Narrowing Plasmon Resonance Linewidth of Au Nanodome Lattices

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Narrowing Plasmon Resonance Linewidth of Au Nanodome Lattices Jinlin Zhang, Woo Ri Ko, Fei Long, Min Hyung Lee, and Jae Yong Suh ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b09003 • Publication Date (Web): 18 Oct 2017 Downloaded from http://pubs.acs.org on October 19, 2017

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ACS Applied Materials & Interfaces

Narrowing Plasmon Resonance Linewidth of Au Nanodome Lattices Jinlin Zhang†, Woo Ri Ko§, Fei Long‡, Min Hyung Lee§*, Jae Yong Suh†* † Department of Physics, Michigan Technological University, Michigan, 49931, USA § Department of Applied Chemistry, Kyung Hee University, Yongin, Gyeonggi 17104, Korea ‡ Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, Michigan, 49931, USA Corresponding Authors: *E-mail: [email protected]. *E-mail: [email protected].

ABSTRACT Gold hollow nanodomes arranged in hexagonal lattices support surface plasmon polaritons (SPPs) propagating at air-Au interface. The cross section heights of the continuous and hierarchical hexagonal nanodome arrays can be altered by a simple thermal treatment, and the change in nanodome size leads to a significant linewidth narrowing of plasmon resonance because of reduced scattering loss. Taking the variation in the SPP intensities into account, the surface modulation depth is found to be around 100 nm for achieving a longer propagation length of SPP. KEYWORDS: hollow nanodomes, surface plasmon polaritions (SPPs), scattering cross section, resonance linewidth, surface modulation depth

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INTRODUCTION Noble metal nanostructures have been a rapid expansion in a wide range of fields, such as nanophotonics, nanoelectronics, catalysis, and biomedicine thanks to their rich and tunable optical properties at the visible and near-infrared frequencies.1, 2 Plasmonic metal nanoparticles in a dielectric surrounding exhibit strong scattering and absorption when excited by external light. Surface plasmons (SPs), collective oscillations of free electrons confined at metaldielectric interface, are typically categorized into two distinct forms: localized surface plasmons (LSPs) and surface plasmon polaritons (SPPs).3 LSPs are non-propagating electromagnetic mode excited at discrete or isolated metal nanostructures. In contrast, SPPs excited on continuous metallic gratings can propagate on the metal surface until the energy dissipates by either heat loss or by radiation into free space, and thus they exhibit dispersive curves with a certain resonance linewidth in the energy-momentum relation.4, 5 A key issue in the applications of SPs is the large material loss (i.e. Ohmic loss) that is hardly controllable since it is related to intrinsic non-radiative damping. SPP scattering, on the other hand, is considered as another loss that contributes to broadening the linewidth (full-width-at-half-maximum, FWHM) of the resonance.6 Thus, the total loss consists of Ohmic loss and scattering loss, given as 1/ τtot = 1/τohmic + 1/τscat where τtot, τohmic, and τscat correspond to the decay times of the total, Ohmic, and scattering losses.7 Hence, a smaller loss of SPP energy appears as a narrowed linewidth implying a longer lifetime of SPP, which is important for sensors,4, 8 nanocircuits,9-10 and plasmonic laser.11


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Mie theory explains how the light extinction spectra including scattering and absorption depend on the size of spherical nanoparticles.12 For spherical particles, the scattering efficiency of particles is given by Qs = σs/πr2 where σs and r are the scattering cross-section and radius of particles, respectively. In the Rayleigh (quasistatic) scattering, Qs is proportional to (r/λ)4, implying that the cross-section σs is proportional to (r/λ)6.12-14 The relationship between scattering and particle size can also be applicable to the nano-patterned continuous metal film. Roland et al. have shown that the scattering efficiency is approximated with the fourth power of the hole size (r4) in the metal film.7 Hiramatsu et al. have investigated the propagation length of SPPs depending on the gold surface morphology and scattering in the mid-infrared range.15 Additionally, it has been reported that the ratio of scattering loss and absorption can be tuned by the height of core-shell SiO2/Au nanocylinder arrays by theoretical simulations.16, 17 In this paper, we first show that a thermal annealing can alter the surface profile of the Au hollow nanodome array film. This simple thermal treatment greatly affects the spectral property of SPPs because of the changes in the size and surface curvature of the nanodomes, which are directly related to the surface modulation depth and thus the scattering cross-section of propagating SPPs. The hollow nanodome array allows a large shrinkage of nanodome volume upon annealing whereas solid nanorods undergo only shape changes. With a reduced height of Au nanodomes, the linewidth of the plasmon resonance decreases due to the reduction in the scattering loss as SPPs propagate on the modulated surface. Importantly, the steady-state SPP intensities measured in reflection and transmission spectra also change upon annealing since the excitation efficiency of SPP strongly depends on the modulation depth. Thereby, an optimized modulation depth (i.e. cross section height of the nanodome) of sample surface exists such that the SPP lifetime is maximized in a two-dimensional (2D) grating nanostructure. In our previous



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report, Au nanodome films were shown to support strong SPPs and interfacial mode coupling.5 Here, we show how narrow resonances in the light transmission and reflection from the Au hexagonal nanodome arrays can be achieved by modifying the surface geometry while maintaining the periodicity of the arrays. RESULTS AND DISCUSSION Two types of hexagonal arrays of Au hollow nanodomes with a long-range order (> 1cm) were fabricated using the templates of periodic nanodomes formed by anodized aluminum oxide (AAO) nanopores. For the sample type Ι, long-range ordered AAO template was fabricated by imprinting a Si stamp of 500 nm spacing hexagonal nanopillars onto polished Al, followed by anodizing in 1 wt% phosphoric acid at an applied voltage of 195 V for 10 minutes. Next, Al was selectively etched in a solution of CuCl2·2H2O:HCl:H2O (3.4:100:100; g:v:v) at 2 °C to expose the nanodome AAO membranes. As-prepared AAO membranes were used as Au deposition templates to create Sample Ι. For fabricating hierarchical nanodome AAO (templates for sample type II), additional pore-opening step was carried out to etch the AAO from the nanodome side using 5 wt% phosphoric acid at 50 °C for 15 minutes. Plasmonic crystals were prepared by depositing 50 nm thick Au on each AAO template. This fabrication method is described in detail in our previous report.5 Figure 1 shows atomic force microscopy (AFM) images (upper panels) of the two structures, and their corresponding cross section height data (lower panels) of unannealed (Fig. 1a, c) and annealed samples (Fig. 1b, d). For annealing, both samples were heated at 200 °C for 30 minutes in air on a hotplate, and were gradually cooled down to room temperature. It is evident from the cross section height data that the nanodome volume decreases via the annealing treatment as both structures maintain their periodicities. The AFM images of


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unannealed and annealed hexagonal Au nanodome array with thickness 50 nm (Sample Ι) (Fig. 1a, b upper panels) display that hexagonal nanodomes are packed closely (See Fig. S1a for scanning electron microscope (SEM) image); meanwhile, cross section SEM image shows the detail of Au hollow nanodome structure (inset of Fig. S1a), and the center-to-center distance between two adjacent nanodomes (periodicity) is 500 nm. For Sample Ι, the average cross section height changed from Z = 155 nm (Fig. 1a low panels) to 105 nm (Fig. 1b low panels) by annealing. The diameter of hexagonal Au nanodomes also decreases by 20%, indicating that the nanodome surface is slightly flattened. In contrast, hierarchical Au hexagonal nanodome array with thickness 50 nm (Sample II) has an elliptical nanorod in between two adjacent Au nanodomes (Fig. 1c, d upper panels). The hollow Au nanodomes of Sample II are connected by Au nanorods, which exist underneath the elliptical nanorods in a perpendicular direction (Fig. S1b). As the average cross-section height changes Z from 120 nm to 35 nm due to the volume shrinkage of the hollow nanodomes, the solid nanorods in cross directions in between nanodomes coalesce into single nanorods. Hence, after annealing, Sample II appears to be a continuous honeycomb structure with smaller scattering centers located at hexagonal lattice points. Noticeably, the quality degradation in Sample II is observed, which is partially responsible for the reduction in SPP intensity. Figure 2a shows the experimental reflection dispersion map of Sample Ι with p-polarized broadband light of incidence angles θ from 5° to 60°. When p-polarized light is incident on Au nanodome array films with angle (θ) and azimuthal angle (φ), the dispersion of the SPP-Bloch wave modes can be characterized under the Bragg coupling condition.18

(1)



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where ω and c are the angular frequency, speed of free space light, k0 is the momentum of light with incident angle θ and azimuthal angle φ. The reciprocal vectors are given by

and where a is the primitive vectors for a hexagonal lattice, and i and j are integer pairs associated with specific SPP modes of the wave vector kspp. εd and εm are the frequencydependent electric permittivity of the adjacent dielectric medium and metal (Au). The major (-1, 0) SPP mode is most dispersive among other SPP modes, and moves to longer wavelengths with increasing incident angle (Fig. 2). The corresponding transmission dispersions were also measured with incidence angle from 0 to 60° (Fig. S2a, b). Individual reflection spectra show an asymmetric Fano line-shape where a large resonance dip is found at the lower energy side of the (-1, 0) SPP-Bloch mode (white solid line in Fig. 2a, b). The Fano lineshape is, in general, a result of the spectral interference between a narrow discrete resonance and a scattering towards a broad continuum.14, 19 In our case, the discrete resonance is the SPPs excited on the periodic nanodome array while the continuum state corresponds to the non-resonant scattering of the SPP into free space.20 After annealing, the reflectivity (%R) at the dip wavelength remains almost the same as that of unannealed sample; however, the relative peak intensity appears to increase since the background reflection substantially increases despite of the less areal density of the nanodomes (Fig. 2c). Most importantly, the linewidth of the resonance dip is significantly reduced upon annealing. The linewidth narrowing occurs only toward the small peaks at the shorter wavelengths that are associated with the (-1, 0) SPP mode. The wavelengths of the small peaks following the Bragg coupling condition stay nearly the same because the array periodicity does not change before and after annealing. Small degree of the blue-shift of the SPP resonances, however, can be attributed to the phase-retardation effect as a result of the reduced cross section height.16 The quality factors Q = λ/ ∆λ, where λ is the resonance center wavelength and ∆λ is 6 Environment ACS Paragon Plus

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FWHM of Fano lineshape, increase by a factor of 1.5~2 at the four representative angles (Fig. 2c). The FWHM is a fit result of the experimental curves to the Breit-Wigner-Fano equation.21 These experimental Q factors of the SPPs excited on continuous unannealed lattices remain below 20, but enhances up to 50 after annealing owing to the smaller nanodome size that reduces the scattering loss of the SPPs along the (-1, 0) mode. For Sample II, in order to demonstrate the narrowed linewidth, the reflection dispersions were measured with a rotated azimuthal angle φ = 5° of incidence, relative to the major crystal axis of the hexagonal lattice (Fig. 3a, b). With this azimuthal angle, the degenerate (-1, 0) SPP mode at air-Au interface is split into two, forming double SPP modes. These split SPP modes are also observed in the transmission dispersions (Fig. S2c, d). Similarly, the linewidths of the major (-1, 0) and (0, -1) SPP modes from annealed Sample II are found to be much narrower than those from unannealed one, indicating again the reduction in scattering loss (Fig. 1c, d). The Q factor of the (-1, 0) SPP mode of annealed Sample II is enhanced up to 143 at an incidence angle of 60°, which is about 7 times larger than those of unannealed sample II (Fig. 3c). The large enhancement of Q factor in Sample II can be qualitatively explained by the relatively large reduction of cross section height Z of the Au nanodomes, compared to the size change of Sample I. The nanodome radius of Sample II reduced by one half leads to the even higher enhanced Q factor although the quartic relationship between the scattering cross section and particle radius could be only applicable in the Rayleigh limit (r ≥ λ/2). However, as opposed to the case of Sample I, the absolute SPP intensities are about twice smaller than those from Sample I. This decrease in the relative SPP intensity is expected to occur at the size regime for Sample II as analyzed with finite-difference time-domain (FDTD) calculations. Also, the small resonance intensity can be partially attributed to the quality degradation caused by the annealing. As shown



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in Figure 1d, Sample II undergoes some structural changes including missing and irregular nanodomes, and broken elliptical nanorods. To confirm the linewidth narrowing of the SPP modes at air-Au interface via cross section height reduction of hexagonal nanodomes, we calculated the transmission and reflection dispersions using FDTD method (Lumerical Inc.) (Fig. 4).5 The dielectric constants of gold were taken from Johnson and Christy.22 The Bloch boundary conditions that correct the phase mismatch with broadband illumination were introduced in the x and y directions of the simulation region to calculate the angle-dependent transmittance and reflectance. For the continuous Au hexagonal nanodome array (Sample I), we varied surface cross-section height Z from 64 to 175 nm (Fig. 4, Fig. S3). The calculated reflections of cross-section heights Z = 155 (Fig. 4 left panel) and 105 nm (Fig. S3c), and the experimental ones (Fig. 2a, b) show excellent agreement in the resonance wavelength and the overall trend in linewidth narrowing. Slight differences in transmission and reflection amplitudes are attributable to minor imperfections in the Au samples such as the small Au nanoparticles residing on the nanodomes, which exist only in the real samples. In transmission spectra, the disappearance of SPP near normal incidence angles is caused by the mode crossing between air-Au and Au-glass interfaces.5 The linewidths of the SPP mode become narrower with decreasing cross-section height Z in both transmission and reflection dispersions (Fig. 4, Fig. S3). Furthermore, the SPP modes slightly blue-shift with decreasing Z (Fig. S4), which confirms the observation from the experimental results (Fig. 2c). While the Q factors monotonically increase with smaller scattering centers, we find the two size regimes for the surface modulation depth that determines the behavior of the SPP resonance intensity. Figure 5 shows the changes in the simulated reflection intensity and linewidth for the (1, 0) SPP mode of Sample I with varying cross section height Z at an incidence angle of θ = 36°.


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With increasing nanodome height above 120 nm, the integrated intensities reach to a saturation point and then exhibit a slight decrease by about 10% (Fig. 5 (a) and (b)). The existence of this maximum in the resonance intensity with increasing nanodome height can be understood from the fact that the SPP excitation occurs predominantly below the skin depth of the metal surface. In the size regime below 120 nm, however, the SPP intensities rapidly drop with decreasing nanodome height both in the reflection and transmission spectra. These two different sizedependences agree with the changes in the experimental integrated intensities of the two types of Au nanodome arrays before and after annealing. Thereby, Sample I falls in the regime of large nanodome size (> 120 nm, Size regime II) so that the SPP intensity markedly increases with the height change from 155 nm to 105 nm upon annealing (Fig. 2c). In contrast, Sample II is in the size regime of small nanodomes (< 120 nm, Size regime I); therefore, the resonance intensity substantially drops with the diminished nanodome height from 120 nm to 35 nm upon annealing (Fig. 3c). Meanwhile, the associated Q factor of the SPPs only enhances with decreasing height, regardless of the size regimes that affect the resonance intensities at the SPP wavelengths. These two factors (Ires integrated intensity and Q-factors) are independent each other as Ires is related to the initial SPP excitation efficiency while Q is the scattering loss of the propagating SPP after excitation. The effective propagation length of SPP wave inside the modulated sample surface can be assumed to be linearly related to both the resonance intensity and linewidth, respectively. On a non-modulated metal surface, the SPP propagation length (LI) is given by LI =

1 2 Im k x

,

where the absorption coefficient of metal is included in the complex plasmon wave vector kx.23 And the Q-factors on such smooth metal surfaces can thus be calculable from the dielectric constants,24 which could vary depending upon the film processing conditions.25 For corrugated or nano-patterned surfaces, the propagation of SPPs is governed by both the internal Ohmic loss



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and scattering loss, which means that the propagation length can be further diminished. In our case, however, that the actual measurement of propagation length is not feasible since the excitation light is illuminated globally on the semi-infinite nano-patterned area. Given our calculated data (Fig. 5), we conclude that the cross point where the two lines for the Q factor and SPP intensity intersect, gives an optimized cross section height of Au nanodomes (Z = 105 nm) for a maximized SPP propagation length inside the patterned area. The values of Q-factor (> 140) found in Size regime I is at a maximum level that is achievable with the SPP modes in continuously-modulated plasmonic lattices. CONCLUSION In summary, we successfully demonstrated that SPP modes at air-Au nanodome interfaces can have narrower linewidths by simple thermal treatment, accompanying the size reduction of the hollow nanodomes and the reduced surface curvature. The enhanced Q factors of the SPP resonances originate from suppressed SPP scattering, supported by electromagnetic calculations. The two size regimes found in this study indicate that the surface modulation depth for a longer propagation length should be controlled at the length scale around 100 nm. By incorporating quantum emitters nearby, we expect that these unique periodic structures supporting narrowed plasmonic resonances may be used to study light-matter interactions on a large surface area. ASSOCIATED CONTENT The Supporting Information is available free of charge on the ACS Publications website at DOI: SEM images of the structures of samples; the experimental transmission dispersions maps; FDTD calculated reflection and transmission dispersions maps; and FDTD reflection and transmission spectra of Sample Ⅰ.


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ACKNOWLEDGEMENTS This research was supported by a research seed grant from the Vice President for Research at Michigan Technological University. This work was also supported by the Basic Science Research Program of the National Research Foundation of Korea, funded by the Ministry of Education (Grant NRF-2017R1A2B4007641). REFERENCES 1. Zhang, N.; Han, C.; Xu, Y.-J.; Foley Iv, J. J.; Zhang, D.; Codrington, J.; Gray, S. K.; Sun, Y., Near-Field Dielectric Scattering Promotes Optical Absorption by Platinum Nanoparticles. Nat. Photonics 2016, 10, 473-482. 2. Brongersma, M. L.; Kik, P. G., Surface Plasmon Nanophotonics. Springer:Berlin, 2007. 3. Maier, S. A., Plasmonics: Fundamentals and Applications. Springer :Berlin, 2007. 4. Barnes, W. L.; Dereux, A.; Ebbesen, T. W., Surface Plasmon Subwavelength Optics. Nature 2003, 424, 824-830. 5. Ko, W. R.; Zhang, J.; Park, H.-H.; Nah, J.; Suh, J. Y.; Lee, M. H., Interfacial Mode Interactions of Surface Plasmon Polaritons on Gold Nanodome Films. ACS Appl. Mater. Interfaces 2016, 8, 20516-20521. 6. Gao, H.; McMahon, J. M.; Lee, M. H.; Henzie, J.; Gray, S. K.; Schatz, G. C.; Odom, T. W., Rayleigh Anomaly-Surface Plasmon Polariton Resonances in Palladium and Gold Subwavelength Hole Arrays. Opt. Express 2009, 17, 2334-2340. 7. Müller, R.; Malyarchuk, V.; Lienau, C., Three-Dimensional Theory on Light-Induced Near-Field Dynamics in A Metal Film with A Periodic Array of Nanoholes. Phys. Rev. B 2003, 68, 205415. 8. Tetz, K. A.; Pang, L.; Fainman, Y., High-Resolution Surface Plasmon Resonance Sensor Based on Linewidth-Optimized Nanohole Array Transmittance. Opt. Lett. 2006, 31, 1528-1530. 9. Bozhevolnyi, S. I. Plasmonic Nano-Guides and Circuits. Pan Stanford Publishing: Singapore, 2008. 10. Ebbesen, T. W.; Genet, C.; Bozhevolnyi, S. I., Surface-Plasmon Circuitry. Phys. Today 2008, 61, 44-50. 11. Kuznetsov, A. I.; Evlyukhin, A. B.; Gonçalves, M. R.; Reinhardt, C.; Koroleva, A.; Arnedillo, M. L.; Kiyan, R.; Marti, O.; Chichkov, B. N., Laser Fabrication of Large-Scale Nanoparticle Arrays for Sensing Applications. ACS Nano 2011, 5, 4843-4849. 12. Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C., The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment. J. Phys. Chem. B 2003, 107, 668-677. 13. Kreibig, U.; Vollmer, M., Optical Properties of Metal Clusters. Springer: Berlin, 1995. 14. Luk'yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T., The Fano Resonance in Plasmonic Nanostructures and Metamaterials. Nat. Mater. 2010, 9, 707-715.



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15. Hiramatsu, N.; Kusa, F.; Imasaka, K.; Morichika, I.; Takegami, A.; Ashihara, S., Propagation Length of Mid-Infrared Surface Plasmon Polaritons on Gold: Impact of Morphology Change by Thermal Annealing. J. Appl. Phys. 2016, 120, 173103. 16. Lin, L.; Yi, Y., Lattice Plasmon Resonance in Core-Shell SiO2/Au Nanocylinder Arrays. Opt. Lett. 2014, 39, 4823-4826. 17. Lin, L.; Yi, Y., Orthogonal and Parallel Lattice Plasmon Resonance in Core-Shell SiO2/Au Nanocylinder Arrays. Opt. Express 2015, 23, 130-142. 18. W. L. Barnes, W. A. M., J. Dintinger, E. Devaux, and T. W. Ebbesen, Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Light through Periodic Arrays of Subwavelength Holes in a Metal Film. Phys. Rev. Lett. 2004, 92, 107401. 19. Fano, U., Effects of Configuration Interaction on Intensities and Phase Shifts. Phys. Rev. 1961, 124, 1866-1878. 20. Genet, C.; van Exter, M. P.; Woerdman, J., Fano-Type Interpretation of Red Shifts and Red Tails in Hole Array Transmission Spectra. Opt. Commun. 2003, 225, 331-336. 21. Yanik, A. A.; Cetin, A. E.; Huang, M.; Artar, A.; Mousavi, S. H.; Khanikaev, A.; Connor, J. H.; Shvets, G.; Altug, H., Seeing Protein Monolayers with Naked Eye through Plasmonic Fano Resonances. Proc. Natl.Acad. Sci. U. S. A. 2011, 108, 11784-11789. 22. Johnson, P. B.; Christy, R.-W., Optical Constants of the Noble Metals. Phys. Rev. B 1972, 6, 4370. 23. Raether, H., Surface Plasmons on Smooth Surfaces. Springer:Berlin, 1988. 24. West, P. R.; Ishii, S.; Naik, G. V.; Emani, N. K.; Shalaev, V. M.; Boltasseva, A., Searching for Better Plasmonic Materials. Laser Photonics Rev. 2010, 4, 795-808. 25. McPeak, K. M.; Jayanti, S. V.; Kress, S. J. P.; Meyer, S.; Iotti, S.; Rossinelli, A.; Norris, D. J., Plasmonic Films Can Easily Be Better: Rules and Recipes. ACS Photonics 2015, 2, 326333.


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Figure 1. AFM topography images (upper panels) of Au hexagonal nanodome structures and the corresponding cross section height data (lower panels) taken along the dashed line in AFM images for (a) unannealed and (b) annealed Sample Ⅰ, and (c) unannealed and (d) annealed Sample Ⅰ.



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Figure 2. Experimental angle-resolved reflection spectra of continuous Au dome lattice (Sample I) with a periodicity of 500 nm and a film thickness of 50 nm. Reflection dispersion maps of (a) unannealed and (b) annealed Sample Ⅰ. The color bar stands for the normalized intensity of optical reflection. Solid white lines are SPP modes at the air-Au interface calculated by the SPPBragg model. (c) Individual reflection spectra taken at four different incidence angles, presenting Fano resonances from unannealed (red solid line) and annealed (black solid line) Sample Ⅰ, the markers ▲ and ♦ are the (-1, 0) SP resonance center wavelength of unannealed (red solid line) and annealed (black solid line) Sample Ⅰ, respectively.


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Figure 3. Experimental angle-resolved reflection spectra of hierarchical Au domes in honeycomb lattice (Sample II) with a periodicity of 500 nm and a film thickness of 50 nm. Reflection dispersion maps of (a) unannealed and (b) annealed Sample Ⅰ. (c) Individual reflection spectra with an azimuthal angle of 5°, exhibiting double Fano resonances from unannealed (red solid line) and annealed (black solid line) Sample Ⅰ, the markers ▲, ♥ and ♦, ■ are the (-1, 0) and (0, -1) SP resonance center wavelength of unannealed (red solid line) and annealed (black solid line) Sample Ⅰ, respectively.



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Figure 4. Calculated (FDTD) reflection and transmission dispersions of Sample Ⅰ with a periodicity of 500 nm and a thickness 50 nm. Reflection spectra (left panel) and the corresponding transmission spectra (right panel) were calculated with the given cross section heights Z of Au nanodomes. Decreasing Z, the peak width of SPP modes become narrower but the intensity decreases.


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Figure 5. Plots of calculated normalized reflection (a) and transmission (b) SPP dip (peak) intensities (left), and Q factor (right) of the corresponding (-1, 0) SPP modes as a function of cross section height Z of Sample Ⅰ at a representative angle of incidence θ = 36°.



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Narrowing Plasmon Resonance Linewidth of Au Nanodome Lattices

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