Interferometric investigation and simulation of refractive index in glass matrixes containing nanoparticles of varying sizes

Michael Gerard Feeney; Rabia Ince; Mehmet Hikmet Yukselici; Cagdas Allahverdi

doi:10.1364/AO.50.003259

Applied Optics
Vol. 50,
Issue 19,
pp. 3259-3267
(2011)
•https://doi.org/10.1364/AO.50.003259

Interferometric investigation and simulation of refractive index in glass matrixes containing nanoparticles of varying sizes

Michael Gerard Feeney, Rabia Ince, Mehmet Hikmet Yukselici, and Cagdas Allahverdi

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Michael Gerard Feeney, Rabia Ince, Mehmet Hikmet Yukselici, and Cagdas Allahverdi, "Interferometric investigation and simulation of refractive index in glass matrixes containing nanoparticles of varying sizes," Appl. Opt. 50, 3259-3267 (2011)

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- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: January 21, 2011
- Revised Manuscript: April 12, 2011
- Manuscript Accepted: May 6, 2011
- Published: June 28, 2011

Abstract

The relationship between refractive index and nanoparticle radii of cadmium selenide (CdSe) nano particles embedded within glass matrixes was investigated experimentally and by simulations. A homemade automated Michelson interferometer arrangement employing a rotating table and a He–Ne laser source at a wavelength of $632.8 nm$ determined the refractive index versus nanoparticle radii of embedded cadmium selenide (CdSe) nanoparticles. The refractive index was found to decrease linearly with nanoparticle radius increase. However, one sample showed a step increase in refractive index; on spectroscopic analysis, it was found that its resonant wavelength matched that of the He–Ne source wavelength. The simulations showed that two conditions caused the step increase in refractive index: low plasma frequency and matched sample and source resonances. This simple interferometer setup defines a new method of determining the radii of nanoparticles embedded in substrates and enables refractive index tailoring by modification of exact annealing conditions.

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Sample	Cycle Temperature ( $° C$ )/time (h)			Absorption Wavelength (nm)	Nanoparticle Radius (nm)
Sample	1	2	3	Absorption Wavelength (nm)	Nanoparticle Radius (nm)
1	$1000 / 0.6$	$625 / 2$	$450 / 23$	514	2.41
2	$1000 / 0.6$	$625 / 1$	$450 / 23$	548	2.50
3	$1000 / 0.6$	$625 / 4$	$450 / 23$	551	2.52
4	$1000 / 0.6$	$625 / 2$	$450 / 23$	594	3.00
5	$1080 / 0.6$	$625 / 1$	$450 / 23$	595	3.01
6	$1080 / 0.6$	$625 / 4$	$450 / 23$	665	4.61

Sample	$n_{sample}$ ( $λ = 632.8 nm$ )	$Δ n_{sample} = n_{sample} - n_{substrate}$ ( $\times 10^{- 3}$ )	$λ_{o}$ (nm)	NP Radius, R (nm)
Substrate/matrix	1.541	0	^a	None
1	1.524	$- 17$	514	2.41
2	1.514	$- 28$	548	2.50
3	1.494	$- 47$	551	2.52
4	1.492	$- 50$	594	3.00
5	1.610	$+ 69$	595	3.01
6	1.510	$- 31$	665	4.61

	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6
$α_{crvst}$ ( $\times 10^{5}$ )	1.00	1.00	1.00	1.00	1.00	1.00
$n_{M}$	1.54	1.54	1.54	1.54	1.54	1.54
$ε_{M}$ ( ${n_{M}}^{2}$ )	2.37	2.37	2.37	2.37	2.37	2.37
$ε_{1}$ ( $nF / m$ )	3.21	6.28	0.39	1.92	0.02	0.64
$ε_{2}$ ( $10^{- 9}$ )	1.45	7.93	0.84	3.19	0.04	1.13
${ε_{2}}^{2}$ ( $\times 10^{- 18}$ )	2.10	62.9	0.70	10.2	0.002	1.28
$α_{com}$	19.4	30.4	5.5	17.9	1.3	4.2
n (λ)	2.06	2.06	2.06	2.06	2.06	2.06
$f_{c}$ ( $\times 10^{- 4}$ )	1.99	3.13	0.56	1.84	0.13	0.43

NP Properties	1	2	3	4	5	6
NP Radius (nm)	2.41	2.50	2.52	3.00	3.01	4.61
NP Volume ( $\times 10^{- 26} m^{3}$ )	5.79	4.84	4.46	3.77	3.15	2.36
$V_{f}$ ( $\times 10^{- 4}$ )	1.43	2.25	0.75	1.50	0.13	0.43
N ( $\times 10^{21} m^{- 3}$ )	3.38	4.81	0.84	1.62	0.12	0.10
CdSe unit cube volume ( $\times 10^{- 29} m^{3}$ ) [22]	7.95	7.95	7.95	7.95	7.95	7.95
Number of ions/NP ( $\times 10^{3}$ )	2.91	2.43	2.24	1.90	1.59	1.19
$N_{e}$ (NP) ( $\times 10^{3}$ )	5.83	4.87	4.49	3.79	3.17	2.38
$N_{e}$ ( $\times 10^{25} m^{- 3}$ )	2.00	3.15	0.57	1.85	0.13	0.43

Sample	N (NP) ( $\times 10^{21} m^{- 3}$ )	$N_{e}$ ( $\times 10^{25} m^{- 3}$ )	$λ_{p}$ ( $μm$ )
1	3.4	2.0	51.3
2	4.8	3.2	57.3
3	0.8	0.6	33.9
4	1.6	1.9	41.4
5	0.1	0.1	13.6
6	0.1	0.4	49.3

Sample	R (nm)	$n_{sample}$ ( $λ = 632.8 nm$ )	$Δ n_{sample}$ ( $\times 10^{- 3}$ )
1	2.41	1.5412	0.2
2	2.50	1.5413	0.3
3	2.52	1.5418	0.7
4	3.00	1.5423	1.0
5	3.01	1.5531	8.6
6	4.61	1.5400	$- 1.2$

Abstract

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Applied Optics