Plasmon hybridization in composite nanostructures with tunable resonances and vertex truncation analysis J. Luo,1,2,* C. K. Qiu,1 W. M. Wang,1 and Q. Lin3 1
State Key Laboratory of Optical Technologies on Nano-fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China 2 3
Graduate University of Chinese Academy of Sciences, Beijing 100039, China
Department of Mechanical Engineering, Columbia University, New York 10027, USA *Corresponding author: [email protected] Received 10 October 2013; revised 23 April 2014; accepted 24 April 2014; posted 1 May 2014 (Doc. ID 199299); published 30 May 2014
An Ag∕SiO2 ∕Ag sandwich delta nanostar with three sharp angles (30°) is proposed. The extinction efficiency property with a variation in environment refractive index has been investigated in detail by the finite difference time domain method. The refractive index response sensitivity is 482.67 nm∕RIU. And the correlations between resonance wavelengths and thickness of the dielectric layer are also established. It reveals that as the thickness increases, the peak wavelength turns to red shift, and a tunable resonance wavelength is achieved through the thickness adjusting of the SiO2 layer. The maximum of the electric field enhancement is 833.776 with the thickness of the dielectric layer h 40 nm. Moreover, the influence of the vertex truncation on the extinction spectra and the refractive index sensitivity has also been analyzed. © 2014 Optical Society of America OCIS codes: (000.4430) Numerical approximation and analysis; (240.6680) Surface plasmons; (290.2200) Extinction; (350.3950) Micro-optics; (310.6628) Subwavelength structures, nanostructures. http://dx.doi.org/10.1364/AO.53.003528
1. Introduction
Noble metal nanoparticles exhibit good performance between the visible and near-infrared range for the abnormal optical properties. The surface plasmon resonance properties of metal nanostructures are highly sensitive to the shape, size, material, and the dielectric environment and have been intensively studied [1–4]. Researchers achieve the tunable resonance by varying the basic size and shape parameters [5,6]. And the nanoparticles are usually fabricated by the wet-chemical approaches and lithographic processes [7,8]. Recently, changes of the thickness of the multilayer nanostructure have been 1559-128X/14/163528-05$15.00/0 © 2014 Optical Society of America 3528
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
used to tailor the resonance position, which can avoid the high cost and sophisticated fabricating process. Besides, the Zhang and co-workers have proposed a metal/dielectric/metal structure of a three-layer sandwich elliptical cylinder [5,9], and the extinction characteristics are adjusted by regulating the thickness of the intermediate dielectric layer. It is found that, as for the resonance wavelength tuning, the longitudinal layer thickness adjusting of the sandwich nanostructures is much more convenient and easier than the geometric size changing of the single layer nanostructure. Substantial attention has been focused on these plasmon hybridization studies [10,11]. The bulk plasmon polariton (BPP) can be excited in the metal-dielectric nanomultilayer structures [12]. And the plasmon coupling of the upper and bottom metal layers will change the surface
plasmon resonance (SPR) properties. The electromagnetic field will be enhanced and the resonance wavelength can be adjusted. The plasmon hybridization phenomenon was first observed and explained on nanosphere dimmers [13,14]. In order to obtain better nanosensing properties, we combine both the sharp tips and the metal– dielectric multilayer structures together. In this paper, we present a sandwich delta nanostar that features an Ag∕SiO2 ∕Ag sandwich delta star nanoplate with three sharp angles of 30°. And the proposed architecture combines several attractive points that can excite high near-field enhancement and achieve tunable resonance wavelength. Moreover, the sharp angle can also develop some hotspots of strong field enhancement. In this study, we analyze the extinction efficiency and local surface plasmon resonance (LSPR) sensing properties using the FDTD method. Furthermore, a detailed numerical analysis of the local electromagnetic field enhancement and resonance wavelength tuning are studied.
Fig. 1. Sketch of the sandwich delta nanostar. The cross section of the nanostar is composed of a central equilateral triangle and three isosceles triangles joined at its sides.
3. Results and Discussion 2. Simulation Modeling
The geometry of a (Ag∕SiO2 ∕Ag) sandwich delta nanostar is defined by four parameters: the length of hemline of the central equilateral triangle, a 18.3 nm; the length of the isosceles triangle, b 35.36 nm; the thickness h 20 nm; and the sharp vertex of the isosceles triangle, α 30°, as depicted in Fig. 1. The thicknesses of up and lower silver layers are both 20 nm, and the central dielectric layer is made of silicon dioxide. But why should we choose the sharp angle as 30°? The effects of vertex features of the single silver nanostructure on its extinction and LSPR properties have been discussed [15]. The analysis shows that a delta-star with a relatively small vertex presents a larger resonant wavelength. And the vertex angle of 30° displays the best figure of merit value for LSPR application. When the photon frequency is coincident with the localized surface plasmon resonance frequency, plenty of free electrons can be drawn among the sharp vertex angles, and it can excite strong electrostatic fields.
The extinction efficiency property of the Ag∕SiO2 ∕Ag sandwich delta nanostar with a variation in environment refractive index is investigated in detail by the finite-difference time-domain (FDTD) method. The FDTD method is of high accuracy and wide application, which is deduced from Maxwell equations. For better calculation of the extinction properties, we adopt the special total-scattering field source (TSFS) and total-scattering field monitor (TSFM) in the simulation. The thickness of the SiO2 layer is 20 nm and the output extinction spectra of different refractive index have been obtained in Fig. 2(a). As the refractive index increases, the peak wavelength gradually shifts red. The refractive index changes from 1.0 to 1.5, and the corresponding resonance wavelength slowly rises from 624.463 to 864.43 nm. The sensing ability of the peak wavelength to the environment refractive index can be estimated by the linear fitting in Fig. 2(b). The refractive index response sensitivity of the sandwich delta nanostar is 482.67 nm∕RIU (refractive index unit), with the linear correlation coefficient 0.99923.
Fig. 2. (a) Output spectra of the extinction efficiency under different refractive index with h 20 nm. (b) Plot of the peak wavelength versus the refractive index (dot line) and its linear fitting (red line). 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3529
Besides, the correlations between resonance wavelengths and thickness of the dielectric layer are established. Changing the thickness of the SiO2 layer, the extinction and near-field enhancement characteristics are also described [see Fig. 3(a)]. It reveals that as the thickness of the SiO2 layer increases, the peak wavelength turns to be red shift. When the thickness grows from 10 to 60 nm, the resonance peak wavelength shifts from 1005.9 to 1117.54 nm, and accompanies with increasing of the extinction efficiency. We apply plasmon hybridization theory to explain the spectral shifts of the coupled nanostructure. The vertical plasmon hybridization is excited between the upper and bottom metal layers, which is perpendicular to the surface plasmon direction. When the thickness of the dielectric layer grows larger, the vertical plasmon coupling gradually reduces. In addition, the shift of peak wavelength increases unconspicuously, when the thickness of the SiO2 layer grows larger than 50 nm. And the tunable wavelength range is 600–640 nm. Besides, the electric field enhanced ability of the nanostructure should also be considered, especially as the LSPR and SERS substrate. The electric field enhancement factor is introduced to evaluate the near-field enhancing capability of the nanostructure. Figure 3(b) displays the correlation between peak wavelength and extinction efficiency of varying dielectric thickness. And the maximum of the electric field enhancement is 833.776 with the thickness of the dielectric layer h 40 nm, as revealed in Fig. 4. 4. Analysis of Vertex Truncation
The sharp vertex is one of the important factors affecting the sensing characteristics of the overall structure. However, as to the actual fabricating process, it is difficult to achieve the idealized sharp angle. Currently, with the development of the micro/nano fabrication technology, the preparation method of the nanostructures usually includes the focused ionbeam lithography, electron-beam lithography, nanosphere lithography, etc. [16–18]. Because of the resolution of these nanofabrication techniques and some uncontrollable processing factors and errors, the sharp features of the prepared nanostructures
Fig. 4. Electric field distribution of x–y plane with the thickness of the dielectric layer h 40 nm.
such as corners and edges are always inevitably truncated. As for our experimental condition, the experiment cannot be carried out currently. But the limit of resolution of these nanofabrication techniques is ubiquitous. And the vertex truncated effect of sharp angle exists commonly. Even though it is the best electron-beam lithography technique, it also can bring in the truncation effect. And its resolution is usually bigger than 2 nm, more commonly to be 5– 10 nm [16]. Therefore, it is essential and important to study the influence on its optical property and sensing characters. The ideal delta-star with three sharp angles of α 30° (black line) and the vertex truncated structure (red line) are described in Fig. 5. The delta-star with truncated vertices can be considered as a combination of an intermediate equilateral triangle (length a 18.3 nm) and three isosceles triangles (waist length b 35.36 nm and hemline a 18.3 nm). Here, we introduce the truncation factor, f , and define it as the ratio of the area of the vertex truncation to the area of the perfect delta nanostar. And the vertex truncation area contains the region of triangle △ABC, deducted the area of camber AB. So the truncated nanostar is composed of three isosceles
Fig. 3. (a) Extinction efficiency with changing thickness of the SiO2 layer. (b) Peak wavelength and extinction efficiency of varying dielectric thickness. 3530
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Fig. 5. Cross section in x–y direction of the vertex truncation (red dot line) and of the idealized angle (black line) (left) and the sandwich delta-star nanoplate with vertex truncation (right).
trapezoids, a camber, and an equilateral triangle. The size and position of the delta-star can be determined by several key points, which are point A, B (0, 0),
Table 1.
A B f
(9.15,30.62) (9.15,30.62) 0%
(8, 26.7716) (10.3, 26.7716) 0.0891%
C (9.15, 30.62), D (18.3, 0), E (9.15, −15.85). And different truncation ratios can be obtained by changing the coordinate of point A, B, and the truncation factors are 0.0891%, 3.11%, 6.68%, 11.6%, and 17.8%, respectively (see in Table 1). We analyze the influence of the vertex truncated nanostructure on the extinction spectra and refractive index sensitivity with different truncation ratios. According to the calculated extinction spectra presented in Fig. 6(a), the LSPR extinction spectrum exhibits a peak at about 624.46 nm for the idealized nanostructure (f 0%). As the truncation ratio increases, the extinction peak wavelength becomes blue shifting and the amplitude of the extinction efficiency decreases. And the peak wavelength of the LSPR spectra gradually shifts from 624.46 to 479.026 nm as the truncation ratio changes from 0% to 17.8%,
Different Truncation Ratios
(7, 23.425) (11.3, 23.425) 3.11%
(6, 20.0787) (12.3, 20.0787) 6.68%
(5, 16.7322) (13.3, 6.7322) 11.6%
(4, 13.3858) (14.3, 13.3858) 17.8%
Fig. 6. (a) Extinction results of the vertex truncated sandwich delta-star nanoplate with the truncation ratio of f 0.0891%, 3.11%, 6.68%, 11.6%, and 17.8%, respectively. (b) Refractive index sensitivity distribution of truncated nanostructure with different truncation ratio.
Fig. 7. Near-field enhancement of sandwich delta nanostar with a truncation of 6.68% (a) and the idealized nanostructure when the thickness of the dielectric layer h 20 nm (b). 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
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which is because of the retardation effect of the electromagnetic field across the nanostructure along with decrease of the characteristic size of the sandwich nanoplate. The refractive index sensing property of the truncated structure has also been calculated as depicted in Fig. 6(b). The refractive index sensitivity decreases strongly as the truncation ratio f increases from 0% to 17.8%. Compared with the perfect structure (f 0%), the sandwich nanostar with sharp vertices exhibits higher sensitivity while the performance of the nanostructure with slightly rounded vertices is much poorer. When f varies from 0.0891% to 11.6%, the refractive index sensitivity falls from 403.122 nm∕RIU to 326.121 nm∕RIU. And comparison of the near-field with truncated vertex and the idealized angle is also made, as depicted in Fig. 7. It is apparent that the near-field distribution of the idealized sharp vertices is more localized than that of the truncated nanostar with the vertex truncation f 6.68%. 5. Conclusions
In this paper, we present a sandwich delta nanostar with three sharp angles of 30°. The extinction efficiency and local surface plasmon resonance (LSPR) sensing properties of the proposed architecture have been studied. And the refractive index response sensitivity of the sandwich delta nanostar is 482.67 nm∕RIU, with the linear correlation coefficient 0.99923. And tunable resonance wavelength is achieved through the thickness adjusting of the SiO2 layer. The maximum of the electric field enhancement is 833.776 with the thickness of the dielectric layer h 40 nm. Furthermore, we also analyze the influence of the vertex truncation on the extinction spectra and refractive index sensitivity. Compared with the perfect structure (f 0%), the sandwich nanostar with sharp vertices exhibits higher sensitivity. Then, it is proved that the presented architecture combines several attractive features. First, adjusting the thickness of dielectric layer is relatively easier than changing the characteristic of the size and shape for achieving the tunable resonance wavelength. Besides, strong near-field enhancement of the tips is effectively collected around the sharp vertex region. And the close proximity of the upper and lower metal layers leads to a hybridization of the vertical plasmon. Hence, this sandwich delta nanostar is approved to be quite appropriate and much more suitable as the LSPR sensing substrate. The author gratefully acknowledges the support of K. C. Wong Education Foundation, Hong Kong, and
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West Light Foundation of the Chinese Academy of Sciences (No. A11K011). References 1. N. Guillot, H. Shen, B. Frémaux, O. Péron, E. Rinnert, T. Toury, and M. Lamy de la Chapelle, “Surface enhanced Raman scattering optimization of gold nanocylinder arrays: influence of the localized surface plasmon resonance and excitation wavelength,” Appl. Phys. Lett. 97, 023113 (2010). 2. F. Hao, C. L. Nehl, J. H. Hafner, and P. Nordlander, “Plasmon resonances of a gold nanostar,” Nano Lett. 7, 729–732 (2007). 3. L. J. Sherry, R. Jin, C. A. Mirkin, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver triangular nanoprisms,” Nano Lett. 6, 2060–2065 (2006). 4. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003). 5. K. H. Su, Q. H. Wei, and X. Zhang, “Tunable and augmented plasmon resonances of Au/SiO2/Au nanodisks,” Appl. Phys. Lett. 88, 1–3 (2006). 6. M. Laroche, S. Albaladejo, R. Gómez-Medina, and J. J. Sáenz, “Tuning the optical response of nanocylinder arrays: an analytical study,” Phys. Rev. B 74, 245422 (2006). 7. F. Fievet, J. P. Lagier, B. Blin, B. Beaudoin, and M. Figlarz, “Homogeneous and heterogeneous nucleations in the polyol process for the preparation of micron and submicron size metal particles,” Solid State Ion. 32, 198–205 (1989). 8. C. L. Haynes and R. P. V. Duyne, “Nanosphere lithography: a versatile nanofabrication tool for studies of size-dependent nanoparticles optics,” J. Phys. Chem. B 105, 5599–5611 (2001). 9. S. Wang, D. F. P. Pile, C. Sun, and X. Zhang, “Nanopin plasmonic resonator array and its optical properties,” Nano Lett. 7, 1076–1080 (2007). 10. J. Fischer, N. Vogel, R. Mohammadi, H. Butt, K. Landfester, C. K. Weiss, and M. Kreiter, “Plasmon hybridization and strong near-field enhancements in opposing nanocrescent dimers with tunable resonances,” Nanoscale 3, 4788–4797 (2011). 11. S. Yin, Q. Deng, X. Luo, C. Du, and Y. Zhang, “The coupled electric field effects on localized surface plasmon resonance in nanoparticle arrays,” J. Appl. Phys. 104, 1–5 (2008). 12. I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402 (2007). 13. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). 14. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004). 15. W. Y. Ma, H. Yang, J. P. Hilton, Q. Lin, J. Y. Liu, L. X. Huang, and J. Yao, “A numerical investigation of the effect of vertex geometry on localized surface plasmon resonance of nanostructures,” Opt. Express 18, 843–853 (2010). 16. Y. Xia and N. J. Halas, “Shaped-controlled synthesis and surface plasmonic properties of metallic nanostructures,” MRS Bull. 30, 338–348 (2005). 17. W. Y. Ma, J. Yao, H. Yang, J. Y. Liu, F. Li, J. P. Hilton, and Q. Lin, “Effects of vertex truncation of polyhedral nanostructures on localized surface plasmon resonance,” Opt. Express 17, 14967–14976 (2009). 18. B. J. Wiley, Y. Chen, J. M. McLellan, Y. Xiong, Z. Y. Li, D. Ginger, and Y. Xia, “Synthesis and optical properties of silver nanobars and nanorice,” Nano Lett. 7, 1032–1036 (2007).
State Key Laboratory of Optical Technologies on Nano-fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China 2 3
Graduate University of Chinese Academy of Sciences, Beijing 100039, China
Department of Mechanical Engineering, Columbia University, New York 10027, USA *Corresponding author: [email protected] Received 10 October 2013; revised 23 April 2014; accepted 24 April 2014; posted 1 May 2014 (Doc. ID 199299); published 30 May 2014
An Ag∕SiO2 ∕Ag sandwich delta nanostar with three sharp angles (30°) is proposed. The extinction efficiency property with a variation in environment refractive index has been investigated in detail by the finite difference time domain method. The refractive index response sensitivity is 482.67 nm∕RIU. And the correlations between resonance wavelengths and thickness of the dielectric layer are also established. It reveals that as the thickness increases, the peak wavelength turns to red shift, and a tunable resonance wavelength is achieved through the thickness adjusting of the SiO2 layer. The maximum of the electric field enhancement is 833.776 with the thickness of the dielectric layer h 40 nm. Moreover, the influence of the vertex truncation on the extinction spectra and the refractive index sensitivity has also been analyzed. © 2014 Optical Society of America OCIS codes: (000.4430) Numerical approximation and analysis; (240.6680) Surface plasmons; (290.2200) Extinction; (350.3950) Micro-optics; (310.6628) Subwavelength structures, nanostructures. http://dx.doi.org/10.1364/AO.53.003528
1. Introduction
Noble metal nanoparticles exhibit good performance between the visible and near-infrared range for the abnormal optical properties. The surface plasmon resonance properties of metal nanostructures are highly sensitive to the shape, size, material, and the dielectric environment and have been intensively studied [1–4]. Researchers achieve the tunable resonance by varying the basic size and shape parameters [5,6]. And the nanoparticles are usually fabricated by the wet-chemical approaches and lithographic processes [7,8]. Recently, changes of the thickness of the multilayer nanostructure have been 1559-128X/14/163528-05$15.00/0 © 2014 Optical Society of America 3528
APPLIED OPTICS / Vol. 53, No. 16 / 1 June 2014
used to tailor the resonance position, which can avoid the high cost and sophisticated fabricating process. Besides, the Zhang and co-workers have proposed a metal/dielectric/metal structure of a three-layer sandwich elliptical cylinder [5,9], and the extinction characteristics are adjusted by regulating the thickness of the intermediate dielectric layer. It is found that, as for the resonance wavelength tuning, the longitudinal layer thickness adjusting of the sandwich nanostructures is much more convenient and easier than the geometric size changing of the single layer nanostructure. Substantial attention has been focused on these plasmon hybridization studies [10,11]. The bulk plasmon polariton (BPP) can be excited in the metal-dielectric nanomultilayer structures [12]. And the plasmon coupling of the upper and bottom metal layers will change the surface
plasmon resonance (SPR) properties. The electromagnetic field will be enhanced and the resonance wavelength can be adjusted. The plasmon hybridization phenomenon was first observed and explained on nanosphere dimmers [13,14]. In order to obtain better nanosensing properties, we combine both the sharp tips and the metal– dielectric multilayer structures together. In this paper, we present a sandwich delta nanostar that features an Ag∕SiO2 ∕Ag sandwich delta star nanoplate with three sharp angles of 30°. And the proposed architecture combines several attractive points that can excite high near-field enhancement and achieve tunable resonance wavelength. Moreover, the sharp angle can also develop some hotspots of strong field enhancement. In this study, we analyze the extinction efficiency and local surface plasmon resonance (LSPR) sensing properties using the FDTD method. Furthermore, a detailed numerical analysis of the local electromagnetic field enhancement and resonance wavelength tuning are studied.
Fig. 1. Sketch of the sandwich delta nanostar. The cross section of the nanostar is composed of a central equilateral triangle and three isosceles triangles joined at its sides.
3. Results and Discussion 2. Simulation Modeling
The geometry of a (Ag∕SiO2 ∕Ag) sandwich delta nanostar is defined by four parameters: the length of hemline of the central equilateral triangle, a 18.3 nm; the length of the isosceles triangle, b 35.36 nm; the thickness h 20 nm; and the sharp vertex of the isosceles triangle, α 30°, as depicted in Fig. 1. The thicknesses of up and lower silver layers are both 20 nm, and the central dielectric layer is made of silicon dioxide. But why should we choose the sharp angle as 30°? The effects of vertex features of the single silver nanostructure on its extinction and LSPR properties have been discussed [15]. The analysis shows that a delta-star with a relatively small vertex presents a larger resonant wavelength. And the vertex angle of 30° displays the best figure of merit value for LSPR application. When the photon frequency is coincident with the localized surface plasmon resonance frequency, plenty of free electrons can be drawn among the sharp vertex angles, and it can excite strong electrostatic fields.
The extinction efficiency property of the Ag∕SiO2 ∕Ag sandwich delta nanostar with a variation in environment refractive index is investigated in detail by the finite-difference time-domain (FDTD) method. The FDTD method is of high accuracy and wide application, which is deduced from Maxwell equations. For better calculation of the extinction properties, we adopt the special total-scattering field source (TSFS) and total-scattering field monitor (TSFM) in the simulation. The thickness of the SiO2 layer is 20 nm and the output extinction spectra of different refractive index have been obtained in Fig. 2(a). As the refractive index increases, the peak wavelength gradually shifts red. The refractive index changes from 1.0 to 1.5, and the corresponding resonance wavelength slowly rises from 624.463 to 864.43 nm. The sensing ability of the peak wavelength to the environment refractive index can be estimated by the linear fitting in Fig. 2(b). The refractive index response sensitivity of the sandwich delta nanostar is 482.67 nm∕RIU (refractive index unit), with the linear correlation coefficient 0.99923.
Fig. 2. (a) Output spectra of the extinction efficiency under different refractive index with h 20 nm. (b) Plot of the peak wavelength versus the refractive index (dot line) and its linear fitting (red line). 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
3529
Besides, the correlations between resonance wavelengths and thickness of the dielectric layer are established. Changing the thickness of the SiO2 layer, the extinction and near-field enhancement characteristics are also described [see Fig. 3(a)]. It reveals that as the thickness of the SiO2 layer increases, the peak wavelength turns to be red shift. When the thickness grows from 10 to 60 nm, the resonance peak wavelength shifts from 1005.9 to 1117.54 nm, and accompanies with increasing of the extinction efficiency. We apply plasmon hybridization theory to explain the spectral shifts of the coupled nanostructure. The vertical plasmon hybridization is excited between the upper and bottom metal layers, which is perpendicular to the surface plasmon direction. When the thickness of the dielectric layer grows larger, the vertical plasmon coupling gradually reduces. In addition, the shift of peak wavelength increases unconspicuously, when the thickness of the SiO2 layer grows larger than 50 nm. And the tunable wavelength range is 600–640 nm. Besides, the electric field enhanced ability of the nanostructure should also be considered, especially as the LSPR and SERS substrate. The electric field enhancement factor is introduced to evaluate the near-field enhancing capability of the nanostructure. Figure 3(b) displays the correlation between peak wavelength and extinction efficiency of varying dielectric thickness. And the maximum of the electric field enhancement is 833.776 with the thickness of the dielectric layer h 40 nm, as revealed in Fig. 4. 4. Analysis of Vertex Truncation
The sharp vertex is one of the important factors affecting the sensing characteristics of the overall structure. However, as to the actual fabricating process, it is difficult to achieve the idealized sharp angle. Currently, with the development of the micro/nano fabrication technology, the preparation method of the nanostructures usually includes the focused ionbeam lithography, electron-beam lithography, nanosphere lithography, etc. [16–18]. Because of the resolution of these nanofabrication techniques and some uncontrollable processing factors and errors, the sharp features of the prepared nanostructures
Fig. 4. Electric field distribution of x–y plane with the thickness of the dielectric layer h 40 nm.
such as corners and edges are always inevitably truncated. As for our experimental condition, the experiment cannot be carried out currently. But the limit of resolution of these nanofabrication techniques is ubiquitous. And the vertex truncated effect of sharp angle exists commonly. Even though it is the best electron-beam lithography technique, it also can bring in the truncation effect. And its resolution is usually bigger than 2 nm, more commonly to be 5– 10 nm [16]. Therefore, it is essential and important to study the influence on its optical property and sensing characters. The ideal delta-star with three sharp angles of α 30° (black line) and the vertex truncated structure (red line) are described in Fig. 5. The delta-star with truncated vertices can be considered as a combination of an intermediate equilateral triangle (length a 18.3 nm) and three isosceles triangles (waist length b 35.36 nm and hemline a 18.3 nm). Here, we introduce the truncation factor, f , and define it as the ratio of the area of the vertex truncation to the area of the perfect delta nanostar. And the vertex truncation area contains the region of triangle △ABC, deducted the area of camber AB. So the truncated nanostar is composed of three isosceles
Fig. 3. (a) Extinction efficiency with changing thickness of the SiO2 layer. (b) Peak wavelength and extinction efficiency of varying dielectric thickness. 3530
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Fig. 5. Cross section in x–y direction of the vertex truncation (red dot line) and of the idealized angle (black line) (left) and the sandwich delta-star nanoplate with vertex truncation (right).
trapezoids, a camber, and an equilateral triangle. The size and position of the delta-star can be determined by several key points, which are point A, B (0, 0),
Table 1.
A B f
(9.15,30.62) (9.15,30.62) 0%
(8, 26.7716) (10.3, 26.7716) 0.0891%
C (9.15, 30.62), D (18.3, 0), E (9.15, −15.85). And different truncation ratios can be obtained by changing the coordinate of point A, B, and the truncation factors are 0.0891%, 3.11%, 6.68%, 11.6%, and 17.8%, respectively (see in Table 1). We analyze the influence of the vertex truncated nanostructure on the extinction spectra and refractive index sensitivity with different truncation ratios. According to the calculated extinction spectra presented in Fig. 6(a), the LSPR extinction spectrum exhibits a peak at about 624.46 nm for the idealized nanostructure (f 0%). As the truncation ratio increases, the extinction peak wavelength becomes blue shifting and the amplitude of the extinction efficiency decreases. And the peak wavelength of the LSPR spectra gradually shifts from 624.46 to 479.026 nm as the truncation ratio changes from 0% to 17.8%,
Different Truncation Ratios
(7, 23.425) (11.3, 23.425) 3.11%
(6, 20.0787) (12.3, 20.0787) 6.68%
(5, 16.7322) (13.3, 6.7322) 11.6%
(4, 13.3858) (14.3, 13.3858) 17.8%
Fig. 6. (a) Extinction results of the vertex truncated sandwich delta-star nanoplate with the truncation ratio of f 0.0891%, 3.11%, 6.68%, 11.6%, and 17.8%, respectively. (b) Refractive index sensitivity distribution of truncated nanostructure with different truncation ratio.
Fig. 7. Near-field enhancement of sandwich delta nanostar with a truncation of 6.68% (a) and the idealized nanostructure when the thickness of the dielectric layer h 20 nm (b). 1 June 2014 / Vol. 53, No. 16 / APPLIED OPTICS
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which is because of the retardation effect of the electromagnetic field across the nanostructure along with decrease of the characteristic size of the sandwich nanoplate. The refractive index sensing property of the truncated structure has also been calculated as depicted in Fig. 6(b). The refractive index sensitivity decreases strongly as the truncation ratio f increases from 0% to 17.8%. Compared with the perfect structure (f 0%), the sandwich nanostar with sharp vertices exhibits higher sensitivity while the performance of the nanostructure with slightly rounded vertices is much poorer. When f varies from 0.0891% to 11.6%, the refractive index sensitivity falls from 403.122 nm∕RIU to 326.121 nm∕RIU. And comparison of the near-field with truncated vertex and the idealized angle is also made, as depicted in Fig. 7. It is apparent that the near-field distribution of the idealized sharp vertices is more localized than that of the truncated nanostar with the vertex truncation f 6.68%. 5. Conclusions
In this paper, we present a sandwich delta nanostar with three sharp angles of 30°. The extinction efficiency and local surface plasmon resonance (LSPR) sensing properties of the proposed architecture have been studied. And the refractive index response sensitivity of the sandwich delta nanostar is 482.67 nm∕RIU, with the linear correlation coefficient 0.99923. And tunable resonance wavelength is achieved through the thickness adjusting of the SiO2 layer. The maximum of the electric field enhancement is 833.776 with the thickness of the dielectric layer h 40 nm. Furthermore, we also analyze the influence of the vertex truncation on the extinction spectra and refractive index sensitivity. Compared with the perfect structure (f 0%), the sandwich nanostar with sharp vertices exhibits higher sensitivity. Then, it is proved that the presented architecture combines several attractive features. First, adjusting the thickness of dielectric layer is relatively easier than changing the characteristic of the size and shape for achieving the tunable resonance wavelength. Besides, strong near-field enhancement of the tips is effectively collected around the sharp vertex region. And the close proximity of the upper and lower metal layers leads to a hybridization of the vertical plasmon. Hence, this sandwich delta nanostar is approved to be quite appropriate and much more suitable as the LSPR sensing substrate. The author gratefully acknowledges the support of K. C. Wong Education Foundation, Hong Kong, and
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