Extracting an accurate model for permittivity from experimental data: hunting complex poles from the real line

M. Garcia-Vergara; G. Demésy; F. Zolla

doi:10.1364/OL.42.001145

Optics Letters
Vol. 42,
Issue 6,
pp. 1145-1148
(2017)
•https://doi.org/10.1364/OL.42.001145

Extracting an accurate model for permittivity from experimental data: hunting complex poles from the real line

M. Garcia-Vergara, G. Demésy, and F. Zolla

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M. Garcia-Vergara, G. Demésy, and F. Zolla, "Extracting an accurate model for permittivity from experimental data: hunting complex poles from the real line," Opt. Lett. 42, 1145-1148 (2017)

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Abstract

In this Letter, we describe a very general procedure to obtain a causal fit of the permittivity of materials from experimental data with very few parameters. Unlike other closed forms proposed in the literature, the uniqueness of this approach lies in its independence on the material or frequency range at stake. Many illustrative numerical examples are given, and the accuracy of the fitting is compared to other expressions in the literature.

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$Ω_{j}$ [P rad/s]	$\| A_{j} \|$ [P rad/s]	$ϕ_{j} [rad]$
Au (Johnson and Christy) $λ : 0.188 - 1.937 μm$
( ${error}_{2} = 3.01 %$ and ${error}_{\infty} = 1.27 %$ )
$3.43 E - 01 + 5.21 E - 02 i$	238.36	−3.14
$4.56 E + 00 + 1.46 E + 00 i$	9.83	−2.12
Cu (Johnson and Christy) $λ : 0.188 - 1.937 μm$
( ${error}_{2} = 6.70 %$ and ${error}_{\infty} = 2.88 %$ )
$4.46 E - 01 + 4.61 E - 02 i$	156.78	−3.12
$3.11 E + 00 + 7.71 E - 01 i$	5.16	−1.07
*Al (Ordal et al.)* $λ : 0.667 - 200 μm$
( ${error}_{2} = 8.36 %$ and ${error}_{\infty} = 11.55 %$ )
$3.24 E - 10 + 1.35 E - 03 i$	4284.43	−1.57
$1.13 E - 01 + 7.16 E - 02 i$	228.84	−3.08
$4.24 E - 01 + 7.94 E - 01 i$	139.21	0.69
*Ag (Babar et al.)* $λ : 0.2066 - 12.40 μm$
( ${error}_{2} = 1.71 %$ and ${error}_{\infty} = 1.87 %$ )
$- 9.14 E - 16 + 6.52 E - 02 i$	1818.56	1.57
$8.37 E + 00 + 2.78 E + 00 i$	6.83	−2.44
$6.30 E + 00 + 4.72 E - 01 i$	1.62	−2.58
$6.73 E + 00 + 2.18 E - 01 i$	0.39	−1.55

$Ω_{j}$ [P rad/s]	$\| A_{j} \|$ [P rad/s]	$ϕ_{j} [rad]$
*GaAs (Jellison et al.) $λ : 0.234 - 0.840 μm$*
( ${error}_{2} = 3.13 %$ and ${error}_{\infty} = 6.23 %$ )
$7.17 E + 00 + 8.55 E - 01 i$	18.54	−2.92
$4.65 E + 00 + 1.00 E + 00 i$	12.34	−2.96
$4.30 E + 00 + 2.57 E - 01 i$	2.37	−1.54
$7.66 E + 00 + 2.40 E - 01 i$	1.79	1.29
*GaP (Jellison et al.)* $λ : 0.234 - 0.840 μm$
( ${error}_{2} = 3.16 %$ and ${error}_{\infty} = 6.78 %$ )
$7.60 E + 00 + 7.60 E - 01 i$	20.56	−3.10
$5.64 E + 00 + 2.40 E - 01 i$	5.02	−2.87
$6.19 E + 00 + 3.51 E - 01 i$	1.96	−2.62
$4.32 E + 00 + 4.49 E - 01 i$	0.68	−1.87
Si (Green and Keevers) $λ : 0.25 - 1.0 μm$
( ${error}_{2} = 1.08 %$ and ${error}_{\infty} = 3.08 %$ )
$7.99 E + 00 + 1.83 E + 00 i$	13.57	2.98
$6.54 E + 00 + 3.74 E - 01 i$	11.50	2.78
$5.49 E + 00 + 6.65 E - 01 i$	10.51	−2.46
$5.12 E + 00 + 1.68 E - 01 i$	4.02	−2.46

$Ω_{j}$ [P rad/s]	$\| A_{j} \|$ [P rad/s]	$ϕ_{j} [rad]$
Au (Johnson and Christy) $λ : 0.188 - 1.937 μm$
( ${error}_{2} = 3.01 %$ and ${error}_{\infty} = 1.27 %$ )
$3.43 E - 01 + 5.21 E - 02 i$	238.36	−3.14
$4.56 E + 00 + 1.46 E + 00 i$	9.83	−2.12
Cu (Johnson and Christy) $λ : 0.188 - 1.937 μm$
( ${error}_{2} = 6.70 %$ and ${error}_{\infty} = 2.88 %$ )
$4.46 E - 01 + 4.61 E - 02 i$	156.78	−3.12
$3.11 E + 00 + 7.71 E - 01 i$	5.16	−1.07
*Al (Ordal et al.)* $λ : 0.667 - 200 μm$
( ${error}_{2} = 8.36 %$ and ${error}_{\infty} = 11.55 %$ )
$3.24 E - 10 + 1.35 E - 03 i$	4284.43	−1.57
$1.13 E - 01 + 7.16 E - 02 i$	228.84	−3.08
$4.24 E - 01 + 7.94 E - 01 i$	139.21	0.69
*Ag (Babar et al.)* $λ : 0.2066 - 12.40 μm$
( ${error}_{2} = 1.71 %$ and ${error}_{\infty} = 1.87 %$ )
$- 9.14 E - 16 + 6.52 E - 02 i$	1818.56	1.57
$8.37 E + 00 + 2.78 E + 00 i$	6.83	−2.44
$6.30 E + 00 + 4.72 E - 01 i$	1.62	−2.58
$6.73 E + 00 + 2.18 E - 01 i$	0.39	−1.55

$Ω_{j}$ [P rad/s]	$\| A_{j} \|$ [P rad/s]	$ϕ_{j} [rad]$
*GaAs (Jellison et al.) $λ : 0.234 - 0.840 μm$*
( ${error}_{2} = 3.13 %$ and ${error}_{\infty} = 6.23 %$ )
$7.17 E + 00 + 8.55 E - 01 i$	18.54	−2.92
$4.65 E + 00 + 1.00 E + 00 i$	12.34	−2.96
$4.30 E + 00 + 2.57 E - 01 i$	2.37	−1.54
$7.66 E + 00 + 2.40 E - 01 i$	1.79	1.29
*GaP (Jellison et al.)* $λ : 0.234 - 0.840 μm$
( ${error}_{2} = 3.16 %$ and ${error}_{\infty} = 6.78 %$ )
$7.60 E + 00 + 7.60 E - 01 i$	20.56	−3.10
$5.64 E + 00 + 2.40 E - 01 i$	5.02	−2.87
$6.19 E + 00 + 3.51 E - 01 i$	1.96	−2.62
$4.32 E + 00 + 4.49 E - 01 i$	0.68	−1.87
Si (Green and Keevers) $λ : 0.25 - 1.0 μm$
( ${error}_{2} = 1.08 %$ and ${error}_{\infty} = 3.08 %$ )
$7.99 E + 00 + 1.83 E + 00 i$	13.57	2.98
$6.54 E + 00 + 3.74 E - 01 i$	11.50	2.78
$5.49 E + 00 + 6.65 E - 01 i$	10.51	−2.46
$5.12 E + 00 + 1.68 E - 01 i$	4.02	−2.46

Abstract

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Tables (2)

Equations (13)

Optics Letters