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The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles
G Model IJLEO-54423; No. of Pages 3
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles Daobin Luo ∗ , Xiang’e Han, Paerhatijiang Tuersun School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China
a r t i c l e
i n f o
Article history: Received 18 July 2013 Accepted 11 January 2014 Available online xxx Keywords: Metallic nanoparticle Optical transmissivity Light scattering
a b s t r a c t We design a method to enhance film optical transimissivity by sphere metallic nanoparticles. The light scatter effect of the nanoparticles is analyzed. We show the optimization design to improve the optical transimissivity of a film with silver nanoparticles, considering the factors of the sphere nanoparticles size and the surface density. The calculated results show that the silver nanoparticles can enhance the film optical transmissivity greatly. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction At present, metal nanoparticles (NPs) have received an extraordinary attention because of their special optical properties, leading to a dramatic improvement in the molecule fluorescence [1,2], light collection in photovoltaics [3], and plasmonic light-harvesting devices [4]. In particular, Mie theory solute the optical absorption and scattering of sphere NPs. Metal nanoparticles are also used for increasing the efficiency of solar cells by light scattering from metal nanoparticles [5,6]. In this paper, we develop a kind of design to enhance film optical transmissivity by sphere metallic NPs. In this model, the Ag NPs are attached on the film uniformly with surface density , and the optical transmissivity of the film is enhanced due to the strong light scattering when the radius of the NPs is in appropriate size. The enhancement rate of film optical transmissivity is calculated also.
2. The theory consideration for the optical characters of the sphere metallic nanoparticle
Based on Mie theory, the scattering cross section and the extinction cross section are 2 (2n + 1)(|an |2 + |bn |2 ) k2
(1)
2 (2n + 1)Re{an + bn } k2
(2)
∞
Csca =
n=1 ∞
Cext =
n=1
The relation of the extinction cross section, absorption cross section and scattering cross section is Cext = Cabs + Csca
(3)
where k = (2/)N is the wave number in the medium, is the wavelength of incidence light in vacuum, N is the refractive indices of the medium. The scattering coefficients an and bn can expressed as an =
m2 jn (mx)[xjn (x)] − jn (x)[mxjn (mx)]
(1)
m2 jn (mx) xhn (x)
(1)
− hn (x)[mxjn (mx)]
(4)
2.1. Mie theory Mie theory is an exact analytical description of the electrodynamic response of spherical objects without assumptions made.
∗ Corresponding author. E-mail address: [email protected] (D. Luo).
bn =
jn (mx)[xjn (x)] − jn (x)[mxjn (mx)]
(1)
jn (mx) xhn (x)
(1)
− hn (x)[mxjn (mx)]
(5)
where x = kR, R is the radius of the nanoparticle, the relative refractive index m = N1 /N, N1 is the refractive indices of the NPs. jn (x) is (1) the Bessel function, hn is the first kind Hankel function, and Re{} denote real part.
http://dx.doi.org/10.1016/j.ijleo.2014.01.128 0030-4026/© 2014 Elsevier GmbH. All rights reserved.
Please cite this article in press as: D. Luo, et al., The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.128
G Model
ARTICLE IN PRESS
IJLEO-54423; No. of Pages 3
D. Luo et al. / Optik xxx (2014) xxx–xxx
2
4.5
9 393
8.498
Qext Qsc a Qabs
8 393,7.715
Q
4
b
Q
7
3.5
6
3
f
Q
Efficiency
Efficiency
sca
5 4
2.5 2 1.5
3
1
2 353,2.326
0.5
1 0 300
350
400
450
500 550 600 Wavelength(nm)
650
700
750
0 20
800
The dielectric function of a metal like Ag NPs is physically described using Drude model ω2
ωP2
+ iω
40
50
60
70 80 Radius(nm)
90
100
110
120
Fig. 2. The efficiency of the different radius at the wavelength 550 nm.
Fig. 1. The extinction, scattering and absorption efficiency.
ε(ω) = 1 −
30
(6)
where ωP is the plasma frequency and is the damping coefficient. indices of the metal nanoparticle It is well know that the refractive ε(ω). can be expressed as N1 = The scattering efficiency, extinction efficiency and the absorption efficiency are Qsca =
Csca R2
(7)
Qext =
Cext R2
(8)
Qabs =
Cabs R2
(9)
uniformly with surface density (per square micrometer), seeing Fig. 3, the transmissivity of the film T will be different to T0 , the sphere metallic nanoparticles will change the film transmissivity due to its scattering characters. We will discuss the total transmissivity of the film at this condition. The total optical flux of the film includes two parts. One is the area with nanoparticle and another is the area of the film without the nanoparticle. The part optical flux due to the nanoparticle is expressed as WAg = Qf SAg I
where Qf is the forward scattering efficiency, SAg = · S · R2 is the total area of the Ag nanoparticles on the film, and I is the incidence intension. The other part optical flux of substrate without nanoparticle is [8] W0 = T0 (SI − Qext SAg I)
2.2. The scattering character of the sphere metallic nanoparticle
where Qext is the extinction efficiency of the nanoparticle. So the total optical flux of the film can expressed as
The extinction spectra from metal spheres can be calculated if the frequency dependent permittivity of the metal is known. To begin with, let us consider a 50 nm radius silver sphere surrounded by air. The extinction, scattering and absorption spectra are shown in Fig. 1. From Fig. 1, we can see that the scattering efficiency will arrive peak when = 393 nm, and the scattering efficiency is more than unit. The efficiency for backscattering Qb is [7]
W = W0 + WAg
1 Qb = 2 | (2n + 1)(−1)n (an + bn )|2 x
(10)
n
and Qsca = Qb + Qf
(11)
where Qf is the forward scattering efficiency. Fig. 2 shows the efficiency of Ag nanoparticles in vacuum vary as the radius at the wavelength 550 nm. Based on Fig. 2, there is a scattering peak when the radius is about 80 nm,and it is obviously that the forward scattering efficiency is far greater than the backscattering efficiency.
(12)
(13)
(14)
and the transmissivity of the film is T=
W IS
(15)
The transmissivity enhancement rate due to the nanoparticles is f =
T T0
(16)
We show the transmissivity enhancement rate at the radius of 80 nm in Fig. 4. From Fig. 4, we can see that the transmissivity rate of the film will be improved by the NPs. For 80 nm NPs, the enhance rate will arrive at peak value about 2 when = 800 nm and surface density = 30 per square micron.
3. Enhanced film optical transmissivity via the Ag sphere metallic nanoparticle Let us consider a film with the transmissivity T0 and the area S. If the sphere metallic nanoparticles are attached to the thin film
Fig. 3. The sketch map of the film with nanoparticles.
Please cite this article in press as: D. Luo, et al., The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.128
G Model IJLEO-54423; No. of Pages 3
ARTICLE IN PRESS D. Luo et al. / Optik xxx (2014) xxx–xxx
3
film optical transmissivity, and the Ag nanoparticles have greatly improved the transmissivity rate of the film in the visible spectrum. Further, we show the optimization design of the surface density and the size of the metallic nanoparticles. Future work will focus on optimized metal nanoparticles surface density and its size, also taking into account interparticle coupling. References
Fig. 4. The transmissivity enhancement rate at the radius of 80 nm.
4. Conclusions In this paper, we have shown that both the metallic nanoparticle size and the surface density are crucial parameters for enhanced
[1] R. Carminati, J.-J. Greffet, C. Henkel, J.M. Vigoureux, Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle, Opt. Commun. 261 (2006) 368–375. [2] P. Anger, P. Bharadwaj, L. Novotny, Enhancement and quenching of singlemolecule fluorescence, Phys. Rev. Lett. 96 (113002) (2006) 1–4. [3] H.A. Atwater, A. Polman, Plasmonics for improved photovoltaic devices, Nat. Mater. 9 (2010) 205–213. [4] A. Alexandre, L. Dang Yuan, Plasmonic light-harvesting devices over the whole visible spectrum, Nano Lett. 10 (2010) 2574–2579. [5] K.R. Catchpole, A. Polman, Design principles for particle plasmon enhanced solar cells, Appl. Phys. Lett. 93 (2008) 191113-1–191113-3. [6] K.R. Catchpole, A. Polman, Plasmonic solar cells, Opt. Express 16 (26) (2008) 21793–21800. [7] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, John Wiley & Sons, New York, 1983. [8] T. Han, F.-Y. Meng, S. Zhang, Theoretical investigation of anti-reflection properties of Ag-nanoparticles, Acta Phys. Sin. 60 (2) (2011) 027303 1–273035.
Please cite this article in press as: D. Luo, et al., The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.128
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles Daobin Luo ∗ , Xiang’e Han, Paerhatijiang Tuersun School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China
a r t i c l e
i n f o
Article history: Received 18 July 2013 Accepted 11 January 2014 Available online xxx Keywords: Metallic nanoparticle Optical transmissivity Light scattering
a b s t r a c t We design a method to enhance film optical transimissivity by sphere metallic nanoparticles. The light scatter effect of the nanoparticles is analyzed. We show the optimization design to improve the optical transimissivity of a film with silver nanoparticles, considering the factors of the sphere nanoparticles size and the surface density. The calculated results show that the silver nanoparticles can enhance the film optical transmissivity greatly. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction At present, metal nanoparticles (NPs) have received an extraordinary attention because of their special optical properties, leading to a dramatic improvement in the molecule fluorescence [1,2], light collection in photovoltaics [3], and plasmonic light-harvesting devices [4]. In particular, Mie theory solute the optical absorption and scattering of sphere NPs. Metal nanoparticles are also used for increasing the efficiency of solar cells by light scattering from metal nanoparticles [5,6]. In this paper, we develop a kind of design to enhance film optical transmissivity by sphere metallic NPs. In this model, the Ag NPs are attached on the film uniformly with surface density , and the optical transmissivity of the film is enhanced due to the strong light scattering when the radius of the NPs is in appropriate size. The enhancement rate of film optical transmissivity is calculated also.
2. The theory consideration for the optical characters of the sphere metallic nanoparticle
Based on Mie theory, the scattering cross section and the extinction cross section are 2 (2n + 1)(|an |2 + |bn |2 ) k2
(1)
2 (2n + 1)Re{an + bn } k2
(2)
∞
Csca =
n=1 ∞
Cext =
n=1
The relation of the extinction cross section, absorption cross section and scattering cross section is Cext = Cabs + Csca
(3)
where k = (2/)N is the wave number in the medium, is the wavelength of incidence light in vacuum, N is the refractive indices of the medium. The scattering coefficients an and bn can expressed as an =
m2 jn (mx)[xjn (x)] − jn (x)[mxjn (mx)]
(1)
m2 jn (mx) xhn (x)
(1)
− hn (x)[mxjn (mx)]
(4)
2.1. Mie theory Mie theory is an exact analytical description of the electrodynamic response of spherical objects without assumptions made.
∗ Corresponding author. E-mail address: [email protected] (D. Luo).
bn =
jn (mx)[xjn (x)] − jn (x)[mxjn (mx)]
(1)
jn (mx) xhn (x)
(1)
− hn (x)[mxjn (mx)]
(5)
where x = kR, R is the radius of the nanoparticle, the relative refractive index m = N1 /N, N1 is the refractive indices of the NPs. jn (x) is (1) the Bessel function, hn is the first kind Hankel function, and Re{} denote real part.
http://dx.doi.org/10.1016/j.ijleo.2014.01.128 0030-4026/© 2014 Elsevier GmbH. All rights reserved.
Please cite this article in press as: D. Luo, et al., The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.128
G Model
ARTICLE IN PRESS
IJLEO-54423; No. of Pages 3
D. Luo et al. / Optik xxx (2014) xxx–xxx
2
4.5
9 393
8.498
Qext Qsc a Qabs
8 393,7.715
Q
4
b
Q
7
3.5
6
3
f
Q
Efficiency
Efficiency
sca
5 4
2.5 2 1.5
3
1
2 353,2.326
0.5
1 0 300
350
400
450
500 550 600 Wavelength(nm)
650
700
750
0 20
800
The dielectric function of a metal like Ag NPs is physically described using Drude model ω2
ωP2
+ iω
40
50
60
70 80 Radius(nm)
90
100
110
120
Fig. 2. The efficiency of the different radius at the wavelength 550 nm.
Fig. 1. The extinction, scattering and absorption efficiency.
ε(ω) = 1 −
30
(6)
where ωP is the plasma frequency and is the damping coefficient. indices of the metal nanoparticle It is well know that the refractive ε(ω). can be expressed as N1 = The scattering efficiency, extinction efficiency and the absorption efficiency are Qsca =
Csca R2
(7)
Qext =
Cext R2
(8)
Qabs =
Cabs R2
(9)
uniformly with surface density (per square micrometer), seeing Fig. 3, the transmissivity of the film T will be different to T0 , the sphere metallic nanoparticles will change the film transmissivity due to its scattering characters. We will discuss the total transmissivity of the film at this condition. The total optical flux of the film includes two parts. One is the area with nanoparticle and another is the area of the film without the nanoparticle. The part optical flux due to the nanoparticle is expressed as WAg = Qf SAg I
where Qf is the forward scattering efficiency, SAg = · S · R2 is the total area of the Ag nanoparticles on the film, and I is the incidence intension. The other part optical flux of substrate without nanoparticle is [8] W0 = T0 (SI − Qext SAg I)
2.2. The scattering character of the sphere metallic nanoparticle
where Qext is the extinction efficiency of the nanoparticle. So the total optical flux of the film can expressed as
The extinction spectra from metal spheres can be calculated if the frequency dependent permittivity of the metal is known. To begin with, let us consider a 50 nm radius silver sphere surrounded by air. The extinction, scattering and absorption spectra are shown in Fig. 1. From Fig. 1, we can see that the scattering efficiency will arrive peak when = 393 nm, and the scattering efficiency is more than unit. The efficiency for backscattering Qb is [7]
W = W0 + WAg
1 Qb = 2 | (2n + 1)(−1)n (an + bn )|2 x
(10)
n
and Qsca = Qb + Qf
(11)
where Qf is the forward scattering efficiency. Fig. 2 shows the efficiency of Ag nanoparticles in vacuum vary as the radius at the wavelength 550 nm. Based on Fig. 2, there is a scattering peak when the radius is about 80 nm,and it is obviously that the forward scattering efficiency is far greater than the backscattering efficiency.
(12)
(13)
(14)
and the transmissivity of the film is T=
W IS
(15)
The transmissivity enhancement rate due to the nanoparticles is f =
T T0
(16)
We show the transmissivity enhancement rate at the radius of 80 nm in Fig. 4. From Fig. 4, we can see that the transmissivity rate of the film will be improved by the NPs. For 80 nm NPs, the enhance rate will arrive at peak value about 2 when = 800 nm and surface density = 30 per square micron.
3. Enhanced film optical transmissivity via the Ag sphere metallic nanoparticle Let us consider a film with the transmissivity T0 and the area S. If the sphere metallic nanoparticles are attached to the thin film
Fig. 3. The sketch map of the film with nanoparticles.
Please cite this article in press as: D. Luo, et al., The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.128
G Model IJLEO-54423; No. of Pages 3
ARTICLE IN PRESS D. Luo et al. / Optik xxx (2014) xxx–xxx
3
film optical transmissivity, and the Ag nanoparticles have greatly improved the transmissivity rate of the film in the visible spectrum. Further, we show the optimization design of the surface density and the size of the metallic nanoparticles. Future work will focus on optimized metal nanoparticles surface density and its size, also taking into account interparticle coupling. References
Fig. 4. The transmissivity enhancement rate at the radius of 80 nm.
4. Conclusions In this paper, we have shown that both the metallic nanoparticle size and the surface density are crucial parameters for enhanced
[1] R. Carminati, J.-J. Greffet, C. Henkel, J.M. Vigoureux, Radiative and non-radiative decay of a single molecule close to a metallic nanoparticle, Opt. Commun. 261 (2006) 368–375. [2] P. Anger, P. Bharadwaj, L. Novotny, Enhancement and quenching of singlemolecule fluorescence, Phys. Rev. Lett. 96 (113002) (2006) 1–4. [3] H.A. Atwater, A. Polman, Plasmonics for improved photovoltaic devices, Nat. Mater. 9 (2010) 205–213. [4] A. Alexandre, L. Dang Yuan, Plasmonic light-harvesting devices over the whole visible spectrum, Nano Lett. 10 (2010) 2574–2579. [5] K.R. Catchpole, A. Polman, Design principles for particle plasmon enhanced solar cells, Appl. Phys. Lett. 93 (2008) 191113-1–191113-3. [6] K.R. Catchpole, A. Polman, Plasmonic solar cells, Opt. Express 16 (26) (2008) 21793–21800. [7] C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles, John Wiley & Sons, New York, 1983. [8] T. Han, F.-Y. Meng, S. Zhang, Theoretical investigation of anti-reflection properties of Ag-nanoparticles, Acta Phys. Sin. 60 (2) (2011) 027303 1–273035.
Please cite this article in press as: D. Luo, et al., The optimization design for improving film optical transmissivity via the sphere metallic nanoparticles, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2014.01.128