August 15, 2014 / Vol. 39, No. 16 / OPTICS LETTERS
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Lattice plasmon resonance in core-shell SiO2/Au nanocylinder arrays Linhan Lin1 and Yasha Yi1,2,* 1
2
Integrated Nano Optoelectronics Laboratory, Department of Electrical and Computer Engineering, University of Michigan, Dearborn, Michigan 48128, USA
Materials Processing Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA *Corresponding author: [email protected] Received June 6, 2014; revised July 10, 2014; accepted July 10, 2014; posted July 11, 2014 (Doc. ID 213670); published August 12, 2014
Core-shell SiO2 ∕Au nanocylinder arrays (NCAs) are studied using finite-difference time-domain simulations. The increase of height induces new surface plasmon resonances along the nanocylinders, i.e., dipole and quadrupole modes. Orthogonal coupling between superstrate diffraction order and the height-induced dipole mode is observed, which could achieve a well-defined lattice plasmon mode even for smaller NCAs in asymmetric environments. Electromagnetic field distribution has been employed to determine the coupling origin. Radiative loss could also be effectively suppressed in these core-shell NCAs, indicating the possibility of future applications in fluorescence enhancement and nanolasers. © 2014 Optical Society of America OCIS codes: (260.3910) Metal optics; (240.6680) Surface plasmons; (260.5740) Resonance; (160.4236) Nanomaterials. http://dx.doi.org/10.1364/OL.39.004823
Metallic nanoparticles (NPs) have attracted much attention due to their remarkable optical properties related to excitation of localized surface plasmon resonances (LSPRs), which exhibit high optical field confinement and sensitivity to the refractive index of local environment [1–5]. It has been widely studied in bio-sensing [6,7], luminescence enhancement [8,9], and surface-enhanced Raman spectroscopy (SERS) [10,11]. Recently, LSPRs were associated with diffraction structures to investigate far-field coupling between the NPs [12–18]. Dipolar interaction between the NPs takes place when a wavelength is close to the Rayleigh anomaly and induces the so-called lattice plasmon modes (LPMs) [19–21]. In the two-dimensional (2D) periodic structures, the in-plane wave vectors are described as below: k∥i;j k∥ i
2π 2π ex j ey . dx dy
(1)
k∥ denotes the horizontal component of the incident plane wave. For normal incidence, k∥ could be ignored. dx and dy mean the lattice constants of the periodic structure. i and j are integers, which correspond to different diffraction orders along the x and y axes. The wave number along the z axis could be calculated by k⊥i;j
s 2π 2 n − k∥2 i;j ; λ
(2)
where λ is the wavelength of incident light. n is the refractive index (RIX) of the superstrate or substrate. Therefore, two sets of diffraction orders could be obtained. According to Meier’s study, when k⊥i;j is a real number, it represents a radiative diffraction order, while an imaginary k⊥i;j corresponds to an evanescent diffraction order. When the diffraction order changes from evanescent to radiative, a strong dipolar interaction takes place and collective modes could be observed, with the 0146-9592/14/164823-04$15.00/0
diffraction edge of the 0; 1 superstrate and substrate sub orders as λair 0;1 dy and λ0;1 n × dy , respectively. LPMs exhibit several novel characteristics compared with LSPRs, especially the significant suppression of the plasmon radiative damping resulting in narrow resonance lineshape, which could be utilized in bio-sensing [22–24], laser action [25–27], or SERS [28]. However, most of the LPMs reported were achieved by fabricating Au NPs on the substrate using electron beam lithography. It has been pointed out that the presence of a substrate could reduce or even suppress the diffraction–LSPR coupling in NP arrays [29]. In order to suppress the effect of the substrate, a homogeneous environment or large NP size is required. Specifically, NP size is crucial to determine resonance wavelength of LSPRs, and therefore the coupling wavelength of LPMs. This will greatly restrict the future applications. Recently, a well-defined collective resonance in Au nanorod arrays was proposed and exhibited excellent tolerance to index asymmetry in the environment [18]. In this Letter, we propose the core-shell SiO2 ∕Au nanocylinder arrays (NCAs), which could be possibly fabricated by coating an Au layer on the SiO2 NCAs. The increase of height generates plasmon modes along the nanocylinders (NCs), which could be coupled with the diffraction orders and induce well-defined LPMs in the asymmetric environment. Core-shell SiO2 ∕Au NCAs were schematically displayed in Fig. 1. The diameter of the NCs is varied from 50 to 200 nm, and the coating Au thickness is 20 nm. The distance between neighboring NCs is defined according to the direction of external electric field, i.e., d∥ when the direction is parallel to the external electric field and d⊥ when the direction is orthogonal to the external electric field. The height of the NCs is varied from 50 to 400 nm. The medium surrounding the structure is air (superstrate) with RIX of 1.0 while the RIX of the SiO2 substrate is 1.44. Three-dimentional (3D) finite-difference time-domain (FDTD) simulations were carried out using OmniSim. © 2014 Optical Society of America
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Fig. 1. Schematic view of the core-shell SiO2 ∕Au NCAs on the glass substrate. d∥ and d⊥ denote the distance between the neighboring NCs along or vertical to the direction of external electric field E. h indicates the height of the NCs. Inset shows the cross section of the core-shell structure, and D represents the diameter of the SiO2 NCs.
A broadband plane wave with E x polarization was launched in the negative direction of the z axis. Perfect match layers (PMLs) were applied above the top and below the bottom z boundary of the unit cell to absorb the transmitted and reflected light. Periodic boundary conditions were applied along the x and y axes to generate the 2D NCAs. A minimal grid size of 3 nm and a Lorentz model for Au permittivity were used in the simulations. In order to study the increase of height on the plasmonic modes in these core-shell NCAs, extinction spectra dependent on the height with D 200 nm and d∥ d⊥ 500 nm are summarized in Fig. 2(a). The extinction cross section is defined as σ ext d⊥ × d∥ × 1 − T. For the structure with height of 50 nm, a single broad LSPR is fixed at around 1000 nm, which is similar to the LSPR reported in Au NP arrays [12]. It originates from the propagation interruption of surface resonance at the interface. However, due to the core-shell coupling, a redshift could be observed compared with the Au NPs of a similar size. This LSPR is almost independent of the height of the NCs. (A slight redshift of ∼20 nm is observed when height increases from 50 to 100 nm.) When
Fig. 2. (a) Extinction cross section of the core-shell SiO2 ∕Au NCAs with D 200 nm, d∥ d⊥ 500 nm, and different heights. (b)–(d) correspond to the distribution of E x component for the plasmon modes at 660, 743, and 1034 nm, respectively, consistent with the extinction peaks shown in (a). Charge density distribution of (e) Q mode at 660 nm and (f) D2 mode at 743 nm.
the height reaches 100 nm, a new extinction peak at ∼600 nm appears. Obvious redshift and broadened linewidth are observed when the height further increases. The peak redshifts to 743 nm for the NCAs with height of 400 nm. In addition, in the extinction spectra for the NCAs with height of 300 and 400 nm, another extinction peak appears at the higher energy side. It is worth noting that the 1; 0 or 0; 1 superstrate diffraction orders could be observed at 500 nm, which is away from all the plasmonic modes. Very weak coupling is found between the 1; 0 or 0; 1 substrate diffraction orders (located at 722 nm) and the newly generated plasmon modes. Therefore, the plasmonic modes shown in these NCAs are similar to the results of single NC. The Ex distributions in the xz plane for these three plasmon resonances are listed in Figs. 2(b)–2(d). The LSPR at 1034 nm shows dipolar distribution at the interface [Fig. 2(d)], which is denoted as D1 mode. In Fig. 2(c), another dipolar distribution (D2 mode) was observed, corresponding to the extinction peak at 743 nm. The electric field along the outside surface of the NCs is consistent with the external electric field, while a reverse electric field is obtained in the SiO2 NCs. This mode is similar to the dipolar bonding mode in the research of Au nanoshells [2,30]. The charge distribution is displayed in Fig. 2(f). The outer surface and inner surface have mutually aligned dipolar distribution. As the wide linewidths and wavelength overlap for D1 and D2 modes, the electric field distributions are not isolated from each other. Specifically, dipolar distribution along the NCs is also observed at 1034 nm, which, however, is irrelevant to D1 mode. The electric field distribution and charge density for the plasmon mode at 660 nm are shown in Figs. 2(b) and 2(e), respectively. A quadrupole-like distribution caused by phase retardation is obtained (Q mode) [30,31]. As the height of NCs exceeds the dipole limit, an anti-aligned dipolar distribution is responsible for the specific electric field distribution [Fig. 2(e)]. Concentration of charge on the outer surface at the top side of the NCs induces an enhancement of the external electric field near the outer surface, while a charge concentration on the inner surface at the bottom side caused by a reverse electric field induces an enhanced electric field in the SiO2 NCs. This phase-retardation effect is also responsible for the redshift and linewidth broadening for both D2 and Q modes [30,32]. Figure 3(c) summarizes the extinction spectra of the core-shell SiO2 ∕Au NCAs (h 400 nm) with d⊥ from 500 to 1200 nm. The 1; 0 superstrate diffraction order could be observed at 500 nm. Because of its ultranarrow linewidth, this diffraction order could only be observed when the resolution of the spectrum is ultrafine. The 1; 0 substrate diffraction order could be observed at ∼722 nm; it overlaps with Q and D2 modes with very weak coupling. However, the 0; 1 superstrate diffraction order could not be observed without coupling. An increase of d⊥ could lead to the redshift of both λair 0;1 and λsub and therefore the coupling between the plas0;1 mon modes and diffraction waves. When d⊥ is smaller than 800 nm, i.e., nd⊥ < λD1 , the allowed substrate diffraction orders are of higher energy than the D1 modes and little radiative coupling could take place. When d⊥
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Fig. 3. Extinction spectra of the core-shell SiO2 ∕Au NCAs with D 200 nm, d∥ 500 nm and (a) h 50 nm, (b) h 300 nm, and (c) h 400 nm. Extinction, absorption, and scattering spectra for the NCAs with D 200 nm, d∥ 500 nm and (d) d⊥ 800 nm, h 50 nm, (e) d⊥ 800 nm, h 400 nm, and (f) d⊥ 1000 nm, h 400 nm.
reaches 800 nm, i.e., λsub 0;1 nd⊥ 1155 nm, which is located on the lower energy side of D1 mode, a sharp LPM with narrower linewidth and higher intensity appears, which is attributed to coupling between the 0; 1 substrate diffraction order and D1 mode. Further increase of d⊥ above 800 nm results in a larger distance between λsub 0;1 and λD1 , and therefore the coupling weakens gradually and vanishes. This LPM is similar to most of the LPMs reported in Au NP arrays and is sensitive to the presence of substrate. Interestingly, another LPM associated with coupling between the 0; 1 superstrate order and D2 mode is observed at a shorter wavelength. When d⊥ increases from 700 to 1000 nm, a sustainable linewidth narrowing, wavelength redshift, and intensity enhancement for D2 mode is observed. However, when d⊥ further increases, the extinction peak disappears and very weak coupling with D1 mode is obtained. In order to confirm the origin of this LPM, the extinction spectra for core-shell NCAs with height of 50 nm are shown for comparison [Fig. 3(a)]. The LPM associated with the D1 mode and 0; 1 substrate diffraction order shows similar behavior with that from the structure with h 400 nm. However, little coupling between the 0; 1 superstrate diffraction order and D1 mode is observed, with only shallow dips in the D1 mode. The height study from 100 to 300 nm has also been carried out (not present here), which demonstrates that the coupling between the 0; 1 superstrate diffraction order and D2 mode is highly dependent on the height, i.e., coupling becomes stronger with enhanced intensity and redshifts when height increases. Figure 3(b) shows that the LPM is located at 900 nm with lower intensity when h 300 nm. Decompositions of extinction spectra into scattering and absorption components are shown in Figs. 3(d)–
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3(f), in which absorption is calculated by σ abs d⊥ × d∥ × 1 − T − R and scattering is calculated by σ scat σ ext − σ abs For the LPM at 1169 nm displayed by the spectra shown in Fig. 3(d), scattering and absorption show nearly equal contributions when h 50 nm. However, the weight of absorption increases and becomes dominant when h 400 nm, indicating efficient suppression of radiative loss. Similar behavior is observed in the D1 mode without coupling (d∥ d⊥ 500 nm, not shown here), indicating suppression of radiative loss in the plasmonic mode is crucial for the associated LPM. Decomposition of LPM at 1000 nm is shown in Fig. 3(f) for h 400 nm and d⊥ 1000 nm, with the data from h 50 nm and d⊥ 1000 nm subtracted to eliminate the effect of D1 mode. The primary contribution of absorption is also obtained, suggesting the possibility of this LPM being applied to luminescence enhancement. It is emphasized that the coupling between the 0; 1 superstrate diffraction order and D2 mode is robust in the presence of a substrate, which could eliminate the restriction on NP size and environment index. The extinction spectra for core-shell NCAs with smaller diameters have been calculated to verify this supposition (Fig. 4). The coupling between the 0; 1 substrate diffraction order and D1 mode is weak when D 100 nm and almost vanishes when D 50 nm. However, strong coupling between the 0; 1 superstrate diffraction order and D2 mode is sustained, with coupling wavelength at 800 and 650 nm when D 100 nm and 50 nm, respectively. It indicates that this robust LPM allows tunability of the resonance wavelength to the visible range by controlling the NC diameter without index matching layer. Electromagnetic (EM) field distributions are summarized in Fig. 5. Considerable field enhancements are observed in E x distributions when LPMs are excited. Figure 5(a) shows the distribution of E x in the xz plane for the LPM at 1169 nm. The wavelength overlap between D1 and D2 modes determines that the field profile from D2 mode could not be eliminated. As the external electric field is orthogonal to the diffraction wave vector in our case, the radiative coupling could be confirmed in the distribution of H z . A similar vertical component of E z has been observed in the parallel LPMs reported in Ref. [18]. A standing-wave profile is obtained from the bottom side of the NCs into the substrate, which should be attributed to the interference of the diffraction waves along the y axis. The enhanced electric-field energy generated from D1 mode is converted into magnetic-
Fig. 4. Extinction spectra of the core-shell SiO2 ∕Au NCAs with h 400 nm and (a) D 100 nm, d∥ 400 nm and (b) D 50 nm, d∥ 300 nm.
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Fig. 5. E x amplitude in xz plane and H z amplitude in yz plane through the NC center with D 200 nm, d∥ 500 nm, h 400 nm and (a), (b) d⊥ 800 nm, λ 1169 nm; (c), (d) d⊥ 1000 nm, λ 1000 nm.
field energy and coupled with the diffraction wave for transfer. The hot spots at the top side of the NCs (D2 associated) are weak and show noncoupling with the diffraction wave, which further confirm the coupling origin of this LPM. The field distributions for the LPM at 1000 nm are shown in Figs. 5(c) and 5(d). The E x distribution shows intensive dipolar distribution on the top side along the NCs. The coupling behavior could also be confirmed in the H z distribution, which is different from the LPM at 1169 nm. The hot spots at the top side of the NCs are coupled with the 0; 1 superstrate diffraction wave, and no coupling behavior for the bottom hot spots is observed, which is consistent with the analysis above. In summary, SiO2 ∕Au core-shell NCAs were studied using FDTD simulations for generation of LPMs. In addition to the coupling between the 0; 1 substrate diffraction order and D1 mode, the increase of height induces new LSPR modes along the NCs, which could be coupled with the 0; 1 superstrate diffraction order. This LPM allows strong coupling in inhomogeneous environments even for NCs with much smaller diameters, which is important to improve the tunability of coupling wavelength. The coupling behavior could be confirmed by the EM field distributions, in which horizontal propagating H z is coupled with the hot spots from the NCs for energy transfer. Efficient suppression of the radiative loss is also observed for both of the LPMs, which is important for the future application in fluorescence enhancement or nanolaser. The coating of Au layer on the SiO2 NCAs would be crucial for the future fabrication. It is considered that employing template for protection of the spacing substrate and postcoating using physical vapor deposition or chemical deposition is available. It should also be noted that according to the coupling mechanism, perfect coating of Au layer is not required for generation of the D2 associated LPM, which is also important for practical applications. The authors would like to acknowledge the financial support from Demetra Energy, Europe and partial support from the University of Michigan.
References 1. C. Oubre and P. Nordlander, J. Phys. Chem. B 108, 17740 (2004). 2. C. Radloff and N. J. Halas, Nano Lett. 4, 1323 (2004). 3. N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, Chem. Rev. 111, 3913 (2011). 4. M. Rycenga, C. M. Cobley, J. Zeng, W. Li, C. H. Moran, Q. Zhang, D. Qin, and Y. Xia, Chem. Rev. 111, 3669 (2011). 5. M. I. Stockman, Opt. Express 19, 22029 (2011). 6. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, Nat. Mater. 8, 867 (2009). 7. H. Shen, G. Lu, T. Zhang, J. Liu, Y. Gu, P. Perriat, M. Martini, O. Tillement, and Q. Gong, Nanotechnology 24, 285502 (2013). 8. B. P. Khanal, A. Pandey, L. Li, Q. Lin, W. K. Bae, H. Luo, V. I. Klimov, and J. M. Pietryga, ACS Nano 6, 3832 (2012). 9. S. Khatua, P. M. R. Paulo, H. Yuan, A. Gupta, P. Zijlstra, and M. Orrit, ACS Nano 8, 4440 (2014). 10. J. Ye, F. F. Wen, H. Sobhani, J. B. Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, Nano Lett. 12, 1660 (2012). 11. V. V. Thacker, L. O. Herrmann, D. O. Sigle, T. Zhang, T. Liedl, J. J. Baumberg, and U. F. Keyser, Nat. Commun 5, 3448 (2014). 12. E. M. Hicks, S. L. Zou, G. C. Schatz, K. G. Spears, R. P. Van Duyne, L. Gunnarsson, T. Rindzevicius, B. Kasemo, and M. Kall, Nano Lett. 5, 1065 (2005). 13. B. Auguie and W. L. Barnes, Phys. Rev. Lett. 101, 143902 (2008). 14. Y. Chu, E. Schonbrun, T. Yang, and K. B. Crozier, Appl. Phys. Lett. 93, 181108 (2008). 15. V. G. Kravets, F. Schedin, and A. N. Grigorenko, Phys. Rev. Lett. 101, 087403 (2008). 16. A. G. Nikitin, T. Nguyen, and H. Dallaporta, Appl. Phys. Lett. 102, 221116 (2013). 17. A. G. Nikitin, Appl. Phys. Lett. 104, 061107 (2014). 18. A. Vitrey, L. Aigouy, P. Prieto, J. M. García-Martín, and M. U. González, Nano Lett. 14, 2079 (2014). 19. M. Meier, A. Wokaun, and P. F. Liao, J. Opt. Soc. Am. B 2, 931 (1985). 20. V. A. Markel, J. Mod. Opt. 40, 2281 (1993). 21. V. A. Markel, J. Phys. B 38, L115 (2005). 22. P. Offermans, M. C. Schaafsma, S. R. K. Rodriguez, Y. Zhang, M. Crego-Calama, S. H. Brongersma, and J. G. Rivas, ACS Nano 5, 5151 (2011). 23. A. I. Kuznetsov, A. B. Evlyukhin, M. R. Goncalves, C. Reinhardt, A. Koroleva, M. L. Arnedillo, R. Kiyan, O. Marti, and B. N. Chichkov, ACS Nano 5, 4843 (2011). 24. B. Spackova and J. Homola, Opt. Express 21, 27490 (2013). 25. W. Zhou and T. W. Odom, Nat. Nanotechnol. 6, 423 (2011). 26. W. Zhou, Y. Hua, M. D. Huntington, and T. W. Odom, J. Phys. Chem. Lett. 3, 1381 (2012). 27. W. Zhou, M. Dridi, J. Y. Suh, C. H. Kim, D. T. Co, M. R. Wasielewski, G. C. Schatz, and T. W. Odom, Nat. Nanotechnol. 8, 506 (2013). 28. L. K. Ausman, S. Li, and G. C. Schatz, J. Phys. Chem. C 116, 17318 (2012). 29. B. Auguie, X. M. Bendana, W. L. Barnes, and F. J. Garcia de Abajo, Phys. Rev. B 82, 155447 (2010). 30. S. L. Westcott, J. B. Jackson, C. Radloff, and N. J. Halas, Phys. Rev. B 66, 155431 (2002). 31. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, J. Phys. Chem. B 107, 668 (2003). 32. J. P. Kottmann and O. J. F. Martin, Opt. Lett. 26, 1096 (2001).
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Lattice plasmon resonance in core-shell SiO2/Au nanocylinder arrays Linhan Lin1 and Yasha Yi1,2,* 1
2
Integrated Nano Optoelectronics Laboratory, Department of Electrical and Computer Engineering, University of Michigan, Dearborn, Michigan 48128, USA
Materials Processing Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA *Corresponding author: [email protected] Received June 6, 2014; revised July 10, 2014; accepted July 10, 2014; posted July 11, 2014 (Doc. ID 213670); published August 12, 2014
Core-shell SiO2 ∕Au nanocylinder arrays (NCAs) are studied using finite-difference time-domain simulations. The increase of height induces new surface plasmon resonances along the nanocylinders, i.e., dipole and quadrupole modes. Orthogonal coupling between superstrate diffraction order and the height-induced dipole mode is observed, which could achieve a well-defined lattice plasmon mode even for smaller NCAs in asymmetric environments. Electromagnetic field distribution has been employed to determine the coupling origin. Radiative loss could also be effectively suppressed in these core-shell NCAs, indicating the possibility of future applications in fluorescence enhancement and nanolasers. © 2014 Optical Society of America OCIS codes: (260.3910) Metal optics; (240.6680) Surface plasmons; (260.5740) Resonance; (160.4236) Nanomaterials. http://dx.doi.org/10.1364/OL.39.004823
Metallic nanoparticles (NPs) have attracted much attention due to their remarkable optical properties related to excitation of localized surface plasmon resonances (LSPRs), which exhibit high optical field confinement and sensitivity to the refractive index of local environment [1–5]. It has been widely studied in bio-sensing [6,7], luminescence enhancement [8,9], and surface-enhanced Raman spectroscopy (SERS) [10,11]. Recently, LSPRs were associated with diffraction structures to investigate far-field coupling between the NPs [12–18]. Dipolar interaction between the NPs takes place when a wavelength is close to the Rayleigh anomaly and induces the so-called lattice plasmon modes (LPMs) [19–21]. In the two-dimensional (2D) periodic structures, the in-plane wave vectors are described as below: k∥i;j k∥ i
2π 2π ex j ey . dx dy
(1)
k∥ denotes the horizontal component of the incident plane wave. For normal incidence, k∥ could be ignored. dx and dy mean the lattice constants of the periodic structure. i and j are integers, which correspond to different diffraction orders along the x and y axes. The wave number along the z axis could be calculated by k⊥i;j
s 2π 2 n − k∥2 i;j ; λ
(2)
where λ is the wavelength of incident light. n is the refractive index (RIX) of the superstrate or substrate. Therefore, two sets of diffraction orders could be obtained. According to Meier’s study, when k⊥i;j is a real number, it represents a radiative diffraction order, while an imaginary k⊥i;j corresponds to an evanescent diffraction order. When the diffraction order changes from evanescent to radiative, a strong dipolar interaction takes place and collective modes could be observed, with the 0146-9592/14/164823-04$15.00/0
diffraction edge of the 0; 1 superstrate and substrate sub orders as λair 0;1 dy and λ0;1 n × dy , respectively. LPMs exhibit several novel characteristics compared with LSPRs, especially the significant suppression of the plasmon radiative damping resulting in narrow resonance lineshape, which could be utilized in bio-sensing [22–24], laser action [25–27], or SERS [28]. However, most of the LPMs reported were achieved by fabricating Au NPs on the substrate using electron beam lithography. It has been pointed out that the presence of a substrate could reduce or even suppress the diffraction–LSPR coupling in NP arrays [29]. In order to suppress the effect of the substrate, a homogeneous environment or large NP size is required. Specifically, NP size is crucial to determine resonance wavelength of LSPRs, and therefore the coupling wavelength of LPMs. This will greatly restrict the future applications. Recently, a well-defined collective resonance in Au nanorod arrays was proposed and exhibited excellent tolerance to index asymmetry in the environment [18]. In this Letter, we propose the core-shell SiO2 ∕Au nanocylinder arrays (NCAs), which could be possibly fabricated by coating an Au layer on the SiO2 NCAs. The increase of height generates plasmon modes along the nanocylinders (NCs), which could be coupled with the diffraction orders and induce well-defined LPMs in the asymmetric environment. Core-shell SiO2 ∕Au NCAs were schematically displayed in Fig. 1. The diameter of the NCs is varied from 50 to 200 nm, and the coating Au thickness is 20 nm. The distance between neighboring NCs is defined according to the direction of external electric field, i.e., d∥ when the direction is parallel to the external electric field and d⊥ when the direction is orthogonal to the external electric field. The height of the NCs is varied from 50 to 400 nm. The medium surrounding the structure is air (superstrate) with RIX of 1.0 while the RIX of the SiO2 substrate is 1.44. Three-dimentional (3D) finite-difference time-domain (FDTD) simulations were carried out using OmniSim. © 2014 Optical Society of America
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Fig. 1. Schematic view of the core-shell SiO2 ∕Au NCAs on the glass substrate. d∥ and d⊥ denote the distance between the neighboring NCs along or vertical to the direction of external electric field E. h indicates the height of the NCs. Inset shows the cross section of the core-shell structure, and D represents the diameter of the SiO2 NCs.
A broadband plane wave with E x polarization was launched in the negative direction of the z axis. Perfect match layers (PMLs) were applied above the top and below the bottom z boundary of the unit cell to absorb the transmitted and reflected light. Periodic boundary conditions were applied along the x and y axes to generate the 2D NCAs. A minimal grid size of 3 nm and a Lorentz model for Au permittivity were used in the simulations. In order to study the increase of height on the plasmonic modes in these core-shell NCAs, extinction spectra dependent on the height with D 200 nm and d∥ d⊥ 500 nm are summarized in Fig. 2(a). The extinction cross section is defined as σ ext d⊥ × d∥ × 1 − T. For the structure with height of 50 nm, a single broad LSPR is fixed at around 1000 nm, which is similar to the LSPR reported in Au NP arrays [12]. It originates from the propagation interruption of surface resonance at the interface. However, due to the core-shell coupling, a redshift could be observed compared with the Au NPs of a similar size. This LSPR is almost independent of the height of the NCs. (A slight redshift of ∼20 nm is observed when height increases from 50 to 100 nm.) When
Fig. 2. (a) Extinction cross section of the core-shell SiO2 ∕Au NCAs with D 200 nm, d∥ d⊥ 500 nm, and different heights. (b)–(d) correspond to the distribution of E x component for the plasmon modes at 660, 743, and 1034 nm, respectively, consistent with the extinction peaks shown in (a). Charge density distribution of (e) Q mode at 660 nm and (f) D2 mode at 743 nm.
the height reaches 100 nm, a new extinction peak at ∼600 nm appears. Obvious redshift and broadened linewidth are observed when the height further increases. The peak redshifts to 743 nm for the NCAs with height of 400 nm. In addition, in the extinction spectra for the NCAs with height of 300 and 400 nm, another extinction peak appears at the higher energy side. It is worth noting that the 1; 0 or 0; 1 superstrate diffraction orders could be observed at 500 nm, which is away from all the plasmonic modes. Very weak coupling is found between the 1; 0 or 0; 1 substrate diffraction orders (located at 722 nm) and the newly generated plasmon modes. Therefore, the plasmonic modes shown in these NCAs are similar to the results of single NC. The Ex distributions in the xz plane for these three plasmon resonances are listed in Figs. 2(b)–2(d). The LSPR at 1034 nm shows dipolar distribution at the interface [Fig. 2(d)], which is denoted as D1 mode. In Fig. 2(c), another dipolar distribution (D2 mode) was observed, corresponding to the extinction peak at 743 nm. The electric field along the outside surface of the NCs is consistent with the external electric field, while a reverse electric field is obtained in the SiO2 NCs. This mode is similar to the dipolar bonding mode in the research of Au nanoshells [2,30]. The charge distribution is displayed in Fig. 2(f). The outer surface and inner surface have mutually aligned dipolar distribution. As the wide linewidths and wavelength overlap for D1 and D2 modes, the electric field distributions are not isolated from each other. Specifically, dipolar distribution along the NCs is also observed at 1034 nm, which, however, is irrelevant to D1 mode. The electric field distribution and charge density for the plasmon mode at 660 nm are shown in Figs. 2(b) and 2(e), respectively. A quadrupole-like distribution caused by phase retardation is obtained (Q mode) [30,31]. As the height of NCs exceeds the dipole limit, an anti-aligned dipolar distribution is responsible for the specific electric field distribution [Fig. 2(e)]. Concentration of charge on the outer surface at the top side of the NCs induces an enhancement of the external electric field near the outer surface, while a charge concentration on the inner surface at the bottom side caused by a reverse electric field induces an enhanced electric field in the SiO2 NCs. This phase-retardation effect is also responsible for the redshift and linewidth broadening for both D2 and Q modes [30,32]. Figure 3(c) summarizes the extinction spectra of the core-shell SiO2 ∕Au NCAs (h 400 nm) with d⊥ from 500 to 1200 nm. The 1; 0 superstrate diffraction order could be observed at 500 nm. Because of its ultranarrow linewidth, this diffraction order could only be observed when the resolution of the spectrum is ultrafine. The 1; 0 substrate diffraction order could be observed at ∼722 nm; it overlaps with Q and D2 modes with very weak coupling. However, the 0; 1 superstrate diffraction order could not be observed without coupling. An increase of d⊥ could lead to the redshift of both λair 0;1 and λsub and therefore the coupling between the plas0;1 mon modes and diffraction waves. When d⊥ is smaller than 800 nm, i.e., nd⊥ < λD1 , the allowed substrate diffraction orders are of higher energy than the D1 modes and little radiative coupling could take place. When d⊥
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Fig. 3. Extinction spectra of the core-shell SiO2 ∕Au NCAs with D 200 nm, d∥ 500 nm and (a) h 50 nm, (b) h 300 nm, and (c) h 400 nm. Extinction, absorption, and scattering spectra for the NCAs with D 200 nm, d∥ 500 nm and (d) d⊥ 800 nm, h 50 nm, (e) d⊥ 800 nm, h 400 nm, and (f) d⊥ 1000 nm, h 400 nm.
reaches 800 nm, i.e., λsub 0;1 nd⊥ 1155 nm, which is located on the lower energy side of D1 mode, a sharp LPM with narrower linewidth and higher intensity appears, which is attributed to coupling between the 0; 1 substrate diffraction order and D1 mode. Further increase of d⊥ above 800 nm results in a larger distance between λsub 0;1 and λD1 , and therefore the coupling weakens gradually and vanishes. This LPM is similar to most of the LPMs reported in Au NP arrays and is sensitive to the presence of substrate. Interestingly, another LPM associated with coupling between the 0; 1 superstrate order and D2 mode is observed at a shorter wavelength. When d⊥ increases from 700 to 1000 nm, a sustainable linewidth narrowing, wavelength redshift, and intensity enhancement for D2 mode is observed. However, when d⊥ further increases, the extinction peak disappears and very weak coupling with D1 mode is obtained. In order to confirm the origin of this LPM, the extinction spectra for core-shell NCAs with height of 50 nm are shown for comparison [Fig. 3(a)]. The LPM associated with the D1 mode and 0; 1 substrate diffraction order shows similar behavior with that from the structure with h 400 nm. However, little coupling between the 0; 1 superstrate diffraction order and D1 mode is observed, with only shallow dips in the D1 mode. The height study from 100 to 300 nm has also been carried out (not present here), which demonstrates that the coupling between the 0; 1 superstrate diffraction order and D2 mode is highly dependent on the height, i.e., coupling becomes stronger with enhanced intensity and redshifts when height increases. Figure 3(b) shows that the LPM is located at 900 nm with lower intensity when h 300 nm. Decompositions of extinction spectra into scattering and absorption components are shown in Figs. 3(d)–
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3(f), in which absorption is calculated by σ abs d⊥ × d∥ × 1 − T − R and scattering is calculated by σ scat σ ext − σ abs For the LPM at 1169 nm displayed by the spectra shown in Fig. 3(d), scattering and absorption show nearly equal contributions when h 50 nm. However, the weight of absorption increases and becomes dominant when h 400 nm, indicating efficient suppression of radiative loss. Similar behavior is observed in the D1 mode without coupling (d∥ d⊥ 500 nm, not shown here), indicating suppression of radiative loss in the plasmonic mode is crucial for the associated LPM. Decomposition of LPM at 1000 nm is shown in Fig. 3(f) for h 400 nm and d⊥ 1000 nm, with the data from h 50 nm and d⊥ 1000 nm subtracted to eliminate the effect of D1 mode. The primary contribution of absorption is also obtained, suggesting the possibility of this LPM being applied to luminescence enhancement. It is emphasized that the coupling between the 0; 1 superstrate diffraction order and D2 mode is robust in the presence of a substrate, which could eliminate the restriction on NP size and environment index. The extinction spectra for core-shell NCAs with smaller diameters have been calculated to verify this supposition (Fig. 4). The coupling between the 0; 1 substrate diffraction order and D1 mode is weak when D 100 nm and almost vanishes when D 50 nm. However, strong coupling between the 0; 1 superstrate diffraction order and D2 mode is sustained, with coupling wavelength at 800 and 650 nm when D 100 nm and 50 nm, respectively. It indicates that this robust LPM allows tunability of the resonance wavelength to the visible range by controlling the NC diameter without index matching layer. Electromagnetic (EM) field distributions are summarized in Fig. 5. Considerable field enhancements are observed in E x distributions when LPMs are excited. Figure 5(a) shows the distribution of E x in the xz plane for the LPM at 1169 nm. The wavelength overlap between D1 and D2 modes determines that the field profile from D2 mode could not be eliminated. As the external electric field is orthogonal to the diffraction wave vector in our case, the radiative coupling could be confirmed in the distribution of H z . A similar vertical component of E z has been observed in the parallel LPMs reported in Ref. [18]. A standing-wave profile is obtained from the bottom side of the NCs into the substrate, which should be attributed to the interference of the diffraction waves along the y axis. The enhanced electric-field energy generated from D1 mode is converted into magnetic-
Fig. 4. Extinction spectra of the core-shell SiO2 ∕Au NCAs with h 400 nm and (a) D 100 nm, d∥ 400 nm and (b) D 50 nm, d∥ 300 nm.
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Fig. 5. E x amplitude in xz plane and H z amplitude in yz plane through the NC center with D 200 nm, d∥ 500 nm, h 400 nm and (a), (b) d⊥ 800 nm, λ 1169 nm; (c), (d) d⊥ 1000 nm, λ 1000 nm.
field energy and coupled with the diffraction wave for transfer. The hot spots at the top side of the NCs (D2 associated) are weak and show noncoupling with the diffraction wave, which further confirm the coupling origin of this LPM. The field distributions for the LPM at 1000 nm are shown in Figs. 5(c) and 5(d). The E x distribution shows intensive dipolar distribution on the top side along the NCs. The coupling behavior could also be confirmed in the H z distribution, which is different from the LPM at 1169 nm. The hot spots at the top side of the NCs are coupled with the 0; 1 superstrate diffraction wave, and no coupling behavior for the bottom hot spots is observed, which is consistent with the analysis above. In summary, SiO2 ∕Au core-shell NCAs were studied using FDTD simulations for generation of LPMs. In addition to the coupling between the 0; 1 substrate diffraction order and D1 mode, the increase of height induces new LSPR modes along the NCs, which could be coupled with the 0; 1 superstrate diffraction order. This LPM allows strong coupling in inhomogeneous environments even for NCs with much smaller diameters, which is important to improve the tunability of coupling wavelength. The coupling behavior could be confirmed by the EM field distributions, in which horizontal propagating H z is coupled with the hot spots from the NCs for energy transfer. Efficient suppression of the radiative loss is also observed for both of the LPMs, which is important for the future application in fluorescence enhancement or nanolaser. The coating of Au layer on the SiO2 NCAs would be crucial for the future fabrication. It is considered that employing template for protection of the spacing substrate and postcoating using physical vapor deposition or chemical deposition is available. It should also be noted that according to the coupling mechanism, perfect coating of Au layer is not required for generation of the D2 associated LPM, which is also important for practical applications. The authors would like to acknowledge the financial support from Demetra Energy, Europe and partial support from the University of Michigan.
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