Accurate determination of dielectric permittivity of polymers from 75&#x2009;&#x2009;GHz to 1.6&#x2009;&#x2009;THz using both S-parameters and transmission spectroscopy

Tianying Chang; Xiansheng Zhang; Xiaoxuan Zhang; Hong-Liang Cui

doi:10.1364/AO.56.003287

Applied Optics
Vol. 56,
Issue 12,
pp. 3287-3292
(2017)
•https://doi.org/10.1364/AO.56.003287

Accurate determination of dielectric permittivity of polymers from 75 GHz to 1.6 THz using both S-parameters and transmission spectroscopy

Tianying Chang, Xiansheng Zhang, Xiaoxuan Zhang, and Hong-Liang Cui

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Tianying Chang, Xiansheng Zhang, Xiaoxuan Zhang, and Hong-Liang Cui, "Accurate determination of dielectric permittivity of polymers from 75 GHz to 1.6 THz using both S-parameters and transmission spectroscopy," Appl. Opt. 56, 3287-3292 (2017)

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Abstract

Interactions of terahertz (THz) electromagnetic radiation with polymer materials have been studied recently with increasing depth and breadth, for purposes of both using polymers in fabricating THz optical components such as lenses, waveplates, waveguides, and sample holders/containers, and employing THz spectral imaging as a new tool for nondestructive testing of polymer composite structures. Either endeavor cannot even begin without a quantitative knowledge of the complex dielectric permittivity, i.e., the propagation and attenuation properties of such polymers in the requisite wave band. In this paper, a number of non-polar and non-magnetic polymers, such as polytetrafluoroethylene, polypropylene, high-density polyethylene, and polymethyl methacrylate, are studied for the purpose of determining their complex dielectric permittivity, including its real part and imaginary parts, in the wide frequency band from millimeter wave to THz wave (75 GHz–1.6 THz), in two ways. The first is a free space method based on a vector network analyzer covering the frequency region from 75 to 500 GHz, and the second is the THz time-domain spectroscopy (THz-TDS), effective for the region of 100 GHz–1.6 THz. The results are consistent with existing data (with discrepancies less than 1% in most cases for both the index of refraction and the absorption coefficient), and where they overlap in frequency coverage, the two methods yield identical results to within measurement error.

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Corrections

Tianying Chang, Xiansheng Zhang, Xiaoxuan Zhang, and Hong-Liang Cui, "Accurate determination of dielectric permittivity of polymers from 75 GHz to 1.6 THz using both S-parameters and transmission spectroscopy: publisher’s note," Appl. Opt. 57, 6032-6032 (2018)
https://opg.optica.org/ao/abstract.cfm?uri=ao-57-21-6032

18 June 2018: A correction was made to Ref. 6.

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	Frequency: 0.075–0.5 THz
	$ϵ_{r}^{'}$	$\tan β (\times 10^{- 3})$
PTFE	2.050–2.069	1.59–3.55
PP	2.266–2.272	2.33–7.55
HDPE	2.353–2.375	0.68–7.95
PMMA	2.646–2.669	17.00–27.10

	Frequency: 0.1–1.6 THz
	$ϵ_{r}^{'}$	$\tan β (\times 10^{- 3})$
PTFE	2.061–2.069	2.64–5.57
PP	2.288–2.295	3.03–3.57
HDPE	2.354–2.368	7.09–7.55
PMMA	2.600–2.671	14.7–60.6

	Frequency (GHz)	$ϵ_{r}^{'}$ This Work	$ϵ_{r}^{'}$ Previously Published [32]
PTFE	76.5	2.05571	$2.057 \pm 0.004$
	85	2.06065	$2.057 \pm 0.004$
	94	2.05964	$2.057 \pm 0.004$
PP	76.5	2.26697	$2.258 \pm 0.002$
PP	85	2.26710	$2.258 \pm 0.002$
	94	2.26626	$2.258 \pm 0.002$
	Frequency (GHz)	$\tan β (\times 10^{- 3})$ This Work	$\tan β (\times 10^{- 3})$ Previously Published
PTFE	76.5	1.72	$0.83 \pm 0.30$
	85	1.64	$0.78 \pm 0.22$
	94	1.61	$0.72 \pm 0.29$
PP	76.5	2.41	$0.61 \pm 0.30$
	85	2.37	$0.56 \pm 0.40$
	94	2.35	$0.57 \pm 0.34$

	Frequency: 0.1–1.6 THz
	Absorption Coefficient $({cm}^{- 1})$
PTFE	0.009–1.0056
PP	0.116–1.211
HDPE	0.183–0.652
PMMA	0.474–39.176

	Frequency: 0.075–0.5 THz
	$ϵ_{r}^{'}$	$\tan β (\times 10^{- 3})$
PTFE	2.050–2.069	1.59–3.55
PP	2.266–2.272	2.33–7.55
HDPE	2.353–2.375	0.68–7.95
PMMA	2.646–2.669	17.00–27.10

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Applied Optics