Empirical comparison between effective medium theory models for the dielectric response of biological tissue at terahertz frequencies

Goretti G. Hernandez-Cardoso; Abhishek K. Singh; Enrique Castro-Camus

doi:10.1364/AO.382383

Applied Optics
Vol. 59,
Issue 13,
pp. D6-D11
(2020)
•https://doi.org/10.1364/AO.382383

Empirical comparison between effective medium theory models for the dielectric response of biological tissue at terahertz frequencies

Goretti G. Hernandez-Cardoso, Abhishek K. Singh, and Enrique Castro-Camus

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Goretti G. Hernandez-Cardoso, Abhishek K. Singh, and Enrique Castro-Camus, "Empirical comparison between effective medium theory models for the dielectric response of biological tissue at terahertz frequencies," Appl. Opt. 59, D6-D11 (2020)

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About this Article
History
- Original Manuscript: November 4, 2019
- Revised Manuscript: December 4, 2019
- Manuscript Accepted: December 6, 2019
- Published: January 17, 2020
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Applied Optics Optics theory and practice in Iberoamerica (2020)

Abstract

We study the use of three effective medium theory models, namely Maxwell–Garnett, Bruggeman, and Landau–Lifshitz–Looyenga, for the dielectric response of biological tissue in the terahertz band of the electromagnetic spectrum. In order to accomplish our objectives, we performed measurements on water-dehydrated basil binary mixtures encompassing the entire concentration range, and we further analyze the dielectric function with the models. Our results indicate that the Landau–Lifshitz–Looyenga and Bruggeman models provide marginally better fit to the experimentally measured dielectric function in the terahertz band. We further discuss the biological relevance of the models in the context of our experimental data based on their fundamental assumptions.

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$X_{w}$	Exp.	MG	$Δ$	BM	$Δ$	LLL	$Δ$
0.0	3.24	3.20	0.04	3.20	0.04	3.20	0.04
0.1	3.60	3.38	0.22	3.43	0.17	3.41	0.19
0.2	3.64	3.57	0.07	3.65	0.01	3.62	0.02
0.3	3.83	3.76	0.07	3.85	0.02	3.83	0.00
0.4	4.02	3.94	0.08	4.04	0.02	4.03	0.01
0.5	4.19	4.13	0.06	4.21	0.02	4.22	0.03
0.6	4.39	4.32	0.07	4.38	0.01	4.40	0.01
0.7	4.49	4.50	0.01	4.54	0.05	4.57	0.08
0.8	4.70	4.67	0.03	4.70	0.00	4.73	0.03
0.9	4.90	4.85	0.05	4.85	0.05	4.88	0.02
1.0	5.04	5.01	0.03	5.01	0.03	5.01	0.03
Average			0.07		0.04		0.04

$X_{w}$	Exp.	MG	$Δ$	BM	$Δ$	LLL	$Δ$
0.0	0.37	0.10	0.27	0.10	0.28	0.10	0.28
0.1	0.43	0.41	0.02	0.37	0.06	0.38	0.04
0.2	0.70	0.75	0.05	0.68	0.02	0.70	0.01
0.3	1.05	1.10	0.05	1.03	0.02	1.04	0.01
0.4	1.43	1.47	0.04	1.40	0.03	1.41	0.02
0.5	1.79	1.87	0.08	1.80	0.02	1.80	0.02
0.6	2.22	2.28	0.06	2.23	0.01	2.23	0.00
0.7	2.71	2.73	0.02	2.69	0.02	2.68	0.03
0.8	3.15	3.19	0.04	3.17	0.02	3.16	0.01
0.9	3.63	3.69	0.06	3.68	0.05	3.67	0.04
1.0	4.34	4.21	0.13	4.21	0.13	4.21	0.13
Average			0.08		0.06		0.05

Mixture	MG	$Δ$	BM	$Δ$	LLL	$Δ$
1.0	1.01	0.01	1.01	0.01	1.01	0.01
0.9	0.92	0.02	0.92	0.02	0.92	0.02
0.8	0.81	0.01	0.81	0.01	0.81	0.01
0.7	0.71	0.01	0.71	0.01	0.71	0.01
0.6	0.60	0.00	0.60	0.00	0.60	0.00
0.5	0.47	0.03	0.47	0.03	0.47	0.03
0.4	0.38	0.02	0.38	0.02	0.38	0.02
0.3	0.27	0.03	0.27	0.03	0.27	0.03
0.2	0.21	0.01	0.20	0.00	0.20	0.00
0.1	0.09	0.01	0.08	0.02	0.08	0.02
0.0	0.00	0.00	0.00	0.00	0.00	0.00
Average		0.01		0.01		0.01

$X_{w}$	Exp.	MG	$Δ$	BM	$Δ$	LLL	$Δ$
0.0	3.24	3.20	0.04	3.20	0.04	3.20	0.04
0.1	3.60	3.38	0.22	3.43	0.17	3.41	0.19
0.2	3.64	3.57	0.07	3.65	0.01	3.62	0.02
0.3	3.83	3.76	0.07	3.85	0.02	3.83	0.00
0.4	4.02	3.94	0.08	4.04	0.02	4.03	0.01
0.5	4.19	4.13	0.06	4.21	0.02	4.22	0.03
0.6	4.39	4.32	0.07	4.38	0.01	4.40	0.01
0.7	4.49	4.50	0.01	4.54	0.05	4.57	0.08
0.8	4.70	4.67	0.03	4.70	0.00	4.73	0.03
0.9	4.90	4.85	0.05	4.85	0.05	4.88	0.02
1.0	5.04	5.01	0.03	5.01	0.03	5.01	0.03
Average			0.07		0.04		0.04

$X_{w}$	Exp.	MG	$Δ$	BM	$Δ$	LLL	$Δ$
0.0	0.37	0.10	0.27	0.10	0.28	0.10	0.28
0.1	0.43	0.41	0.02	0.37	0.06	0.38	0.04
0.2	0.70	0.75	0.05	0.68	0.02	0.70	0.01
0.3	1.05	1.10	0.05	1.03	0.02	1.04	0.01
0.4	1.43	1.47	0.04	1.40	0.03	1.41	0.02
0.5	1.79	1.87	0.08	1.80	0.02	1.80	0.02
0.6	2.22	2.28	0.06	2.23	0.01	2.23	0.00
0.7	2.71	2.73	0.02	2.69	0.02	2.68	0.03
0.8	3.15	3.19	0.04	3.17	0.02	3.16	0.01
0.9	3.63	3.69	0.06	3.68	0.05	3.67	0.04
1.0	4.34	4.21	0.13	4.21	0.13	4.21	0.13
Average			0.08		0.06		0.05

Abstract

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Tables (3)

Equations (14)

Applied Optics