Localized Heating of Nanostructures by Coherent Laser Pulses

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Localized Heating of Nanostructures by Coherent Laser Pulses Vassilios Yannopapas J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp4033639 • Publication Date (Web): 14 Jun 2013 Downloaded from http://pubs.acs.org on June 15, 2013

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The Journal of Physical Chemistry

Localized Heating of Nanostructures by Coherent Laser Pulses Vassilios Yannopapas∗,† Department of Materials Science, University of Patras, GR-26504 Patras, Greece, and Department of Physics, National Technical University of Athens, GR-15780 Athens, Greece E-mail: [email protected]

Abstract By performing rigorous numerical simulations, we show that it is possible to create a nanoscale temperature distribution in a collection of metallic nanoparticles with the aid of laser coherent control, without the need for nanofabrication. For coherent laser pulses of nanosecond duration and optimized geometrical configurations of the nanoparticles, the temperature distribution can last for up to thousands of nanoseconds due to the larger relaxation times of the various cooling mechanisms. By using optimized laser pulses obtained by an adaptive-control process, one can address locally the temperature of a given target-nanoparticle paving the way for nanoscale chemical-reaction control via laser fields.

Keywords: Metallic nanoparticles, heat transfer, coherent control, nanosecond laser pulses, surface plasmons. Introduction. The ability to control locally temperature and heating is of paramount importance in various disciplines such as biology, chemistry and electronics. In the microscale, arrays of microheaters have been used in biological applications such as for rapid thermal lysis ∗ To

whom correspondence should be addressed of Materials Science, University of Patras, GR-26504 Patras, Greece ‡ Department of Physics, National Technical University of Athens, GR-15780 Athens, Greece † Department

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of cells, 1 protein synthesis 2 and programmed manipulation. 3 Microheater arrays have also been used for the functionalization of electronic and optoelectronic devices with nanomaterials. 4 In the nanoscale, several case studies of strong temperature localization have been reported, e.g., nanoparticle-assisted lysis of cancer cells with nanoscale precision (without affecting neighboring normal tissue), 5 thermal data recording via thin-film nanoheaters for high-density optical data storage, 6 ultrafast switching of phase-change materials via localized heating, 7,8 accelerated response of hydrogen sensors based on Joule-heated nanowires, 9,10 and chemical-reaction control via selective heating of nanowire arrays. 11 In the all above cases, localized heating is achieved via advanced nanomaterials (nanowires or carbon nanotubes) and sophisticated devices (thermal cantilevers or atomic-force microscopes) heated by electrodes or by expensive laser systems with nanoscale focus. Here we propose a novel method for localized heating of nanostructures by laser light without resorting to laborious experimental setups. Namely, we combine the laser excitation of localized electromagnetic (EM) modes such as surface plasmons in metallic nanostructures, with the concept of coherent control, i.e., the modification of the output data of a device by the phase carried by the input data. 12 Coherent control of light has been mainly applied to quantum systems (atoms, molecules and quantum dots) wherein their quantum state is determined by the interference of the different quantum pathways induced by an external optical field with properly designed amplitude, phase and polarization. 13 By transferring this concept in the nanoscale science, coherent control over nanostructures can be achieved by their illumination with ultrashort laser chirped pulses. 14 In case where a given nanostructure supports localized EM modes such as surface plasmons or exciton-polaritons, nanoscale spatial control and femtosecond temporal control of light is possible by the same pulse. Although the coherent control of nanostructures is usually driven by simple chirped pulses, 14–20 most efficient spatiotemporal control is achieved by adaptive feedback schemes and learning algorithms. 21–30 Quite naturally, the generation of an optical near-field landscape in, say, a plasmonic nanostructure by a laser field leads to a corresponding temperature landscape. However, a temperature

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landscape is not proportional to a near-field landscape due to the various cooling mechanisms taking place when an object is heated above the temperature of the environment. For the case of collections of nanoparticles (NPs), the cooling mechanisms are the heat transfer among the NPs, the Stefan-Boltzmann cooling and the heat exchange via inelastic collisions with ambient air atoms. 31 As we will show below, for laser pulses of nanosecond duration, the cooling rates cannot catch up with the laser heating of the NPs allowing for the depiction of a temperature landscape which can last up to a few thousands of nanoseconds. The final temperature distribution of such a plasmonic nanostructure results from the interplay between the laser-induced heating and the different cooling mechanisms which renders the geometrical arrangement of the NPs critical for the appearance of a temperature landscape. In what follows, we will present the theory for simulating the temperature distribution of a collection of NPs irradiated by laser pulses. It is a many-body theory for the exchange of heat among the NPs and/ or their environment in the context of fluctuational electrodynamics 32–37 and of EM Green’s tensor formalism. The EM Green’s tensor and the optical field are calculated in the framework of the discrete-dipole approximation (DDA). 38–40 By applying this theory to representative case studies, we show that the size and geometrical arrangement of the NPs are decisive factors for the occurrence of a distinct temperature landscape when the NPs are illuminated by chirped pulses. However, by exploiting the wave interference induced by two different laser beams we increase the degrees of freedom of our system allowing for the application of adaptive control via genetic/ evolutionary algorithms in order to exercise selective heating of individual NPs irrespective of the geometrical arrangement of the NPs. Theory. Consider a collection of a finite number N of metallic NPs. The NPs are illuminated by an arbitrary laser field and are therefore heated and begin to exchange energy. The corresponding energy balance equation for the i-th NP of the collection reads as follows dTi 4 3 π Si ρs;i cs;i = Cabs;i (t)I p (t) 3 dt N

4 −4Cabs;i σB [Ti4 (t) − Tenv ] + 3G0 ∑ T i j [T j (t) − Ti (t)] j=1

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s −4π Si2 ξ F

i kB Tenv h Ti (t) −1 p 8π mg Tenv

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(1)

where Ti , Si , ρs;i , cs;i are the temperature, radius, density and specific heat of the i-th NP, respectively. Tenv is the temperature of the surrounding medium (ambient Ar atoms in our case). The left-hand side of eq 1 is the variation of the thermal energy of the NP per unit time. The first term of the right-hand side of eq 1 is the power absorbed by the NP where I p (t) is the intensity of the laser pulse and Cabs,i the absorption cross section of the NP given by 38–40 Cabs,i (t) =

4πω ℑ[pi (t) · Ei (t)∗ ] c|E0inc (t)|2

(2)

where ω is the angular frequency, c the speed of light in vacuum and E0inc the amplitude of the laser field. pi is the dipole moment and Ei is the local electric field of the i-th NP given by Ei = αi−1 pi where αi (ω ) is the polarizability of the i-th NP. pi are given by the coupled-dipole equations of the DDA method 0 pi (t) = αi (ω )[Einc j (t) + ∑ Gi j (ω )p j (t)],

(3)

j6=i

where G0i j (ω ) is the electric part of the free-space Green’s tensor given by " # exp(ikr ) ikr − 1 i j i j G0i j (ω ) = k2 (ˆri j ⊗ rˆi j − 13 ) + (3ˆri j ⊗ rˆi j − 13 ) 4 π ri j ri2j

(4)

and Einc j the electric field of the incident laser pulse at the position of the j-th NP. The polarizability of a spherical NP is provided by the Clausius-Mossotti relation

αi (ω ) = 4πε0 Si3

ε (ω ) − εm ε (ω ) + 2εm

(5)

where εm is the dielectric function of the medium surrounding the NP (air in our case - εm = 1) and

ε (ω ) is the dielectric function of the NP. The second term of the right-hand side of eq 1 is the modified Stefan-Boltzmann law which

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provides the power of thermal radiation emitted by each NP due to the temperature difference with the environment (σB is the Stefan-Boltzmann constant). Cabs,i is the (thermal) average absorption cross section of the i-th NP provided by Cabs,i = 15/(4π 3 )

Z ∞ 0

dxg(x)Cabs,i (x)

(6)

with g(x) = x3 /[exp(x) − 1]2 , x = h¯ ω /kB T . The third term of the right-hand side of eq 1 expresses the radiative heat transfer among the NPs. 41 G0 = π 2 kB2 T /(3h) (kB being the Boltzmann constant and h Planck’s constant) is the quantum of thermal conductance. T i j is the average transmission coefficient 42 given by T i j = (3/π ) 2

Z ∞ 0

dx f (x)Ti j (x)

(7)

with f (x) = x2 exp(−x)/[exp(x) − 1]2 , x = h¯ ω /kB T and 41 4 ω Ti j (ω ) = ( )4 ℑαi (ω )ℑα j (ω )Tr[Gi j (ω )G†i j (ω )] 3 c

(8)

Ti j ∈ [0, 1] and it is analogous to the transmission probability of electrons in the Landauer formalism. 42 f (x) is a function reminiscent of the mean energy of a harmonic oscillator. 42 Gi j (ω ) is the EM Green’s tensor for the collection of NPs and is found by solving the following linear system of 3N equations £ ¤ ω2 0 δ α − G ( ω ) Gk j (ω ) = G0i j (ω ). ik k ∑ ik 2 c k

(9)

The fourth term of the right-hand side of eq 1 is the heat exchange via inelastic collisions between the NPs and the ambient atoms surrounding the NPs (in our case Ar atoms). 43,44 F = 3 are the degrees of freedom for Ar, p the pressure of the Ar gas and mg the atomic mass of Ar.

ξ = 0.2 quantifies the degree of inelasticity of the NP-Ar atom collision. 44 Results and discussion. We consider a chain of five spherical NPs (see Figure 1a) described by a generic, Drude-type dielectric formula, i.e., ε (ω ) = 1 − ω p2 /[ω (ω + iγ )] where ω p is the 5



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plasma frequency and γ = 0.05ω p is the inverse of the free-electron relaxation time. The use of a generic dielectric function makes the present formalism applicable to all plasmonic materials such as noble metals in the optical and semiconductors in the infrared regime. 45 The NPs have the same radius S = 0.2c/ω p and the temperature of the environment is 300 K. The density of bulk gold is ρs = 19.3 g/cm3 and the corresponding specific heat cs = 0.129 Jg−1 K−1 . Figure 1 shows the temporal evolution of the absorption cross-section Cabs and the temperature for the NPs of the linear chain of Figure 1a for a normally incident, right-circularly polarized chirped pulse of nanosecond duration. We observe that the temperature of all NPs [the curves for the first (second) NP coincide with those of the fifth (fourth) NP due to the symmetry of the structure and the type of incident laser pulse] remains almost constant up to 15 ns as the characteristic time scale for all cooling mechanisms is orders of magnitude larger than the lifetime of the pulse. 31 Essentially there is no cooling of the NPs at this time scale allowing the NPs maintain a constant temperature for tens or even hundreds of nanoseconds after switching off the pulse. A chirped pulse sweeps through the different plasmon resonances of the NP chain as a result of the linear increase of the carrier frequency. The two different peaks appearing in Figure 1a for the first, third and fifth NPs correspond to surface plasmon modes of orthogonal polarization oscillations. Namely, the high- (low-) frequency peak in the absorption spectrum of Figure 1a is excited by incident light which is polarized parallel (normal) to the chain axis. So, for linearly polarized light, only one of the peaks appears in the absorption cross section. By using circularly polarized light both modes contribute to the power absorbed by the above NPs resulting in the two peaks in the absorption cross-section Cabs for both NPs. The second and fourth NPs reside at a minimum of the optical near field as evidenced by the very low absorption cross section. However, these NPs (the second and fourth) are more heated than the first and fifth ones which absorb a much larger proportion of the incident laser power. This is due to the fact that the second and fourth NPs gain energy from the heat transfer among the NPs whilst the first and fifth NPs lose. The above clearly manifests that the temperature distribution is far from being proportional to the optical near-field distribution and the cooling of NPs should be taken into account. We note that, the rate

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of energy losses from the inelastic collision with air atoms (for the given ambient air pressure) as well as the Stefan-Boltzmann cooling are lower than that of heat exchange among the NPs. 31 Figure 2 shows the final temperatures of a linear chain of 5 NPs (see Figure 1a) for different NP radii. The distance among the NPs as well as the parameters of the chirped pulse are the same as those considered in Figure 1. We observe that the largest temperature difference occurs for NP radius S = 0.2c/ω p where the highest temperature belongs to the middle (third) NP. Since a given temperature distribution lasts enough time (up to 50 times the duration of a nanosecond pulse 31 ) after switching off the laser pulse, one can refer to ‘final’ temperatures of the NPs. In this context, the final temperature of each NP is determined by two competing factors: the rate of radiation absorption by the NP and the rate of heat exchange among the NPs. The heating rate of the NPs is inversely proportional to the volume of the NP leading to high temperatures for small sizes for the same pulse duration. On the other hand, by increasing the size of the NPs while keeping the interparticle distance constant, means that the surfaces of the NPs come closer increasing the rate of heat exchange among the NPs. However, a higher heat-exchange rate does not tell us anything about the sign of the net energy gained or lost by a given NP as a result of the heat exchange. It is obvious that we cannot predict intuitively the temperature distribution for the chain of NPs. We can only speculate that the low (high) temperatures compared to the temperature of the environment, 300 K, for large (small) radii is due to the slow (fast) absorption of incident radiation by the NPs compared to the duration of the pulse. In order to increase the external control over the temperature distribution of the NP chain of Figure 1a we should introduce more parameters determining the optical near-field. To this end, we assume that two different laser pulses with different linear polarizations (S and P) are incident obliquely on the NP chain. This enables us to exercise an adaptive control scheme, in our case an evolutionary algorithm 46 (PIKAIA code 47 ), for implementing a given temperature distribution on the NP chain. In Figure 3 we have searched for an optimized function ω (t) imparting the highest temperature to the first NP (No. 1 in the inset) in contrast to the trend observed in Figure 1 where the middle NP reaches the highest temperature as it absorbs more power than the edge ones for

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the entire frequency spectrum. The optimized time function of frequency ω (t) is shown in the inset of Figure 3. Evidently, using this function ω (t) for both laser beams (simulated as plane waves) we have heated preferentially the first NP over the rest of the NPs without literally focusing our laser beam on this NP. In other words, we have created an ultra-small heat spot with two plane-wave pulses without the need of laborious nano-heating devices. To give an estimate of the heat spot: for gold NPs, h¯ ω p ' 9 eV which gives a radius S = 0.2c/ω p ' 4.4 nm and a centerto-center interparticle distance of d = c/ω p ' 22 nm. We note that the wave interference of the scattered fields generated by each incident beam is essential for the preferential heating of the edge NPs via the evolutionary algorithm. In Figure 4 we show adaptive control to a more symmetric configuration, i.e., to a square of NPs. Again, the optimized frequency function of the inset allows for selective heating of a particular NP of the square, despite the geometrical equivalence of the 4 NPs. In Figure 5 we show the spatial distribution of temperature within a planar fractal aggregate of NPs after switching off the incident pulse. The temperature varies from 302K to 395K depending on the position within the aggregate creating a rich temperature landscape. Evidently, such a fractal temperature landscape can find application, e.g., in chemical-reaction control provided that the chemical process is faster than the characteristic cooling/ relaxation time of the nanostructure. We note that for the fractal aggregate of Figure 5, the heating exchange among the NPs should also include the contribution of magnetic thermal fluctuations in the third term of eq 1 41 due to the close proximity of the NPs, a factor which would relatively modify the spatial distribution of temperature in the fractal aggregate. A final note on the experimental verification of the phenomena reported here. First of all, for a direct quantitative comparison of theory and experiment, an experimentally obtained dielectric function 48 for the gold NPs should be assumed in order to include the interband transitions taking place in bulk gold which is an additional factor leading to heating of the NPs. Furthermore, the NPs are usually placed on top of a substrate which must be made of thermally insulating material in order to reproduce the computational/ theoretical setup presented here.

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Conclusion We have presented a theory for simulating the temperature landscape generated in plasmonic nanostructures irradiated by laser fields. In particular, we have shown that via the aid of the surface plasmon excitations, one can individually address the temperature in metallic nanostructures with nanoscale accuracy, i.e., it is possible to impart different temperatures in different nanoparticles by coherent laser fields. The temperature distribution (profile) in a certain nanostructure can be controlled in time via coherent laser pulses such as chirped pulses as well as more complicated pulses generated by adaptive optimization techniques. The several cooling mechanisms are practically inert for nanosecond pulses allowing for a certain temperature distribution among the nanoparticles to last up to several hundreds of nanoseconds. The latter may find application in chemistry as one can, for example, exercise spatial and temporal control over the process of chemical reactions taking place at the surface of the nanoparticles. 49 Furthermore, it can find application in NP-assisted hyperthermic lysis of malignant cells without affecting nearby normal tissue by adaptive control of two laser beams illuminating the target area.

Acknowledgement The author wishes to thank Dr A. Bakandritsos for helpful discussions.

References (1) Privorotskaya, N.; Liu, Y S.; Lee, J.; Zeng, H.; Carlisle, J. A.; Radadia, A.; Millet, L.; Bashir, R.; King, W. P. Rapid Thermal Lysis of Cells Using Silicon-Diamond Microcantilever Heaters. Lab Chip 2010, 10, 1135–1141. (2) Ginet, P.; Montagne, K.; Akiyama, S.; Rajabpour, A.; Taniguchi, A.; Fujii, T.; Sakai, Y.; Kim, B.; Fourmy, D.; Volz, S. Towards Single Cell Heat Shock Response by Accurate Control on Thermal Confinement with an On-Chip Microwire Electrode. Lab Chip 2011, 11, 1513– 1520.

9



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Page 10 of 18

(3) Huber, D. L.; Manginelli, R. P.; Samara, M. A.; Kim, B. I.; Bunker, B.C. Programmed Adsorption and Release of Proteins in A Microfluidic Device. Science, 2003, 301, 352–354. (4) Hong, Y. J.; Kim, Y. J.; Jeon, J. M.; Kim, M.; Choi, J. H.; Baik, C. W.; Kim, S. I.; Park, S. S.; Kim, J. M.; Yi, G. C. Selective Formation of GaN-based Nanorod Heterostructures on SodaLime Glass Substrates by a Loal Heating Method. Nanotechnology 2011, 22, 205602. (5) Lapotko, D. O.; Lukianova, E.; Oraevsky, A. A. Selective Laser Nano-Thermolysis of Human Leukemia Cells with Microbubbles Generated Around Clusters of Gold Nanoparticles. Lasers Surg. Med. 2006, 38, 631–642. (6) Hamann, H. F.; O’Boyle, M.; Martin, Y.C.; Rooks, M.; Wickramasinghe, H. K. Ultra-HighDensity Phase-Change Storage and Memory. Nat. Mater. 2006, 5, 383–387. (7) Lee, S. H.; Jung, Y.; Agarwal, R. Highly Scalable Non-Volatile and Ultra-Low-Power PhaseChange Nanowire Memory. Nat. Nanotechnol. 2007, 2, 626–630. (8) Xiong, F.; Liao, A.; Pop, E. Inducing Chalcogenide Phase Change with Ultra-Narrow Carbon Nanotube Heaters. Appl. Phys. Lett. 2009, 95, 243103. (9) Yang, F.; Taggart, D. K.; Penner, R. M. Joule Heating a Palladium Nanowire Sensor for Accelerated Response and Recovery to Hydrogen Gas. Small 2010, 6, 1422–1429. (10) Offermans, P.; Tong, H. D., van Rijn, C. J. M.; Merken, P, Brongersma, S. H.; Crego-Calama, M. Ultralow-power Hydrogen Sensing with Single Palladium Nanowires. Appl. Phys. Lett. 2009, 94, 223110. (11) Jin, C. Y.; Li Z.; Williams, R. S.; Lee, K. C.; Park, I. Localized Temperature and Chemical Reaction Control in Nanoscale Space by Nanowire Array. Nano Lett. 2011, 11, 4818–4825. (12) Tuchscherer, P.; Rewitz, C.; Voronine, D.; García de Abajo, F. J.; Pfeiffer, W.; Brixner, T. Analytic Coherent Control of Plasmon Propagation in Nanostructures. Opt. Express 2009, 17, 14235–14259. 10


Page 11 of 18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(13) Brumer, P.; Shapiro, M. (eds.) Principles of the Quantum Control of Molecular Processes, Wiley: New York, 2003. (14) Stockman, M. I.; Faleev, S. V.; Bergman, D. J. Coherent Control of Femtosecond Energy Localization in Nanosystems. Phys. Rev. Lett. 2002, 88, 067402. (15) Stockman, M. I., Bergman, D. J.; Kobayashi, T. Coherent Control of Nanoscale Localization of Ultrafast Optical Excitation in Nanostystems. Phys. Rev. B 2004, 69, 054202. (16) Stockman, M. I.; Hewageegana, P. Nanolocalized Nonlinear Electron Photoemission under Coherent Control. Nano Lett. 2005, 5, 2325–2329. (17) Stockman, M. I., Kling, M. F.; Kleineberg, U.; Krausz, F. Attosecond Nanoplasmonic-Field Microscope. Nature Photon. 2007, 1, 539–544. (18) Stockman, M. I. Ultrafast Nanoplasmonics under Coherent Control. New. J. Phys. 2008, 10, 025031. (19) Lévêque, G.; Martin, O. J. F. Narrow-Band Multiresonant Plasmon Nanostructure for the Coherent Control of Light: An Optical Analog of the Xylophone. Phys. Rev. Lett. 2008, 100, 117402. (20) Yannopapas, V.; Vitanov, N. V. Coherent Control of Surface Exciton-Polaritons in Collections of Semiconductor Nanoparticles: A Theoretical Study. Phot. Nanostruct. Fundam. Appl. 2011, 9, 196–200. (21) Brixner, T.; García de Abajo, F. J.; Schneider, J.; Pfeiffer, W. Nanoscopic Ultrafast SpaceTime-Resolved Spectroscopy. Phys. Rev. Lett. 2005, 95, 093901. (22) Kubo, A.; Onda, K.; Petek, H.; Sun, Z.; Jung, Y. S.; Kim, H. K. Femtosecond Imaging of Surface Plasmon Dynamics in a Nanostructured Silver Film Nano Lett. 2005, 5, 1123–1127. (23) Sukharev, M.; Seideman, T. Phase and Polarization Control as a Route to Plasmonic Nanodevices. Nano Lett. 2006, 6, 715–719. 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 18

(24) Brixner, T.; García de Abajo, F. J.; Schneider, J.; Spindler, C.; Pfeiffer, W. Ultrafast Adaptive Optical Near-Field Control. Phys. Rev. B 2006, 73, 125437 (25) Brixner, T.; García de Abajo, F. J.; Spindler, C.; Pfeiffer, W. Adaptive Ultrafast Nano-optics in a Tight Focus. Appl. Phys. B 2006, 84, 89–95. (26) Sukharev, M.; Seideman, T. Coherent Control of Light Propagation via Nanoparticle Arrays J. Phys. B 2007, 40, S283-S298. (27) Aeschlimann, M.; Bauer, M.; Bayer, D.; Brixner, T.; García de Abajo, F. J.; Pfeiffer, W.; Rohmer, M.; Spindler, C.; Steeb, F. Adaptive Subwavelength Control of Nano-Optical Fields. Nature (London) 2007, 446, 301–304. (28) Choi, S.; Park, D.; Lienau, C.; Jeong, M. S.; Byeon, C. C.; Ko, D.; Kim, D. S.; Femtosecond Phase Control of Spatial Localization of the Optical Near-Field in a Metal Nanoslit Array. Opt. Express 2008, 16, 12075–12083. (29) Huang, J. S.; Voronine, D. V.; Tuchscherer, P.; Brixner, T.; Hecht, B. Deterministic SpatioTemporal Control of Nano-Optical Fields in Optical Antennas and Nano Transmission Lines. Phys. Rev. B 2009, 79, 195441. (30) Utikal, T.; Stockman, M. I., Heberle, A. P.; Lippitz, M.; Giessen, H. All-Optical Control of the Ultrafast Dynamics of a Hybrid Plasmonic System. Phys. Rev. Lett. 2010, 104, 113903. (31) Yannopapas, V.; Vitanov, N. V. Spatiotemporal Control of Temperature in Nanostructures Heated by Coherent Laser Fields. Phys. Rev. Lett. 2013, 110, 044302. (32) Agarwal, G.; Quantum Electrodynamics in the Presence of Dielectrics and Conductors. I. Electromagentic-Field Response Functions and Black-Body Fluctuations in Finite Geometries. Phys. Rev. A 1975, 11, 253–264. (33) Carminati, R.; Greffet, J. J. Near-Field Effects in Spatial Coherence of Thermal Sources. Phys. Rev. Lett. 1999, 82, 1660-1663. 12


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(34) Shchegrov, A. V.; Joulain, K.; Carminati, R.; Greffet, J. J. Near-Field Spectral Effects due to Electromagnetic Surface Excitations. Phys. Rev. Lett. 2000, 85, 1548–1552. (35) Henkel, C.; Joulain, K.; Carminati, R.; Greffet, J. J. Spatial Coherence of Thermal Near Fields. Opt. Commun. 2000, 186, 57–67. (36) Joulain, K.; Mulet, J. P.; Marquier, F.; Carminati, R.; Greffet, J. J. Surface Electromagnetic Waves Thermally Excited: Radiative Heat Transfer, Coherence Properties and Casimir Forces Revisited in the Near Field. Surf. Sci. Rep. 2005, 57, 59–112. (37) Yannopapas, V.; Vitanov, N. V. Fluctuational Electrodynamics in the Presence of Finite Thermal Sources. Phys. Rev. Lett. 2007, 99, 053901. (38) Purcell, E. M.; Pennypacker, C. R., Scattering and Absorption of Light by Non-Spherical Dielectric Grains Astrophys. J. 1973, 186, 705–714. (39) Flatau, P. J. Improvements in the Discrete-Dipole Approximation Method of Computing Scattering and Absorption. Opt. Lett. 1997, 22, 1205–1207. (40) Yurkin, M. A.; Hoekstra, A. G. The Discrete Dipole Approximation: An Overview and Recent Developments. J. Quant. Spec. Rad. Transfer 2007, 106, 558–589. (41) Ben-Abdallah, P.; Biehs, S. A.; Joulain, K. Many-Body Radiative Heat Transfer Theory. Phys. Rev. Lett. 2011, 107, 114301. (42) Biehs, S. A.; Rousseau, E.; Greffet, J. J. Mesoscopic Description of Radiative Heat Transfer at the Nanoscale. Phys. Rev. Lett. 2010, 105, 234301. (43) Bäuerle, D. Laser Processing and Chemistry , Springer: Berlin, 2000. (44) Landström, L.; Elihn, K.; Boman, M.; Granqvist, C. G.; Heszler, P. Analysis of Thermal Radiation from Laser-Heated Nanoparticles Formed by Laser-Induced Decomposition of Ferrocene. Appl. Phys. A 2005, 81, 827–833. 13



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(45) West, P. R.; Ishii, S.; Naik, G. V.; Emani, N. K.; Shalaev, V. M.; Boltasseva, A. Searching for Better Plasmonic Materials. Laser Photonics Rev. 2010, 4, 795–808. (46) Ashlock, D. Evolutionary Computation for Modeling and Optimization, Springer: Berlin, 2006. (47) Carbonneau, P.; Knapp, B. A User’s Guide to PIKAIA 1.0, NCAR Technical Note 418+IA (Boulder: National Center for Atmospheric Research). (48) Johnson, R. B.; Christy, R. W. Optical Constants of the Noble Metals Phys. Rev. B 1972, 6, 4370. (49) Xie, W.; Walkenfort, B.; Schlücker, S. Label-Free SERS Monitoring of Chemical Reactions Catalyzed by Small Gold Nanoparticles Using 3D Plasmonic Superstructures. J. Am. Chem. Soc. 2013, 135, 1657–1660.

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-2 -15

(a)

(b) T(K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cabs(10 m )

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t (ns)

Figure 1: (Color online) Temporal evolution of absorption cross section Cabs (a) and of the temperature (b) for each NP of the chain shown in (a). The chain contains 5 metallic NPs of radius S = 0.2c/ω p , separated by distance d = c/ω p . The NPs are illuminated by a normally incident chirped pulse I = I0 exp[−((t − t0 )/τ )2 ] cos(ω1t + 2πβ t 2 ), t0 = τ with τ = 1ns, I0 = 107 W/m2 , ω1 /ω p = 0.37, and β /ω p2 = 0.092/(4πτ ). The ambient pressure p = 103 Pa. Note that the curves for the first (second) NP coincide with those of the fifth (fourth) NP due to the symmetry of the structure and the type of incident laser pulse.

15


S=0.1c/ S=0.2c/ S=0.3c/ S=0.4c/ S=0.5c/

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p p p p p

P

(a) /

-15

-2

Cabs(10 m )

Figure 2: (Color online) The final temperatures (at time t = 15 ns) for linear chains of 5 metallic NPs of different radii as shown in the inset. In all cases the NPs are separated by distance d = c/ω p . The incident (chirped) pulse and the ambient pressure are the same as in Figure 1.

t (ns)

(b) T(K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

T(K)


t (ns)

Figure 3: Temporal evolution of the absorption cross section Cabs (a) and of the temperature (b) for the 5 NPs of the chain shown in (a). The NPs are illuminated by two laser fields (with instantaneous frequencies given by the inset) incident both at a polar angle of 350 , azimuthal angle of 450 , corresponding to S and P polarization, respectively. The envelope function of the pulse is a Gaussian function I = I0 exp[−((t − t0 )/τ )2 ], t0 = τ with τ = 1ns, I0 = 108 W/m2 . The ambient pressure is p = 103 Pa.

16


(a) /

-15

P

-2

t (ns)

T(K)

(b)

t (ns)

Figure 4: Temporal evolution of the absorption cross section Cabs (a) and of the temperature (b) for the 4 NPs of the square shown in (a). The NPs are illuminated by two laser fields (with instantaneous frequencies given by the inset) incident both at a polar angle of 450 , azimuthal angle of 450 , corresponding to S and P polarization, respectively. The envelope function of the pulse is a Gaussian function I = I0 exp[−((t − t0 )/τ )2 ], t0 = τ with τ = 1ns, I0 = 108 W/m2 . The ambient pressure is p = 103 Pa.

2

1.5

p/c

1

y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cabs(10 m )

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0.5

0

-0.5

-1

-2

-1.5

-1

-0.5

0

x

0.5

1

1.5

2

p/c

Figure 5: Temperature distribution at t = 15ns in a fractal aggregate of 100 metallic NPs of radius S = 0.2c/ω p irradiated by a a chirped pulse I = I0 exp[−((t − t0 )/τ )2 ] cos(ω1t + 2πβ t 2 ), τ = 2t0 with t0 = 1ns, I0 = 109 W/m2 , ω1 /ω p = 0.37, and β /ω p2 = 0.092/(4π ).

17



2

1.5

p/c

1

y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.5

0

-0.5

-1

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x p/cdistribution in a fractal aggregate of metallic Figure 6: TOC figure: Snapshot of the temperature NPs irradiated by a a chirped laser pulse.

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Localized Heating of Nanostructures by Coherent Laser Pulses

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