Chapter 2 Simulation Method, Fabrication Process, and
2.4 Measurement Setup
Fig. 2.5 shows the configuration and photography of upright transmission spectroscopy. Light from a halogen lamp was polarized by a polarizer, collimated and focused by a 20x objective lens on the sample at normal incidence. Alignment between the incident light and the sample can be adjusted by 3-axes stage where the sample is mounted. This adjustment can be monitored by the projection of the pattern on a simple screen. Output signal was collected by another 20x objective lens and coupled into multimode fiber (MMF), which was finally analyzed by an optical spectrum analyzer (OSA). The extinction spectra as shown in the following are given by –log (P/P0), where P and P0 are the power of transmitted light with and without passing through the patterns.
On the other hand, in order to investigate the optical sensing performance of these devices, we change the environmental refractive index of elliptical gold nanodisk and nanoring by immersing the fabricated device in index match liquid (n = 1.3~1.39), and obtaining their transmission spectra by the upright transmission spectroscopy.
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Figure 2.5: (a) Photography and (b) configuration of upright transmission spectroscopy. (c) Partial enlarged detail of upright transmission spectroscopy.
2.4 Summary
In this chapter, we introduced the fundamental theory of finite element method for our simulations. And we described the nano-fabrication processes for realizing the elliptical gold nanoring, which are composed of e-beam lithography, thermal evaporation, and lift-off. Finally, we described the configuration of upright transmission spectroscopy and the method of sensing performance measurement of fabricated devices.
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Chapter 3 Optical Properties of Plasmonic Modes in Elliptical Gold Nanoring
3.1 Introduction
In this chapter, the optical responses of elliptical nanostructure with different aspect ratios are investigated. The elliptical gold nanodisc, nanohole and nanoring are simulated for comparison under longitudinal and transverse polarizations. The plasmonic properties of elliptical gold nanoring are understood by the combination of plasmonic behaviors with elliptical gold nanodisc and nanohole. In addition, we also fabricated the elliptical gold nanodisc and nanoring arrays and analyzed their optical responses. The resonance wavelength and mode profiles are studied for understanding plasmons behavior of elliptical nanostructure with gradually varied aspect ratio.
Finally, the plasmon hybridization of elliptical gold nanoring is discussed.
3.2 Elliptical Nanodisc
In simulation, the fixed short-axis dimension Ly and the height t of elliptical nanodisc are set to be 275nm and 50 nm. The aspect ratio R which is defined as the length of long axis divided by the length of short axis is varied from 1 to 1.58 by elongating the long-axis dimension Lx, as shown in Fig. 3.1. The surrounding medium is assumed to be air. We use the Lorentz-Drude model to describe the gold dielectric function and consider the dispersion of ITO. Incident plane waves of power 1 W and
Figure 3.1: Scheme of elliptical gold nanodisc.
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Figure 3.2: Simulated extinction spectra of elliptical gold nanodisc with varied aspect ratio under (a) longitudinal and (b) transverse polarizations.
wavelength ranges from 400 to 1700 nm are employed to excite the elliptical gold nanodisc. The incident electric field parallel to the long axis is defined as longitudinal polarization, and another direction perpendicular to the short axis is defined as transverse polarization.
The simulated extinction spectra of elliptical gold nanodisc for longitudinal and transverse polarizations are shown in Fig 3.2. Under longitudinal polarization, the distinct dipole mode red shifts with broaden band width as the aspect ratio is increased. However, it blue shifts slightly under transverse polarization. These results are confirmed with previous experiment [28]. To indentify the plasmon modes of
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elliptical gold nanodisc, we simulated the mode profiles with vector field are shown in Fig 3.3. The multipole plasmon of the elliptical gold nanodisc has been studied in previous studies [28]. It indicates that high order modes can be excited by elongating the nanodisc for both longitudinal and transverse polarizations.
Figure 3.3: Simulated mode profiles with vector field and charge distribution of elliptical gold nanodisc under (a) longitudinal and (b) transverse polarizations at aspect ratio R = 1.58.
The measured extinction spectra of elliptical gold nanodisc with different aspect ratios for longitudinal and transverse polarizations are verified by the simulated result, as shown in Fig. 3.4. The peak wavelengths of dipole modes show the red-shift and blue-shift behaviors for longitudinal and transverse polarizations. The red shift of high order mode is also observed in experiment.
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Figure3.4: Measured extinction spectra of elliptical gold nanodisc with varied aspect ratio under (a) longitudinal and (b) transverse polarizations.
3.3 Elliptical Nanohole
For the elliptical gold nanohole, the fixed short-axis dimension Ly and the height t are set to be 125 nm and 50 nm in our simulation. The aspect ratio R is varied from 1 to 2.28 by elongating the long-axis dimension Lx, as shown in Fig. 3.5. For metal thin film, the transmission or scattering intensity are studied for searching the resonance wavelength usually. Figure 3.6 shows the behavior of resonance wavelength
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completely opposite to the case of elongated metal particles. A simple analytical model qualitatively explains this observation in terms of the different orientations of the induced dipole moments in holes and particles [29]. The charge distribution of induced dipole in metal film for nanohole is opposite to that of induced dipole for the metallic nanoparticle with the same size. This effect changes not only the trend of peak wavelength shift but also the behavior of amplitude for scattering light [29].
Figure 3.5: Scheme of elliptical gold nanohole.
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Figure 3.6: Simulated extinction spectra of elliptical gold nanohole with varied aspect ratio under (a) longitudinal and (b) transverse polarizations.
The cavity mode is shown in Fig. 3.7. The mode profile indicates that the field intensity of transverse mode is stronger than that of longitudinal mode. In addition, the vector field of cavity mode is plotted for studying the dipole oscillation. The charge distribution of induced cavity mode for nanohole is opposite to that of induced dipole mode for nanodisc by studying the direction of electromagnetic field.
Figure3.7: Simulated mode profile with vector field and charge distribution of elliptical gold nanohole under (a) longitudinal and (b) transverse polarizations at aspect ratio R = 2.28.
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3.4 Elliptical Nanoring
Fig. 3.8 shows the scheme of elliptical gold nanoring with uniform ring width W, fixed short axis Ly and varied long axis. For elliptical gold nanoring in simulation, uniform ring width W, fixed short-axis dimension Ly and thickness are set to 150, 200 and 50 nm. The aspect ratio is varied from 1 to 1.58 in simulation. The extinction spectra are obtained for longitudinal and transverse polarizations in Fig. 3.9. By gradually elongated the gold nanoring, resonance modes red shift for both longitudinal and transverse polarizations. This phenomenon can be described by plasmon hybridization which is presented as the disc-like behavior under longitudinal and cavity-like behavior under transverse polarization.
Figure 3.8: Scheme of hybridized elliptical gold nanoring
Interestingly, there is only two mode at R=1 aspect ratio which are identified as bonding and antibonding modes. However, there are four plasmonic modes at R=1.58 under both longitudinal and transverse polarization, as shown in Fig. 3.10. The plasmonic high order mode can be induced by elongated the nanostructure under both longitudinal and transverse polarizations. The second-order hexapolar antibonding mode around 680nm is induced by the ring width effect which breaks the symmetries of elliptical gold nanoring in appendix A. These plasmonic modes are the result of coupling between inner and outer surfaces by the interaction of plasmon hybridization, which is introduced in next section.
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Figure 3.9: Simulated extinction spectra of elliptical gold nanoring with varied aspect ratio under (a) longitudinal and (b) transverse polarizations.
Figure 3.11 shows the extinction spectra for longitudinal and transverse polarizations with different aspect ratios R from 0.95 to 1.54. Under longitudinal polarization, there are two plasmonic modes at R = 0.95 and R = 1.11, which are bonding and antibonding mode. As the aspect ratio is 1.27, there are two plasmonic modes which are bonding and hexapolar antibonding mode. For R = 1.43 and R = 1.54, the additional two plasmonic modes are induced, which are hexapolar bonding and second-order hexapolar antibonding modes. Under transverse polarization, the bonding and antibonding mode are observed at R = 0.95 and R = 1.11. As the aspect ratio is 1.27, there are two plasmonic modes which are bonding and dipolar antibonding mode. For R = 1.43, the additional plasmonic mode is induced, which is quadrupolar antibonding mode. For R = 1.54, the hexapolar bonding mode is appeared. These modes will be discussed in detail by the concept of plasmon hybridization in next section
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Figure 3.10: Simulated mode profile with vector field of elliptical gold nanoring under (a) longitudinal and (b) transverse polarizations at aspect ratio R = 1.58.
Figure 3.11: Measured extinction spectra of elliptical gold nanoring with varied aspect ratio under (a) longitudinal and (b) transverse polarizations.
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3.5 Characterization of Plasmon Hybridization in Elliptical Gold Nanoring
The plasmon hybridization for elliptical gold nanoring is similar with spheroid nanoshell. The energy level diagrams are shown in Fig. 3.12 for longitudinal and transverse polarizations. For the plasmonic properties under longitudinal polarization, the plasmon energy of bonding mode is close to the energy of nanodisc so the plasmonic properties of elliptical gold nanoring are dominated by disc mode. On another hand, the plasmon energy of antibonding mode is close to the energy of nanohole so the plasmonic properties of elliptical gold nanoring are dominated by cavity mode. For the plasmonic properties under transverse polarization, the plasmon energy of bonding mode is close to the energy of nanohole so the plasmonic properties of elliptical gold nanoring are dominated by cavity mode. In addition, the plasmon energy of antibonding mode is close to the energy of nanodisc so the plasmonic properties of elliptical gold nanoring are dominated by cavity's mode.
These optical behaviors of plasmon hybridization are shown in the resonance wavelength, mode profile and field enhancement.
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Figure 3.12: An energy level diagram of plasmon hybridization in elliptical gold nanoring for (a) longitudinal and (b) transverse polarizations.
3.5.1 Disc-like Optical Properties of Elliptical Gold Nanoring
The plasmonic behavior of elliptical gold nanoring with different aspect ratios under longitudinal polarization is similar with that of dipole mode for elliptical
Figure 3.13: Peak wavelength-shift trend of elliptical gold nanodisc, nanohole and nanoring with varied aspect ratio under longitudinal polarization.
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Figure 3.14: Mode profile with vector field for (a) bonding mode of elliptical gold nanoring and (b) dipole mode of elliptical gold nanodisc with different aspect ratios under longitudinal polarization.
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gold nanodisc. This optical behavior is described in resonance wavelength shift. Fig.
3.13 shows red-shift of bonding mode of elliptical gold nanoring as the aspect ratio is increased also in elliptical gold nanodisc. In addition, high order mode of elliptical gold nanoring and nanodisc are appeared as the aspect ratio is increased. These optical properties of elliptical gold nanoring and nanodisc are similar because the plasmon energy of longitudinal bonding mode is close to that of dipole mode of nanodisc. For vector field distribution, the plasmon mode of elliptical gold nanoring is compared with that of nanodisc in Fig. 3.14. For bonding mode under longitudinal polarization, the nanodisc mode dominated behavior is observed from R = 1.29, which the vector field in the region of metal is the same as that of elliptical nanodisc and the field distribution is similar with the plasmonic modes of elliptical nanodisc. For antibonding mode under transverse polarization, the plasmonic property is dominated by nanodisc mode in both vector field and field distribution. However, the antibonding mode under transverse polarization would be introduced in 3.5.3.
3.5.2 Cavity-like Optical Properties of Elliptical Gold Nanoring
Figure 3.15: Peak wavelength-shift trend of elliptical gold nanodisc, nanohole and nanoring with varied aspect ratio under transverse polarization.
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Figure 3.16: Mode profile with vector field for (a) bonding mode of elliptical gold nanoring and (b) cavity mode of elliptical gold nanohole with different aspect ratios under transverse polarization.
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The plasmonic behavior of elliptical gold nanoring with different aspect ratio under transverse polarization is similar with that of cavity mode for elliptical gold nanohole, as shown in Fig. 3.15. However, the optical spectra of elliptical gold nanohole with different aspect ratios show red shifts because the plasmon oscillation of cavity mode is different with dipole mode’s behavior. The plasmonic properties of nanohole have been investigated by B. Sepulveda in the experiment and simulation which are mentioned before [29]. For mode profile with vector field, the transverse bonding mode of elliptical gold nanoring is compared with the cavity mode of nanohole, as shown in Fig. 3.16. For bonding mode under transverse polarization, the plasmonic properties of elliptical gold nanoring is similar with that of elliptical gold nanohole mode from R=1.43. The vector field of transverse bonding mode is the same as that of cavity mode in the region of metal and the field distribution is similar with the plasmonic modes of elliptical nanohole. For antibonding mode under longitudinal polarization, the plasmonic properties are similar with with that of cavity mode for elliptical gold nanohole in both vector field and field distribution. The mode profile with vector field of antibonding mode under transverse polarization would be introduced in next section.
3.5.3 Plasmon Hybridization in High-order Mode
As the aspect ratio is increased, the high order mode would be induced in both longitudinal and transverse polarizations. These high-order mode profiles are varied with different aspect ratio because the plasmon interaction between the inner and outer surface of elliptical gold nanoring is changed with plasmon coupling of different plasmonic modes. For the hexapolar bonding mode, the plasmon hybridization can be seen as the coupling between high order elliptical disc mode and cavity mode in mode profile, as shown in Fig. 3.17. The extinction spectrum shows the splitting of antibonding mode into two modes since the aspect ratio is at R=1.29 in both longitudinal and transverse polarizations in Fig. 3.18 (a) and Fig. 3.19 (a).For the longitudinal antibonding mode, the plasmon coupling is different due to varied
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plasmonic mode relative with different aspect ratios, as shown in fig. 3.18. At R=1,
Figure 3.17: High order bonding mode profile with vector field distribution for (a) longitudinal and (b) transverse polarization at R=1.58.
The dipole mode of nanodisc couples with the cavity mode. As the nanostructure is elongated, the hexapole mode or the second-order hexapole mode couples with cavity mode, which results in the hexapolar antibonding mode or second-order hexapolar antibonding mode. For the transverse antibonding mode, the plasmon coupling is also
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different due to varied plasmonic mode relative with different aspect ratio, as shown
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Fig. 3.18: (a) Extinction spectra of simulation and experiment for antibonding mode with different aspect ratios under longitudinal polarization. Mode profile of plasmon hybridization for (b) antibonding mode at R=1, (c) hexapolar antibonding at R=1.29, and (d) second-order hexapolar antibonding mode at R=1.29.
in fig. 3.19. At R=1, the dipole mode of nanodisc couples with the cavity mode. As the gold nanoring is elongated, the second-order dipole mode or the quadruple mode couples with cavity mode, which results in the hexapolar antibonding mode and second-order hexapolar antibonding mode.
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Fig. 3.19: (a) Extinction spectra of antibonding modes for simulation and experiment under transverse polarization. Mode profile of plasmon hybridization in (b) antibonding mode at R=1, (C) dipolar antibonding at R=1.29, and (d) quadrupolar antibonding at R=1.29.
3.6 Electric Field Enhancement
The near field is enhanced within the region nearby the surface of plasmonic nanostructure. However, the enhanced electric field can be tuned by the parameters, as shape, aspect ratio and other geometry factors. For recently studies, the field intensity enhancement of spheroid nanoshell is studied by tuning the aspect ratio [11]. The electric field intensity of spheroid nanoshell at aspect ratio R = 4 is enhanced around 400 fold relative to that of the ambient field. For our study, electric field enhancement is calculated for elliptical gold nanodisc and nanoring with different aspect ratios. The field intensity enhancement is defined as the field at monitor (EO) divided by the ambient field (EI). We select one monitor for and two monitors for elliptical gold nanodisc and nanoring. Under longitudinal polarization, the electric field intensity is increased as the aspect ratio is increased in elliptical gold nanodisc and nanoring.
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Fig. 3.20: A two dimensional spatial profile of the electric field intensity for elliptical gold (a) nanodisc and (b) nanoring with varied aspect ratio under longitudinal polarization. (c) The field intensity enhancement (EO/EI) as the function of aspect ratio for elliptical gold nanodisc and nanoring under longitudinal polarization.
The maximum field intensity enhancement under longitudinal polarization is up to 13.5 and 14.2 at R = 1.58 for elliptical gold nanodisc and nanoring respectively, as shown in Fig. 3.20. Furthermore, the field intensity enhancement of elliptical gold nanoring under longitudinal polarization is higher than that of elliptical gold nanodisc
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Fig. 3.21: A two dimensional spatial profile of the electric field intensity for elliptical gold (a) nanodisc and (b) nanoring with varied aspect ratio under transverse polarization. (c) The field intensity enhancement (EO/EI) as the function of aspect ratio for elliptical gold nanodisc and nanoring under transverse polarization.
due to coupling between the inner and outer surface plasmons. For disc-like optical properties, the field intensity enhancement at outer surface of elliptical gold nanoring is near that of elliptical gold nanodisc at large aspect ratio.
Under transverse polarization, the monitor at the inner surface of elliptical gold nanoring is studied for electric field intensity of the transverse bonding mode. The electric field intensity is increased as the aspect ratio is increased in elliptical gold
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nanoring due to the strong cavity mode induced by enlarging the region of hole inside the elliptical gold nanoring. However, the electric field intensity is decreased as the aspect ratio is increased in elliptical gold nanodisc, as shown in Fig. 3.21. This factor results in the different sensing performance which is discussed in chapter 4.
3.7 Summary
We simulated the optical properties of elongated nanostructure including elliptical gold nanoring, nanodisc and nanohole. The aspect ratio dependent optical properties were investigated under longitudinal and transverse polarizations.
Interestingly, the optical property of elliptical gold nanoring is disc-like or cavity-like at different condition, including polarization, aspect ratio and energy level. The shift trend of resonance wavelength shows red shift as the nanostructure is elongated in both longitudinal and transverse polarizations. It can be explained by plasmon hybridization as the interaction of disc and cavity mode. In addition, the mode profile with vector field is studied for understanding plasmon hybridization in elliptical gold nanoring. The induced longitudinal second-order hexapolar antibonding mode and transverse quadrupolar antibonding mode are attributed to the interaction of high order disc mode and cavity mode since R=1.29 aspect ratio. Furthermore, the electric field intensity enhancement is calculated for elliptical gold nanodisc and nanoring.
The results show that the field intensity enhancement of elliptical gold nanoring is increased under both longitudinal and transverse polarizations. In addition, bonding mode is stronger than dipole mode due to the coupling between the inner and outer surface plasmons.
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Chapter 4 Index Sensing Properties of Elliptical Gold Nanoring
4.1 Introduction
In this chapter, we simulated the optical sensing performance by changing the environmental refractive index of the elliptical gold nanostructure. Both the sensitivity and figure of merit (FOM) are discussed, including elliptical gold nanodisc and nanoring. In addition, the experiment has been done to confirm the simulation result by immersing the samples into different environments.
4.2 Index Sensing Performance of Elliptical Gold Nanoring
There is a red shift in the plasmon resonance wavelength of metallic nanoparticles [30][31] as the medium refractive index is increased since the Coulombic restoring force acting on the polarized charges is reduced in the higher refractive index medium [22]. The refractive index sensitivity of a particular nanoparticle is usually reported in nanometers of peak shift per refractive index unit (nm/RIU). Fig. 4.1 shows a plot of the simulated dipole mode wavelength of elliptical nanodisk as a function of the refractive index of surrounding medium. When the
There is a red shift in the plasmon resonance wavelength of metallic nanoparticles [30][31] as the medium refractive index is increased since the Coulombic restoring force acting on the polarized charges is reduced in the higher refractive index medium [22]. The refractive index sensitivity of a particular nanoparticle is usually reported in nanometers of peak shift per refractive index unit (nm/RIU). Fig. 4.1 shows a plot of the simulated dipole mode wavelength of elliptical nanodisk as a function of the refractive index of surrounding medium. When the