Local Dielectric Environment Dependent Local Electric Field

Article pubs.acs.org/JPCC

Local Dielectric Environment Dependent Local Electric Field Enhancement in Double Concentric Silver Nanotubes Jian Zhu, Jian-Jun Li, and Jun-Wu Zhao* The Key Laboratory of Biomedical Information Engineering of the Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China S Supporting Information *

ABSTRACT: The local dielectric environment dependent local field enhancement properties in double concentric silver nanotubes have been obtained by using the plasmon hybridization method and quasi-static calculation. Because of the inserted silver nanotube, the geometrical parameter controlled intertube coupling greatly improves the tunability of the local dielectric dependent enhancement of local electric field. In the inner dielectric core, the most intense local field factor peak corresponds to the |ω+−⟩ plasmon mode, and the major local field factor peak usually changes nonmonotonously as the inner core or spacer layer dielectric is increased. The maximum local field could be obtained by fine-tuning the local dielectric constant in the double tubes with thick inner and outer tube thickness. In the dielectric spacer layer, the most intense local field factor peak corresponds to the |ω−−⟩ plasmon mode. The intense local field could be obtained with small spacer layer dielectric constant and reaches the maximum value when the double tube has thick inner and outer tube thickness. This inner core and spacer layer dielectric dependent local field enhancement provides the potential application of the real time tubular nanosensor based on local field induced fluorescence enhancement and surface-enhanced Raman scattering (SERS).

1. INTRODUCTION Localized electric field enhancement of metallic nanostructures have attracted much attention because of various promising applications, including surface enhancement fluorescence,1,2 surface-enhanced Raman scattering (SERS),3,4 and second- and third-order nonlinear optical response.5−7 The local field effect of metal nanoparticles could be attributed to the surface plasmon resonance (SPR). As a result of the coupled oscillations of incident light and free electrons at the metal− dielectric interface, SPR leads to intense optical absorption, scattering, and strong enhancement of polarized local electronic field. Because of the coupling of surface plasmon resonance from different metallic surfaces, the local electric fields are normally concentrated and enhanced at the gaps or junctions between adjacent nanoparticles in the aggregates.8 For spherical metallic dimer, the local field enhancements increase monotonically with decreasing gap separation.9,10 The hot spot of local field has also been found at the gap of the Ag nanowire dimer; the physical origin has been attributed to the dipolar bonding © 2012 American Chemical Society

hybridization of the transverse surface plasmons of the two component nanowires.3 The plasmonic optical properties of gold nanoring dimers have been investigated by Tsai et al.10 The local field intensity at the gap distance of 10 nm of gold nanoring dimers has been enhanced 23% compared to that for gold nanodisk dimers with the same diameter. Recently, local plasmonic coupling between a triangular gold island pair has been observed experimentally.11 The strong local field coupling between two adjacent gold triangles gives direct evidence to the local field enhancement in plasmonic nanoantenna effect. However, plasmonic coupling also takes place between different metallic surfaces of multilayered core−shell nanostructure.12,13 As is known that the plasmon hybridization method is generalized to calculate the plasmon modes and optical properties of dielectric−metal core−shell nanostructures.14 For example, the plasmon modes of the single Received: October 29, 2012 Revised: December 6, 2012 Published: December 14, 2012 584

dx.doi.org/10.1021/jp310676s | J. Phys. Chem. C 2013, 117, 584−592

The Journal of Physical Chemistry C

Article

the repulsive effects on the restoring force of plasmon oscillation. However, in the single-walled gold nanotube, only the inter surface coupling of the tube wall affect the SPR properties. In order to improve the tunability of the SPR and local field enhancement, a metal nanotube with small diameter has been inserted into the singlewalled nanotube in this study. In this double concentric metal nanotube, the intertube plasmon coupling greatly affects the SPR and local electric field. It was found that the local electric field in both inner core and spacer layer are greatly dependent on the dielectric constant of inner core, spacer layer, and outer surrounding. What’s more, we also compared the local dielectric dependent local field enhancement in the silver double tubes with different geometric parameters.

nanoshell or nanotube could be understood as resulting from the hybridization of the solid particle plasmons corresponding to outer surface of the shell and of the cavity plasmons corresponding to the inner surface.14 Thus, the strong local electric field could also be obtained in one multilayered nanoshell or nanotube. These multilayered core−shell nanostructures produce intense local electric field resulting from plasmons strongly coupled at the metal−dielectric interfaces. Although the plasmon hybridization in the multilayered concentric spherical nanoshells is similar to that of multilayered concentric cylindrical nanostructures, there are some differences of plasmonic optical properties between spherical nanoshells and cylindrical nanotubes. The physical mechanism of the differences is resulted from the symmetry type and the surface curvature. For example, the spherical symmetry leading to the spherical nanoshells have more intense surface curvature and surface charge density, which will affect the plasmon shift and local field enhancement. By using the calculation based on Green’s integral theorem, the extinction cross-section as a function of the incident wavelength for gold, silver, and cooper nanotubes with a two-dimensional core−shell structure has been studied.15 It has been found that the thickness of the metal wall influences the plasmon−plasmon interaction. The SPR properties of two-layered gold nanowires have also been studied by using the vector wave function method.16 Both the plasmonic shifting and bandwidth are dependent on the incidence angle and polarization. SPR and local field enhancement of multiple dielectric-core−gold-shell nanocylinder pairs have been investigated by the finite difference time domain (FDTD) method.17 It has been found that the interaction between the dipolar mode of the nanoscale gold cylinder results in the lightning-rod plasmon mode in the infrared band. Gurwich et al. have developed a formalism for solving the problem of scattering of electromagnetic waves by an infinite multilayered cylinder.17 By using this approach, the Mie scattering coefficients could be obtained without involving matrix calculations. Furthermore, the number of layers and the incident angle in the calculation are arbitrary.17 In Moradi’s report, a metal nanowire has been inserted into a metallic nanotube to fabricate a nanowire/double-shell structure.18 Because of the hybridization between the three free plasmon modes, the plasmonic tunability in the three layered nanotube is better than that of the two layered metallic nanotubes. The optical properties of metallic core−shell nanostructure are also greatly dependent on the local dielectric environment.19 Calculation results based on time-dependent density functional method indicated that the energies of the dipolar plasmon resonances depend greatly on the dielectric constant of the inner core or embedding medium. Regrettably, because of the closed metallic surface, the inner core dielectric constant is fixed when the metallic spherical nanoshells are prepared. However, cylindrical metallic nanostructures that have opened end faces, which lead to the inner core dielectric constant, become changeable. What’s more, the cylindrical nanostructure can act as conduits for molecule and condensed matter transport, which provide the potential application of real time optical sensing based on inner core dielectric dependent changing of SPR and local field enhancement. In recent years, both gold and platinum nanotube arrays have been fabricated experimentally.20,21 Our previous theoretical study shows that the core refractive index sensitivity of gold nanotube can be improved by reducing the wall thickness or the surrounding dielectric constant.22 The physical origin has been attributed to

2. MODEL AND PROCEDURE In the present work, a silver nanotube with small diameter has been inserted into a large silver nanotube to fabricate a double concentric nanotube structure, as shown in Figure 1a. This nanostructure consists of a dielectric core with a radius of r1, an inner silver tube with a thickness of r2 − r1, a dielectric spacer layer with a thickness of r3 − r2, and an outer silver tube with a thickness of r4 − r3. The dielectric constants of the refractive medium from inside to outside are ε1, ε2, ε3, ε4, and ε5,

Figure 1. (a) Schematic representation of an infinitely long double concentric silver nanotube. The radius from inner to outer is r1, r2, r3, and r4, respectively. (b) Plasmon hybridization and induced polarizations in the double concentric silver nanotube (top view). 585



Article

Figure 2. Absorption spectrum of silver double nanotubes with different geometry, (a) thick inner tube and thin outer tube, the thickness of inner and outer tubes are 10 and 3 nm, respectively; (b) thin inner tube and thick outer tube, the thickness of inner and outer tubes are 3 and 10 nm, respectively; (c) thick inner tube and thick outer tube, the thickness of both inner and outer tubes are 10 nm; (d) thin inner tube and thin outer tube, the thickness of both inner and outer tubes are 3 nm. The insets are top views of the silver double nanotubes.

respectively. It is important to note that the dielectric function of the inner and outer silver tube are wavelength-dependent and approximated by the Drude model.23 In this study, we consider one double concentric nanotube infinitely extended along the z axis and illuminated by light of wavelength λ. This incident light travels in the forward z direction and the incident electric field, E⃗ 0, is polarized in the x axis direction. As the incident field is polarized perpendicular to the tubes and the overall diameter of the tubes is much smaller than the light wavelength (in this study, the overall diameter is fixed at 48 nm), the quasi-static theory could be employed in the calculation.24 Therefore, the solution for the local electric field in each region of the double nanotube could be derived from Laplace’s equation25,26 ⎛ A⎞ ⇀ E1 = ⎜1 − 1 ⎟⇀ E0 E0 ⎠ ⎝

(1)

⎛ A ⎞ C ⇀ E2 = ⎜1 − 2 ⎟⇀ E0 + 22 (cos ϕ⇀ er + sin ϕ⇀ eϕ) E0 ⎠ r ⎝

(2)

⎛ A ⎞ C ⇀ E3 = ⎜1 − 3 ⎟⇀ E0 + 23 (cos ϕ⇀ er + sin ϕ⇀ eϕ) E0 ⎠ r ⎝

(3)

⎛ A ⎞ C ⇀ E4 = ⎜1 − 4 ⎟⇀ E0 + 24 (cos ϕ⇀ er + sin ϕ⇀ eϕ) E r ⎝ 0⎠

(4)

C ⇀ E5 = ⇀ E0 + 25 (cos ϕ⇀ er + sin ϕ⇀ eϕ) r

(5)

the details of coefficients (including A1, A2, A3, A4, C2, C3, C4, and C5), initial values, and boundary conditions could be found in the Supporting Information. By using the optical scattering theory, the absorption cross-section of the double concentric silver nanotube could be written as Cabs =

2π ⎛ C5 ⎞ Im⎜ ⎟ λ ⎝ r4 2 ⎠

(6)

Figure 1b shows the plasmon hybridization and the induced polarizations in the double concentric silver nanotube. The corresponding detail energy level diagram of these four plasmon modes have been reported in the refs 13 and 27. Our report in this article is a theoretical study, so we have no experimental section of the synthesis method. However, both metallic multilayered nanoshells and nanotube arrays have been fabricated experimentally recently.12,20,21,28 Xia et al. described the synthesis of bilayered concentric nanoshells with an overall diameter of around 50 nm consisting of a gold core, a tunable 586



Article

Figure 3. Local field factor of silver double nanotubes as a function of wavelength and (a,b) inner hole dielectric constant; (c,d) spacer layer dielectric constant; and (e,f) outer surrounding dielectric constant. (a,c,e) Local field in the inner dielectric hole with r = 0 and ϕ = 0. (b,d,f) Local field in the dielectric spacer layer with r = r2 and ϕ = 0. [r1,r2,r3,r4] = [2,12,21,24] nm.

silica spacer layer, and an outermost gold nanoshell.12 These multilayered nanoshells have been synthesized by layering silica and gold layers onto 20 nm gold nanoparticles, and the thickness of the silica middle layer can be controlled by the reaction conditions. In the report of Prodan et al., four-layered concentric gold nanoshells have been prepared by growth of two gold layers on the silica core.28 The gold nanotubes could be fabricated by electrodeposition into thin film porous alumina templates. Hendren et al. reported that the arrays of gold nanotubes with polypyrrole cores were grown on glass substrates by electrodeposition into thin film porous anodic alumina (AAO) templates,20 and then, the hollow nanotubes

were obtained when the polypyrrole was removed by plasma etch and the AAO was dissolved by chemical etch. Bridges et al. presented the template synthesis solution-suspendable gold nanotubes, which is accomplished by the sequential deposition of materials in an AAO template.29 The synthesis method includes deposition of sacrificial metal base materials, electropolymerization of a polymer core, core collapse by hydrophobic effects, deposition of a gold tube, and the removal of all sacrificial materials. Although the double metal nanotubes have seldom been reported, we hope this structure could be fabricated by growth of the second metal layer on the solution-suspendable gold nanotubes. 587



Article


3. RESULTS AND DISCUSSION

second peak at about 445 nm corresponds to the symmetric coupling between the inner and outer antibonding tube plasmon mode, which is denoted as |ω−+ ⟩. The third peak at about 485 nm corresponds to the symmetric coupling between the inner and outer bonding tube plasmon mode, which is denoted as |ω+−⟩. The fourth peak at the longest wavelength of 1230 nm corresponds to the antisymmetric coupling between the inner and outer bonding tube plasmon mode, which is denoted as |ω−−⟩. When the dielectric spacer layer is thick, the intersurface coupling in the silver tube takes major effect on the plasmon hybridization. Thus, the fourth SPR peak red shifts as the silver nanostructure has a thin outer tube, as shown in Figure 2a,d, whereas a blue shift occurs as the nanostructure has a thick outer tube, as shown in Figure 2b. However, the intertube coupling between inner and outer tubes takes major

3.1. Absorption Spectrum Properties of Silver Double Nanotubes. The calculated absorption spectra of double concentric silver nanotube with different geometrical parameters are shown in Figure 2. In this calculation, the inner dielectric core, dielectric spacer layer, and outer surrounding have the same dielectric constant ε1 = ε3 = ε5 = 3. One can find the absorption spectra could, at most, display four SPR peaks corresponding to the four plasmon resonant modes resulted from the plasmonic hybridization of the inner and outer silver tubes, which is in agreement with the results given in ref 30. As shown in Figure 2a, the first peak at about 400 nm corresponds to the antisymmetric coupling between the inner and outer antibonding tube plasmon mode, which is denoted as |ω++⟩. The 588



Article


decreased from 16 to 9 nm, as shown in Figure 2a,d. These geometry-dependent SPR shifting properties are also similar to the report of Moradi.30 3.2. Local Field Enhancement of Silver Double Nanotubes with Thick Inner Tube and Thin Outer Tube. In this section, we study the local dielectric constant (including ε1, ε3, and ε5) dependent local field factor (|E⃗ |/|E⃗ 0|) spectrum of silver double nanotubes with thick inner tube and thin outer tube. The geometrical parameters are set as [r1,r2,r3,r4] = [2,12,21,24] nm. Thus, the inner tube has a thick thickness of 10 nm, and the outer tube has a thin thickness of 3 nm. Because the nanotubes can act as conduits for molecule and condensed matter transport, we are interested

effect on the plasmon hybridization when the dielectric spacer layer is thin. For the |ω++⟩ and |ω−−⟩ modes of the nanostructure with thin spacer layer, plasmon resonance of the inner tube is oppositely aligned with the plasmon of the outer tube, which weakens the dipole moment of the |ω++⟩ and |ω−−⟩ modes, as shown in Figure 2c. Therefore, the first and last peaks in Figure 2c are very weak. The resonance wavelength positions are also dependent on the spacer layer thickness. When the outer tube thickness is 10 nm, decreasing the spacer layer thickness from 9 to 2 nm leads to the |ω−−⟩ mode greatly red shifting, whereas the |ω+−⟩ mode blue shifts slightly, as shown in Figure 2b,c. These plasmon shifting properties could also be observed as the outer tube thickness is 3 nm and the spacer layer thickness is 589



Article


in the local field enhancement in the dielectric inner core and spacer layer. Therefore, we calculated the local field at two different spatial points. One point is in the dielectric core with the position r = 0 and ϕ = 0; the other point is in the dielectric spacer layer with the position r = r2 and ϕ = 0. As shown in Figure 3a,c,e, in the inner dielectric hole, the local field factor spectra only have one distinct peak corresponding to the |ω+−⟩ plasmon mode. It is interesting to note that, increasing the inner core dielectric constant leads to a nonmonotonic change of the peak intensity and slight red shift, which is similar to that of the cylindrical gold nanohole.31 As shown in Figure 3c, increasing the spacer layer dielectric constant ε3 also leads to the local field factor peak becoming intense first and then fading down. However, the dielectric constant dependent

changing of the local field factor becomes gentle, and the hot spot corresponding to the maximum local field factor right shifts. In Figure 3e, we studied the effect of the outer surrounding dielectric constant on the changing of the local field factor. It is obvious that the local field factor peak has a monotone increasing when ε5 is increased. However, the local field factor spectra in the dielectric spacer layer have three distinct peaks corresponding to the |ω−+ ⟩, |ω+−⟩, and |ω−−⟩ plasmon mode respectively, as shown in Figure 3b,d,f. The major peak corresponding to |ω−−⟩ mode at longer wavelength is not sensitive to the changing of the inner core dielectric constant. However, increasing the inner core dielectric constant leads to the middle wavelength peak corresponding to the |ω+−⟩ mode to fade down, whereas the shorter wavelength peak gets 590



Article

intense. Figure 3d shows the spacer layer dielectric constant dependent local field spectra. One can find that the major peak corresponding to |ω−−⟩ mode red shifts and fades down rapidly as the ε3 is increased. Figure 3f shows the surrounding dielectric constant dependent local field spectra. One can find that the major peak corresponding to |ω−−⟩ mode gets intense rapidly as the ε5 is increased, which is contrary to the effect of ε3. Figure 3 also tells us that the maximum local field in the inner core is always greater than that of the spacer layer. Furthermore, the greatest local field in the silver double nanotubes with thick inner tube and thin outer tube could be obtained with small ε3 in the spacer layer and large ε5 in the inner core. 3.3. Local Field Enhancement of Silver Double Nanotubes with Thin Inner Tube and Thick Outer Tube. In this section, we study the local dielectric dependent local field factor spectrum of silver double nanotubes with thin inner tube and thick outer tube. The geometrical parameters are set as [r1,r2,r3,r4] = [2,5,14,24] nm. Thus, the inner tube has a thin thickness of 3 nm, and the outer tube has a thick thickness of 10 nm. In the dielectric spacer layer, the peak corresponding to the |ω−−⟩ mode has a shorter wavelength, which is attributed to the thick outer tube resulted weak intersurface plasmon coupling. However, the influences from the local dielectric constants on the local field factor are similar to that of the double tubes with thick inner tube and thin outer tube, as shown in Figure 4b,d,f. In the inner dielectric core, the local field spectra have three distinct peaks corresponding to the |ω−+ ⟩, |ω+−⟩, and |ω−−⟩ modes, respectively, which is different from that of the double tubes with thick inner tube and thin outer tube. Furthermore, the intensity of the strongest peak corresponding to the |ω+−⟩ mode also changes nonmonotonously as the ε1 or ε3 is increased, as shown in Figure 4a,c. However, the inner core dielectric constant dependent changing of the local field factor is gentler than the effect from the spacer layer dielectric constant, which is different from that of the double tubes with thick inner tube and thin outer tube. In Figure 4, one could find that the maximum local field in the inner core is also always greater than that of the spacer layer. Furthermore, the greatest local field in the silver double nanotubes with thin inner tube and thick outer tube could also be obtained with small ε3 in the spacer layer and large ε5 in the inner core. However, by comparing with the double nanotubes with thick inner tube and thin outer tube, the double nanotubes with thin inner tube and thick outer tube present greater local field factor in both inner core and spacer layer. 3.4. Local Field Enhancement of Silver Double Nanotubes with Thick Inner Tube and Thick Outer Tube. In this section, we study the local dielectric dependent local field factor spectrum of silver double nanotubes with thick inner tube and thick outer tube. The geometrical parameters are set as [r1,r2,r3,r4] = [2,12,14,24] nm. Thus, both the inner and outer tubes have a thick thickness of 10 nm. In the dielectric spacer layer, the influences from the local dielectric constants on the local field factor are similar to that of the double tubes with thick inner tube and thin outer tube, as shown in Figure 5b,d,f. However, by comparing with the double nanotubes with other geometrical parameters, both the intensity and wavelength of the peak corresponding to the |ω−−⟩ mode are more sensitive to the spacer layer dielectric constant, as shown in Figure 5d. What’s more, the local field factor in the spacer layer could reach 70 when ε3 = 1.0, which is more intense than that of the double tubes with other geometrical parameters. In the dielectric inner core, the ε1 or ε3

dependent nonmonotonic intensity changes of the major peak corresponding to the |ω+−⟩ mode are also similar to that of the double tubes with thick inner tube and thin outer tube, as shown in Figure 5a,c. However, the ε5 dependent intensity changing becomes nonmonotonic, as shown in Figure 5e. Therefore, the maximum local field factor in the dielectric inner core takes place with specific value of ε5, but not large ε5. Furthermore, the maximum local field factor could also be obtained with a specific value of ε1 or ε3. As shown in Figure 5a,c,e, the maximum local field factor reaches 80 when ε1 is approaching 3.0 or ε3 and ε5 is approaching 3.5. 3.5. Local Field Enhancement of Silver Double Nanotubes with Thin Inner Tube and Thin Outer Tube. In this section, we study the local dielectric dependent local field factor spectrum of silver double nanotubes with thin inner tube and thin outer tube. The geometrical parameters are set as [r1,r2,r3,r4] = [2,5,21,24] nm. Thus, both the inner and outer tubes have a thin thickness of 3 nm. As shown in Figure 6b,d,f, the influences from the local dielectric constants on the local field factor in the dielectric spacer layer are similar to that of the double tubes with thick inner tube and thin outer tube. In the dielectric inner core, the intensity of the strongest peak corresponding to the |ω+−⟩ mode also changes nonmonotonously as the ε3 is increased, as shown in Figure 6c. However, the ε1 dependent intensity change of the peak becomes monotonic, as shown in Figure 6a. Furthermore, the maximum local field factor in the dielectric inner core also takes place with large ε5, as shown in Figure 6e. Figure 6 also tells us that the maximum local fields in the double tubes with thin inner and outer tubes are weaker than that of double tubes with other geometrical parameter. 3.6. Intertube Interaction Based Physical Mechanism of the Local Dielectric Dependent Local Field Enhancement. As we know, the local electric field of the metallic nanostructure is the sum of the polarized field and the incident field. The intensity of the polarized field is greatly dependent on the SPR and the local dielectric environment.32 In the single-walled metal tube, the local electric field is affected by the tube thickness and the intersurface plasmon coupling.31 In this study, two coaxial silver nanotubes constitute a double-tube structure. Not only intersurface coupling but also intertube coupling influences the SPR and local field enhancement. In the double tubes with both thick inner and outer silver tubes, the dielectric spacer layer becomes very thin, as shown in Figure 5. Thus, the intertube coupling becomes intense. For |ω+−⟩ mode, the outer tube polarization is conformably aligned with the inner tube polarization. Therefore, the local field in the inner core is greater for double tubes with thin spacer layer, as shown in Figure 5a,c,e. For |ω−−⟩ mode, the local field is mainly resulted from the different typs of charges of inner surface of outer tube and outer surface of inner tube. Therefore, the local field in the spacer layer is greater for double tubes with thin spacer layer, as shown in Figure 5d. In the double tubes with both thin inner and outer silver tubes, the dielectric spacer layer becomes very thick, as shown in Figure 6. Thus, the intertube coupling becomes weak. Therefore, the local field in the inner core is weaker for double tubes with thick spacer layer, as shown in Figure 6a,c,e, and the local field in the spacer layer is weaker for double tubes with thick spacer layer, as shown in Figure 6d. The thick spacer layer induced weak intertube coupling also leading to the local field in the inner core could not easily be affected by the polarized field in the outer surrounding. Thus, the local field of the inner core is mainly 591



Article

affected by ε1, and then, the ε1 dependent intensity change of the inner core field becomes monotonic, as shown in Figure 6a.

(9) Olk, P.; Renger, J.; Wenzel, M. T.; Eng, L. M. Nano Lett. 2008, 8, 1174. (10) Tsai, C. Y.; Lin, J. W.; Wu, C. Y.; Lin, P. T.; Lu, T. W.; Lee, P. T. Nano Lett. 2012, 12, 1648. (11) Chen, W.; Kirilyuk, A.; Kimel, A.; Rasing, T. Appl. Phys. Lett. 2012, 100, 163111. (12) Xia, X.; Liu, Y.; Backman, V.; Ameer, G. A. Nanotechnology 2006, 17, 5435. (13) Radloff, C.; Halas, N. J. Nano Lett. 2004, 4, 1323. (14) Brandl, D. W.; Nordlander, P. J. Chem. Phys. 2007, 126, 144708. (15) Ekeroth, R. M. A.; Lester, M.; Scaffardi, L. B.; Schinca, D. C. Plasmonics 2011, 6, 435. (16) Wu, D. J.; Liu, X. J.; Li, B. J. Appl. Phys. 2011, 109, 083540. (17) Gurwich, I.; Shiloah, N.; Kleiman, M. J. Quant. Spectrosc. Radiat. Transfer 1999, 63, 217. (18) Moradi, A. J. Opt. Soc. Am. B 2012, 29, 625. (19) Prodan, E.; Lee, A.; Nordlander, P. Chem. Phys. Lett. 2002, 360, 325. (20) Hendren, W. R.; Murphy, A.; Evans, P.; O’Connor, D.; AWurtz, G.; Zayats, A. V.; Atkinson, R.; Pollard, R. J. J. Phys.: Condens. Mater. 2008, 20, 362203. (21) Chen, C.; Loo, J.; Deng, M.; Kox, R.; Huys, R.; Bartic, C.; Maes, G.; Borghs, G. J. Phys. Chem. C 2009, 113, 5472. (22) Zhu, J.; Deng, X. C. Sens. Actuators, B 2011, 155, 843. (23) Perenboom, J. A. A. J.; Wyder, P.; Meier, F. Phys. Rep. 1981, 78, 173. (24) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer: New York, 1995. (25) Haus, J. W.; Zhou, H. S.; Takami, S.; Hirasawa, M.; Honma, I.; Komiyama, H. J. Appl. Phys. 1993, 73, 1043. (26) Khosravi, H.; Daneshfar, N.; Bahari, A. Phys. Plasmas 2010, 17, 053302. (27) Peña-Rodríguez, O.; Pal, U. J. Phys. Chem. C 2010, 114, 4414. (28) Prodan, E.; Radloff, C.; Halas, N. J.; Nordlander, P. Science 2003, 302, 419. (29) Bridges, C. R.; DiCarmine, P. M.; Seferos, D. S. Chem. Mater. 2012, 24, 963. (30) Moradi, A. Phys. Plasmas 2012, 19, 062102. (31) Zhu, J. J. Nanopart. Res. 2011, 13, 87. (32) Zhu, J. Appl. Surf. Sci. 2007, 253, 8729.

4. CONCLUSIONS Local dielectric environment dependent local field enhancement properties in double concentric silver nanotubes have been studied by using the quasi-static theory. In the inner dielectric core, the most intense local field factor peak corresponds to the |ω+−⟩ plasmon mode. In most cases, this major local field factor peak changes nonmonotonously as the ε1 or ε3 is increased. The ε1 dependent monotonic change of this local field factor peak only takes place with thin inner and outer tubes, whereas the ε5 dependent nonmonotonic change only takes place with thick inner and outer tubes. Because of the intense intertube coupling, the intense local field could always be obtained by tuning the local dielectric constant in the double tubes with thick inner and outer tubes. On the contrary, the weak local field could be obtained in the double tubes with thin inner and outer tubes. In the dielectric spacer layer, the most intense local field factor peak corresponds to the |ω−−⟩ plasmon mode, and this major local field factor peak always changes monotonously as the local dielectric constant is increased. The intense local field could be obtained with small ε3 and reaches the maximum value when the double tube has thick inner and outer tubes.

■

ASSOCIATED CONTENT

■

AUTHOR INFORMATION

S Supporting Information *

Solution for the local electric field in each region of the double nanotube. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author

*Phone: 86-29-82664224. Fax: 86-29-82664224. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Program for New Century Excellent Talents in University, the Fundamental Research Funds for the Central Universities, and the National Natural Science Foundation of China under grant Nos. 11174232, 61178075, 81101122.

■

REFERENCES

(1) Yeshchenko, O. A.; Kondratenko, S. V.; Kozachenko, V. V. J. Appl. Phys. 2012, 111, 124327. (2) Selvan, S. T.; Hayakawa, T.; Nogami, M. J. Phys. Chem. B 1999, 103, 7064. (3) Du, C. L.; You, Y. M.; Chen, T.; Zhu, Y.; Hu, H. L.; Shi, D. N.; Chen, H. Y.; Shen, Z. X. Plasmonics 2011, 6, 761. (4) Liusman, C.; Li, H.; Lu, G.; Wu, J.; Boey, F.; Li, S.; Zhang, H. J. Phys. Chem. C 2012, 116, 10390. (5) Hubert, C.; Billot, L.; Adam, P. M.; Bachelot, R.; Royer, P.; Grand, J.; Gindre, D.; Dorkenoo, K. D.; Fort, A. Appl. Phys. Lett. 2007, 90, 181105. (6) Lu, C. C.; Hu, X. Y.; Zhang, Y. B.; Li, Z. Q.; Yang, H.; Gong, Q. H. Plasmonics 2012, 7, 159. (7) Olesiak-Banska, J.; Gordel, M.; Kolkowski, R.; Matczyszyn, K.; Samoc, M. J. Phys. Chem. C 2012, 116, 13731. (8) Halas, N. J.; Lal, S.; Chang, W. S.; Link, S.; Nordlander, P. Chem. Rev. 2011, 111, 3913. 592


Local Dielectric Environment Dependent Local Electric Field

Recommend Documents