Determination of the complex refractive index of a subwavelength-diameter platinum or gold pipe by light scattering

Fumiaki Tajima; Yoshio Nishiyama

doi:10.1364/JOSAA.33.001654

Determination of the complex refractive index of a subwavelength-diameter platinum or gold pipe by light scattering

Fumiaki Tajima and Yoshio Nishiyama

Journal of the Optical Society of America A
Vol. 33,
Issue 9,
pp. 1654-1660
(2016)
•https://doi.org/10.1364/JOSAA.33.001654

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Fumiaki Tajima and Yoshio Nishiyama, "Determination of the complex refractive index of a subwavelength-diameter platinum or gold pipe by light scattering," J. Opt. Soc. Am. A 33, 1654-1660 (2016)

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Related Topics
Table of Contents Category
- Materials
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Fiber optics (060.2310)
- Optical properties (160.4760)
- Scattering, polarization (290.5855)

About this Article
History
- Original Manuscript: May 5, 2016
- Revised Manuscript: July 3, 2016
- Manuscript Accepted: July 5, 2016
- Published: August 2, 2016

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Abstract

The complex refractive indices of Pt and Au pipes that are subwavelength in diameter have been found to be different from those of metal thin films for the first time. The metal pipe is made from a spider silk of half-wavelength diameter clad with Pt or Au and illuminated by a plane-polarized laser of wavelength 660 nm at normal incidence. The angular distribution of the light intensity scattered by the pipe is measured and fitted using theoretical calculations based on the corresponding model. The fitting results have lead to the optimum values and uncertainty ranges of the indices and the diameter of the pipe. A field emission scanning electron microscope confirms the diameter from the optical estimation and reveals an image of the surface of the pipe.

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Sample	$n / r$	$E_{⊥}$	$E_{∥}$
$A_{1}$	$n_{1}$	${1.548}_{- 0.077}^{+ 0.092}$	${1.554}_{- 0.180}^{+ 0.159}$
	$r_{1} (nm)$	$139_{- 17}^{+ 17}$	$140_{- 11}^{+ 13}$
	${\tilde{n}}_{2}$ (Pt)	${2.06}_{- 0.27}^{+ 0.19} + {0.21}_{- 0.34}^{+ 0.22} i$	${1.81}_{- 0.43}^{+ 0.45} + {0.41}_{- 0.38}^{+ 0.30} i$
	$r_{2} (nm)$	$193_{- 7}^{+ 16}$	$200_{- 20}^{+ 29}$
	$U_{I}^{\min}$ (%)	1.8	4.3
$A_{2}$	$n_{1}$	${1.570}_{- 0.061}^{+ 0.063}$	${1.612}_{- 0.430}^{+ 0.320}$
	$r_{1} (nm)$	$127_{- 8}^{+ 11}$	$127_{- 16}^{+ 33}$
	${\tilde{n}}_{2}$ (Pt)	${1.86}_{- 0.19}^{+ 0.21} + {0.41}_{- 0.24}^{+ 0.19} i$	${2.11}_{- 0.35}^{+ 0.50} + {0.36}_{- 0.24}^{+ 0.23} i$
	$r_{2} (nm)$	$178_{- 11}^{+ 10}$	$183_{- 20}^{+ 19}$
	$U_{I}^{\min}$ (%)	2.6	4.0
$B_{1}$	$n_{1}$	${1.566}_{- 0.037}^{+ 0.043}$	${1.542}_{- 0.127}^{+ 0.117}$
	$r_{1} (nm)$	$135_{- 9}^{+ 10}$	$136_{- 8}^{+ 9}$
	${\tilde{n}}_{2}$ (Au)	${1.61}_{- 0.19}^{+ 0.15} + {1.31}_{- 0.15}^{+ 0.14} i$	${6.86}_{- 0.06}^{+ 0.06} + {0.33}_{- 0.03}^{+ 0.07} i$
	$r_{2} (nm)$	$185_{- 6}^{+ 5}$	(185)
	$U_{I}^{\min}$ (%)	2.4	2.5
$B_{2}$	$n_{1}$	${1.575}_{- 0.130}^{+ 0.140}$	${1.780}_{- 0.340}^{+ 0.230}$
	$r_{1} (nm)$	$107_{- 9}^{+ 8}$	$104_{- 8}^{+ 12}$
	${\tilde{n}}_{2}$ (Au)	${1.46}_{- 0.27}^{+ 0.27} + {1.56}_{- 0.14}^{+ 0.25} i$	${6.10}_{- 0.36}^{+ 0.40} + {0.48}_{- 0.25}^{+ 0.35} i$
	$r_{2} (nm)$	$148_{- 5}^{+ 5}$	(148)
	$U_{I}^{\min}$ (%)	3.0	2.1

Metal	Johnson and Christy [15]	Lynch and Hunter [16]	ATR Measurement
Pt	—	$2.41 + 4.30 i$	$2.50 + 4.32 i$
Au	$0.14 + 3.697 i$	$0.165 + 3.28 i$	$0.312 + 3.53 i$

Sample	$n / r$	$E_{⊥}$	$E_{∥}$
$A_{1}$	$n_{1}$	${1.548}_{- 0.077}^{+ 0.092}$	${1.554}_{- 0.180}^{+ 0.159}$
	$r_{1} (nm)$	$139_{- 17}^{+ 17}$	$140_{- 11}^{+ 13}$
	${\tilde{n}}_{2}$ (Pt)	${2.06}_{- 0.27}^{+ 0.19} + {0.21}_{- 0.34}^{+ 0.22} i$	${1.81}_{- 0.43}^{+ 0.45} + {0.41}_{- 0.38}^{+ 0.30} i$
	$r_{2} (nm)$	$193_{- 7}^{+ 16}$	$200_{- 20}^{+ 29}$
	$U_{I}^{\min}$ (%)	1.8	4.3
$A_{2}$	$n_{1}$	${1.570}_{- 0.061}^{+ 0.063}$	${1.612}_{- 0.430}^{+ 0.320}$
	$r_{1} (nm)$	$127_{- 8}^{+ 11}$	$127_{- 16}^{+ 33}$
	${\tilde{n}}_{2}$ (Pt)	${1.86}_{- 0.19}^{+ 0.21} + {0.41}_{- 0.24}^{+ 0.19} i$	${2.11}_{- 0.35}^{+ 0.50} + {0.36}_{- 0.24}^{+ 0.23} i$
	$r_{2} (nm)$	$178_{- 11}^{+ 10}$	$183_{- 20}^{+ 19}$
	$U_{I}^{\min}$ (%)	2.6	4.0
$B_{1}$	$n_{1}$	${1.566}_{- 0.037}^{+ 0.043}$	${1.542}_{- 0.127}^{+ 0.117}$
	$r_{1} (nm)$	$135_{- 9}^{+ 10}$	$136_{- 8}^{+ 9}$
	${\tilde{n}}_{2}$ (Au)	${1.61}_{- 0.19}^{+ 0.15} + {1.31}_{- 0.15}^{+ 0.14} i$	${6.86}_{- 0.06}^{+ 0.06} + {0.33}_{- 0.03}^{+ 0.07} i$
	$r_{2} (nm)$	$185_{- 6}^{+ 5}$	(185)
	$U_{I}^{\min}$ (%)	2.4	2.5
$B_{2}$	$n_{1}$	${1.575}_{- 0.130}^{+ 0.140}$	${1.780}_{- 0.340}^{+ 0.230}$
	$r_{1} (nm)$	$107_{- 9}^{+ 8}$	$104_{- 8}^{+ 12}$
	${\tilde{n}}_{2}$ (Au)	${1.46}_{- 0.27}^{+ 0.27} + {1.56}_{- 0.14}^{+ 0.25} i$	${6.10}_{- 0.36}^{+ 0.40} + {0.48}_{- 0.25}^{+ 0.35} i$
	$r_{2} (nm)$	$148_{- 5}^{+ 5}$	(148)
	$U_{I}^{\min}$ (%)	3.0	2.1

Metal	Johnson and Christy [15]	Lynch and Hunter [16]	ATR Measurement
Pt	—	$2.41 + 4.30 i$	$2.50 + 4.32 i$
Au	$0.14 + 3.697 i$	$0.165 + 3.28 i$	$0.312 + 3.53 i$

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