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Abstract
We study the angle-dependent optical reflectance spectrum of a metasurface consisting of a periodic array of film-coupled plasmonic nanopatch particles. The nanopatch metasurface exhibits a strong, angle-independent absorption resonance at a wavelength defined by the nanopatch geometry and relative density. When the nanopatches are arranged in a regular lattice, a second, sharp absorption dip is present that varies strongly as a function of the incidence angle. This second resonance is a collective effect involving the excitation of surface plasmon modes and relates to a Wood’s anomaly. Using an analytical model, we compute the surface modes of the structure and confirm details about the various mechanisms that contribute to the reflection spectra. The measured reflectance spectra are in excellent agreement with both analytical calculations and full-wave numerical simulations.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Conducting or semiconducting nanoparticles can strongly couple to light due to the excitation of electrical currents by the incident electric field. Depending on the nanoparticle geometry, the restoring force imposed by the polarization of an individual nanoparticle can lead to a plasmon resonance, in which the overall electronic response is resonantly enhanced, leading to a large scattering cross section as well as large, local optical fields. The wavelengths where plasmonic resonances occur relate not only to the nanoparticle geometry, but also to the dielectric function of the plasmonic material. Thus, the resonances of the individual plasmonic structures that compose the periodic system can occur for wavelengths of light much larger than the size of the structure. Plasmon resonant nanoparticles have become an important tool for nanophotonic applications because of their ability to enhance many optical processes.
When a collection of plasmon resonant nanoparticles is arranged into a periodic lattice, the inherently strong electronic response of the nanoparticles can be used to enhance scattering phenomena related to the underlying periodicity. In the context of a metasurface, an array of plasmonic resonators above a metallic film can not only efficiently couple to incident light, leading to near total absorption, but can also enhance a series of grating-like surface modes known as Wood’s anomalies. These modes, related to diffraction, represent a collective interaction between the nanoparticles mediated by surface plasmons. The participation of both localized and propagating surface plasmons associated with a periodic arrangement of film-coupled nanoparticles is a useful platform to understand a host of interesting complex wave propagation phenomena.
The nanopatch antenna [1] geometry—consisting of a planar nanoparticle spaced above a metal film by an insulating layer—is particularly compelling as a platform for plasmonics. The film-coupled nanoparticle system in general leverages planar fabrication and deposition techniques, leading to extremely reproducible and tightly controlled properties [2–4]. Moreover, the nanopatch allows two independent approaches to tune its resonance frequency: adjusting the thickness of the gap between patch and film, and adjusting the overall size of the patch. Through the careful application of these two methods, the strength of the local fields that exists between the patch and film can be varied while maintaining a constant resonance frequency, enabling field enhancement effects to be probed in a systematic way [5]. Film-coupled nanopatch arrays have been used to demonstrate perfect absorbing systems [6–9], enhanced spontaneous emission [10–12], enhanced Raman scattering [3,13], and many other interesting and relevant optical phenomena.
The modes of interest associated with the nanopatch array—including the “gap” mode as well as the various lattice modes—can be probed using angular reflectance spectroscopy. Lin et al. investigated arrays of film-coupled nanocubes, fabricated using colloidally synthesized gold nanocubes attached to a gold film via DNA linkers [14]. Comparing with finite-difference based simulations, the authors were able to identify both a gap mode, which produced an absorption dip insensitive to the incidence angle of excitation, as well as a lattice mode, which produced an absorption at a wavelength that varied as a function of excitation angle. Lin et al. showed that these modes could be made to cross and hybridize, simultaneously enabling efficient coupling to the system as well as producing strong local fields underneath the nanocubes.
Our goal in the present study is to delve deeper into the structure of the surface modes, understanding their contributions to the line width and the underlying mechanisms. While field plots of the modes can help distinguish extended, surface modes from localized, gap modes [14], additional analysis is required to gain a more quantitative understanding of the fundamental mechanisms at play. Building on a series of analytical treatments for both individual nanopatch antennas as well as arrays of nanopatch antennas [15–17], we are able to provide a complete description of the reflectance spectra, accounting for both the absorption dip magnitudes and line widths. Measurements on well-controlled, lithographically patterned nanopatch samples provide clean spectra that compare extremely well to both numerical simulations as well as the analytical predictions.
2. Experimental details
An illustration of the nanopatch array geometry we consider is shown in Fig. 1. The distance between each of the patches (lattice constant) is a = 450nm. Each nanopatch has side length W = 100nm and height H = 50nm. The thickness of the spacer layer is h = 13nm, with a dielectric constant of εg = 2.4025. The nanopatches and film are gold, while the spacer layer is Al2O3 fabricated through atomic layer deposition (ALD). The underlying gold film has a thickness of l = 100nm. Light is obliquely incident on the plane of the structure and has transverse magnetic (TM, or p-) polarization (electric field in the plane of incidence).
Fig. 1 Top view and side view of the nanopatch array geometry. Lattice constant a = 450nm ; patch side length W = 100nm ; patch height H = 50nm ; thickness of Al2O3 ALD layer h = 13nm ; thickness of gold film l = 100nm.
The periodic array of nanopatches was fabricated as follows. First, on the top of a commercial template-stripped gold film with a thickness of 100nm (Platypus Technologies), an 13nm thick Al2O3 layer was deposited using a Kurt J. Lesker Co. plasma-enhanced atomic layer deposition (PE-ALD) system from precursors trimethylaluminum (TMA) and water at 200 °C : the template stripped chips were loaded into the chamber and allowed to equilibrate at the temperature for 20 minutes. Immediately following, 157 cycles of TMA (40 ms pulse, 10 s argon purge) and water (140 ms pulse, 10 s argon purge) were deposited to fabricate a 13 nm Al2O3 thin film. The Al2O3 layer grown under this condition has a dielectric constant around 2.4. On the top of the ALD layer, a photo resist (PMMA A2 950k) was spin-coated to reach a thickness of 120nm and baked at 180 °C for 2 minutes. Then arrays of nanopatches were patterned using electron-beam lithography (EBL) at 50kV on an Elionix ELS-7500 EX E-Beam Lithography System, with a dose of 1200μC/cm2. After the EBL exposure, the exposed photo resist was developed in a mixture of MIBK (4-Methyl-2-pentanone) and IPA (Isopropyl alcohol) with a volume ratio of 1 : 3 for 70s and thoroughly rinsed with IPA, thus forming a resist mask with nanopatch patterns. Subsequently, a 50nm thick gold layer was deposited on the resist mask using a CHA Solution electron beam (E-Beam) evaporator. Eventually, the remaining photo resist was lifted off with acetone for 30 minutes and thoroughly rinsed with IPA. The area with nanopatch arrays is 2mm × 3mm.
Figure 2 shows the scanning electron microscopic (SEM) top-view image of the fabricated structures. The side length of the patches is 100nm as measured from SEM.
Fig. 2 Top view of a scanning electron microscope (SEM) image of the sample. The side length of nanopatches is confirmed to be 100nm.
To characterize the reflectance of the sample, a custom reflectance spectrometer was assembled, capable of angle-resolved reflectance measurements over the visible spectrum. As illustrated in the diagram of Fig. 3, the light source used in the system is a tungsten-halogen lamp with an effective blackbody temperature of 2796 K, providing a spectral range of 360 to 2,600 nm. The light source is directly coupled into a fiber optic cable with a core diameter of 400μm and a numerical aperture (NA) of 0.39. Light emerging from the fiber is focused onto a 500μm pinhole using an achromatic doublet lens to create a spatial filter and provide a cleaner beam profile. The light passes through a second achromatic doublet lens and a polarizer before coming to focus 21cm after passing through the lens onto the metasurface sample. The beam size on sample is about 0.8mm at normal incidence.
Fig. 3 Measurement diagram. (a) Optical path. (i) fiber coupler; (ii) achromatic doublet lens; (iii) pinhole; (iv) achromatic doublet lens; (v) polarizer; (vi) coaxial rotational stages; (vii) fiber coupler. (b) Incidence diagram. TM light is incident onto the sample parallel to the patch sides.
The sample rotation stage is coaxial with a second rotation stage, with the axis of rotation aligned such that it is located on the surface of the sample. The second rotation stage controls the position of the fiber optic cable (core diameter 400μm and NA 0.39) used to gather the light from the sample and send it to a connected Czerny-Turner style spectrometer. The spectrometer covers a wavelength range from 500 to 1,000 nm and has a full width at half maximum (FWHM) accuracy of 0.6 nm at 633 nm.
Ray tracing of the optical system was performed to maximize the light throughput while minimizing the deviation from the intended angle of the light incident on the metasurface. The change in beam diameter between sample and fiber detector as well as the distance between them were measured in the ray tracing model and the calculated value for the deviation from the intended angle was a range of ± 0.5986°.
3. Simulations
Simulated spectra were obtained using a commercial full-wave, finite-element based numerical solver (COMSOL Multiphysics). A periodic nanopatch geometry was modeled by placing perfectly matched layers (PMLs) above and below the structure and applying Floquet periodic conditions on the sides. Scattering boundary conditions were implemented on the ports. The predicted reflectance spectra as a function of the angle of incidence were obtained (Fig. 4). Figure 4 is a two-dimensional summary of the reflectance spectrum as a function of the incident angle, and Figure 5 is a representative reflectance spectrum at an incident angle of 40°. Reflectance resonances are evident in Fig. 5 and their dispersion as a function of incidence angle and wavelength are traced out in Fig. 4. Consistent with the simulation results, the measured gap mode—occurring near 800nm—is relatively broad and mostly insensitive to the angle of incidence of the incoming light, while the lattice mode emerges around 650nm and red shifts with increasing angle of incidence, eventually hybridizing with the gap mode in an avoided crossing. The agreement between the experiments and simulations is excellent, suggesting that the full-wave modeling captures all of the relevant wave scattering dynamics. Note that we have chosen the spacing to intentionally observe the lattice mode; were the spacing much smaller than the wavelength, or the nanopatches arranged randomly, the lattice would not be present.
Fig. 4 Comparison among theory, simulation and experiment. The black diamonds are the reflection resonance wavelength for theoretical predication and the red dots are experimental results while the 2D colormap represents the reflectance from COMSOL simulation. Note the broad gap mode at 800nm remains constant, while the sharp lattice mode (Wood’s anomaly) red shifts as a function of incidence angle, interacts strongly with the gap mode at 42° and eventually cross over to 850nm. The consistence of theory and simulation with experimental results confirms validity of the analytical model.
Fig. 5 Representative spectrum comparison among theory, simulation and experiment. At incident angle 40°, the the lattice mode approaches the gap mode, so the interaction between the two is strong. The dip around 600nm is the second order gap mode. We didn’t include this second order term in the analytical evaluation.
4. Analysis
The lattice mode has a strong connection to the Wood’s anomaly. The Wood’s anomaly [18] is manifest as a reflection dip occurring at or near the Rayleigh wavelength defined by [19]
where n is an integer, a is the period of the grating, and θ is the angle of incidence. Equation (1) is the grating equation, which determines the angles of diffracted orders. As Fano later pointed out, the Wood’s anomalies can be separated into two categories [20]. The first is a sharp anomaly that occurs exactly at the Rayleigh wavelengths, characterized by a sudden, discontinuous change in the intensity of the refracted light from the grating. The second is a diffuse anomaly, which produces a smoother change in the intensity of the diffracted beam; Fano described this latter anomaly, which coincides with a resonant surface mode, as beginning at the sharp anomaly and extending for a wide interval towards the longer wavelengths.A complete analytic treatment of the nanopatch array is made possible using a combination of coupled mode theory and effective medium approaches. The modes of an isolated nanopatch consist of a series of cavity-like resonances, with fields strongly localized between the metal patch and the film. The lowest order cavity mode results in an effective magnetic polarizability of the patch of the form
Here, ω̃0 = ω0(1 − i/2Q) is the complex resonance frequency. The Q-factor, defined as the ratio of the energy stored in the resonator to the energy dissipated per cycle by the damping processes, was calculated using Eq. (13) (expression for energy stored), Eq. (19) (Ohmic loss) and Eq. (23) (radiation loss) in [16]. ∊g is the dielectric constant of the gap layer (the ALD layer in experiment). We note further that the nanopatch antenna can be modeled as an isotropic magnetic dipole in the plane of the metal film but anisotropic out of the plane [16], and therefore this scalar expression is only valid for TM incidence.For the array of nanopatch antennas, the interaction among the elements through propagating surface plasmon modes modifies the effective polarizability to
where the interaction constant is given by [21] where ; ∊ is the dielectric constant of gold; d is the distance between the dipole array and the metal film (which is zero here); a is the lattice constant as in Fig. 1; β is the surface plasmon propagation constant. The three terms in Eq. (4) are the interaction constants of a chosen magnetic dipole, a 1D array of dipoles along the chosen dipole and the 2D dipole lattice excluding the 1D array [21].Separating out the cos(kxνa) in the third term into exponentials yields a geometric series in the summation over ν which may be evaluated exactly, yielding
where H1 is the Hankel function. This now creates a dispersive, effective polarizability that depends on wavenumber, In our coordinate system (shown in Fig. 1), TM incidence will be defined as when ϕ = 0, and hence ky = 0.From the above equations we can determine the TM reflectivity as comprising the field reflected off the bare metal film plus the field radiated by the lattice of dipoles,
where rTM is the reflection coefficient of the gold film under TM polarization.While the intrinsic polarizability in Eq. (2) is independent of the array, the effective polarizability in Eq. (3) is modified by interactions both through the radiative field and through surface plasmons that propagate along the film surface. The interactions through the radiative field mostly effect the radiative contribution to the quality factor, while the effect of surface plasmons is given by the interaction constant in Eq. (5). The interaction through surface plasmons not only introduces a frequency shift and line broadening to the fundamental gap mode of the nanopatch, but also introduce artifacts at certain wavelengths where collective surface modes occur. Examining Eqs. (3) and (5) more closely, it is clear that when
the effective polarizability becomes singular, which gives rise to a resonance in the reflection coefficient. The singularity in the effective polarizability is the condition for a surface eigenmode, i.e. a source-free solution to Maxwell’s equations. In practice the product α(ω)C(ω, k) will not yield a real number for real frequencies, and so the surface mode manifests itself as a resonance with a finite linewidth in the reflection spectrum.In the limit of very small dipoles, i.e. α(ω) → 0, the surface mode can only exist when the interaction constant diverges, i.e. C(ω, k) → ∞. Examining Eq. (5) more closely, the third term in the sum diverges when (Γμ ± kx)a = 2πν, where ν is any integer. Using the definition of Γμ, this occurs when
Hence it is clear that the wavelengths where the interaction constant diverges are defined in a manner similar to the grating equation (Eq. (1)), but modified by the plasmon dispersion properties of the metal as [21]. Once again, the surface plasmon propagation constant will always be complex-valued for lossy materials, and so the condition in Eq. (9) can never be precisely satisfied in practice, which again leads to a surface mode resonance with a finite linewidth, in the limit of vanishingly small dipoles.For non-vanishing dipoles, solving the surface mode condition in Eq. (8) numerically yields the frequency for which the diffusive Wood’s anomaly occurs for any given incident angle. Analytical results based on this model are presented in Fig. 4 and Fig. 5, where both the experimental results and full-wave simulations validate the theory. Although the sharp anomaly cannot be clearly seen for this particular geometry either in experiment or in theory, the wavelength of the diffuse anomaly is well-predicted for all incidence angles, as well as its depth and width. Note that the dip around 600nm in the experimental and simulation spectra comes from second order of the gap mode. We didn’t include the second order term in our analytical calculation to keep the calculation simple and also the second order term is not of interest in this work.
In conclusion, we have presented a detailed analysis of the reflectance spectra of periodic arrays of film-coupled nanopatch antennas. We have focused our study on a theory that describes the diffuse Wood’s anomaly using an effective medium formalism by directly summing up the interactions between the nanopatches through surface plasmons, as distinct from the interaction through radiation modes. The diffuse anomaly is predicted to occur when these interactions allow for a surface mode to exist, and we confirm experimentally that this purely analytic theory can predict the experimental wavelength, resonance depth and width of the diffuse anomaly without the use of fit parameters. With a deeper understanding of the interplay between the surface and localized plasmons, we gain additional insight to design future devices based on the nanopatch platform with considerable control.
Funding
Air Force Office of Scientific Research (Grant No. FA9550-12-1-0491).
Acknowledgment
We acknowledge Dr. Aaron D. Franklin and Felicia McGuire in Duke University for helping to do the ALD process.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References and links
1. R. Esteban, T. V. Teperik, and J. J. Greffet, “Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances,” Phys. Rev. Lett. 104, 026802 (2010). [CrossRef] [PubMed]
2. J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, and D. R. Smith, “Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film,” Nano Lett. 8, 2245 (2008). [CrossRef] [PubMed]
3. R. T. Hill, J. J. Mock, Y. Urzhumov, D. S. Sebba, S. J. Oldenburg, S.-Y. Chen, A. A. Lazarides, A. Chilkoti, and D. R. Smith, “Leveraging nanoscale plasmonic modes to achieve reproducible enhancement of light,” Nano Lett. 10, 4150 (2010). [CrossRef] [PubMed]
4. T. Maurer, P.-M. Adam, and G. Leveque, “Coupling between plasmonic films and nanostructures: from basics to applications,” Nanophotonics 4, 363 (2015). [CrossRef]
5. G. M. Akselrod, J. Huang, T. Hoang, P. T. Bowen, L. Su, D. R. Smith, and M. H. Mikkelsen, “Large-Area Metasurface Perfect Absorbers from Visible to Near-Infrared,” Adv. Mater. 27, 8028 (2015). [CrossRef] [PubMed]
6. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342 (2010). [CrossRef] [PubMed]
7. C. Wu, B. Neuner, G. Shvets, J. John, A. Milder, B. Zollars, and S. Savoy, “Large-area wide-angle spectrally selective plasmonic absorber,” Phys. Rev. B 84, 075102 (2011). [CrossRef]
8. K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic superabsorbers,” Nat. Comm. 2, 517 (2011). [CrossRef]
9. A. Moreau, C. Ciraci, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Controlled-reflectance surfaces with film-coupled nanoantennas,” Nature 492, 86 (2012). [CrossRef] [PubMed]
10. C. Belacel, B. Habert, F. Bigourdan, F. Marquier, J.-P. Hugonin, S. Michaelis de Vasconcellos, X. Lafosse, L. Coolen, C. Schwob, C. Javaux, B. Dubertret, J.-J. Greffet, P. Senellart, and A. Maitre, “Controlling spontaneous emission with plasmonic optical patch antennas,” Nano Lett. 13, 1516 (2013). [CrossRef] [PubMed]
11. Z. Wu and Y. Zheng, “Radiative enhancement of plasmonic nanopatch antennas,” Plasmonics 11, 213 (2016). [CrossRef]
12. G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciraci, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Phot. 8, 835 (2014). [CrossRef]
13. M. Yi, D. Zhang, P. Wang, X. Jiao, S. Blair, X. Wen, Q. Fu, Y. Lu, and H. Ming, “Plasmonic interaction between silver nano-cubes and a silver ground plane studied by surface-enhanced Raman scattering,” Plasmonics 6, 515 (2011). [CrossRef]
14. Q.-Y. Lin, Z. Li, K. A. Brown, M. N. O’Brien, M. B. Ross, Y. Zhou, S. Butun, P.-C. Chen, G. C. Schatz, V. P. Dravid, K. Aydin, and C. A. Mirkin, “Strong coupling between plasmonic gap modes and photonic lattice modes in DNA-assembled gold nanocube arrays,” Nano Lett. 15, 4699 (2015). [CrossRef] [PubMed]
15. C. Ciraci, J. B. Lassiter, A. Moreau, and D. R. Smith, “Quasi-analytic study of scattering from optical plasmonic patch antennas,” J. Appl. Phys. 114, 163108 (2013). [CrossRef]
16. P. Bowen and D. R. Smith, “Coupled-mode theory for film-coupled plasmonic nanocubes,” Phys. Rev. B 90, 195402 (2014). [CrossRef]
17. P. Bowen, A. Baron, and D. R. Smith, “Theory of patch-antenna metamaterial perfect absorbers,” Phys. Rev. A 93, 063849 (2016). [CrossRef]
18. R. W. Wood, “On a Remarkable Case of Uneven Distribution of Light in a Diffraction Grating Spectrum,” Proc. Phys. Soc. London 18, 269 (1902). [CrossRef]
19. L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 14, 60 (1907). [CrossRef]
20. U. Fano, “The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves),” J. Opt. Soc. Am. 31, 213 (1941). [CrossRef]
21. P. Bowen, B. Tidwell, and D. R. Smith, “Effective Medium Description of a Metasurface Composed of a Periodic Array of Nanoantennas Coupled to a Metallic Film,” Physical Review A 95, 033822 (2017). [CrossRef]
