2.1 Metallic nanoparticles and localized surface plasmons
Metal nano-objects support electronic resonances known as LSPs that can be excited upon illumination. The frequency of LSP resonances strongly depends on the morphology of the metal nano-object and its dielectric environment. For instance, elongating a sphere into a rod-like shape tends to red-shift the LSP resonance. For noble metals, such as gold, silver or copper, this property allows accurate tuning of LSP resonances from the visible to the near-infrared (NIR) frequency range.
Recent advances in both bottom-up and top-down fabrication techniques offer a tremendous variety of metal NP sizes and shapes. On the one hand, chemists have developed synthesis procedures to produce colloidal noble metal NPs with numerous geometries including rods, cubes, triangles, shells, stars, etc. . On the other hand, techniques such as e-beam lithography and focused ion beam milling are convenient means to design planar metal nanostructures on a flat substrate with a resolution down to a few tens of nanometers. Examples of colloidal gold NPs and lithographically prepared gold nanostructures are presented in Fig. 1.
Figure 1. Scanning electron microscopy images that illustrate the wide variety of available gold NP morphologies: a–f) colloidal gold NPs synthesized using seed-mediated chemical approaches; g) lithographic gold nanostructures made using e-beam lithography. (Reprinted with permission of RSC.)
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The origin of LSP resonances in metal NPs can be simply derived for a metal sphere that is much smaller than the illumination wavelength and can be considered as an electromagnetic dipole. In this case, the sphere polarizability reads
where R is th radius of the sphere. In this expression, the polarizability α is defined such that the complex amplitude of the polarization vector of the NP reads . Equation (1) shows that a resonance occurs at the frequency ω at which . For a gold sphere smaller than ∼30 nm in water, this occurs for nm. However, for larger spheres, this dipolar approximation is no longer valid and more complex models, such as Mie theory [4, 5], , accounting for retardation effects, are required. For more sophisticated geometries, numerical simulations are needed (see Section 'Numerical methods').
Figure 2. (online color at: www.lpr-journal.org) a) Evolution of the maximum absorption and scattering for increasing diameters of gold NPs. It is shown that spherical gold NPs smaller than 90 nm are more efficient absorbers than scatterers. b) Absorption and scattering cross-section spectra for a gold nanosphere in water, 88 nm in diameter. For this precise diameter, the absorption and scattering maxima are equal. However, due to the spectral shift, absorption can be either dominant or negligible depending on the considered wavelength.
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Note that this conclusion is valid when considering the respective maxima of both cross-section spectra, but not the cross-sections at an arbitrary wavelength. Indeed, as shown in Fig. 2 b, for an 88 nm NP, even though the respective maxima of the absorption and scattering spectra are equal, absorption can be either dominant or negligible depending on the wavelength. This is the consequence of the spectral shift that usually occurs between absorption and scattering spectra for large or non-spherical NPs.
Consequently, even though spherical gold NPs are usually better absorbers than scatterers, the illumination wavelength must be specified to determine what is the actual dominant energy conversion pathway. It is worth noticing that, for this reason, considering experimental extinction spectra to estimate the absorption efficiency of a plasmonic structure, as sometimes seen in the literature , is not always reliable.
Tuning the plasmonic resonance frequency of a NP can be easily achieved by changing its morphology. Any deviation from the spherical shape tends to red-shift the resonance. Experimental results presented in Fig. 3 illustrate the red-shift of the plasmon resonance of a gold nanorod while increasing its aspect ratio.
Figure 3. (online color at: www.lpr-journal.org) Experimental extinction spectra measured on matrices of lithographic gold nanorods of increasing lengths L, 40 nm thick and 60 nm wide, lying on a glass substrate.
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In the following, we focus on the absorption processes and the subsequent heat generation.
2.2 Delivered heat power
The power absorbed (and delivered) by a NP can be simply expressed using the absorption cross-section σabs introduced in the previous section:
were I is the irradiance of the incoming light (power per unit surface). In the case of a plane wave, .
Figure 4. (online color at: www.lpr-journal.org) a) Heat power delivered by a single gold nanorod (50 × 12 nm) as a function of the illumination wavelength calculated using Green's dyadic tensor technique. b) Representation of the heat power density within the nanorod for different illumination wavelengths.
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2.3 Temperature profile under continuous-wave illumination
While the computation of the delivered heat power Q turns out to be a full-optical problem as explained in the previous section, the determination of the steady-state temperature distribution inside and outside the NP is based on the resolution of the heat diffusion equation:
where is the thermal conductivity. For a spherical NP of radius R, simple calculations lead to a temperature increase :
where is the temperature increase of the NP. Interestingly, while the heat power density can be highly non-uniform within the NP as clearly observed in Fig. 4 , the temperature at equilibrium is, on the contrary, generally perfectly uniform inside the NP . This is due to the much larger thermal conductivity of metals as compared with that of the surroundings (liquid, glass, etc.). The actual temperature increase experienced by a NP is dependent on numerous parameters, namely its absorption cross-section, its shape, the thermal conductivity of the surrounding medium and the wavelength and irradiance of the incoming light. For a spherical NP, the NP temperature increase is related to the absorbed power according to 
where κs is the thermal conductivity of the surrounding medium.
The establishment of this steady-state temperature profile is usually very fast when working with NPs. The typical duration τtr of the transient regime is not dependent on the temperature increase but on the characteristic size L of the system (for instance the radius R for a sphere) :
where ρ is the mass density of the NP and cp its specific heat capacity at constant pressure. For example, for spherical NPs of diameters 10 nm, 100 nm and 1 μm, one gets τtr of the order of 0.1 ns, 10 ns and 1 μs, respectively.
For non-spherical NPs, there is no simple analytical expression giving the NP temperature increase as a function of the absorbed heat power Q and numerical simulations are required. However, Baffou et al.  have recently proposed to use a dimensionless geometrical correction factor β defined such that the NP temperature increase reads
where Req is the equivalent NP radius. The value of beta for a large set of geometries with axial symmetry (namely rods, ellipsoids, discs and tori) are given in Ref. .
A last feature that is worth discussing is the possible influence of the surface thermal resistivity at the surface of a NP immersed in a liquid [17, 18], [19, 20]. A thermal resistivity may occur because of the material discontinuity, which acts as a thermal impedance. This resistivity can play a significant role in the heat release since it can reach appreciable values when the liquid does not wet the solid. The wetting depends on the nature of the interface and, in particular, on a possible molecular coating. Namely, hydrophobic coatings are associated with poor thermal conductivities. The direct consequence of a finite interface conductivity G (or resistivity ) is a temperature discontinuity at the NP interface such that
However, in the steady-state regime, this surface resistivity has no effect on the temperature outside the NP, in the surrounding medium. As evidenced in Eq. (10), the temperature outside the medium is only dependent on the heat power Q released by the NP. A finite surface conductivity G has only an effect on the temperature within the NP. It can also contribute in making any transient regime longer. The incidence of such a resistivity can be quantified using the Kapitza number λK defined such that
The surface resistivity can be neglected in any thermal process if . For gold NPs in water, usual values of the interface conductivity G range from 50 MW/(m2K) to ∞ [20, 17]. For NP radii ranging from 5 to 50 nm, typical Kapitza numbers λK thus range from 2 to ∼0. As an example, gold nanorods coated with cetyltrimethylammonium bromide (CTAB) molecules are endowed with a typical surface conductivity of MW/(m2K) . If the nanorods are, say, 50 × 12 nm in size, the effective radius is nm and Eq. (20) yields . Hence, in this case, the surface resistivity does not have any significant effect.
2.4 Nanoparticle heating under pulsed illumination
The use of pulsed illumination (from the femtosecond to the nanosecond range) to heat metal NPs markedly increases the range of applications of noble metal NPs. Compared to continuous-wave (CW) illumination, a new class of effects can be triggered, such as shorter temperature and pressure variations [21-23], further temperature confinement , acoustic wave generation , vibration modes [24-26], bubble formation [27-31], NP shape modification [32-35] and melting [32, 36],  and extreme thermodynamics conditions [38-42]. In this section, we briefly discuss the thermodynamics of metal NPs under pulsed illumination and in particular the influence of parameters such as pulse duration, pulsation rate and size of the NP.
The absorption of laser pulse energy by a gold NP can be described as a three-step process [43, 44], each of these steps involving different time scales as follows.
Step 1. Electronic absorption: During the interaction with the laser pulse, part of the incident pulse energy is absorbed by the gas of free electrons of the NP, much lighter and reactive than the ion lattice. The electronic gas thermalizes very fast to a Fermi–Dirac distribution over a time scale 100 fs . This leads to a state of non-equilibrium within the NP: the electronic temperature Te of the electronic gas increases while the temperature of the lattice (phonons) Tp remains unchanged.
Step 3. External heat diffusion: The energy diffusion from the NP to the surroundings usually occurs at longer characteristic time scale τtr (see Eq. (13)) and leads to a cooling of the NP and a heating of the surrounding medium. The time scale of this process depends on the size of the NP and ranges from 100 ps to a few nanoseconds. For small NPs (<20 nm), this third step can overlap in time with the electron–phonon thermalization  (as discussed hereafter).
During this process, the total absorbed energy reads
where f is the pulsation rate and F the fluence of the laser pulse (energy per unit area).
Different regimes can be observed depending on the pulse duration compared with τtr (see Eq. (13)). When the pulse duration is short enough (typically <0.1 ns) and/or the NP is small enough (typically <100 nm in diameter), the three steps can be considered to happen successively. In this regime, the initial temperature increase reaches its maximal value :
where V is the volume of the NP. (The expression is only valid for moderate temperature increase so that cAu remains constant.) In this case, the duration of the heating of the medium is of the order of τtr.
If we consider now the regime were the pulse duration exceeds τtr, the three steps will overlap in time. In other words, heat gets absorbed and delivered in the surroundings simultaneously. In this case, the maximum temperature increase inside the NP will not reach and the heating duration will simply equal the pulse duration. This situation is usually obtained when using nanosecond pulses on gold NPs.
Figure 5. (online color at: www.lpr-journal.org) Figure comparing the spatial extension of the temperature profile in CW and pulsed illuminations. a) Radial profiles of temperature in both cases. In the case of pulsed illumination, temperature profiles at different normalized time are represented (dashed lines) along with the associated temperature envelope. b) Three-dimensional representation of the temperature profile around a NP under CW illumination. c) Three-dimensional representation of the temperature envelope around a NP subsequent to a single femtosecond-pulse illumination. (Reprinted with permission of APS.)
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where the fit parameters are and .