Time-domain numerical scheme based on low-order partial-fraction models for the broadband study of frequency-dispersive liquid crystals

Konstantinos P. Prokopidis; Dimitrios C. Zografopoulos

doi:10.1364/JOSAB.33.000622

Journal of the Optical Society of America B
Vol. 33,
Issue 4,
pp. 622-629
(2016)
•https://doi.org/10.1364/JOSAB.33.000622

Time-domain numerical scheme based on low-order partial-fraction models for the broadband study of frequency-dispersive liquid crystals

Konstantinos P. Prokopidis and Dimitrios C. Zografopoulos

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Konstantinos P. Prokopidis and Dimitrios C. Zografopoulos, "Time-domain numerical scheme based on low-order partial-fraction models for the broadband study of frequency-dispersive liquid crystals," J. Opt. Soc. Am. B 33, 622-629 (2016)

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Abstract

A novel finite-difference time-domain formulation for the modeling of electromagnetic wave propagation in frequency-dispersive liquid crystals with random orientation is presented. The dispersion of the complex ordinary and extraordinary permittivities of nematic liquid crystals is described by a generalized model based on the sum of partial fractions. The proposed dispersive model encompasses traditional approaches, such as Drude, Drude–Lorentz, and modified-Lorentz functions; it can also capture arbitrary dispersion properties of experimentally characterized nematic mixtures via the vector fitting technique. The accuracy of the formulation is demonstrated in a series of benchmark examples in optical and terahertz frequencies.

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Equations (32)

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Parameter	Ordinary	Extraordinary
$ε_{\infty}$	2.3	3.6
$c_{1}$	$- 5.7270 \times 10^{10}$	$1.8228 \times 10^{11}$
$a_{1}$	$- 6.5067 \times 10^{11}$	$- 5.5560 \times 10^{12}$
$c_{2}$	$1.3223 \times 10^{12}$	$4.4321 \times 10^{12}$
$a_{2}$	$- 7.2691 \times 10^{12}$	$- 1.9473 \times 10^{13}$
$c_{3}, c_{4}$	$- 6.3760 \times 10^{10} \pm j 9.3668 \times 10^{9}$	$- 4.3250 \times 10^{10} \pm j 8.3911 \times 10^{10}$
$a_{3}, a_{4}$	$- 2.8033 \times 10^{12} \pm j 4.5283 \times 10^{12}$	$- 3.1091 \times 10^{12} \pm j 5.4429 \times 10^{12}$
$c_{5}, c_{6}$	$- 3.6274 \times 10^{9} \pm j 1.3598 \times 10^{9}$	$1.9796 \times 10^{11} \pm j 1.2855 \times 10^{11}$
$a_{5}, a_{6}$	$- 2.4428 \times 10^{12} \pm j 1.1532 \times 10^{13}$	$- 3.665 \times 10^{12} \pm j 1.1864 \times 10^{13}$
$c_{7}, c_{8}$	$- 7.0440 \times 10^{9} \mp j 1.2297 \times 10^{10}$	$- 7.949 \times 10^{11} \mp j 2.686 \times 10^{11}$
$a_{7}, a_{8}$	$- 1.6795 \times 10^{12} \pm j 1.2340 \times 10^{13}$	$- 4.849 \times 10^{12} \pm j 1.219 \times 10^{13}$
$c_{9}, c_{10}$	$3.9011 \times 10^{11} \mp j 3.4830 \times 10^{11}$	$1.7033 \times 10^{8} \mp j 4.1227 \times 10^{8}$
$a_{9}, a_{10}$	$- 3.1816 \times 10^{12} \pm j 2.7504 \times 10^{13}$	$- 1.206 \times 10^{10} \pm j 1.4938 \times 10^{13}$

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Journal of the Optical Society of America B