E., Ludlam, G. A. H., Degl’Innocenti, R., Dawson, R. J., Peruffo, M., & Lin, H. (2022) · Journal of Membrane Science · doi:10.1016/j.memsci.2022.120329 · Cited by 20 · see citing works
Self-citationComplex dielectric properties of anhydrous polycrystalline glucose in the terahertz region
Sun, P., & Zou, Y. L. (2015) · Optical and Quantum Electronics · doi:10.1007/s11082-015-0273-4 · Cited by 19 · see citing works
Cassar, Q., Dandolo, C. L. K., Guillet, J.-P., Roux, M., Fauquet, F., Perraud, J.-B., & Mounaix, P. (2020) · Journal of Infrared Millimeter and Terahertz Waves · doi:10.1007/s10762-020-00733-y · Cited by 18 · see citing works
Choi, J., Kwon, W. S., Kim, K., & Kim, S. (2016) · NDT & E International · doi:10.1016/j.ndteint.2016.02.011 · Cited by 16 · see citing works
Liu, D., & Qi, F. (2023) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2023.3242337 · Cited by 13 · see citing works
A Time-Domain Adjoint Variable Method for Materials With Dispersive Constitutive Parameters
Ahmed, O. S., Bakr, M. H., Li, X., & Nomura, T. (2012) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2012.2207736 · Cited by 12 · see citing works
Self-citationModeling and parameter retrieving in time domain spectroscopy of material and metamaterial
Mičica, M., Mitryukovskiy, S. I., Froberger, K., Peretti, R., Eliet, S., Vanwolleghem, M., & Lampin, J. (2018) · SPIE Conference on Nonlinear Optics and its Applications · doi:10.1117/12.2306932 · Cited by 10 · see citing works
Terahertz conductivity mapping of thin films on smart textiles
Jäckel, A., Hupfer, M. L., Castro-Camus, E., Mittleman, D. M., Schmidl, G., Gawlik, A., Plentz, J., & Koch, M. (2024) · Scientific Reports · doi:10.1038/s41598-024-73113-4 · Cited by 9 · see citing works
Ellrich, F., Klier, J., Weber, S., Jonuscheit, J., & von Freymann, G. (2016) · International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) · doi:10.1109/irmmw-thz.2016.7758614 · Cited by 8 · see citing works
Retrieving material and metamaterial parameters directly from time-domain spectroscopy time trace
Peretti, R., Mitryukovskiy, S., Kevin, F., & Lampin, J.-F. (2018) · 2018 43rd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) · doi:10.1109/irmmw-thz.2018.8510300 · Cited by 7 · see citing works
Nsengiyumva, W., Mwizerwa, J. P., Makin, A. M., Thirunavukkarasu, N., Chen, X., Shuncong Zhong, A., Wu, L., & Zheng, L. (2025) · Polymer Testing · doi:10.1016/j.polymertesting.2025.108970 · Cited by 6 · see citing works
Morikawa, O., 藤田, 正., & Hangyo, M. (2013) · Japanese Journal of Applied Physics · doi:10.7567/jjap.52.112401 · Cited by 6 · see citing works
Seyyed-Kalantari, L., Ahmed, O. S., Bakr, M. H., & Nikolova, N. K. (2017) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2017.2736580 · Cited by 5 · see citing works
Self-citationStock, D., Wigger, A. K., & Bolívar, P. H. (2021) · Journal of the Optical Society of America B · doi:10.1364/josab.415144 · Cited by 5 · see citing works
Time-Resolved Detection of Terahertz Response in Photodynamically Induced Plasmonic Metasurfaces
Novikov, I. A., Kir'yanov, M. A., Stadnichuk, V. I., Dolgova, T. V., & Fedyanin, A. A. (2024) · Journal of Experimental and Theoretical Physics Letters · doi:10.1134/s0021364024601052 · Cited by 4 · see citing works
Optimization of terahertz fingerprint and identification capabilities by using PSO algorithm
Latreche, F. Y., Lazoul, M., Boutemedjet, A., & Coutaz, J. (2022) · Optik · doi:10.1016/j.ijleo.2022.169354 · Cited by 3 · see citing works
Extraction of effective parameters in terahertz time-domain spectroscopy
Pellegrini, P. E. S., Gabrielli, L. H., dos Santos, L. M., & Ribessi, R. L. (2017) · SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (IMOC) · doi:10.1109/imoc.2017.8121029 · Cited by 1 · see citing works
Model-Based Material Parameter Estimation for Terahertz Reflection Spectroscopy
Kniffin, G. P. (2000) · doi:10.15760/etd.241 · Cited by 1 · see citing works
Complex dielectric properties of anhydrous polycrystalline glucose in the terahertz region
Sun, P., Liu, W., Zou, Y. L., Jia, Q. Z., & Li, J. Y. (2015) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2078430
Stock, D., Kahl, M., Wigger, A. K., Wong, T. M., Kolb, A., & Bolívar, P. H. (2019) · Terahertz, RF, Millimeter, and Submillimeter-Wave Technology and Applications · doi:10.1117/12.2515642
Alves-Lima, D., Li, X.-R., Coulson, B., Nesling, E., Ludlam, G., Degl'Innocenti, R., Dawson, R., Peruffo, M., & Lin, H. (2022) · Social Science Research Network · doi:10.2139/ssrn.3993219 · Cited by 19 · see citing works
Self-citationLatreche, F. Y., Lazoul, M., & Boutemedjet, A. (2022) · International Multi-Conference on Systems, Signals & Devices (SSD) · doi:10.1109/ssd54932.2022.9955855
Novikov, I. A., Kir'yanov, M. A., Stadnichuk, V. I., Dolgova, T. V., & Fedyanin, A. A. (2024) · Письма в Журнал экспериментальной и теоретической физики · doi:10.31857/s1234567824090040
Materials parameters extraction in Terahertz Time-Domain Spectroscopy using genetic algorithm
Kaouther, C. A., & Lazoul, M. (2025) · Journal of Optics · doi:10.1007/s12596-025-02991-2
Yao, Y., Mao, S., Wang, Z., Yang, Z., Yan, S. Q., & Ding, H. (2026) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2026.3684613
Multilayered film monitoring using terahertz reflective time-domain spectroscopy
Choi, J., Kwon, W. S., Kim, K.-S., & Kim, S. (2015) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.2185381
- Authors
- Ahmed, O. S., Swillam, M. A., Bakr, M. H., & Li, X.
- Affiliations
- McMaster University (CA)
- University of Toronto (CA)
- Venue
- Journal of Lightwave Technology
- Published
- 2010-06
- Volume
- 28
- Issue
- 11
- Pages
- 1685-1692
- ISSN
- 0733-8724 (ISSN-L)
- 1558-2213
- OpenAlex
- W2168119881
- Semantic Scholar
- 396ea1fd48974a25243087ab24be86b617f175fa
- Cited by
- 36
- References
- 19
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 4 · 2023: 1 · 2022: 3 · 2021: 4 · 2020: 2 · 2019: 2 · 2018: 3 · 2017: 3 · 2016: 3 · 2015: 3 · 2013: 2 · 2012: 2
- FWCI
- 1.01
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Lightwave Technology (publishedVersion)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Microwave and Dielectric Measurement Techniques
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- terahertz time-domain spectroscopy, parameter extraction, complex refractive index, optimization algorithms, doped semiconductors, surface plasmon polaritons, carbon nanotubes
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