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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12145–12158
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Plasmon assisted thermal modulation in nanoparticles

A. L. Lereu, R. H. Farahi, L. Tetard, S. Enoch, T. Thundat, and A. Passian  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 12145-12158 (2013)
http://dx.doi.org/10.1364/OE.21.012145


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Abstract

Single-particle interactions hold the promise of nanometer-scale devices in areas such as data communications and storage, nanolithography, waveguides, renewable energy and therapeutics. We propose that the collective electronic properties possessed by noble metal nanoparticles may be exploited for device actuation via the unapparent mechanism of plasmon-assisted heat generation and flux. The temperature dependence of the dielectric function and the thermal transport properties of the particles play the central role in the feasibility of the thermally-actuated system, however the behavior of these thermoplasmonic processes is unclear. We experimentally and computationally analyzed modulation via thermoplasmonic processes on a test system of gold (Au) nano-islands. Modulation and energy transport in discontinuous domains exhibited quantitatively different characteristics compared to thin films. The results have implications for all surface plasmon based nano-devices where inevitable small-scale thermal processes are present.

© 2013 OSA

1. Introduction

As the current integrated circuit (IC) technology is approaching its dimensional and performance thresholds, alternative replacement technologies are being sought. The expectation is that the replacement technology will be as radically different as semiconductor-based ICs were to vacuum tubes. One intriguing concept is an all-optical plasmonic device [1

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003) [CrossRef] [PubMed] .

5

5. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55–58 (2009) [CrossRef] .

], featuring individual nanostructures and nanoparticles that support surface plasmon excitation and coupling. Relying on the fast time scale plasmonic response of the host nanoparticles, optical switching and modulation could be designed with the desired features of fast switching time and continuous operation with high repetition rate without device degradations. Most all-optical processes involved in such applications, both passive [6

6. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005) [CrossRef] [PubMed] .

8

8. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1, 402–406 (2007) [CrossRef] .

] and active [9

9. T. Kawazoe, T. Yatsui, and M. Ohtsu, “Nanophotonics using optical near fields,” J. Non-Cryst. Solids 352, 2492–2495 (2006) [CrossRef] .

15

15. N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10, 1741–1746 (2010) [CrossRef] [PubMed] .

], typically only consider the effect of fast plasmonic processes, while neglecting the consequences and the fate of the deposited optical energy and losses. Excitation of surface modes [16

16. B. E. Sernelius, Surface Modes in Physics (Wiley-VCH Verlag Berlin GmbH, 2001) [CrossRef] .

] in nanostructures, as the basis for future devices and components of plasmonics, nanophotonics, and in general nanooptics, must often be considered in conjunction with the after effects of plasmon decay, notably the potential shift induced in the plasmon dispersion relations. This is a universal phenomenon encompassing all plasmonic processes. Practically, in any plasmonic application, the plasmon excitation energy is supplied optically or by use of electrons. However, plasmons’ finite “lifetime” implies that they undergo decay and the portion of the energy that is not emitted in form of photons generates heat, either directly or indirectly via secondary processes. Non-radiative decay of surface plasmons result in the deposit of thermal energy into the surface plasmon supporting nanoparticle and the surrounding media, which owing to the temperature dependence of the dielectric function changes the plasmon resonance conditions. Furthermore the thermal response of the substrate and the surrounding media, primarily in form of thermal expansion and thus mechanical deformation of the plasmon supporting structure, will impact the plasmon dispersion geometrically [17

17. A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006) [CrossRef] .

, 18

18. A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol., A 26, 836–841 (2008) [CrossRef] .

]. Applications and specific attention to the consequence of non-radiative decay of plasmons have been reported in planar structures [17

17. A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006) [CrossRef] .

20

20. A. L. Lereu, A. Passian, J. P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects of surface plasmons,” Appl. Phys. Lett. 86, 154101–154103 (2005) [CrossRef] .

], solid nanospheres [21

21. J. Y. Bigot, J. C. Merle, O. Cregut, and A. Daunois, “Electron dynamics in copper metallic nanoparticles probed with femtosecond optical pulses,” Phys. Rev. Lett. 75, 4702–4705 (1995) [CrossRef] [PubMed] .

23

23. M. Hu and G. V. Hartland, “Heat dissipation for au particles in aqueous solution: relaxation time versus size,” J. Phys. Chem. B 106, 7029–7033 (2002) [CrossRef] .

], nanoshells [22

22. S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B 103, 8410–8426 (1999) [CrossRef] .

, 24

24. M. Perner, S. Gresillon, J. Marz, G. von Plessen, J. Feldmann, J. Porstendorfer, K. J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000) [CrossRef] [PubMed] .

], and nanorods [22

22. S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B 103, 8410–8426 (1999) [CrossRef] .

, 24

24. M. Perner, S. Gresillon, J. Marz, G. von Plessen, J. Feldmann, J. Porstendorfer, K. J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000) [CrossRef] [PubMed] .

]. Decay of energy associated with resonance plasmon excitation in nanofilms and nanoparticles is inherent in many cases and as a result many applications are emerging in which such decay energy is being utilized. Examples include cancer therapy [25

25. L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” PNAS 100, 13549–13554 (2003) [CrossRef] [PubMed] .

30

30. R. Bardhan, S. Lal, A. Joshi, and N. J. Halas, “Theranostic nanoshells: from probe design to imaging and treatment of cancer,” Acc. Chem. Res. 44, 936–946 (2011) [CrossRef] [PubMed] .

], or biological cells or tissues studies [31

31. M. Essone Mezeme and C. Brosseau, “Engineering nanostructures with enhanced thermoplasmonic properties for biosensing and selective targeting applications” Phys. Rev. E. 87, 012722–012731 (2013) [CrossRef] .

] digital microfluidics [19

19. A. Passian, S. Zahrai, A. L. Lereu, R. H. Farahi, T. L. Ferrell, and T. Thundat, “Nonradiative surface plasmon assisted microscale Marangoni forces,” Phys. Rev. E 73,066311–066316 (2006) [CrossRef] .

, 32

32. R. H. Farahi, A. Passian, T. L. Ferrell, and T. Thundat, “Marangoni forces created by surface plasmon decay,” Opt. Lett. 30, 616–618 (2005) [CrossRef] [PubMed] .

34

34. A. L. Lereu, A. Passian, R. H. Farahi, S. Zahrai, and T. Thundat, “Plasmonic Marangoni forces,” JEOS:RP 1, 06030–06034 (2006) [CrossRef] .

], light-by-light modulation [3

3. A. L. Lereu, “Modulation - plasmons lend a helping hand,” Nature Photon. 1, 368–369 (2007) [CrossRef] .

, 18

18. A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol., A 26, 836–841 (2008) [CrossRef] .

, 20

20. A. L. Lereu, A. Passian, J. P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects of surface plasmons,” Appl. Phys. Lett. 86, 154101–154103 (2005) [CrossRef] .

, 35

35. A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett. 30, 41–43 (2005) [CrossRef] [PubMed] .

, 36

36. P. Shankar and N. K. Viswanathan, “All-optical thermo-plasmonic device,” Appl. Opt. 50, 5966–5969 (2011) [CrossRef] [PubMed] .

], and light-by-electric current and electric current-by-light modulations [37

37. A. Passian, A. L. Lereu, E. T. Arakawa, R. H. Ritchie, T. Thundat, and T. L. Ferrell, “Opto-electronic versus electro-optic modulation,” Appl. Phys. Lett. 85, 2703–2705 (2004) [CrossRef] .

40

40. J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010) [CrossRef] [PubMed] .

].

Exactly how a plasmonic device would look like or function is still being contemplated [41

41. H. Wei, Z. Wang, X. Tian, M. Käll, and H. Xu, “Cascaded logic gates in nanophotonic plasmon networks,” Nat. Commun. 2, 387–391 (2011) [CrossRef] [PubMed] .

43

43. D. Solis Jr., B. Willingham, S. L. Nauert, L. S. Slaughter, J. Olson, P. Swanglap, A. Paul, W-S. Chang, and S. Link, “Electromagnetic energy transport in nanoparticle chains via dark plasmon modes,” Nano Lett. 12, 1349–1353 (2012) [CrossRef] [PubMed] .

]. The simplest embodiment is a system of a few metal nanoparticles that would interact to transmit data contained in a modulation and one unobvious coupling mechanism is heat. Such a scenario is depicted in Fig. 1, where pumping photons of wavelength λp impinging on the nanoparticles results in excitation and non-radiative decay of the surface plasmons. The effects of the decay process will amount to a shift in the dispersion relations of the nanoparticle(s) as a result of geometric dependence and the induced variation in the dielectric function of the metal used [18

18. A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol., A 26, 836–841 (2008) [CrossRef] .

]. These effects on or in the local vicinity (proportional to the excitation wavelength) of the nanoparticle may be probed by multiple energy photons (of wavelengths λ1, λ2, ..., λn), as shown in Fig. 1(a). Thus, a modulation in the pump photons with λp would be transferred to those with λn, n = 1, 2, 3,.... Moreover, a modulation of λp could be transferred to an adjacent nanoparticle where it is sensed by λn, as shown in Fig. 1(b). In a two-particle system, the interaction may be direct plasmon coupling and thermal effects, influenced by geometry (such as cross-sectional area a and shape factor s), boundary domain distance d and the surrounding media. Apart from direct thermal influence, the phononics of the second particle in Fig. 1(b) may be a result of an initial surface plasmon coupling from the first particle.

Fig. 1 The simplest plasmonic device may be a system of one or two gold nanoparticles. (a) Nanoparticles are optically excited with a pump beam having wavelength λp and may be probed with a number of beams having wavelengths λn, n = 1, 2, 3,... for optical, electronic and mechanical changes. (b) A two-particle system with separation distance dλ where the interaction may be direct plasmon coupling in addition to thermal effects. Geometric dependencies such as cross-sectional area a and roundness factor s affect absorption efficiency and coupling.

2. Experiment

Fig. 2 Analysis of the test system of non-annealed (a,c,e) and annealed (b,d,f) Au islands. SEM images (a,b) of the synthesized islands, where islands, to be geometrically extracted for further computational analysis, are marked in colors. The histograms of the size (c,d) and roundness (e,f) distributions of the entire SEM image are Gaussian fitted (red). Annealing reduced the number and increased the size of the islands through coalescence. The roundness factor was higher in the annealed case (smax = 0.834) than in the non-annealed case (smax = 0.752).

The size, shape and thickness of the synthesized islands were statistically analyzed by processing the SEM images, plotted in Figs. 2(c)–2(f). A total of nna = 336 non-annealed islands and na = 272 annealed islands were identified. The histograms (blue) and Gaussian fits (red) represent the distributions of island size in terms of area a Figs. 2(c)–2(d) and the circular symmetry of the particles in terms of factor s Figs. 2(e)–2(f). The effect of annealing was the increase in the size of the islands and a reduction in the number of smaller islands (≤ 200 nm2) due to coalescence Figs. 2(c)–2(d). The maximum number of islands occcured at ana = 122 nm2 for the non-annealed case (c) and aa = 134 nm2 for the annealed case (d). From the roundness measurement presented in Figs. 2(e)–2(f), we observed an increase in maximum roundness s from sna = 0.75 for the non-annealed case (e) and sa = 0.83 as a result of annealing (f). By comparing the ratio of occupancy r=i=1nai/aT, where aT is the total area of the SEM image, a decrease after annealing (rna = 0.421, ra = 0.407) was determined. Assuming uniform thickness, the island thickness (tna = 8.3 nm, ta = 8.6 nm) was estimated from r and fabrication parameters. The increase of the thickness of the annealed islands agrees well with the increasing roundness factor s and the observed increase in separation distance d.

The boundaries of selected islands on the SEM images marked in Figs. 2(a) and 2(b) were numerically extracted and used as inputs for computational analysis of the electric field distribution in Fig. 3. Under excitation of polarized light the 3D field distribution for the inner four islands (outlined in yellow) in Figs. 2(a) and 2(b) was computed and visualized in z plane where the maximum field occurs, as shown in Fig. 3(a) and Fig. 3(b), respectively. These results reveal random field enhancements (hot spots) that are dependent on a, s, d and polarization. When the adjacent islands (outlined in purple and blue) in Figs. 2(a) and 2(b) are brought into consideration, as shown in Figs. 3(c) and 3(d), the contribution of the adjacent islands have altered the field distribution of the inner four islands from their original isolated state. Since the field distribution in the center does not change appreciably after consideration of islands beyond those marked in blue, the simulation was limited to these islands (spanning a region of 75 nm radius). Such interaction distances will have implications in the pump and probe size in a plasmonic circuit. The field distribution will also, under proper conditions, translate into where heat will be generated. For a few-particle system that depends on controlled interactions between specific nanoparticles, the effects of adjacent structures and location of field enhancement are critical to the function of the thermoplasmonic device. These results also have implications in surface enhanced Raman scattering (SERS), for example, where uneven field enhancement and heating at the nanoscale will occur with nonuniform particle distribution; for this reason controlled nanoparticle assemblies are being sought to optimize SERS [49

49. F. S. Ou, M. Hu, I. Naumov, A. Kim, W. Wu, A. M. Bratkovsky, X. Li, S. R. Williams, and Z. Li, “Hot-spot engineering in polygonal nanofinger assemblies for surface enhanced raman spectroscopy,” Nano Lett. 11, 2538–2542 (2011) [CrossRef] [PubMed] .

, 50

50. J. Ye, F. Wen, H. Sobhani, J. Britt Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic nanoclusters: near field properties of the fano resonance interrogated with sers,” Nano Lett. 12, 1660–1667 (2012) [CrossRef] [PubMed] .

]. Moreover, the temperature dependence of optical processes of nanoparticles affecting the efficiency of SERS can be significant [36

36. P. Shankar and N. K. Viswanathan, “All-optical thermo-plasmonic device,” Appl. Opt. 50, 5966–5969 (2011) [CrossRef] [PubMed] .

, 51

51. C. W. Chen, H. P. Chiang, P. T. Leung, and D. P. Tsai, “Temperature dependence of enhanced optical absorption and raman spectroscopy from metallic nanoparticles,” Solid State Commun. 148, 413–416 (2008) [CrossRef] .

].

Fig. 3 The 3D computation of the electric field distribution of the non-annealed (a,c) and annealed (b,d) Au islands designated in the SEM images from Figs. 2(a) and 2(b). (a,b) The cross sectional visualization of the distribution of the maximum near-field root-mean-square modulus exhibited by the four isolated gold islands outlined in yellow due to scattering with polarized light. (c,d) The field distribution taking into account adjacent islands outlined in purple and blue. The inclusion of adjacent islands have altered the field distribution and enhancement of the inner four islands. Since the field distribution in the center did not appreciably change after a threshold number of adjacent islands were taken into consideration, the simulation was restricted to this selection (spanning 75 nm radius). The color scale varies from min 8.6 × 10−4 V/m to max 15.1 V/m.

A quartz prism substrate was employed to support both the nano-islands and continuous film samples. The prism configuration was necessary to alter the photon momentum so that collective electron oscillations can be excited by photons on the continuous film. The samples were illuminated with a pump laser of wavelength λp = 808 nm that was amplitude modulated at fp and focused to diameter Dp = 5 μm. An unmodulated probe having wavelength λ1 = 532 nm is reflected off the sample into a photodetector and its response R was measured with lock-in detection referenced at fp. The probe response captures primarily the localized volumetric effect (expansion) caused by the deposit of thermal energy from plasmon decay, which shifts the dielectric function and thus the surface plasmon dispersion relations of the system. In metal thin films we previously measured the shift in the plasmon dispersion relation over the entire visible spectrum with controlled temperature and incident angle [18

18. A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol., A 26, 836–841 (2008) [CrossRef] .

]. While measurement of angular dependence would not be crucial for the islands, as opposed to thin films, [52

52. S. Yamaguchi, “Optical absorption of heat treated very thin silver films and its dependence on angle of incidence,” J. Phys. Soc. Jpn. 17, 1172–1180 (1962) [CrossRef] .

] variations in the plasmon excitation parameters were expected to occur in the island samples. The probe λ1 was engaged to perform a series of 200 μm linescans in the x direction across the pump λp excitation region at fixed modulation frequency fp = 200 Hz and power level Pp = 150 mW, plotted in Fig. 4(a). The non-annealed islands (blue) produced comparable signal strength to the continuous film at x = 0 (black), although less Au mass is contributing to the thermal processes involved. The linescans of both island samples were spatially sharper (full width at half maximum FWHM = 22 μm) than the continuous film (FWHM = 52 μm), as demonstrated more clearly in the normalized presentation in the inset Fig. 4(a). Since surface boundary scattering and grain boundary scattering are the main mechanisms for reduced thermal conductivity in thin films (compared to bulk) [53

53. T. Q. Qiu and C. L. Tien, “Size effects on nonequilibrium laser-heating of metal-films,” J. Heat Trans-T ASME 115, 842–847 (1993) [CrossRef] .

, 54

54. G. Chen and P. Hui, “Thermal conductivities of evaporated gold films on silicon and glass,” Appl. Phys. Lett. 74, 2942–2944, (1999) [CrossRef] .

], discontinuous films would exhibit an even greater reduction. Thus we see a broader profile of the continuous metal film due to better in-plane heat dissipation compared to a more localized heating from disrupted thermal transport by the boundaries of the nanoparticles. We note that whereas the experimental conditions for optimized plasmon creation were designed for the continuous film, these conditions were not optimized for the islands. Shown in Fig. 4(b), the overall lower response produced by annealed islands (red), at greater interparticle distances, may be explained by the shift in absorption where the maximum absorption for the non-annealed and annealed cases occurred at λ = 694 nm and λ = 570 nm, respectively. The broad absorption spectrum for the non-annealing islands is resulting from the broad distribution in size of the constituting particles. The spectral properties of the islands are expected to undergo a change as a result of annealing. In addition to the variations resulting from polarization state and incidence angle of the excitation photons, such spectral shifts in the scattering cross section, polarizability, and absorption spectra of nanoparticles are known to result from both material dependencies (the dielectric function) and geometric factors (local curvature [55

55. A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425–115435, (2005) [CrossRef] .

] and distribution). This can be readily seen from the plasmon dispersion relations of an oblate/prolate spheroidal nanoparticle as a function of the shape factor η (the ratio of the major to minor axis), volume and dielectric function. Within the dipole approximation, in the nonretarded regime, and assuming a local dielectric function, it can readily be shown that the absorption spectrum undergoes a blue shift as η → 1, that is, in the spherical limit [56

56. S. W. Kennerly, J. W. Little, R. J. Warmack, and T. L. Ferrell, “Optical properties of heated Ag films,” Phys. Rev. B 29, 2926–2929 (1984) [CrossRef] .

]. Furthermore, in this limit, the polarizability scales with the cube of the spheres diameter, red-shifting the spectrum for larger particles. As seen from the analysis in Fig. 4, in our case the reshaping and increased particle separation effects and structural transformation of the lattice of the melted particles [57

57. U. Kreibig and L. Genzel, “Optical-absorption of small metallic particles,” Surf. Sci. 156, 678–700 (1985) [CrossRef] .

] are dominant amounting to a net blue shift. Our results further agree with Gupta et al [58

58. G. Gupta, D. Tanaka, Y. Ito, D. Shibata, M. Shimojo, K. Furuya, K. Mitsui, and K. Kajikawa, “Absorption spectroscopy of gold nanoisland films: optical and structural characterization,” Nanotechnol. 20, 025703–025711, (2009) [CrossRef] .

], who more recently revisited the annealing induced reshaping and the consequent blue-shift in Au islands.

Fig. 4 Test results from the measurement of the probe beam having wavelength λ1 = 532 nm due to a modulated excitation of wavelength λp = 808 nm on Au nano-islands and a continuous Au film. (a) Linescans (normalized in inset) across the λp excitation region centered at x = 0. (b) The absorption spectra for the two samples, non-annealed (blue) and annealed (red). (c) Frequency responses at Pp = 150 mW and x = 0. (d) Power responses at fp = 200 Hz and x = 0.

3. Results and discussion

In order to evaluate modulation ability, the probe λ1 was fixed at x = 0 where the signal is maximum while fp was varied, as shown in Fig. 4(c). The frequency response at 0.2 ≤ fp ≤ 3 kHz and Pp = 150 mW was measured and fitted with the function f (x) = a + bxγ. The highest signal was at the lowest frequency where the thermal processes evolved to higher temperatures and then relaxed. In Fig. 4(c), the heating and cooling ability of the continuous film (black curve) appeared to obey the power law of x−0.50 (square law) for thermal waves [59

59. J. Opsal, A. Rosencwaig, and D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt. 22, 3169–3176 (1983) [CrossRef] [PubMed] .

], based on the fit coefficients (a = 5.5 × 10−4, b = 0.133, γ = −0.46). Thermal waves depend on the thermal diffusion length μ=2α/ω, where α is the thermal diffusivity and ω is the frequency of the periodic heat generation [60

60. B. Rief, “Thermal-wave transient behaviour,” Can. J. Phys. 64, 1303–1306 (1986) [CrossRef] .

]. On the other hand the non-annealed islands (blue), having hindered heat dissipation by discontinuous domains, obeyed a power law of x−0.20, with fit coefficients (a = −7.2 × 10−3, b = 0.052, γ = −0.20). In the annealed case (red), cooling ability was further reduced due to greater separation distances; the power law of x−0.09 was obeyed with fit coefficients of (a = −5.6 × 10−3, b = 0.012, γ = −0.09). In Fig. 4(c), our collective measurements suggest a decreasing power law with increasing island separation distance; morphology may be linked to the power law as well. The temporal limitations of these processes begin to be exposed as the frequency increases; in this case the modulation frequencies are less than 5 kHz.

Measurements of the power dependence at x = 0, 1 ≤ Pp ≤ 176 mW and fp = 200 Hz confirmed that the results of the frequency experiments were within a linear power regime, shown in Fig. 4(d). The results in Fig. 4(d) were also repeatable with the power varied from 176 mW to 1 mW at the same location, a verification that the measurements were below the damage threshold of the sample. For the annealed islands curve (red), the onset of nonlinearity occurring in the last two data points in Fig. 4(d) can be due to longer thermal relaxation time associated with greater separation distance. If the increased thermal delivery to the surface does not damage the Au coatings, it is predicted that nonlinearity in the response of the continuous film and the non-annealed islands may be observed with higher Pp. Given that the current experimental parameters were not optimized for the islands, it would be reasonable to consider the operating conditions of Pp =5 mW and fp = 2 kHz. Using an average island area ana = 199.8 nm2, aa = 238.9 nm2, the energy deposited on the individual average island was estimated to be Jna = 12.7 pJ, Ja = 15.2 pJ per modulation cycle. Assuming a thickness of 10 nm and using the specific heat capacity of gold C = 0.129 J/(g °C), the theoretical amount of energy to heat an individual average island by 10 °C is Jna = 4.97 × 10−17 J, Ja = 5.95 × 10−17 J, neglecting temperature dependencies. From these estimates very low power requirements could potentially be achieved. As an additional verification of the volumetric surface response contributing to the probe signal presented in Fig. 4, the non-annealed islands were characterized by tapping mode atomic force microscopy (AFM), shown in Fig. 5. In Fig. 5 topographic AFM images were obtained before (1 μm×1 μm and 70.3 μm×70.3 μm scans on the left) and after (70.3 μm×70.3 μm scan on the right) pumping. A peak deformation of 12 nm due to surface expansion was measured in the region of surface plasmon excitation from a continuous focused diode laser pump at 635 nm and 5 mW. We have also observed similar topographic variations in fabricated nanorods array via near field scanning optical microscopy (NSOM) characterization (see appendix).

Fig. 5 AFM characterization of non-annealed islands before (left) and after (right) excitation with a pump laser. The deformation observed on the right in the excitation region is consistent with the profiles obtained by the laser probe measurements in Fig. 4(a). The scan sizes are chosen to image the nanoparticles (1 μm×1 μm) and the deformation over a wide area (70.3 μm×70.3 μm) adapted to the illumination region.

Although plasmonic (∝ petahertz [22

22. S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B 103, 8410–8426 (1999) [CrossRef] .

]) and thermal processes (∝ gigahertz [61

61. X. Chen, Y. Chen, M. Yan, and M. Qiu, “Nanosecond photothermal effects in plasmonic nanostructures,” ACS Nano 6, 2550–2557 (2012) [CrossRef] [PubMed] .

]) can be very fast, substrate effects are here implicated in the observed limited modulation exhibited by the test systems. In both the continuous film and the nano-island cases, the importance of the choice of the substrate for the thermoplasmonic system lies primarily in two factors: 1) the introduction of a given substrate alters the excitation and resonance conditions of the surface plasmons in the metal nanostructures, a process that is reflected in the plasmon dispersion relations of the system, and 2) the thermal properties of the substrate-nanostructure interface determine energy transport from the nanostructure into the substrate (and vice versa), a process that can significantly alter the thermoplasmonic modulation rate. To elaborate on the latter we computationally analyzed the thermal response of a microstructure composed of similar materials as in the test system. Employing the finite elements (FE) numerical approach to solving the heat diffusion equation, we obtained the transient temperature distribution of two thermally dissimilar materials, aluminum (Al) and silica. In Fig. 6, microrod structures of length L = 10 μm and radius 0.1L are considered for the case of all-Al, all-silica, and half-Al (lower) half-silica (upper). An initial condition of T (z, 0) = 300 K and a boundary condition of T(0, t) = 320 K are assumed. In the top row of Fig. 6, the computed temperature at z = L is plotted as a function of time over the first microsecond and the instantaneous temperature distribution of the microrod is mapped at t = 1 μs. The temperature T(z) and the temperature gradient ∇T(z) as functions of z at selected times up to 1 μs are plotted in the middle and bottom rows, respectively. In the case of Al, Fig. 6(a), the structure reaches a nearly uniform temperature distribution T(z) within a microsecond, whereas in silica, Fig. 6(b), a large temperature gradient remains. The thermal transport can be seen to be severely hindered in the Al-silica composite, Fig. 6(c). The heating and cooling characteristics of the Au thin film and island samples on quartz are expected to behave similarly to the simulations for Al and silica. Characteristics of the modeled thermal transport can be observed in the experimental data: First, the linescans in Fig. 4(a) show that the temperature distribution is more confined (lower FWHM) for the nanoisland samples compared to the continuous Au film which would rapidly dissipate heat similar to the Al rod Fig. 6(a). Second, the thermal interface resistance in the Al-silica system Fig. 6(c) suggests that similar processes are occurring in our test system composed of metal film or islands on a quartz substrate. The obstructed thermal transport prevents the film or islands from quickly restoring to thermal equilibrium through the substrate after each cycle, thus limiting the modulation ability shown in Fig. 4(c).

Fig. 6 Computational determination of the transient temperature distribution T(z, t) for (a) Al, (b) silica, and (c) half-Al (lower) half-silica (upper) microrods. With an initial condition of T(z, 0) = 300 K, the application of the boundary condition of T(0, t) = 320 K allows the study of the heat diffusion throughout the structure. Top section: T(L) in the first microsecond and an instantaneous temperature map of the structure at t = 1μs. Middle section: T(z) at selected time intervals. Bottom section: temperature gradient ∇T(z) at selected time intervals.

Analysis of the transient surface temperature distribution T(t) for the selected annealed islands identified in the SEM image in Fig. 2(b) also resulted in fast thermal transport when residing on silica glass, shown in Fig. 7. To study the thermal transport, a boundary condition of T(0, t) = 320 K was assumed for one center island with an initial condition of T(0) = 300 K. At t = 0.1 ns, the surface temperature of the center island is reduced to 306.2 K and the temperature has risen in the adjacent islands Fig. 7(a). By t =15 ns the surface temperature has already been distributed to all the surrounding islands Fig. 7(d). Thus, high thermoplasmonic modulation rates are possible, however the optimization via substrate choice may warrant a tradeoff between the magnitude of the plasmon shift and the interfacial thermal resistance. The results indicate that it may be possible to extend the low-power, high-spatial resolution thermoplasmonic modulation system to higher modulation frequencies. The discontinuous domain boundaries not only localize heat, but enable fast heat dissipation due to their high surface-to-volume ratio [62

62. G. V. Hartland, “Measurements of the material properties of metal nanoparticles by time-resolved spectroscopy,” Phys. Chem. Chem. Phys. 6, 5263–5274 (2004) [CrossRef] .

64

64. P. Keblinski, D. G. Cahill, A. Bodapati, C. R. Sullivan, and T. A. Taton, “Limits of localized heating by electromagnetically excited nanoparticles,” J. Appl. Phys. 100, 054305–054309 (2006) [CrossRef] .

]. Heat transfer between a solid nanostructure and a gaseous environment such as the surrounding air can be dominant over other heat loss channels under certain conditions [65

65. C. Cheng, W. Fan, J. Cao, S-G. Ryu, J. Ji, C. P. Grigoropoulos, and J. Wu, “Heat transfer across the interface between nanoscale solids and gas,” ACS Nano 5, 10102–10107 (2011) [CrossRef] [PubMed] .

]. The material properties of the surrounding media must be chosen to maximize the heat transfer for optimized modulation performance. With the length scales associated with the energy carriers comparable to the nanostructure dimensions (the phonon mean free path of gold is 40 nm, for example), heat transfer in a nanosystem would not be necessarily governed by the Fourier law [66

66. M. I. Flik, B. I. Choi, and K. E. Goodson, “Heat-transfer regimes in microstructures,” J. Heat Trans-T ASME 114, 666–674 (1992) [CrossRef] .

, 67

67. G. Chen, “Particularities of heat conduction in nanostructures,” J. Nanopart. Res. 2, 199–204 (2000) [CrossRef] .

]. Amidst increasingly smaller electronic, photonic, and photovoltaic devices as well as the incorporation of nanoparticles in metamaterials, microscale/nanoscale heat transfer has been receiving attention in the last decade [68

68. S. Volz, (Ed.), , “Thermal Nanosystems and Nanomaterials,” in Topics in Applied Physics, 1st ed.118, (Springer-Verlag Berlin, Heidelberger Platz 3, Berlin, Germany, 2010).

] with specific studies in thermal boundary resistance in multilayer optoelectronics [69

69. E. Gesikowska and W. Nakwaski, “An impact of multi-layered structures of modern optoelectronic devices on their thermal properties,” Opt. Quant. Electron. 40, 205–216 (2008) [CrossRef] .

], new models for heat transfer in nanofluids [70

70. R. Stana, I. Casian Botez, V. P. Paun, and A. Marcel, “New model for heat transfer in nanostructures,” J. Comput. Theor. Nanos. 9, 55–66 (2012) [CrossRef] .

], and thermal management in microelectronic devices using carbon nanotubes and graphene sheets [71

71. J. Kou, H. Qian, H. Lu, Y. Liu, Y. Xu, F. Wu, and J. Fan, “Optimizing the design of nanostructures for improved thermal conduction within confined spaces,” Nanoscale Res. Lett. 6, 422–429 (2011) [CrossRef] [PubMed] .

73

73. Z. Xu and M. J. Buehler, “Hierarchical nanostructures are crucial to mitigate ultrasmall thermal point loads,” Nano Lett. 9, 2065–2072 (2009) [CrossRef] [PubMed] .

]. Although most of the small-scale heat transfer discourse makes no mention of plasmonic decay processes of nanostructures, the findings are very applicable to systems where localized plasmonic decay occurs.

Fig. 7 Computational determination of the transient surface temperature distribution T (x,y,t) shows high thermoplasmonic modulation rates are possible for the annealed islands freestanding in vacuum. Temperature distributions are shown at various times t after an initial condition of T(x,y,0) = 300 K and the application of the boundary condition of T (xci, yci, t) = 320 K on the center island. (a) t = 0.1 ns, (b) t = 1.0 ns, (c) t = 1.5 ns, and (d) t = 15 ns.

4. Conclusions

Appendix: Characterization of Nanorods using near-field scanning optical microscopy

For further study of volumetric effects in nanostructures due to thermoplasmonic processes, scanning near-field optical microscopy (NSOM) analysis was conducted on a Au array of 400 nm long, 100 nm wide and 40 nm thick nanorods fabricated on an ITO-quartz substrate, shown in Fig. 8. NSOM images in the transmission mode configuration were obtained by near-field illumination of the sample through an aperture probe and collection of the scattered light through with an objective. The near-field illumination at 632.8 nm was linearly polarized (direction indicated with arrows), creating resonance conditions for these nanorods. The 632.8 nm was then filtered to avoid blinding the photodetector. Another light source, an Ar laser at the 514 nm line and 8 mW, was configured to obliquely impinge the sample from the top and illuminate the scanned region to create additional plasmonic activity. The effects on the near-field optical (photon counts) and simultaneous topographical (z height) measurements when the Ar laser is on (unblocked) and off (blocked) are examined. The cross sections shown in Fig. 8(a) are from the 4 μm×4 μm images in Figs. 8(b) and 8(c), where the horizontal line indicates the location where the cross sections were extracted. The Ar excitation is blocked from reaching the NSOM photodetector, so that the optical signal does not overload the detector. The topographical cross sections reveal new formations in the nanorod structure when the Ar excitation is applied, which may be interpreted as thermal expansion due to localized heating. Note that the optical signal is unchanged between the two measurements which rejects the possibility of change in the z (tip-sample distance).

Fig. 8 NSOM characterization of Au nanorods to demonstrate volumetric changes from plasmonic events induced by a secondary Ar laser. (a) Cross sections of the simultaneous optical and topographical signals. (b) Topographic image with Ar off (blocked). (c) Topographic image with Ar on (unblocked). The horizontal line on the images indicate the location where cross sections were taken. Changes in topography show possible thermal expansion due to additional thermoplasmonic processes created by the Ar excitation. The non-changing optical signal let assume that the distance probe-sample is unchanged wether the Ar laser is on or off.

Acknowledgments

References and links

1.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003) [CrossRef] [PubMed] .

2.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006) [CrossRef] [PubMed] .

3.

A. L. Lereu, “Modulation - plasmons lend a helping hand,” Nature Photon. 1, 368–369 (2007) [CrossRef] .

4.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9, 897–902 (2009) [CrossRef] [PubMed] .

5.

K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3, 55–58 (2009) [CrossRef] .

6.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005) [CrossRef] [PubMed] .

7.

P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005) [CrossRef] [PubMed] .

8.

D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics 1, 402–406 (2007) [CrossRef] .

9.

T. Kawazoe, T. Yatsui, and M. Ohtsu, “Nanophotonics using optical near fields,” J. Non-Cryst. Solids 352, 2492–2495 (2006) [CrossRef] .

10.

W. Dickson, G. A. Wurtz, P. R. Evans, R. J. Pollard, and A. V. Zayats, “Electronically controlled surface plasmon dispersion and optical transmission through metallic hole arrays using liquid crystal,” Nano Lett. 8, 281–286 (2008) [CrossRef] .

11.

R. A. Pala, K. T. Shimizu, N. A. Melosh, and M. L. Brongersma, “A nonvolatile plasmonic switch employing photochromic molecules,” Nano Lett. 8, 1506–1510 (2008) [CrossRef] [PubMed] .

12.

E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett. 100, 123901–123904 (2008) [CrossRef] [PubMed] .

13.

W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9, 4403–4411 (2009) [CrossRef] [PubMed] .

14.

C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express 17, 10757–10766 (2009) [CrossRef] [PubMed] .

15.

N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10, 1741–1746 (2010) [CrossRef] [PubMed] .

16.

B. E. Sernelius, Surface Modes in Physics (Wiley-VCH Verlag Berlin GmbH, 2001) [CrossRef] .

17.

A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films 497, 315–320 (2006) [CrossRef] .

18.

A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol., A 26, 836–841 (2008) [CrossRef] .

19.

A. Passian, S. Zahrai, A. L. Lereu, R. H. Farahi, T. L. Ferrell, and T. Thundat, “Nonradiative surface plasmon assisted microscale Marangoni forces,” Phys. Rev. E 73,066311–066316 (2006) [CrossRef] .

20.

A. L. Lereu, A. Passian, J. P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects of surface plasmons,” Appl. Phys. Lett. 86, 154101–154103 (2005) [CrossRef] .

21.

J. Y. Bigot, J. C. Merle, O. Cregut, and A. Daunois, “Electron dynamics in copper metallic nanoparticles probed with femtosecond optical pulses,” Phys. Rev. Lett. 75, 4702–4705 (1995) [CrossRef] [PubMed] .

22.

S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B 103, 8410–8426 (1999) [CrossRef] .

23.

M. Hu and G. V. Hartland, “Heat dissipation for au particles in aqueous solution: relaxation time versus size,” J. Phys. Chem. B 106, 7029–7033 (2002) [CrossRef] .

24.

M. Perner, S. Gresillon, J. Marz, G. von Plessen, J. Feldmann, J. Porstendorfer, K. J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000) [CrossRef] [PubMed] .

25.

L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” PNAS 100, 13549–13554 (2003) [CrossRef] [PubMed] .

26.

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209, 171–176 (2004) [CrossRef] .

27.

D. Pissuwan, S. M. Valenzuela, and M. B. Cortie, “Therapeutic possibilities of plasmonically heated gold nanoparticles,” Trends Biotechnol. 24, 62–67 (2006) [CrossRef] .

28.

J. Z. Zhang, “Biomedical Applications of Shape-Controlled Plasmonic Nanostructures: A Case Study of Hollow Gold Nanospheres for Photothermal Ablation Therapy of Cancer,” J. Phys. Chem. Lett. 1, 686–695 (2010) [CrossRef] .

29.

J. Y. Chen, C. Glaus, R. Laforest, Q. Zhang, M. Yang, M. Gidding, M. J. Welch, and Y. Xia, “Gold nanocages as photothermal transducers for cancer treatment,” Small 6, 811–817 (2010) [CrossRef] [PubMed] .

30.

R. Bardhan, S. Lal, A. Joshi, and N. J. Halas, “Theranostic nanoshells: from probe design to imaging and treatment of cancer,” Acc. Chem. Res. 44, 936–946 (2011) [CrossRef] [PubMed] .

31.

M. Essone Mezeme and C. Brosseau, “Engineering nanostructures with enhanced thermoplasmonic properties for biosensing and selective targeting applications” Phys. Rev. E. 87, 012722–012731 (2013) [CrossRef] .

32.

R. H. Farahi, A. Passian, T. L. Ferrell, and T. Thundat, “Marangoni forces created by surface plasmon decay,” Opt. Lett. 30, 616–618 (2005) [CrossRef] [PubMed] .

33.

R. H. Farahi, A. Passian, S. Zahrai, A. L. Lereu, T. L. Ferrell, and T. Thundat, “Microscale Marangoni actuation: all-optical and all-electrical methods,” Ultramicroscopy 106, 815–821 (2006) [CrossRef] [PubMed] .

34.

A. L. Lereu, A. Passian, R. H. Farahi, S. Zahrai, and T. Thundat, “Plasmonic Marangoni forces,” JEOS:RP 1, 06030–06034 (2006) [CrossRef] .

35.

A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett. 30, 41–43 (2005) [CrossRef] [PubMed] .

36.

P. Shankar and N. K. Viswanathan, “All-optical thermo-plasmonic device,” Appl. Opt. 50, 5966–5969 (2011) [CrossRef] [PubMed] .

37.

A. Passian, A. L. Lereu, E. T. Arakawa, R. H. Ritchie, T. Thundat, and T. L. Ferrell, “Opto-electronic versus electro-optic modulation,” Appl. Phys. Lett. 85, 2703–2705 (2004) [CrossRef] .

38.

T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. 85, 5833–5835 (2004) [CrossRef] .

39.

A. Passian, A. L. Lereu, R. H. Farahi, T. L. Ferrell, and T. Thundat, “Thermoplasmonics in thin metal films,” in Trends in solid film researchA. R. Jost, eds. (Nova Science Publishers, Hauppauge NY, 2007), pp. 69–109.

40.

J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express 18, 1207–1216 (2010) [CrossRef] [PubMed] .

41.

H. Wei, Z. Wang, X. Tian, M. Käll, and H. Xu, “Cascaded logic gates in nanophotonic plasmon networks,” Nat. Commun. 2, 387–391 (2011) [CrossRef] [PubMed] .

42.

S. V. Boriskina and B. M. Reinhard, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale 4, 76–90 (2012) [CrossRef] .

43.

D. Solis Jr., B. Willingham, S. L. Nauert, L. S. Slaughter, J. Olson, P. Swanglap, A. Paul, W-S. Chang, and S. Link, “Electromagnetic energy transport in nanoparticle chains via dark plasmon modes,” Nano Lett. 12, 1349–1353 (2012) [CrossRef] [PubMed] .

44.

A. Passian, A. Wig, A. L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area surface plasmon interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy 100, 429–436 (2004) [CrossRef] [PubMed] .

45.

A. Passian, A. Wig, A. L. Lereu, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Photon tunneling via surface plasmon coupling,” Appl. Phys. Lett. 85, 3420–3422 (2004) [CrossRef] .

46.

F. P. Incropera, D. P. Dewitt, T. L. Bergman, and A. S. Lavine, Fundamentals of Heat and Mass Transfer, 6th ed. (John Wiley & Sons, Inc., 2007).

47.

A. Popescu, L. M. Woods, J. Martin, and G. S. Nolas, “Model of transport properties of thermoelectric nanocomposite materials,” Phys. Rev. B 79, 205302–205308 (2009) [CrossRef] .

48.

D. Cederkrantz, N. Farahi, K. A. Borup, B. B. Iversen, M. Nygren, and A. E. C. Palmqvist, “Enhanced thermoelectric properties of mg2si by addition of tio2 nanoparticles,” J. Appl. Phys. 111, 023701–023707 (2012) [CrossRef] .

49.

F. S. Ou, M. Hu, I. Naumov, A. Kim, W. Wu, A. M. Bratkovsky, X. Li, S. R. Williams, and Z. Li, “Hot-spot engineering in polygonal nanofinger assemblies for surface enhanced raman spectroscopy,” Nano Lett. 11, 2538–2542 (2011) [CrossRef] [PubMed] .

50.

J. Ye, F. Wen, H. Sobhani, J. Britt Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic nanoclusters: near field properties of the fano resonance interrogated with sers,” Nano Lett. 12, 1660–1667 (2012) [CrossRef] [PubMed] .

51.

C. W. Chen, H. P. Chiang, P. T. Leung, and D. P. Tsai, “Temperature dependence of enhanced optical absorption and raman spectroscopy from metallic nanoparticles,” Solid State Commun. 148, 413–416 (2008) [CrossRef] .

52.

S. Yamaguchi, “Optical absorption of heat treated very thin silver films and its dependence on angle of incidence,” J. Phys. Soc. Jpn. 17, 1172–1180 (1962) [CrossRef] .

53.

T. Q. Qiu and C. L. Tien, “Size effects on nonequilibrium laser-heating of metal-films,” J. Heat Trans-T ASME 115, 842–847 (1993) [CrossRef] .

54.

G. Chen and P. Hui, “Thermal conductivities of evaporated gold films on silicon and glass,” Appl. Phys. Lett. 74, 2942–2944, (1999) [CrossRef] .

55.

A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425–115435, (2005) [CrossRef] .

56.

S. W. Kennerly, J. W. Little, R. J. Warmack, and T. L. Ferrell, “Optical properties of heated Ag films,” Phys. Rev. B 29, 2926–2929 (1984) [CrossRef] .

57.

U. Kreibig and L. Genzel, “Optical-absorption of small metallic particles,” Surf. Sci. 156, 678–700 (1985) [CrossRef] .

58.

G. Gupta, D. Tanaka, Y. Ito, D. Shibata, M. Shimojo, K. Furuya, K. Mitsui, and K. Kajikawa, “Absorption spectroscopy of gold nanoisland films: optical and structural characterization,” Nanotechnol. 20, 025703–025711, (2009) [CrossRef] .

59.

J. Opsal, A. Rosencwaig, and D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt. 22, 3169–3176 (1983) [CrossRef] [PubMed] .

60.

B. Rief, “Thermal-wave transient behaviour,” Can. J. Phys. 64, 1303–1306 (1986) [CrossRef] .

61.

X. Chen, Y. Chen, M. Yan, and M. Qiu, “Nanosecond photothermal effects in plasmonic nanostructures,” ACS Nano 6, 2550–2557 (2012) [CrossRef] [PubMed] .

62.

G. V. Hartland, “Measurements of the material properties of metal nanoparticles by time-resolved spectroscopy,” Phys. Chem. Chem. Phys. 6, 5263–5274 (2004) [CrossRef] .

63.

Z. Ge, Y. Kang, T. A. Taton, P. V. Braun, and D. G. Cahill, “Thermal transport in au-core polymer-shell nanoparticles,” Nano Lett. 5, 531–535 (2005) [CrossRef] [PubMed] .

64.

P. Keblinski, D. G. Cahill, A. Bodapati, C. R. Sullivan, and T. A. Taton, “Limits of localized heating by electromagnetically excited nanoparticles,” J. Appl. Phys. 100, 054305–054309 (2006) [CrossRef] .

65.

C. Cheng, W. Fan, J. Cao, S-G. Ryu, J. Ji, C. P. Grigoropoulos, and J. Wu, “Heat transfer across the interface between nanoscale solids and gas,” ACS Nano 5, 10102–10107 (2011) [CrossRef] [PubMed] .

66.

M. I. Flik, B. I. Choi, and K. E. Goodson, “Heat-transfer regimes in microstructures,” J. Heat Trans-T ASME 114, 666–674 (1992) [CrossRef] .

67.

G. Chen, “Particularities of heat conduction in nanostructures,” J. Nanopart. Res. 2, 199–204 (2000) [CrossRef] .

68.

S. Volz, (Ed.), , “Thermal Nanosystems and Nanomaterials,” in Topics in Applied Physics, 1st ed.118, (Springer-Verlag Berlin, Heidelberger Platz 3, Berlin, Germany, 2010).

69.

E. Gesikowska and W. Nakwaski, “An impact of multi-layered structures of modern optoelectronic devices on their thermal properties,” Opt. Quant. Electron. 40, 205–216 (2008) [CrossRef] .

70.

R. Stana, I. Casian Botez, V. P. Paun, and A. Marcel, “New model for heat transfer in nanostructures,” J. Comput. Theor. Nanos. 9, 55–66 (2012) [CrossRef] .

71.

J. Kou, H. Qian, H. Lu, Y. Liu, Y. Xu, F. Wu, and J. Fan, “Optimizing the design of nanostructures for improved thermal conduction within confined spaces,” Nanoscale Res. Lett. 6, 422–429 (2011) [CrossRef] [PubMed] .

72.

Z. Xu and M. J. Buehler, “Nanoengineering heat transfer performance at carbon nanotube interfaces,” ACS Nano 3, 2767–2775 (2009) [CrossRef] [PubMed] .

73.

Z. Xu and M. J. Buehler, “Hierarchical nanostructures are crucial to mitigate ultrasmall thermal point loads,” Nano Lett. 9, 2065–2072 (2009) [CrossRef] [PubMed] .

OCIS Codes
(120.6810) Instrumentation, measurement, and metrology : Thermal effects
(230.4110) Optical devices : Modulators
(160.4236) Materials : Nanomaterials
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 22, 2013
Revised Manuscript: March 22, 2013
Manuscript Accepted: March 23, 2013
Published: May 10, 2013

Citation
A. L. Lereu, R. H. Farahi, L. Tetard, S. Enoch, T. Thundat, and A. Passian, "Plasmon assisted thermal modulation in nanoparticles," Opt. Express 21, 12145-12158 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12145


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References

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424, 824–830 (2003). [CrossRef] [PubMed]
  2. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311, 189–193 (2006). [CrossRef] [PubMed]
  3. A. L. Lereu, “Modulation - plasmons lend a helping hand,” Nature Photon.1, 368–369 (2007). [CrossRef]
  4. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “Plasmostor: a metal-oxide-si field effect plasmonic modulator,” Nano Lett.9, 897–902 (2009). [CrossRef] [PubMed]
  5. K. F. MacDonald, Z. L. Samson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3, 55–58 (2009). [CrossRef]
  6. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett.94, 053901 (2005). [CrossRef] [PubMed]
  7. P. Muhlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science308, 1607–1609 (2005). [CrossRef] [PubMed]
  8. D. Pacifici, H. J. Lezec, and H. A. Atwater, “All-optical modulation by plasmonic excitation of CdSe quantum dots,” Nat. Photonics1, 402–406 (2007). [CrossRef]
  9. T. Kawazoe, T. Yatsui, and M. Ohtsu, “Nanophotonics using optical near fields,” J. Non-Cryst. Solids352, 2492–2495 (2006). [CrossRef]
  10. W. Dickson, G. A. Wurtz, P. R. Evans, R. J. Pollard, and A. V. Zayats, “Electronically controlled surface plasmon dispersion and optical transmission through metallic hole arrays using liquid crystal,” Nano Lett.8, 281–286 (2008). [CrossRef]
  11. R. A. Pala, K. T. Shimizu, N. A. Melosh, and M. L. Brongersma, “A nonvolatile plasmonic switch employing photochromic molecules,” Nano Lett.8, 1506–1510 (2008). [CrossRef] [PubMed]
  12. E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, “Optical control over surface-plasmon-polariton-assisted THz transmission through a slit aperture,” Phys. Rev. Lett.100, 123901–123904 (2008). [CrossRef] [PubMed]
  13. W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett.9, 4403–4411 (2009). [CrossRef] [PubMed]
  14. C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express17, 10757–10766 (2009). [CrossRef] [PubMed]
  15. N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett.10, 1741–1746 (2010). [CrossRef] [PubMed]
  16. B. E. Sernelius, Surface Modes in Physics (Wiley-VCH Verlag Berlin GmbH, 2001). [CrossRef]
  17. A. Passian, A. L. Lereu, R. H. Ritchie, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Surface plasmon assisted thermal coupling of multiple photon energies,” Thin Solid Films497, 315–320 (2006). [CrossRef]
  18. A. L. Lereu, A. Passian, R. H. Farahi, N. F. van Hulst, T. L. Ferrell, and T. Thundat, “Thermoplasmonic shift and dispersion in thin metal films,” J. Vac. Sci. Technol., A26, 836–841 (2008). [CrossRef]
  19. A. Passian, S. Zahrai, A. L. Lereu, R. H. Farahi, T. L. Ferrell, and T. Thundat, “Nonradiative surface plasmon assisted microscale Marangoni forces,” Phys. Rev. E73,066311–066316 (2006). [CrossRef]
  20. A. L. Lereu, A. Passian, J. P. Goudonnet, T. Thundat, and T. L. Ferrell, “Optical modulation processes in thin films based on thermal effects of surface plasmons,” Appl. Phys. Lett.86, 154101–154103 (2005). [CrossRef]
  21. J. Y. Bigot, J. C. Merle, O. Cregut, and A. Daunois, “Electron dynamics in copper metallic nanoparticles probed with femtosecond optical pulses,” Phys. Rev. Lett.75, 4702–4705 (1995). [CrossRef] [PubMed]
  22. S. Link and M. A. El-Sayed, “Spectral properties and relaxation dynamics of surface plasmon electronic oscillations in gold and silver nanodots and nanorods,” J. Phys. Chem. B103, 8410–8426 (1999). [CrossRef]
  23. M. Hu and G. V. Hartland, “Heat dissipation for au particles in aqueous solution: relaxation time versus size,” J. Phys. Chem. B106, 7029–7033 (2002). [CrossRef]
  24. M. Perner, S. Gresillon, J. Marz, G. von Plessen, J. Feldmann, J. Porstendorfer, K. J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett.85, 792–795 (2000). [CrossRef] [PubMed]
  25. L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” PNAS100, 13549–13554 (2003). [CrossRef] [PubMed]
  26. D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett.209, 171–176 (2004). [CrossRef]
  27. D. Pissuwan, S. M. Valenzuela, and M. B. Cortie, “Therapeutic possibilities of plasmonically heated gold nanoparticles,” Trends Biotechnol.24, 62–67 (2006). [CrossRef]
  28. J. Z. Zhang, “Biomedical Applications of Shape-Controlled Plasmonic Nanostructures: A Case Study of Hollow Gold Nanospheres for Photothermal Ablation Therapy of Cancer,” J. Phys. Chem. Lett.1, 686–695 (2010). [CrossRef]
  29. J. Y. Chen, C. Glaus, R. Laforest, Q. Zhang, M. Yang, M. Gidding, M. J. Welch, and Y. Xia, “Gold nanocages as photothermal transducers for cancer treatment,” Small6, 811–817 (2010). [CrossRef] [PubMed]
  30. R. Bardhan, S. Lal, A. Joshi, and N. J. Halas, “Theranostic nanoshells: from probe design to imaging and treatment of cancer,” Acc. Chem. Res.44, 936–946 (2011). [CrossRef] [PubMed]
  31. M. Essone Mezeme and C. Brosseau, “Engineering nanostructures with enhanced thermoplasmonic properties for biosensing and selective targeting applications” Phys. Rev. E.87, 012722–012731 (2013). [CrossRef]
  32. R. H. Farahi, A. Passian, T. L. Ferrell, and T. Thundat, “Marangoni forces created by surface plasmon decay,” Opt. Lett.30, 616–618 (2005). [CrossRef] [PubMed]
  33. R. H. Farahi, A. Passian, S. Zahrai, A. L. Lereu, T. L. Ferrell, and T. Thundat, “Microscale Marangoni actuation: all-optical and all-electrical methods,” Ultramicroscopy106, 815–821 (2006). [CrossRef] [PubMed]
  34. A. L. Lereu, A. Passian, R. H. Farahi, S. Zahrai, and T. Thundat, “Plasmonic Marangoni forces,” JEOS:RP1, 06030–06034 (2006). [CrossRef]
  35. A. Passian, A. L. Lereu, E. T. Arakawa, A. Wig, T. Thundat, and T. L. Ferrell, “Modulation of multiple photon energies by use of surface plasmons,” Opt. Lett.30, 41–43 (2005). [CrossRef] [PubMed]
  36. P. Shankar and N. K. Viswanathan, “All-optical thermo-plasmonic device,” Appl. Opt.50, 5966–5969 (2011). [CrossRef] [PubMed]
  37. A. Passian, A. L. Lereu, E. T. Arakawa, R. H. Ritchie, T. Thundat, and T. L. Ferrell, “Opto-electronic versus electro-optic modulation,” Appl. Phys. Lett.85, 2703–2705 (2004). [CrossRef]
  38. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett.85, 5833–5835 (2004). [CrossRef]
  39. A. Passian, A. L. Lereu, R. H. Farahi, T. L. Ferrell, and T. Thundat, “Thermoplasmonics in thin metal films,” in Trends in solid film researchA. R. Jost, eds. (Nova Science Publishers, Hauppauge NY, 2007), pp. 69–109.
  40. J. Gosciniak, S. I. Bozhevolnyi, T. B. Andersen, V. S. Volkov, J. Kjelstrup-Hansen, L. Markey, and A. Dereux, “Thermo-optic control of dielectric-loaded plasmonic waveguide components,” Opt. Express18, 1207–1216 (2010). [CrossRef] [PubMed]
  41. H. Wei, Z. Wang, X. Tian, M. Käll, and H. Xu, “Cascaded logic gates in nanophotonic plasmon networks,” Nat. Commun.2, 387–391 (2011). [CrossRef] [PubMed]
  42. S. V. Boriskina and B. M. Reinhard, “Molding the flow of light on the nanoscale: from vortex nanogears to phase-operated plasmonic machinery,” Nanoscale4, 76–90 (2012). [CrossRef]
  43. D. Solis, B. Willingham, S. L. Nauert, L. S. Slaughter, J. Olson, P. Swanglap, A. Paul, W-S. Chang, and S. Link, “Electromagnetic energy transport in nanoparticle chains via dark plasmon modes,” Nano Lett.12, 1349–1353 (2012). [CrossRef] [PubMed]
  44. A. Passian, A. Wig, A. L. Lereu, P. G. Evans, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Probing large area surface plasmon interference in thin metal films using photon scanning tunneling microscopy,” Ultramicroscopy100, 429–436 (2004). [CrossRef] [PubMed]
  45. A. Passian, A. Wig, A. L. Lereu, F. Meriaudeau, T. Thundat, and T. L. Ferrell, “Photon tunneling via surface plasmon coupling,” Appl. Phys. Lett.85, 3420–3422 (2004). [CrossRef]
  46. F. P. Incropera, D. P. Dewitt, T. L. Bergman, and A. S. Lavine, Fundamentals of Heat and Mass Transfer, 6th ed. (John Wiley & Sons, Inc., 2007).
  47. A. Popescu, L. M. Woods, J. Martin, and G. S. Nolas, “Model of transport properties of thermoelectric nanocomposite materials,” Phys. Rev. B79, 205302–205308 (2009). [CrossRef]
  48. D. Cederkrantz, N. Farahi, K. A. Borup, B. B. Iversen, M. Nygren, and A. E. C. Palmqvist, “Enhanced thermoelectric properties of mg2si by addition of tio2 nanoparticles,” J. Appl. Phys.111, 023701–023707 (2012). [CrossRef]
  49. F. S. Ou, M. Hu, I. Naumov, A. Kim, W. Wu, A. M. Bratkovsky, X. Li, S. R. Williams, and Z. Li, “Hot-spot engineering in polygonal nanofinger assemblies for surface enhanced raman spectroscopy,” Nano Lett.11, 2538–2542 (2011). [CrossRef] [PubMed]
  50. J. Ye, F. Wen, H. Sobhani, J. Britt Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic nanoclusters: near field properties of the fano resonance interrogated with sers,” Nano Lett.12, 1660–1667 (2012). [CrossRef] [PubMed]
  51. C. W. Chen, H. P. Chiang, P. T. Leung, and D. P. Tsai, “Temperature dependence of enhanced optical absorption and raman spectroscopy from metallic nanoparticles,” Solid State Commun.148, 413–416 (2008). [CrossRef]
  52. S. Yamaguchi, “Optical absorption of heat treated very thin silver films and its dependence on angle of incidence,” J. Phys. Soc. Jpn.17, 1172–1180 (1962). [CrossRef]
  53. T. Q. Qiu and C. L. Tien, “Size effects on nonequilibrium laser-heating of metal-films,” J. Heat Trans-T ASME115, 842–847 (1993). [CrossRef]
  54. G. Chen and P. Hui, “Thermal conductivities of evaporated gold films on silicon and glass,” Appl. Phys. Lett.74, 2942–2944, (1999). [CrossRef]
  55. A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B71, 115425–115435, (2005). [CrossRef]
  56. S. W. Kennerly, J. W. Little, R. J. Warmack, and T. L. Ferrell, “Optical properties of heated Ag films,” Phys. Rev. B29, 2926–2929 (1984). [CrossRef]
  57. U. Kreibig and L. Genzel, “Optical-absorption of small metallic particles,” Surf. Sci.156, 678–700 (1985). [CrossRef]
  58. G. Gupta, D. Tanaka, Y. Ito, D. Shibata, M. Shimojo, K. Furuya, K. Mitsui, and K. Kajikawa, “Absorption spectroscopy of gold nanoisland films: optical and structural characterization,” Nanotechnol.20, 025703–025711, (2009). [CrossRef]
  59. J. Opsal, A. Rosencwaig, and D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt.22, 3169–3176 (1983). [CrossRef] [PubMed]
  60. B. Rief, “Thermal-wave transient behaviour,” Can. J. Phys.64, 1303–1306 (1986). [CrossRef]
  61. X. Chen, Y. Chen, M. Yan, and M. Qiu, “Nanosecond photothermal effects in plasmonic nanostructures,” ACS Nano6, 2550–2557 (2012). [CrossRef] [PubMed]
  62. G. V. Hartland, “Measurements of the material properties of metal nanoparticles by time-resolved spectroscopy,” Phys. Chem. Chem. Phys.6, 5263–5274 (2004). [CrossRef]
  63. Z. Ge, Y. Kang, T. A. Taton, P. V. Braun, and D. G. Cahill, “Thermal transport in au-core polymer-shell nanoparticles,” Nano Lett.5, 531–535 (2005). [CrossRef] [PubMed]
  64. P. Keblinski, D. G. Cahill, A. Bodapati, C. R. Sullivan, and T. A. Taton, “Limits of localized heating by electromagnetically excited nanoparticles,” J. Appl. Phys.100, 054305–054309 (2006). [CrossRef]
  65. C. Cheng, W. Fan, J. Cao, S-G. Ryu, J. Ji, C. P. Grigoropoulos, and J. Wu, “Heat transfer across the interface between nanoscale solids and gas,” ACS Nano5, 10102–10107 (2011). [CrossRef] [PubMed]
  66. M. I. Flik, B. I. Choi, and K. E. Goodson, “Heat-transfer regimes in microstructures,” J. Heat Trans-T ASME114, 666–674 (1992). [CrossRef]
  67. G. Chen, “Particularities of heat conduction in nanostructures,” J. Nanopart. Res.2, 199–204 (2000). [CrossRef]
  68. S. Volz, (Ed.), , “Thermal Nanosystems and Nanomaterials,” in Topics in Applied Physics, 1st ed.118, (Springer-Verlag Berlin, Heidelberger Platz 3, Berlin, Germany, 2010).
  69. E. Gesikowska and W. Nakwaski, “An impact of multi-layered structures of modern optoelectronic devices on their thermal properties,” Opt. Quant. Electron.40, 205–216 (2008). [CrossRef]
  70. R. Stana, I. Casian Botez, V. P. Paun, and A. Marcel, “New model for heat transfer in nanostructures,” J. Comput. Theor. Nanos.9, 55–66 (2012). [CrossRef]
  71. J. Kou, H. Qian, H. Lu, Y. Liu, Y. Xu, F. Wu, and J. Fan, “Optimizing the design of nanostructures for improved thermal conduction within confined spaces,” Nanoscale Res. Lett.6, 422–429 (2011). [CrossRef] [PubMed]
  72. Z. Xu and M. J. Buehler, “Nanoengineering heat transfer performance at carbon nanotube interfaces,” ACS Nano3, 2767–2775 (2009). [CrossRef] [PubMed]
  73. Z. Xu and M. J. Buehler, “Hierarchical nanostructures are crucial to mitigate ultrasmall thermal point loads,” Nano Lett.9, 2065–2072 (2009). [CrossRef] [PubMed]

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