Complete Light Annihilation in an Ultrathin Layer of Gold

Letter pubs.acs.org/NanoLett

Complete Light Annihilation in an Ultrathin Layer of Gold Nanoparticles Mikael Svedendahl,† Peter Johansson,†,‡ and Mikael Kal̈ l*,† †

Department of Applied Physics, Chalmers University of Technology, 41296 Göteborg, Sweden School of Science and Technology, Ö rebro University, 70182 Ö rebro, Sweden

‡

S Supporting Information *

ABSTRACT: We experimentally demonstrate that an incident light beam can be completely annihilated in a single layer of randomly distributed, widely spaced gold nanoparticle antennas. Under certain conditions, each antenna dissipates more than 10 times the number of photons that enter its geometric cross-sectional area. The underlying physics can be understood in terms of a critical coupling to localized plasmons in the nanoparticles or, equivalently, in terms of destructive optical Fano interference and so-called coherent absorption. KEYWORDS: Perfect absorption, localized surface plasmon, metamaterials, optical heating, optical near fields, optical absorption

O

a layer of gold-nanodisk antennas. We focus on maximizing the effective absorption cross section per nanodisk for a single wavelength and incidence angle using a minimum amount of absorbing material. Our goal is thus to couple the maximum amount of light energy to the subwavelength nanodisk antennas, where the energy may be utilized for various optical near-field applications,1−5 in particular laser-based surface enhanced spectroscopies. Plasmons can be generated in a variety of conducting nanostructures. Gold particles are of particular importance because of their potential in biomedical applications and because the LSPR condition is easily satisfied for light in the visible wavelength range. We studied the optical properties of disordered layers of gold nanodisks on glass substrates (see the schematics in Figure 1). The samples were mounted on a hemispherical prism, through which they were illuminated with polarized light (see the Materials and Methods section). The samples have meta-material-like properties with distinct reflection and transmission angles and negligible diffuse scattering.16,17 Illuminating such samples from the backside (that is, through the glass substrate) at high or low angles of incidence (Figures 1A and 1C, respectively) typically results in strong specular reflection. However, for certain nanodisk densities, morphologies, and incidence wavelengths, we found that the reflected beam was completely lost for an illumination angle just above the critical angle of the glass/air interface, θc (Figure 1B). This corresponds to the complete annihilation of the incident light due to critical coupling and destructive Fano interference

ptimal light management leading to complete confinement of photons to nanoscale surface structures may lead to substantial enhancement and new developments in solar harvesting, photocatalysis, biophotonics, optical sensing, and molecular spectroscopy applications.1−5 Optical antennas are notable in that they enhance light−matter interactions through the resonant amplification of optical near fields, thus enabling the confinement of light on length scales much smaller than the classical diffraction limit. Maximizing light absorption in a layer of optical antennas entails minimizing both light reflection from and light transmission through the layer. Reflection is typically reduced by impedance matching or by critical coupling, both of which involve the careful optimization of the refractive-index mismatch between the absorbing layer and the surrounding medium; light transmission, on the other hand, is typically eliminated by using a backside mirror or by illuminating the surface under conditions that lead to total internal reflection.6−15 These techniques for maximizing light absorption require, however, a substantial amount of absorbing material. Yet, a recent theoretical study by Garcia de Abajo and co-workers9 predicts that complete optical absorption should be possible in a single layer of widely spaced, periodically arranged subwavelength particles: If each particle supports a localized surface plasmon resonance (LSPR) with a sufficiently large oscillator strength and if the layer structure and illumination conditions are designed for critical coupling and for zero transmittance, then the absorption cross section of the individual nanoparticles is maximized and all of the incident light is efficiently converted into optical near fields. The fewer the number of nanoparticles required to fulfill the complete photon annihilation conditions, the larger the absorption enhancement will be for each individual particle. Here, we experimentally demonstrate complete light annihilation based on localized surface plasmon resonances in © 2013 American Chemical Society

Received: March 7, 2013 Revised: June 12, 2013 Published: June 25, 2013 3053

dx.doi.org/10.1021/nl400849f | Nano Lett. 2013, 13, 3053−3058

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Figure 2. Experimental examples of complete light annihilation. (a, b) Two gold nanodisk arrays with different heights and surface densities can be excited by using a specific reflection configuration to (c) achieve zero reflection above the critical angle. The inset in (c) shows that the optically denser sample (black) can be efficiently excited using p-polarized light, whereas the optically less dense sample (orange) can be efficiently excited using s-polarized light.

measurements of the two samples conducted at normal incidence, which clearly shows the differences in optical density and resonance energy. Note that, because of their high aspect ratios, the out-of-plane plasmon excitation of the nanodisks is very weak and has negligible influence on the optical properties of the layers within the wavelength range studied here. The optical response of the plasmonic surfaces used here can be analyzed through an island film theory.18−20 The theory utilizes excess charge and current densities related to the polarizability of individual islands, here corresponding to the gold nanodisks, to reformulate the boundary conditions at the interface. The new boundary conditions in turn lead to modified Fresnel reflection and transmission coefficients that can be used to simulate the optical properties of the supported nanodisk layer. Figure 3 shows the experimentally determined angular dependence of the reflections, together with simulations based on the actual layer parameters.18 The theoretical and experimental data exhibit excellent agreement, although the dip position is slightly shifted for the experimentally acquired p-polarized reflections compared with that for the analytical predictions. It can be shown that the island film theory is equivalent to the aforementioned two-layer interference theory.9 The basic concept, which we can understand as an interference-controlled absorption process, is illustrated through full electrodynamics simulations in Figure 4. We here approximate the sample as an infinite periodic array of rectangular nanoparticles, which allows us to use the Green’s tensor method for stratified media to calculate the optical fields around the particle layer.21 We plotted the field components that surround a layer illuminated at an angle higher than the critical angle (θi = 45°) with ppolarized light. For the particular parameters used in the simulation, this illumination configuration yields 0.5% reflection at a photon energy of 1.72 eV, that is, almost complete light annihilation. For a bare glass−air interface, the incident and reflected fields form a standing-wave pattern (Figure 4a). The evanescent transmitted fields on the air side of the interface can excite the nanoparticles, which in turn produce scattered fields

Figure 1. Illustration of complete light annihilation in a nanodisk array. Critical coupling is achieved by tuning the incident angle, θi, above the critical angle. When the incident angle matches the critical coupling angle, θcc, no light is leaving the surface and the absorption in the nanodisks is (B) consequently maximized, whereas (A) larger and (C) smaller incident angles decrease the absorption.

between the light reflected from the nanoparticles and the light reflected from the substrate interface.18 As indicated in Figure 1B, the phenomenon is accompanied by heating of the nanoparticles and the presence of strongly enhanced optical near fields. The critical-coupling condition depends on the incidence angle, the incidence polarization, the refractive-index difference between the supporting substrate and the surrounding medium, and the oscillator strength and the surface density of the absorbing nanodisks. The experimental data shown in Figure 2 demonstrate complete light annihilation in two gold nanodisk layers with similar resonance frequencies but very different surface densities. The sizes of the gold nanodisks in the two samples were roughly the same, with diameter/height approximately 120 nm/20 nm for sample 1 (Figure 2a) and approximately 110 nm/27 nm for sample 2 (Figure 2b). As the resonance position of plasmonic nanodisks largely depends on their aspect ratio, these different sizes resulted in a slight difference in resonance energy. However, the most significant difference between the samples was in the number of nanodisks per unit area: ρ = 20.1 μm−2 for sample 1 and 9.9 μm−2 for sample 2. The different surface coverages resulted in complete light annihilation at similar incidence angles and similar photon energies, but using perpendicular incidence polarizations (pand s-polarization); see Figure 2c. The inset shows extinction 3054


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Figure 3. Incident angle dependences of (a, d) the experimentally observed reflections, compared with (b, e) theoretical predictions, for both p- (left column) and s-polarized (right column) light. The angular dependences of the reflections above the critical angle for (a−c) p- and (d−f) s-polarized light. The logarithm of the reflections is color-coded for the surface plots shown in (a, b) and (d, e), with dark areas illustrating a reflectance below 1%. For clarity, (c) and (f) show the data on a linear scale, with the individual spectra taken at various incidence angles, as indicated by the line plots.

that add up along the reflection angle (Figure 4b). But the reflected and scattered fields are almost of the same magnitude and out-of-phase. Hence, the reflected and scattered light interferes destructively, leading to a complete cancellation of the reflection (Figure 4c) and, therefore, trapping of the light within the nanoparticles leading to enhanced absorption (Figure 4d). To experimentally explore the enhanced absorption phenomenon, we studied sample 2 using a heat camera while illuminating it with a diode laser at various incident angles.22 The main results are shown in Figure 5, where parts a−d are false-color infrared images (the bright spots in the middle of the samples correspond to the illuminated area). The angular dependence of the measured temperature is shown in Figure 5e. Poor spatial resolution limited the measurements because the field of view of a single pixel in the camera (200 μm) is larger than the beam focal spot (80 μm). We therefore performed steady-state finite-element simulations to estimate the maximum temperature of the spot. Figure 5g illustrates the simulated temperature distribution within one unit cell in a homogeneously illuminated infinite nanodisk array. The nanodisk is found to primarily dissipate energy into the glass substrate rather than into the air, which leads to a homogeneous temperature within the unit cell. The experiment

can therefore be simulated by using the illuminated area of the glass−air boundary as a homogeneous heat source (Figure 5f). The mean temperature in the field of view of a pixel was used as a basis for the theoretical fit shown in Figure 5. The measured temperature may be approximately described by Tm = ΔT + T0, where ΔT = kA(θi) cos θi, k is a phenomenological scaling factor that is mainly dependent on the thermal conductivities of the surrounding materials, and T0 is the ambient temperature in the lab, 22 °C. The estimated maximum temperature rise in the sample is approximately 40 °C, as measured near the critical coupling angle. This final temperature is mainly determined by the thermal conductivities of the surrounding materials, which can be engineered to achieve either higher local temperatures or effective cooling.23,24 The conditions required for total light annihilation can be determined from the island film theory.18−20 For light that is incident above the critical angle, the general total light annihilation conditions for s- and p-polarization are given respectively by ω ρα(ω) = nt|cos θt| + in i cos θi (1) c nt n ω ρα(ω) = − +i i c |cos θt| cos θi 3055

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Figure 4. Full electrodynamic calculation demonstrating complete light annihilation leading to total optical absorption. (a) The fields surrounding a bare interface at z = −20 nm contain both incident and reflected fields, which form a standing wave pattern. (b) The nanoparticles that are excited by the transmitted fields scatter light that adds up only along the reflection angle. (c) The superposition of the two components yields the total field, which only contains an incoming field, no reflected fields, and strongly enhanced near fields. (d) The absorbed power per unit volume of a nanoparticle thus exhibits an angular dependence, which is maximized at the critical coupling condition, illustrated here by the cross sections of a nanoparticle excited at 45° and 0° incidences, respectively. The incident polarization is parallel to the diagonal of the nanoparticles. See Supporting Information S2 and Figure S1 for further simulation details and comparison of field patterns.

Here θ and n are the angle and index of refraction, with subindices i and t denoting the incidence and transmission media, and ρ is the surface density of nanoparticles, each with complex frequency-dependent in-plane polarizability α(ω) = α′(ω) + iα″(ω). Similar conditions can be derived for nanoparticles with a significant out-of-plane polarizability. Interestingly, a large single particle absorption (∝ α″(ω)) is not really necessary to achieve total light annihilation because the equivalence in eq 1 for an arbitrarily small absorption can be compensated for by a high incidence angle, θi. For example, s-polarized light incident at 85° on a glass−air boundary can be completely absorbed by nanoparticles that have a real polarizability, α′, almost 10 times larger than the imaginary part, α″. However, the total annihilation of light incident at the critical angle is completely determined by α″. Furthermore, this angle determines the minimum surface density of nanoparticles that is required to achieve total light annihilation. The experimental data for sample 2, which exhibited complete absorption near θc, correspond to an effective absorption cross section 10.6 times the geometrical cross section. In addition, the surface polarization needed for total light absorption is related to the refractive-index mismatch of the two media. A lower refractive-index contrast pushes the critical angle up toward grazing incidence, leading to a lower surface polarization being needed for critical coupling. A glass−water interface, for example, requires less nanoparticle coverage than the glass−air boundary (Figure 2) to achieve complete light annihilation.25

It can be shown that eqs 1 and 2 correspond to complete coherent absorption,26,27 a concept based on the relation between material loss and gain upon time inversion, as shown in Supporting Information S1. In the present case, the complete annihilation condition can be viewed as the time-inverted deexcitation of a leaky surface mode that is confined within the optically less dense medium but is leaking to the substrate. Interestingly, the time-inverted description suggests 100% absorption without suppressing transmission, that is, for angles θi < θc, if two coherent beams converge from opposite sides of the surface. Depending on the optical path and the coherence of the light source, this could be achieved by positioning a mirror a certain distance away from the boundary. However, it can be shown that this approach requires a larger ρ to achieve complete absorption than fulfilling eq 1 at θi = θc. Critical coupling at θc thus maximizes the absorption cross section for a given boundary and refractive-index contrast. Furthermore, we should point out that the phenomenon we describe here is conceptually different to absorbers with plasmonic structures near a thick metal film, which exhibit high absorption due to antiparallel currents in the structure and the film due to significant coupling between these components.6 This coupling lead to enhanced fields primarily located in the spacer layer, which needs to be considered when using the design for specific applications. We expect eqs 1 and 2 to be useful for the design of polarization-insensitive absorbers. For example, the two conditions may be satisfied independently by fabricating 3056


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Figure 5. Experimental verification that complete light annihilation leads to substantial heating of the nanoparticle layer. (a−d) Illuminating the sample with 660 nm laser light at various angles of incidence results in varying surface temperatures. (e) The angular dependence is well-described by theory. (f, g) The maximum temperature in the center of the focused light beam can be estimated from simulations of heat conduction in glass and in gold. A spatially limited illumination area yields a lower maximum temperature than a continuously illuminated infinite array of nanoparticles. The inset in (e) illustrates the experimental configuration used for these measurements.

wavelength of 660 nm) and imaged by a thermal camera (FLIR Systems, ThermoVision A20) using the shortest working distance of the camera objective (30 cm). This heat camera is sensitive to infrared (IR) radiation over the spectral range of 7− 13 μm. Owing to the volume and emissivity differences of the materials used in this study (gold nanoparticles and bulk glass), the detected radiation is assumed to emerge mainly from the substrate, from which the mean temperature of the illuminated spot was measured. Gold Nanodisk Arrays. The samples were fabricated by hole-mask colloidal lithography (HCL)16 on microscope cover slides. HCL is a versatile technique that allows precise control of the arrays oscillator strengths, resonance frequency, and nearest-neighbor distances. However, the samples do not have any long-range periodicity or order. Colloidal polystyrene beads were first self-assembled onto a substrate that was covered with PMMA, after which a thin gold film was deposited onto the sample. The surface coverage can be tuned e.g. by introducing salt into the polystyrene bead solution. The salt concentrations in the bead solutions that were used to obtain the arrays in samples 1 and 2 were 5 and 0 mM, respectively. The

anisotropic plasmonic nanoparticles with their major axes aligned parallel and perpendicular to the plane of incidence. Furthermore, the methodology described in this paper is not limited to plasmonic absorbers. 100% absorption may also be possible using other materials and resonances with other optical properties, such as quantum dots or J-aggregates.7,10 Materials and Methods. Optical Measurements. The samples were positioned on a hemispherical glass prism with an intermediate layer of a refractive index-matching oil and mounted in the center of two rotational stages. The illumination and collection optics were mounted on optical rails, which were fastened onto their respective rotational stages. A fiber-coupled halogen lamp (Ocean Optics HL-2000) was used as an illumination source. The reflected light was collected by a multimode optical fiber that was connected to a computer-controlled spectrometer (B&W Tek BRC711E). All of the spectra were normalized to using the bare interface reflected spectra of the respective polarization collected above the critical angle. Thermal Measurements. The samples were illuminated by a weakly focused laser diode (Arima Lasers, ADL-66505TL, peak 3057


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(7) Tischler, J. R.; Bradley, M. S.; Bulovic, V. Opt. Lett. 2006, 31 (13), 2045−2047. (8) Driessen, E. F. C.; de Dood, M. J. A. Appl. Phys. Lett. 2009, 94 (17), 171109. (9) Thongrattanasiri, S.; Koppens, F. H. L.; Javier Garcia de Abajo, F. Phys. Rev. Lett. 2012, 108 (4), 047401. (10) Pirruccio, G.; Lozano, G.; Zhang, Y.; Rodriguez, S. R. K.; Gomes, R.; Hens, Z.; Rivas, J. G. Phys. Rev. B 2012, 85 (16), 165455. (11) Spinelli, P.; Verschuuren, M. A.; Polman, A. Nat. Commun. 2012, 3, 692. (12) Mizuno, K.; Ishii, J.; Kishida, H.; Hayamizu, Y.; Yasuda, S.; Futaba, D. N.; Yumura, M.; Hata, K. Proc. Natl. Acad. Sci. U. S. A. 2009, 106 (15), 6044−6047. (13) Hagglund, C.; Apell, S. P. Opt. Express 2010, 18 (19), A343− A356. (14) Pala, R. A.; White, J.; Barnard, E.; Liu, J.; Brongersma, M. L. Adv. Mater. 2009, 21 (34), 3504−3509. (15) Teperik, T. V.; Garcia de Abajo, F. J.; Borisov, A. G.; Abdelsalam, M.; Bartlett, P. N.; Sugawara, Y.; Baumberg, J. J. Nat. Photonics 2008, 2 (5), 299−301. (16) Fredriksson, H.; Alaverdyan, Y.; Dmitriev, A.; Langhammer, C.; Sutherland, D. S.; Zaech, M.; Kasemo, B. Adv. Mater. 2007, 19 (23), 4297−4302. (17) Svedendahl, M.; Chen, S.; Dmitriev, A.; Kall, M. Nano Lett. 2009, 9 (12), 4428−4433. (18) Svedendahl, M.; Käll, M. ACS Nano 2012, 6 (8), 7533−7539. (19) Mendoza-Galvan, A.; Jarrendahl, K.; Dmitriev, A.; Pakizeh, T.; Kall, M.; Arwin, H. Opt. Express 2011, 19 (13), 12093−12107. (20) Bedeaux, D.; Vlieger, J. Optical Properties of Surfaces; Imperial Collage Press: London, 2001. (21) Johansson, P. Phys. Rev. B 2011, 83 (19), 195408. (22) Edman Jönsson, G.; Miljkovic, V. D.; Dmitriev, A. Preprint at http://arxiv.org/abs/1301.4700, 2013. (23) Baffou, G.; Quidant, R.; Javier Garcia de Abajo, F. ACS Nano 2010, 4 (2), 709−716. (24) Wang, K.; Schonbrun, E.; Steinvurzel, P.; Crozier, K. B. Nat. Commun. 2011, 2, 469. (25) Otte, M. A.; Estevez, M. C.; Regatos, D.; Lechuga, L. M.; Sepulveda, B. ACS Nano 2011, 5 (11), 9179−9186. (26) Chong, Y. D.; Ge, L.; Cao, H.; Stone, A. D. Phys. Rev. Lett. 2010, 105 (5), 053901. (27) Wan, W.; Chong, Y.; Ge, L.; Noh, H.; Stone, A. D.; Cao, H. Science 2011, 331 (6019), 889−892.

polystyrene beads were then removed by tape stripping, and the exposed PMMA was etched away. Finally, the metal was deposited and the hole mask was removed, resulting in an array of cylindrical metal particles. Heat Simulations. Heat simulations were performed using the heat transfer model in the COMSOL Multiphysics 3.5a software. Steady-state solutions only require that the heat conductivity, k, of the respective material is known. In these simulations, we used kglass = 1.05 W m−1 K−1, kAu = 318 W m−1 K−1, and kair = 0.024 W m−1 K−1. The power flux from the layer was approximated as the incoming laser power over the illuminated area multiplied by the angle-dependent absorption of the nanoparticles, A(θi). Green’s Tensor Calculations. The theoretical calculations are based on the Green’s function method,21 which was generalized for a 2D periodic array of point sources. The calculations are performed in two steps. In the first step, the electric field is calculated inside one of the particles, taking into account the incident field and the scattered fields from all of the surrounding particles. In the second step, based on the result from the first step (and Bloch’s theorem), the total field is determined anywhere in space.

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ASSOCIATED CONTENT

S Supporting Information *

A discussion of the coherent absorption, further details of the Green’s tensor simulations, and estimates of the diffuse scattering losses. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge S. Chen and V. Claudio for sample fabrication, G. Edman-Jönsson for technical assistance with the heat camera, and B. Sernelius and J. Garcia de Abajo for insightful comments and discussions. This work was financially supported by Vinnova, the Swedish Foundation for Strategic Research, and the Swedish Research Council.

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Complete Light Annihilation in an Ultrathin Layer of Gold

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