Spherical metallic nanoparticle arrays for super-resolution imagingChang Chun Yan, Dao Hua Zhang, and Dong Dong Li Citation: Journal of Applied Physics 109, 063105 (2011); doi: 10.1063/1.3553875 View online: http://dx.doi.org/10.1063/1.3553875 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/109/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Self-organized ordered silver nanoparticle arrays obtained by solid state dewetting Appl. Phys. Lett. 105, 203102 (2014); 10.1063/1.4901715 Metallic nanoparticles grown in the core of femtosecond laser micromachined waveguides J. Appl. Phys. 115, 193507 (2014); 10.1063/1.4875485 Super-resolution spatial frequency differentiation of nanoscale particles with a vibrating nanograting Appl. Phys. Lett. 100, 011101 (2012); 10.1063/1.3673470 Super-resolution imaging using a three-dimensional metamaterials nanolens Appl. Phys. Lett. 96, 023114 (2010); 10.1063/1.3291677 Self-organized metallic nanoparticle and nanowire arrays from ion-sputtered silicon templates Appl. Phys. Lett. 93, 063106 (2008); 10.1063/1.2959080

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

193.61.135.80 On: Thu, 04 Dec 2014 16:32:51

Spherical metallic nanoparticle arrays for super-resolution imaging

Chang Chun Yan, Dao Hua Zhang,a) and Dong Dong LiSchool of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore

(Received 5 November 2010; accepted 7 January 2011; published online 21 March 2011)

We report super-resolution imaging in a metamaterial system comprising spherical silver nanoparticle

chain arrays, where each chain consists of nanoparticles with a smaller particle added to the end. Our

simulations reveal that silver nanoparticale chains have subwavelength resolution capability at visible

wavelengths and that the field intensity in the imaging plane varies with the number of layers of

nanoparticles, their polarization, and their coupling. By adding a smaller nanoparticle at the end of

each chain, the resolution capability is significantly enhanced, and high-quality super-resolution

imaging can be realized for incident waves polarized along the chain direction. VC 2011 AmericanInstitute of Physics. [doi:10.1063/1.3553875]

I. INTRODUCTION

Since the proposal of a perfect lens by Pendry,1 super-

lenses2 and hyperlenses3,4 made of metamaterials have been

widely investigated for their subwavelength imaging and super-

resolution capabilities. These lenses are able to carry high

spatial frequency waves from objects to images based on the

enhancement of surface plasmon resonance. By the same prin-

ciple, researchers have recently demonstrated subwavelength

imaging (both theoretically and experimentally) by using either

metallic nanorod arrays5–8 or reconstructed metal nanorod

arrays.9 Recently, we reported simulated deep subwavelength

resolution in the far field using a metal-dielectric multilayer

structure with slits opened on the covering metal layer.10

Spherical metallic nanoparticles are often used to guide

waves through a coupling between two nanoparticles,11–13

and these waves generally exhibit slow-wave properties.14

They can also be used for producing patterns15 and detec-

tion16 based on surface plasmon resonance that occurs in the

nanoparticles. There are also reports of the structures com-

prising a coupled pair of two-dimensional arrays of metal

nanospheres17,18 or oblate plasmonic nanoellipsoids19 in a

dielectric host medium for superlenses. Recently, Morits

et al.20 generalized a method of electromagnetic characteri-

zation of metasurfaces using a double layer of plasmonic

nanospheres. In addition, these metallic nanoparticles may

have applications for tailoring the transmittance of integrated

optical waveguides,21 optical sensing,22 and switching.22,23

For imaging applications of metallic nanoparticles, most

of the reported structures are constructed by two nanoparticle

layers with identical size; the distance between the two

coupled layers is usually less than the incident wavelength k.

In this paper, we report an imaging application for a spherical

metallic nanoparticle chain array with different numbers of

nanoparticles in each chain. We also propose the addition of

one nanoparticle with a smaller diameter at the end of each

chain to enhance the output field. The spherical metallic nano-

particle chain arrays we propose differ from the coupled pair

structures, because they directly transmit the information of

an object to the imaging plane along the nanoparticle chains

and the position of the imaging plane varies with the number

of nanoparticles in each chain. The numerical results show

that subwavelength resolution at visible wavelengths exists in

the chain array. By adding a smaller nanoparticle on the imag-

ing side, the output field intensity is significantly enhanced.

II. STRUCTURE

Figure 1 shows a schematic of the studied metamaterial,

which is made up of a spherical silver nanoparticle chain

array surrounded by air. This array is arranged in a tetragonal

lattice where the distances between two neighboring nano-

particles are d in the x and y directions and two radii in the zdirection. The Radio Frequency (RF) Module for COMSOL

Multiphysics 3.5 is used for our investigation, as this module

has the ability to design electromagnetic structures and ana-

lyze their response to electromagnetic waves.

In our simulations, the silver nanoparticles are smaller

than the electron mean free path, which is about 50 nm for sil-

ver.24 In this case, size effects become significant. The size-

dependent contributions to permittivity involve several aspects,

which include quantum size effect,25 chemical interface

FIG. 1. (Color online) Schematic representation of a spherical silver nano-

particle chain array. The diameter of each nanoparticle is DL¼ 20 nm and dis the distance between the two neighboring nanoparticles in the x-y plane.a)Electronic mail: edhzhang@ntu.edu.sg.

0021-8979/2011/109(6)/063105/5/$30.00 VC 2011 American Institute of Physics109, 063105-1

JOURNAL OF APPLIED PHYSICS 109, 063105 (2011)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

193.61.135.80 On: Thu, 04 Dec 2014 16:32:51

effect,26 and interband susceptibility.27 The contribution of

interband susceptibility to permittivity can be neglected when

the interband transition is below 3.9 eV in silver.27 This contri-

bution thus is not significant in our case, as the excitation

source we selected (508 nm in wavelength with an energy of

2.4457 eV) is much smaller than 3.9 eV. The first two effects

mainly affect the imaginary part of the permittivity, as the

damping frequency is much smaller than the incident fre-

quency. These make the imaginary part larger,28 which usually

results in faster damping of the plasma waves along the nano-

particles but does not significantly affect the resonance wave-

length in our structure. For simplicity, we used the permittivity

of silver extracted from Ref. 29 in our simulations.

III. FIELD PROPERTIES IN SPHERICAL SILVERNANOPARTICLE CHAINS

A. Field intensity distributions in chains with identicalnanoparticles

Before discussing the imaging performance of silver

nanoparticle chain arrays, we need insight on field propaga-

tion in nanoparticle chains. We first investigate the field

propagation in chains consisting of one, two, three, and four

identical spherical nanoparticles with diameters of 20 nm.

The simulation region is set to 100 nm� 100 nm� 140 nm

and the chain is located in the center of the region. A small

cylinder with a height of 0.2 nm and a radius of 0.1 nm is

positioned 5 nm away from one end of this chain. The cur-

rent flowing through the cylinder along the central axis is set

to 1 A, which can be regarded as an electric dipole excitation

source because of its small dimension. Its polarization is in

the z direction which is similar to that of the metallic nano-

rods proposed by Ono et al.5 All the boundaries are assumed

to be perfectly matched by the definition of the boundary

conditions. The maximum mesh sizes for the nanoparticles

and for the cylinder are set to 2 nm and 0.02 nm, respec-

tively, while the maximum mesh size for the other regions is

4 nm. The generalized minimal residual method (GMRES) is

selected as the solver and the relative error for the last two

iterations is set to be less than 10�3.

We calculated the field intensities (jEj2) in these chains as

functions of wavelength. We found that there is a stronger in-

tensity distribution near the wavelength of 508 nm. The

FIG. 2. (Color online) Field intensity distributions in the silver nanoparticle

chains consisting of different numbers of nanoparticles with diameters of 20

nm. (a) One nanoparticle; (b) two nanoparticles; (c) three nanoparticles; (d)

four nanoparticles.

FIG. 3. Field intensity at the end of the silver nanoparticle chain consisting

of two big and one small diameter-varied nanoparticles. The diameters of

the big nanoparticle are fixed at 20 nm.

FIG. 4. (Color online) Field intensity distributions in the two silver nanopar-

ticle chains consisting of (a) two big nanoparticles and (b) two big and one

small nanoparticles. (c) Electric intensities in the dotted lines shown in Figs.

4(a) and 4(b), respectively. The diameters of the big and small nanoparticles

are 20 nm and 8 nm, respectively.

063105-2 Yan, Zhang, and Li J. Appl. Phys. 109, 063105 (2011)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

193.61.135.80 On: Thu, 04 Dec 2014 16:32:51

intensity distributions for all four cases are shown in Figs.

2(a)–2(d). We can see that in each chain, the plasmonic waves

excited by the source on the surface of the first nanoparticle

can be coupled to the neighboring nanoparticle and then to the

next. However, we can also see that the transmitted field

mainly locates in the region between two neighboring nano-

particles30–32 and the intensities at the ends of the chains are

significantly weakened, which is not desirable for imaging.

B. Field intensity distributions in chains with a smallernanoparticle at the output end

When the nanoparticle at the output end is bigger, its sur-

face field density is lower due to its large surface area. Con-

versely, if the nanoparticle is smaller, the field density may

become higher due to the reduction of its surface area. To

examine this, we reconstructed the chains by adding a smaller

diameter nanoparticle to them. Here, we take a chain with two

large nanoparticles and one small nanoparticle as an example.

The maximum mesh size of the small nanoparticle is set to 1

nm while the rest of the parameters remain unchanged. Figure

3 shows the field intensity at the end of the restricted chain as

a function of the diameter of the smaller particle. It is seen that

the field intensity has no significant change when the diameter

of the added smaller ball is between 12 nm and 20 nm as well

as below 6 nm. The maximum occurs when the diameter of

the smaller ball is about 8 nm.

The simulated field intensity distribution in the recon-

structed chain with a small nanoparticle of 8 nm diameter is

shown in Fig. 4. For comparison, the field intensity distribution

for the two-particle chain (without a smaller nanoparticle) is

included in the figure. Evidently, the intensity at the end of the

reconstructed chain is much stronger although the wave needs

to propagate a slightly longer distance due to the addition of

the small nanoparticle. It is noted that a stronger intensity dis-

tribution still occurs near the wavelength of 508 nm, which

indicates that addition of the small nanoparticle almost has no

effect on this resonance wavelength. To evaluate the two inten-

sities, we drew two dotted lines in Figs. 4(a) and 4(b) and then

plotted the intensity distributions along them as shown in Fig.

4(c). It is found that the peak values in the two dotted lines in

Figs. 4(a) and 4(b) are 6.3� 10�4 V2/m2 and 7.4� 10�3 V2/

m2, and the corresponding full widths at half maximum

(FWHM) are 11 nm and 5 nm, respectively. These results indi-

cate that the wave intensity is enhanced about 12 times while

the FWHM is reduced to about 45% by simply adding a

smaller nanoparticle.

In the silver nanoparticle chains, the plasmonic wave trav-

els along the surface of the nanoparticles. When a smaller par-

ticle is added at the output end, the plasmonic wave will be

affected at the end and will propagate in a more convergent

way. When the added small particle has the size matched with

the big particles in the chain with optimized convergence, the

maximum field intensity will appear at the output end. Obvi-

ously, this kind of reconstructed nanoparticle chain is advanta-

geous for imaging applications.

C. Effects of polarization

We simulated the field intensity distribution of the

reconstructed chain shown in Fig. 4(b) again, after the cylin-

der was rotated 90 degrees. This means that the polarization

of the excitation source is rotated to the x or y direction. Like-

wise, we also plotted the field intensity distribution on the

dotted line. The result is shown in Fig. 5, where the distribu-

tion for the z polarization is included for comparison. From

Figure 5, we find that the field intensity for the z polarization

is about five orders of magnitude stronger than that for ypolarization, and the field intensity at the output end of the

chain for the y polarization is not a maximum but a minimum.

Furthermore, different from the case of z polarization, the

FIG. 5. Field intensity distributions in the dotted line in Fig. 4(b) for differ-

ent polarizations.

FIG. 6. (Color online) Coupled field intensity distributions in two neighbor-

ing nanoparticle chains with spacings of (a) 0 nm, (b) 5 nm, (c) 10 nm, and

(d) 20 nm. (e) Field intensity distributions in the dotted lines in Figs. 6(a)–

6(d). A and B denote the points of the image plane for the nanoparticle

chains with and without a source, respectively. The insert shows the

enlarged field distributions around point B for the four cases.

063105-3 Yan, Zhang, and Li J. Appl. Phys. 109, 063105 (2011)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

193.61.135.80 On: Thu, 04 Dec 2014 16:32:51

intensity distribution is unsymmetrical, which will inevitably

influence image quality. Hence, in the following discussions,

excitation polarized in the z direction will be chosen.

D. Coupling between two reconstructed nanoparticlechains

To study the coupling interference between two neigh-

boring chains, we first added an identical chain next to the

first, with spacings (d–DL) of 0 nm, 5 nm, 10 nm, and 20 nm,

respectively. The field intensity distributions corresponding

to the four spacings were then simulated and the results are

shown in Figs. 6(a)–6(d). The letter A is the point at the out-

put end of the chains with the source, while B is the point for

the added chains; both are in the imaging plane. From these

figures, we find that the coupling weakens with the increase

of spacing. To give a quantitative comparison, we draw dot-

ted lines at the output ends for the four cases, and the field

intensity distributions in these lines are plotted in Fig. 6(e).

We see that the ratios of the field intensities at point B to

those at point A in Figs. 6(a)–6(d) are 0.576, 0.083, 0.034,

and 0.006, respectively, indicating a monotonic decrease

with an increase in spacing.

IV. IMAGING WITH THE NANOPARTICLE CHAINARRAY

On the basis of the above results and analyses, we then

performed imaging with the reconstructed silver nanoparticle

chain array. The array studied was composed of 6� 6 recon-

structed chains with a spacing of 20 nm. Each chain in the

array consists of two big spheres with a diameter of 20 nm

and one small sphere with a diameter of 8 nm. The structure

is identical to the one shown in Fig. 1, except for the addition

of the small silver sphere at the end of each chain in the zdirection. The excitation source, made up of 10 electric

dipoles, forms a U shape. The source is located 5 nm away

from the end of this array (z¼�5 nm) and polarized along

the z direction. The region involved in the calculation is

300 nm� 300 nm� 200 nm. The maximum mesh sizes for

the nanoparticles and for the cylinder are the same as those set

above, while the maximum mesh size for the other regions is

changed from 4 nm to 8 nm in order to reduce memory con-

sumption. The simulation results in the planes of z¼�5 nm,

z¼ 48 nm, z¼ 58 nm, and z¼ 78 nm are shown in Figs. 7(a)–

7(d), and the field intensity distributions along the dotted lines

are correspondingly illustrated in Figs. 7(e)–7(h). As seen

from these figures, the U shape is highly resolved in the image

plane of z¼ 48 nm and the resolution becomes worse with

increasing distance from the excitation source. The FWHMs

at the imaging planes of z¼ 48 nm, z¼ 58 nm, and z¼ 78 nm

are 5 nm, 20 nm, and 81 nm, respectively. The corresponding

ratios of these FWHMs to the wavelength (508 nm) are

0.0098k, 0.0394k, and 0.1594k, respectively.

V. CONCLUSIONS

In conclusion, subwavelength resolution in spherical sil-

ver nanoparticle chains is studied and an imaging system

based on the nanoparticle chain arrays, where each chain

consists of similar sized nanoparticles with an added smaller

one, is proposed and simulated. The simulation results show

that by adding a small silver nanoparticle at the end of each

chain, the field intensity at the output end can be significantly

improved and subwavelength-resolution images for visible

frequencies can be formed.

ACKNOWLEDGMENTS

The project is supported by National Research Founda-

tion (NRF-G-CRP 2007-01), and A*Star (092154009), Sin-

gapore. The authors would like to thank Xuzhou Normal

University for their permission for Dr. Yan to join the

research team at Nanyang Technological University and Dr.

Ng Tsu Hau for his suggestions.

1J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).2N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).

FIG. 7. (Color online) Field intensity distributions for the reconstructed sil-

ver nanoparticle chain array, where each chain has two big and one small

nanoparticles, at the planes of (a) z¼�5 nm (source positions), (b) z¼ 48

nm (the output/imaging plane 53 nm away from the sources), (c) z¼ 58 nm,

(d) z¼ 78 nm. (e), (f), (g), and (h) are the field intensity distribution in the

dotted lines in (a) to (d), respectively.

063105-4 Yan, Zhang, and Li J. Appl. Phys. 109, 063105 (2011)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

193.61.135.80 On: Thu, 04 Dec 2014 16:32:51

3Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).4I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, Science 315, 1699 (2007).5A. Ono, J. Kato, and S. Kawata, Phys. Rev. Lett. 95, 267407 (2005).6G. Shvets, S. Trendafilov, J. B. Pendry, and A. Sarychev, Phys. Rev. Lett.

99, 053903 (2007).7S. Kawata, A. Ono, and P. Verma, Nat. Photonics 2, 438 (2008).8B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Srid-

har, Appl. Phys. Lett. 96, 023114 (2010).9X. Wu, J. Zhang, and Q. Gong, Opt. Express 17, 2818 (2009).

10C. C. Yan, D. H. Zhang, Y. Zhang, D. D. Li, and M. A. Fiddy, Opt.

Express 18, 14794 (2010).11M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. 23,

1331 (1998).12S. A. Maier, P. G. Kik, and H. A. Atwater, Appl. Phys. Lett. 81, 1714 (2002).13W. H. Weber and G. W. Ford, Phys. Rev. B 70, 125429 (2004).14O. Zhuromskyy, O. Sydoruk, E. Shamonina, and L. Solymar, J. Appl.

Phys. 106, 104908 (2009).15A. F. Koenderink, J. V. Hernandez, F. Robicheaux, L. D. Noordam, and A.

Polman, Nano Lett. 7, 745 (2007).16D. M. Schaadt, B. Feng, and E. T. Yu, Appl. Phys. Lett. 86, 063106

(2005).17P. Alitalo, C. Simovski, A. Viitanen, and S. Tretyakov, Phys. Rev. B 74,

235425 (2006).18C. R. Simovski, A. J. Viitanen, S. A. Tretyakov, J. Appl. Phys. 101,

123102 (2007).

19C. Mateo-Segura, C. R. Simovski, G. Goussetis, and S. Tretyakov, Opt.

Lett. 34, 2333 (2009).20D. Morits and C. Simovski, Phys. Rev. B 82, 165114 (2010).21R. Quidant, C. Girard, J. C. Weeber, and A. Dereux, Phys. Rev. B 69,

085407 (2004).22S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter,

Appl. Phys. Lett. 84, 3990 (2004).23M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62,

R16356 (2000).24U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters

(Springer-Verlag, Berlin, 1995).25W. P. Halperin, Quantum size effects in metal particles, Rev. Mod. Phys.

58, 533 (1986).26H. Hovel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, Phys. Rev. B

48, 18178 (1993).27A. Hilger, M. Tenfelde, and U. Kreibig, Appl. Phys. B 73, 361 (2001).28V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H. K. Yuan, W. Cai, and

V. M. Shalaev, Opt. Express 16, 1186 (2008).29E. D. Palik, Handbook of Optical Constants of Solids (Academic Press,

New York, 1991).30M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. 23,

1331 (1998).31D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, Nano Lett. 4,

153 (2004).32M. Y. Ng and W. C. Liu, Opt. Express 14, 4504 (2006).

063105-5 Yan, Zhang, and Li J. Appl. Phys. 109, 063105 (2011)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

193.61.135.80 On: Thu, 04 Dec 2014 16:32:51