Thermal Signatures of Plasmonic Fano Interferences: Toward the

Letter pubs.acs.org/JPCL

Thermal Signatures of Plasmonic Fano Interferences: Toward the Achievement of Nanolocalized Temperature Manipulation Christopher L. Baldwin,† Nicholas W. Bigelow,‡ and David J. Masiello*,†,‡ †

Department of Physics, University of Washington, Seattle, Washington 98195-1560, United States Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States

‡

S Supporting Information *

ABSTRACT: A consequence of thermal diffusion is that heat, even when applied to a localized region of space, has the tendency to produce a temperature change that is spatially uniform throughout a material with a thermal conductivity that is much larger than that of its environment. This implies that the degree of spatial correlation between the heat power supplied and the temperature change that it induces is likely to be small. Here, we show, via theory and simulation, that through a Fano interference, temperature changes can be both localized and controllably directed within certain plasmon-supporting metal nanoparticle assemblies. This occurs even when all particles are composed of the same material and contained within the same diffraction-limited spot. These anomalous thermal properties are compared and contrasted across three different nanosystems, the coupled nanorod−antenna, the heterorod dimer, and the nanocube on a substrate, known to support both spatial and spectral Fano interferences. We conclude that the presence of a Fano resonance is not sufficient by itself to induce a controllably nanolocalized temperature change. However, when present in a nanosystem of the right composition and morphology, temperature changes can be manipulated with nanoscale precision, despite thermal diffusion. SECTION: Plasmonics, Optical Materials, and Hard Matter anipulating the nonradiative flow of energy within and around plasmon-supporting metal nanostructures has been a focus of intense study over the past several years. Roughly a decade ago, the photothermal properties of plasmonsupporting metal nanostructures, particularly nanoparticles, began receiving attention for their role in stable imaging techniques1,2 and cancer therapy3−10 due to their ability to effectively localize heat into nanometer-scale domains following the absorption of light. Researchers have since extended their use of this feature toward a variety of applications ranging from catalysis11−19 to the welding/adhering of biological tissue20,21 to waste sterilization.22 These applications have given impetus for a series of experimental and theoretical studies, and we refer the reader to any of the multiple review articles addressing the efficiency and potency of plasmon-mediated heat generation.23,24 On the experimental side, researchers have used multiple techniques to infer the temperature of plasmonically active nanoparticles. These tools range from observing the melting of ice25 and the melting of nanoparticles26 to the characterization of rotational Brownian motion of fluorophores27−30 and the measurement of temperature-induced refractive index changes.31,32 Theoretical efforts have largely focused on continuum treatments based on coupling Maxwell’s equations and the heat diffusion equation. The distribution of generated heat and the steady-state temperature field have been calculated analytically for the simplest geometries33 and numerically for more complicated arrangements.34−37

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© 2014 American Chemical Society

These studies have reported temperature increases spanning multiple orders of magnitude, from a few Kelvin29,38 to hundreds of Kelvin.17,26 Many have focused on the influence of nanoparticle size, morphology, and aggregation scheme on heat generation.39 An early paper found that plasmoninduced heating in a gold colloidal solution was a collective effect, with an individual nanoparticle contributing minimally to the temperature rise of its environment.38 More recently, researchers examined arrays of gold nanoparticles and determined that localized heating occurred for small particle numbers, but a collective effect emerged as the particle number increased.32 Furthermore, it has been established that, due to thermal diffusion, the temperature fields are much more evenly distributed than the electric fields that generate them.30 Even though heat generation is restricted to certain regions of a nanoparticle,28,34 the high thermal conductivity of noble metals translates into a uniform temperature increase throughout a particular particle.35,36 However, simulations have demonstrated that in a chain of nanoparticles, one can potentially control which particles in the chain become hottest, even if one cannot affect the distribution within a particle.35 These works paint a picture of plasmon-induced heating in which the effects tend to be spatially uniform but can be localized by properly designing the system. Received: February 26, 2014 Accepted: March 26, 2014 Published: March 26, 2014 1347

dx.doi.org/10.1021/jz500421z | J. Phys. Chem. Lett. 2014, 5, 1347−1354

The Journal of Physical Chemistry Letters

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Our approach is inspired by the theory of coupled dipoles48 or the discrete dipole approximation (DDA);49 the numerical implementation of the latter is now widely employed to simulate the optical scattering properties of arbitrary plasmonic nanostructures. We call our formalism the thermal discrete dipole approximation (T-DDA) because it involves breaking the target + environment system into a collection of Cartesian points xi that are both electrically and thermally conductive and solving the coupled Maxwell−heat diffusion equations at these points. First, the system is exposed to an optical field. Each point is electrically polarized by an external electric field E0 and brought into self-consistency with the electric dipole field of all other points according to the standard DDA prescription. Subsequently, each point is powered by the locally scattered electric field Esca according to q(xi) = σiabs(ω)I(xi,ω)/a3 = (3nω/8π)|Esca(xi,ω)|2 Im(εi(ω) − 1)/(εi(ω) + 2), where σiabs and I are the absorption cross section and incident field intensity experienced by the ith dipole and n is the refractive index of the environment. The resulting temperature is brought into self-consistency with all neighboring points through heat diffusion. For example, two neighboring points xi and xj at respective temperatures T(xi) and T(xj), separated by a distance a, will experience an amount of heat flowing between them given by

Concurrently, the Fano interferences that exist in coupled plasmonic systems are being extensively explored.40−44 Their narrow spectral widths and sensitivity to geometric/environmental changes makes Fano resonances promising candidates as, for example, nanoscale rulers45 and molecular sensors.46,47 However, as of yet, research has focused mainly on the radiative features of Fano interferences, with no attention given to the resonances’ nonradiative signatures. The purpose of this Letter is to explore, via theory and simulation, the degree to which temperature changes can be controllably nanolocalized through the excitation of a Fano interference with far-field light. Three different plasmonsupporting metal nanostructures immersed in water will serve to exemplify the degree of temperature control that would be expected in a similar experiment. The destructive interference occurring within their Fano resonances can suppress and even completely quench the scattering of light across a limited spectral region and can be spectrally tuned by deforming some geometric property of the target system. We find that by exploiting the dependence of photothermal heating on the magnitude of the locally scattered electric field, the spatial location of thermal hot and cold spots may be tuned at different optical frequencies within the Fano resonance. This is achieved through the design of target geometries that scatter weakly within the transparency window of a Fano resonance. In the absence of interference, such delicate optical control of heating and the resulting temperature changes would not occur. Additionally, the Fano resonances occurring in certain plasmonic nanosystems indicate that light is extinguished differently at different points in space, again due to interference. This implies that certain parts of a nanoscopic target may absorb and scatter different amounts of optical energy and heat up in a spatially dependent manner, opening the possibility to spectrally and spatially control temperature on the nanoscale. The latter is particularly unusual because we would expect materials of the same composition placed within the same diffraction-limited spot to reach the same steady-state temperature. Yet, in the following, we will show via theory and simulation that the temperature can be controllably increased or decreased within precise nanoscopic regions in space (well below the diffraction limit) in a metal nanoparticle aggregate composed of only one material, despite heat diffusion. Two counterexamples will also be discussed in detail to demonstrate that the spatial localization of temperature change is not a universal property of all Fano resonances. These qualitative thermal features are robust against small variations in the nanosystem geometry, even though the Fano interference pattern may shift. The thermal properties of three different nanoparticle systems that support Fano interferences will be explored in the following via theory and simulation. Before discussing these examples, we first briefly describe here our methodology and save a more detailed explanation for the Supporting Information (SI). We are interested in describing the steady-state temperature distribution within general plasmon-supporting nanostructures of arbitrary morphology, size, aggregation scheme, and material composition, immersed in an arbitrary homogeneous environment and driven by an external optical frequency continuous wave radiation source. For these systems, it is typical to solve the steady-state heat diffusion equation ∇·[κ(x)∇T (x)] + q(x) = 0

8(x i , x j) =

2κiκj κi + κj

a[T (x j) − T (x i)]

(2)

where 8 (xi,xj) is the quantity of heat power flowing into xi from xj. Note that when the two points have identical conductivities, the coefficient 2κiκj/(κi + κj) in eq 2, which can be thought of as a thermal polarizability, reduces to their common thermal conductivity κ. Energy conservation then relates a point’s temperature to that of its neighbors by requiring that the total heat flow from neighbors into the ith point must be equal and opposite to the heat power entering from the field, given by q(xi)a3. This gives a system of linear equations determining the temperature at each point of the general form ′

∑ 8(x i, x j) + q(x i)a3 = 0 (3)

j

where the prime denotes that the sum is over the six nearest neighbors xj of the ith point only. In a region of space with one common thermal conductivity κ, these equations reduce to κa[T (x i + aex̂ ) + T (x i − aex̂ ) + T (x i + aeŷ ) + T (x i − aeŷ ) + T (x i + aeẑ ) + T (x i − aeẑ ) − 6T (x i)] + q(x i)a3 = 0

(4)

which contains a second-order central difference discretization of the Laplacian operator. These T-DDA equations provide an approximate discretization of the steady-state heat diffusion equation in eq 1, accounting for the nonradiative flow of energy through thermal conduction. The methodology does not invoke the uniform temperature approximation35,36 but does neglect the effects of blackbody radiation and mass transport, as has commonly been done in the existing literature.23,35,37 The explicit dependence of the temperature field and heat power density upon the excitation frequency ω is omitted in the notation of all equations, although accounted for in the calculations. Unlike the electromagnetic field, which can transport energy through nondispersive and nondiffractive media and even vacuum, the thermal field T(x) requires a conductive medium (i.e., κ ≠ 0) to transport energy. This means that the

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that still accounts for the effects of an infinite environment. This is accomplished by writing eq 1 as

environment surrounding the target must also be explicitly accounted for in the solution of the heat diffusion equation, even if κ is a constant. One of the main advantages of the DDA concept (over, e.g., the finite difference time domain method) is its scaling with the number of target points and the nonnecessity to explicitly discretize the environment when it is not significantly optically active. However, this advantage is no longer enjoyed in the case of thermal diffusion, even when the environment is only moderately thermally conductive. To circumvent the necessity to discretize both the target and the environment and solve eq 3 in both domains, we employ a combination of projection operator and Green’s function techniques to construct a computationally tractable solution

⎧ ⎛ 2κ(x)κ0 ⎞ ⎫ ⎨κ0∇2 + ⎜ − κ0⎟∇2 ⎬T (x) + q(x) = 0 ⎝ κ (x) + κ 0 ⎠ ⎭ ⎩ ⎪

⎪

⎪

⎪

(5)

where the first term describes how heat would flow through the infinite homogeneous background medium of thermal conductivity κ0, while the second term incorporates the new thermal contributions stemming from the introduction of the (finite) target. Discretization of eq 5 yields an infinite linear system equivalent to 3 but now of the form (A + B)ijT(xj) + q(xi)a3 = 0i, with solution

⎡(PG P)[1 − B(PG P)]−1 ⎤ [1 − (PG0P)B]−1 (PG0P̅ ) 0 0 ⎢ ⎥ q(x )a3 T (x i ) = j −1 −1 ⎢(PG ⎥ P )[1 − B ( PG P )] PG P + ( PG P ) B [1 − ( PG P ) B ] ( PG P ) ̅ ̅ ̅ ̅ ̅ ⎣ 0 0 0 0 0 0 ⎦ij

where G0 = −A−1 and P and P̅ are projectors onto the target and environment regions. The details of this projection procedure are described in the SI. With the T-DDA formalism sufficiently described, we are now in a position to elucidate the spatial and spectral correlations between the heat power supplied to the system through an optical Fano interference and the resulting nanoscale temperature distribution. The connections between these thermal properties will be discussed through the examination of three different plasmon-supporting nanosystems that have been well-studied in the literature and are known to support optical Fano resonances in their scattering spectra.41,43,50 All calculations assume that each system is immersed within an infinite water environment at room temperature and is driven by a plane wave with 1 mW/μm2 intensity, corresponding to an incident field strength of |E0| = 8.7 × 105 V/m. Coupled Nanorod−Antenna System. Fano interferences are well-known to induce regions of transparency in the optical scattering spectra of certain plasmonically active nanosystems. It is also true that the Fano effect may cause destructive interferences in space, leaving specific locations in the shadows while other locations are illuminated within the same diffraction-limited spot. One such example of the latter effect can be found in the coupled nanorod−antenna system recently described in ref 43. This system consists of four gold nanobars arranged as shown in Figure 1. The outer two gold bars are referred to as nanorods due to their high aspect ratio, and the inner two are referred to as antennas because their induced polarization Dant relative to that of the outer rods Drod will dictate the interference visible in the far-field scattering spectrum. What is especially interesting about this system is that it supports both spatial and spectral Fano interferences. The lower left panel of Figure 1 shows a clear example of the destructive and spectrally localized effects of interference on the scattering efficiency, σsca/σgeo (black curve), for a particular value of nanorod length S = 120 nm and antenna spacing d = 25 nm, while the upper two panels of Figure 2 and the left panel of Figure 3 display how different regions in spacewithin the same nanorod−antenna systemare powered (q is the heat power density defined above) in drastically different ways through constructive and destructive interferences occurring at different excitation wavelengths within the Fano resonance.

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In their previous paper,43 Martin and co-workers discuss the spectral and spatial tunability of this Fano interference by changing either S or d relative to the fixed antennas (here chosen to be 70 nm in length), and we refer the reader to their paper for a more complete discussion of the system’s optical properties. Here, we focus on the thermal properties that are manifested as a result of this spatial and spectral interference. The lower right panel of Figure 1 shows the temperature spectra of the nanorod (red) and antenna (blue) structures across the Fano resonance, as computed via the T-DDA driven by a plane wave directed normally to the four-particle system

Figure 1. The coupled nanorod−antenna system composed of two gold nanorods (red) and two gold antennas (blue) arranged in the above configuration is well-known to support a Fano interference between its super- and subradiant plasmon modes, Drod + Dant and Drod − Dant, when excited by far-field light.43 As the rod length (S ) and antenna gap (d) are tuned relative to the fixed antennas (here chosen to be 70 nm in length), the spectral location of maximal destructive interference can be tuned across the optical spectrum. The lower left panel displays the scattering (black) and absorption (magenta) spectra of the nanorod−antenna system immersed in a water environment for the particular case where S = 20 nm and d = 25 nm. The resulting temperature spectra of the individual rods (red) and antennas (blue) are presented in the lower right panel. The former displays a pronounced Fano interference in the scattering spectrum near 780 nm, while the latter surprisingly shows that temperature differences exceeding 20 K can be attained between nanorod and antenna units within the same nanoparticle aggregate and within the same diffraction-limited spot, even in the presence of thermal diffusion. 1349



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matter, and for the purposes of this temperature spectrum, we choose the position of the center of mass of the lower rod and left antenna, respectively. On the basis of this temperature spectrum, it is especially interesting to point out that at different excitation wavelengths within the Fano resonance profile, the temperature on the nanorods can be controllably directed to be either higher than, lower than, or the same as that of the antennas, even though all four particles are composed of the same material (gold). This is counterintuitive because we normally think of heat as flowing isotropically throughout materials of the same composition when contained within the same diffraction-limited spot. Yet, here, this is not always the case. The reason is the spatial interference between super-radiant, Drod + Dant, and subradiant, Drod − Dant, hybridized dipolar plasmons that allows each component within the linear combination A(λ)[Drod + Dant] + B(λ)[Drod − Dant] to be specifically optically excited and powered at different wavelengths λ. Spatial maps of the resulting temperature field T(x) for the particular cases where A = B = 1/2, A = −B = 1/2, and A = 1, B = 0 are displayed in Figures 2 and 3, corresponding to the three wavelengths denoted by vertical lines in the temperature spectra shown in Figure 1. The left and right columns of Figure 2 show the heat power density (upper panels) and resulting temperature change (lower panels) suffered by the nanorod−antenna system at an excitation wavelength of 830 and 760 nm, respectively. The left column corresponds to the case where the nanorods are predominantly polarized as Drod = (1/2)[Drod + Dant] + (1/2)[Drod − Dant] at 830 nm, while the right column corresponds to the case where the antennas are predominantly polarized as Dant = (1/2)[Drod + Dant] + (−1/2)[Drod − Dant] at 760 nm. The lower two panels clearly show the spatial localization of the temperature increase on either the nanorods or the antennas as directly reflecting the corresponding localization of the heat power density, which is due to interference effects. However, note that while the heat power delivered to the hotter set of particles is many times larger than that delivered to the colder particles, the resulting relative temperature difference is only around 20−30%. Thus, thermal diffusion plays a significant role in dictating the steady-state temperature distribution, even with the presence of an insulating water region between particles, and it is not a priori obvious how localized the temperature distribution will be. Nonetheless, the two quantities, heat power density q(x) and the resulting temperature distribution T(x), are correlated both spatially and spectrally. The spectral correlation is due completely to the

Figure 2. Heat power is supplied in a spatially localized manner to the coupled nanorod−antenna system upon optical excitation due to interference effects. The upper two panels show spatial maps of the heat power density q(x) for two different excitation wavelengths near the Fano interference maximum, corresponding to the black vertical lines at 760 and 830 nm in the spectra in Figure 1. At both wavelengths, q(x) is nanolocalized to either the rods or the antennas and differs in magnitude by a factor of 4−15 between them when integrated over the entire particle volume. Yet, in the presence of the thermal diffusion, it is not obvious to what extent the resulting temperature distribution will reflect these differences. The lower two panels display spatial maps of the temperatures T(x), determined via the T-DDA, corresponding to the same excitation wavelengths. In both cases, the temperature increase remains localized to the exact same nanoparticles where the heat power density is localized. However, at both wavelengths, the difference in temperatures between the rods and antennas is significantly reduced to approximately a factor of 20%.

and polarized as shown in Figure 1. In the calculations, the four gold nanobars are immersed in water, and the dielectric and thermal conductivity data for both are chosen to be their bulk values; the former are taken from Palik,51 and the latter are taken as κAu = 318 W/m·K and κwater = 0.60 W/m·K. Because these values correspond to room-temperature measurements, all reported temperature changes are taken with respect to ∼300 K in the following. Each particle’s width and height are fixed at 40 nm, and the spacing between the nanorods and antennas is fixed at 20 nm. Due to the significant differences between κAu and κwater, the temperature within a particular gold particle in the assembly is nearly uniform. This means that the location on each rod where we map the temperature does not

Figure 3. Away from the Fano interference, the entire nanorod−antenna system is uniformly powered by the external field. This is clearly evident in the left panel displaying the heat power density q(x) corresponding to the black vertical line at 600 nm in the spectra shown in Figure 1. The spatial distribution of the resulting temperature increase is displayed in the middle panel and can be seen to be nearly uniform across the system, in accordance with the heat power density. The right panel displays three temperature profiles extracted along the vertical black lines in the temperature maps at 830 (red), 760 (blue), and 600 (black). This plot makes it especially clear the extent to which temperature changes can be controllably nanolocalized in space at different excitation wavelengths due to the unique Fano interference supported by this system. 1350



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optical Fano interference, while the spatial correlation means that the regions of low thermal conductivity (i.e., the water) are capable of trapping thermal energy within a single particle to a noticeable degree. This means that the interference found in this system gives rise to the formation of thermal hot spots (nanolocalized regions of increased temperature) of systematically controllable location that is tunable by the varying the excitation wavelength. As a counterexample, the left two panels of Figure 3 display the more common case where the heat power density and resulting temperature increase is nearly uniform across all four particles at 600 nm. This is due to the fact that the 600 nm excitation wavelength is outside of the Fano resonance window and the requisite interference is lost. The right panel of Figure 3 also shows a cross-sectional cut of the temperature profiles (taken along the vertical black lines in Figures 2 and 3) at 600, 760, and 830 nm to more clearly visualize the nanoscopic spatial dependence of T(x). By changing the relative particle dimensions and spacings, these surprising thermal properties offering the possibility to controllably manipulate temperature changes at specific points in space within the same diffractionlimited spotcan be tuned to occur at other excitation wavelengths across the optical spectrum. Catalytic applications may someday exploit these ideas to control the spatial locations of desired chemical transformations. Nanorod Heterodimer. The previous example demonstrated that Fano interferences can be exploited to control the spatial localization of increased or decreased temperature in nanoparticle aggregates of the same material composition as a function of excitation wavelength. Here, we explore a second system composed of a colinear Pd−Ag heterorod dimer (κPd = 71.8 W/m·K, κAg = 429W/m·K) immersed in water that supports an optical Fano resonance but does not allow for the temperature to be controllably increased or decreased at different nanoscopic points in space by tuning the excitation wavelength. The optical properties of this system, depicted in the upper panel of Figure 4, have already been reported elsewhere,50 and the interference between the dimer’s superradiant (Pd dipole plus Ag quadrupole, D0 + Q0) and subradiant (Pd dipole minus Ag quadrupole, D0 − Q0) plasmon modes has been implicated in its Fano resonance profile. We present this case here as a counterexample to demonstrate that not all Fano interferences offer the ability to direct the nanolocalization of increased/decreased temperature to different points in space. It illustrates how differences in relative electrical and thermal conductivities affect heat flow. In the spectral regime where the Ag quadrupole plasmon overlaps the Pd dipole plasmon, Im εPd(ω)/Im εAg(ω) ≈ 30. Yet, the thermal conductivity of Ag is about six times larger than that of Pd. This has the effect of heat power being preferentially supplied to the Pd rod that is unable to diffuse appreciably across the 1 nm water gap to the Ag rod due to the poor thermal conduction properties of water. Even though the Ag rod is better at conducting heat, it is unable to quench the resulting high temperature induced in the nearby Pd rod. Consequently, the Pd rod remains hotter than the Ag rod across the entire spectral window of the Fano resonance. The Pd rod is immersed within a thermal hot zone that remains pinned to it. This is evident in Figure 4, where the dimer’s optical scattering/absorption spectra (middle panel) and associated temperature spectra (bottom panel) are displayed. A spatial profile of the dimer’s temperature field T(x) is also computed in Figure 5, corresponding to a 460 nm excitation wavelength, where the largest temperature difference (∼10 K)

Figure 4. The Pd−Ag heterorod dimer displayed in the upper panel is known to support a Fano resonance due to the interference between its super- and subradiant, D0 + Q0 and D0 − Q0, plasmon modes excited by far-field light.50 The scattering (black) and absorption (magenta) spectra of this dimer system immersed in water are displayed in the middle panel. The spectral region of destructive interference can be moved around the optical spectrum by tuning the relative lengths of each rod, effectively shifting the spectral location of the narrow Ag quadrupole plasmon resonance with respect to the broad Pd dipole plasmon resonance. The resulting temperature spectra for the Pd (red) and Ag (blue) rods within the dimer are displayed in the lower panel. It is important to note that the temperature is always hotter on the Pd rod than that on the Ag rod across the entire spectral window. This is due to the greater lossiness of Pd over Ag, even though Ag is more thermally conductive. Another interesting feature of this temperature spectrum is that the degree of temperature increase can be tuned as a function of excitation wavelength. Said differently, thermal hot spots arise on either side of the Fano resonance, while a thermal cold spot appears in the region of maximally destructive interference. The latter (and correspondingly the former) can be tuned to occur within a particular spectral window through prior design of the relative rod lengths within the dimer.

Figure 5. The temperature profile T(x) of the Pd−Ag heterorod dimer is computed at 460 nm, where the system attains its maximal temperature increase. This excitation wavelength is indicated in Figure 4 by the black vertical lines in both the scattering/absorption and temperature spectra. It is interesting to note that the 1 nm water gap between the rods is not thermally conductive enough for the temperature on the Pd rod to be significantly quenched by the more thermally conductive Ag rod. This is why the Pd rod remains hotter than the Ag rod across the Fano resonance. This pinning of the nanolocalized temperature increase on the Pd particle is interesting in and of itself because it represents another example where temperature changes can be localized to fixed nanoscopic regions of space, even in the presence of thermal diffusion. 1351



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is attained between the Pd and Ag rods. It is interesting to point out that while the Pd rod is always hotter than the Ag rod, at the spectral location of maximal destructive interference (near 540 nm), neither rod is appreciably heated. This implies that the destructive nature of this Fano interference induces a relative thermal cold spot that is located spectrally in between two thermal hot spots. Without this destructive interference feature, there would be a significant temperature increase across this entire spectral window and no temperature decrease would be achieved near 540 nm. This behavior is quite interesting by itself because it provides a way to systematically heat or cool a predefined region in space (biased toward the Pd particle) as a function of excitation wavelength through a spectral window where this controllability would normally be absent. Nanocube. As a third example of the effects of a Fano resonance upon the nanoscale flow of heat, we consider the case of the nanocube immersed in water and subjected to a driving optical frequency field. In the presence of a substrate that serves to break the symmetry of the system, the cube is well-known to support a Fano interference between its superradiant D0 + Q0 (dipole plus quadrupole plasmons) and subradiant D0 − Q0 (dipole minus quadrupole plasmons) hybridized plasmon modes.41 Figure 6 displays an illustration

Figure 7. Due to the interference between the nanocube’s super- and subradiant plasmons, heat power can be supplied by the exciting field in a spatially anisotropic manner. The upper two panels display spatial maps of the heat power density q(x) corresponding to the 480 and 530 nm excitation wavelengths denoted by the black vertical lines in Figure 6. These wavelengths are chosen to excite either the bottom (substrate) or top (water) localized hybridized plasmon of the cube. While the heat power density is highly spatially anisotropic, this does not necessarily mean that the resulting temperature field will reflect this anisotropy. The lower two panels display spatial maps of the resulting temperature increase at the same two excitation wavelengths. It is clearly visible that both temperature maps are nearly isotropic in space, meaning that the temperature is nearly uniform throughout the entire cube despite the fact that q(x) is not. The white/black horizontal lines are drawn to represent the upper boundary of the Si substrate.

within the Fano resonance profile and are distinguished by the two peaks in the cube’s scattering spectrum (vertical black lines in the middle panel of Figure 6). The upper two panels of Figure 7 show spatial maps of the heat power density q(x) supplied to the cube at each of these excitation wavelengths corresponding to the super- and subradiant plasmons. It is clearly visible that heat power is correspondingly localized toward the substrate or water side of the cube, as might be expected. However, the question remains of whether or not the resulting temperature increase will remain localized to these same spatial locations in the presence of thermal diffusion. The coupled nanorod−antenna system discussed previously serves as an example of a similar situation where the heat power density q(x) can be systematically localized at different points in space, the location of which is controllable by scanning the excitation wavelength. What is interesting about this system is that the resulting temperature distribution T(x) also remains largely localized to the same points in space as q(x). However, this is not the case for the cube. The lower two panels of Figure 7 show spatial maps of the resulting temperature fields corresponding to the excitation of super- and subradiant plasmons. It is clearly visible that the cube’s temperature is nearly uniform throughout its entire volume and inherits no signatures of the substrate- or water-localized heat power density. The temperature spectrum corresponding to a point on the top face (water side) and a point on the bottom face (substrate side) is shown in the lower panel of Figure 6 to further illustrate that the temperature is uniform throughout the cube across the entire Fano spectrum. Unlike the coupled nanorod−antenna system, there is no region of low thermal conductivity to separate the top face from the bottom face of

Figure 6. The nanocube on a substrate is well-known to support a Fano resonance due to the interference between its super- and subradiant, D0 + Q0 and D0 − Q0, plasmon modes excited by far-field light.43 The scattering (black) and absorption (magenta) spectra of the nanocube immersed in water are displayed in the middle panel. The spectral region of destructive interference can be moved around the optical spectrum by tuning the distance between the cube and substrate. The lower panel displays the resulting temperature spectra corresponding to a point on the bottom (substrate side, red) and top (water side, blue) face of the cube. Notice that the computed temperature is nearly identical between top and bottom faces.

of the cube−substrate geometry (upper panel) as well as the scattering/absorption spectrum (middle panel) for a (40 nm)3 silver cube positioned 8 nm above a Si substrate. A unique feature of the cube is that its super-radiant D0 + Q0 plasmon mode at 530 nm is localized to the substrate, while its subradiant D0 − Q0 plasmon mode at 480 nm is localized toward the water environment above. Each of these hybridized plasmons can be accessed at different excitation wavelengths 1352



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(2) Cognet, L.; Tardin, C.; Boyer, D.; Choquet, D.; Tamarat, P.; Lounis, B. Single Metallic Nanoparticle Imaging for Protein Detection in Cells. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 11350−11355. (3) Gobin, A. M.; Lee, M. H.; Halas, N. J.; James, W. D.; Drezek, R. A.; West, J. L. Near-Infrared Resonant Nanoshells for Combined Optical Imaging and Photothermal Cancer Therapy. Nano Lett. 2007, 7, 1929−1934. (4) Jain, P. K.; El-Sayed, I. H.; El-Sayed, M. A. Au Nanoparticles Target Cancer. Nano Today 2007, 2, 18−29. (5) Zhao, W.; Karp, J. M. Tumour Targeting: Nanoantennas Heat Up. Nat. Mater. 2009, 8, 453−454. (6) Skirtach, A. G.; Dejugnat, C.; Braun, D.; Susha, A. S.; Rogach, A. L.; Parak, W. J.; Möhwald, H.; Sukhorukov, G. B. The Role of Metal Nanoparticles in Remote Release of Encapsulated Materials. Nano Lett. 2005, 5, 1371−1377. (7) Jain, P. K.; Huang, X.; El-Sayed, I. H.; El-Sayed, M. A. Noble Metals on the Nanoscale: Optical and Photothermal Properties and Some Applications in Imaging, Sensing, Biology, and Medicine. Acc. Chem. Res. 2008, 41, 1578−1586. (8) Hirsch, L. R.; Stafford, R. J.; Bankson, J. A.; Sershen, S. R.; Rivera, B.; Price, R. E.; Hazle, J. D.; Halas, N. J.; West, J. L. NanoshellMediated Near-Infrared Thermal Therapy of Tumors under Magnetic Resonance Guidance. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 13549− 13554. (9) O’Neal, D.; Hirsch, L. R.; Halas, N. J.; Payne, J.; West, J. L. Photo-Thermal Tumor Ablation in Mice Using Near InfraredAbsorbing Nanoparticles. Cancer Lett. 2004, 209, 171−176. (10) Ye, E.; Win, K. Y.; Tan, H. R.; Lin, M.; Teng, C. P.; Mlayah, A.; Han, M.-Y. Plasmonic Gold Nanocrosses with Multidirectional Excitation and Strong Photothermal Effect. J. Am. Chem. Soc. 2011, 133, 8506−8509. (11) Christopher, P.; Xin, H.; Linic, S. Visible-Light-Enhanced Catalytic Oxidation Reactions on Plasmonic Silver Nanostructures. Nat. Chem. 2011, 3, 467−472. (12) Hou, W.; Hung, W. H.; Pavaskar, P.; Goeppert, A.; Aykol, M.; Cronin, S. B. Photocatalytic Conversion of CO2 to Hydrocarbon Fuels via Plasmon-Enhanced Absorption and Metallic Interband Transitions. ACS Catal. 2011, 1, 929−936. (13) Grabow, L. C.; Mavrikakis, M. Mechanism of Methanol Synthesis on Cu through CO2 and CO Hydrogenation. ACS Catal. 2011, 1, 365−384. (14) Hung, W. H.; Aykol, M.; Valley, D.; Hou, W.; Cronin, S. B. Plasmon Resonant Enhancement of Carbon Monoxide Catalysis. Nano Lett. 2010, 10, 1314−1318. (15) Hou, W.; Liu, Z.; Pavaskar, P.; Hung, W. H.; Cronin, S. B. Plasmonic Enhancement of Photocatalytic Decomposition of Methyl Orange under Visible Light. J. Catal. 2011, 277, 149−153. (16) Pollock, H. M.; Hammiche, A. Micro-Thermal Analysis: Techniques and Applications. J. Phys. D: Appl. Phys. 2001, 34, R23U−R53. (17) Cao, L.; Barsic, D. N.; Guichard, A. R.; Brongersma, M. L. Plasmon-Assisted Local Temperature Control to Pattern Individual Semiconductor Nanowires and Carbon Nanotubes. Nano Lett. 2007, 7, 3523−3527. (18) Adleman, J. R.; Boyd, D. A.; Goodwin, D. G.; Psaltis, D. Heterogenous Catalysis Mediated by Plasmon Heating. Nano Lett. 2009, 9, 4417−4423. (19) Neumann, O.; Urban, A. S.; Day, J.; Lal, S.; Nordlander, P.; Halas, N. J. Solar Vapor Generation Enabled by Nanoparticles. ACS Nano 2013, 7, 42−49. (20) Ratto, F.; Matteini, P.; Rossi, F.; Menabuoni, L.; Tiwari, N.; Kulkarni, S. K.; Pini, R. Photothermal Effects in Connective Tissues Mediated by Laser-Activated Gold Nanorods. Nanomed. Nanotechnol. 2009, 5, 143−151. (21) Matteini, P.; Ratto, F.; Rossi, F.; Centi, S.; Dei, L.; Pini, R. Chitosan Films Doped with Gold Nanorods as Laser-Activatable Hybrid Bioadhesives. Adv. Mater. 2010, 22, 4313−4316. (22) Neumann, O.; Feronti, C.; Neumann, A. D.; Dong, A.; Schell, K.; Lu, B.; Kim, E.; Quinn, M.; Thompson, S.; Grady, N.; Nordlander,

the cube. This serves as an important counterexample, demonstrating that a Fano interference by itself is not sufficient to achieve a nanolocalized and directable temperature increase. However, if present in a system of the right geometry, material composition, and aggregation scheme, a Fano resonance may enable such unusual thermal behavior. In conclusion, plasmon-supporting metal nanostructures offer the possibility to focus light to nanoscopic dimensions well below the diffraction limit. The heat power induced by these highly spatially localized near-fields is often similarly localized to the same points in space at the same frequencies due to the simple connection between these quantities. However, in the presence of thermal diffusion, it is not a priori obvious to what extent the resulting temperature changes induced will be correlated spatially and spectrally with the applied heat power as diffusion tends to delocalize the temperature field. In this Letter, we demonstrate that temperature changes can surprisingly be localized and even controllably directed to the same nanoscopic regions of space as the heat power through the excitation of a Fano resonance. Three different nanostructures that support optically driven Fano interferences are presented to elucidate the conditions under which temperature changes may be controllably directed on the nanoscale despite thermal diffusion. We find that the presence of a Fano interference is by itself not sufficient to induce such temperature control; however, when present within a nanostructure of the right composition and morphology, such control is predicted to be achievable. Specifically, we find that the interference must localize the scattered electric field to different equally absorbing regions separated by a barrier of low thermal conductivity such as water. When these conditions are met, the qualitative thermal properties are found to be robust against small variations in the nanosystem geometry. The successful realization of these ideas bears impact upon a variety of future applications ranging from thermoplasmonic chemical catalysis11−19 and photothermal cancer therapy3−10 to phononic information processing, nanoscale patterning, thermal rectification, and the more efficient cooling of computer processor chips.23,52−56

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ASSOCIATED CONTENT

S Supporting Information *

Computational details of the T-DDA method are described. 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]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation’s CAREER program under Award Number CHE-1253775 and through XSEDE resources under Award Number PHY-130045 (D.J.M.). The authors acknowledge useful discussions with Dr. Charles Cherqui from the University of Washington.

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REFERENCES

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