Ultrafast Surface Plasmonic Switch in Non-Plasmonic Metals

Ultrafast Surface Plasmonic Switch in Non-Plasmonic Metals


We demonstrate that ultrafast carrier excitation can drastically affect electronic structures and induce brief surface plasmonic response in non-plasmonic metals, potentially creating a plasmonic switch. Using first-principles molecular dynamics and Kubo-Greenwood formalism for laser-excited tungsten we show that carrier heating mobilizes electrons into collective inter and intraband transitions leading to a sign flip in the imaginary optical conductivity, activating plasmonic properties for the initial non-plasmonic phase. The drive for the optical evolution can be visualized as an increasingly damped quasi-resonance at visible frequencies for pumping carriers across a chemical potential located in a -band pseudo-gap with energy-dependent degree of occupation. The subsequent evolution of optical indices for the excited material is confirmed by time-resolved ultrafast ellipsometry. The large optical tunability extends the existence spectral domain of surface plasmons in ranges typically claimed in laser self-organized nanostructuring. Non-equilibrium heating is thus a strong factor for engineering optical control of evanescent excitation waves, particularly important in laser nanostructuring strategies.


I Introduction

Collective non-equilibrium effects on transport properties in metallic systems are topics of current interest as non-standard behaviors play an increasing role in optics, thermodynamics or magnetism. Ultrafast laser electronic heating can mobilize localized states, inducing massive nonlinear contributions to optical and thermal transport or structural metastability. Understanding the intimate electronic mechanisms of optical coupling in excited solids and controlling excitation transients is therefore of prime importance as new applications are emerging in ultrafast optics, plasmonics and heat control strategies. If consequences for transport are readily expectable Desjarlais et al. (2002); Chen et al. (2013), and the role of nonequilibrium electronic transfer was early recognized Elsayed-Ali et al. (1987); Schoenlein et al. (1987), subtle atomistic effects can be inferred at the level of the band structure with unexpectedly strong consequences. Charge transfer and screening during non-equilibrium concur to a dynamic self-adjustment of thermal and optical properties to accommodate swift excitation. Recoules et al. Recoules et al. (2006) proved that participation of localized orbitals in noble metals enforces the lattice cohesion. Non-equilibrium charge supply allows large variations of thermal characteristics in transition metals Lin et al. (2008), fluidifying energy transport Petrov et al. (2013). Non-thermal distributions can restrict the collisional phase-space around the Fermi level, severely damping electron-phonon coupling Mueller and Rethfeld (2013). Furthermore, electronic occupation of delocalized states and filling from localized reservoirs (e.g. -bands in transition metals) redefine classical views on free electron density Bévillon et al. (2014), introducing significant dynamics in optical behaviors. Tuning ultrafast optical response via electronic reactions was thus proposed for active large bandwidth modulation in ultrafast plasmonics MacDonald et al. (2009). Engineering macroscopic optical response on ultrafast scales equally relates to the onset of optical resonances Luk’yanchuk et al. (2010); Hessel and Oliner (1965) on excited surfaces with spectral and spatial disturbances, e.g. Wood’s anomalies. One debated example concerns ultrafast laser nanostructuring of solids in self-assembled regular patterns. The universal phenomenon - observed half a century ago Birnbaum (1965) - carries application potential in functional surfaces Zorba et al. (2008), color-coded optical traceability and multidimensional information storage Dusser et al. (2010); Zhang et al. (2014), or feedback-driven nanolithography Öktem et al. (2013). Key questions in laser-induced periodic surface structures (LIPSS) concern the origin of spatially-modulated energy patterns Sipe et al. (1983) and the interplay between optical resonances and nonlinear feedback. Electromagnetic calculations indicate the involvement of surface waves inducing collective motion Sipe et al. (1983). Among them, surface plasmon (SP) with its ability to enhance electromagnetic energy on nanoscales holds a determinant role.

The potential involvement of SPs interference in laser nanostructuring is in close relation to surface optical indices. Thus the experimentally-observed onset of polarization-dependent periodic structures for non-plasmonic metals, as demonstrated on tungsten Vorobyev and Guo (2008), is intriguing in optical ranges theoretically forbidden by predictions based on ambient optical indices. A typical example of ultrafast LIPSS at 800 \sinm is provided in Fig. 1(a), showing quasi-wavelength periodicity. The positive real permittivity of W precludes normally the generation of electronic surface waves and plasmon polariton coupling. The possibility to excite collective material motion pinpoints to a more intricated dynamic response of the system. We investigate the impact of ultrafast heating on electronic structures capable of initiating a large excursion of optical properties, namely an excitation-driven plasmonic state in otherwise non-plasmonic solid non-Drude-like metal. First-principles approaches are chosen to interrogate electronic-driven evolution of optical properties and their consequences on plasmonic behaviors at time and spatial scales difficultly accessible by experiments.

Ii Calculation details

The calculations correspond to ultrashort pulse irradiation conditions enabling LIPSS around the damage threshold (90 \simJ cm^-2 absorbed fluence). Transient electron and lattice temperatures in W for single ultrashort pulse irradiation (Fig. 1(b)) are estimated using a two-temperature hydrodynamic code (Esther) Colombier et al. (2012) which describes the energy balance using Helmholtz optical formalism and electron-phonon relaxation with temperature-dependent transport properties Lin et al. (2008); Bévillon et al. (2014). Electronic temperatures on the rising heat cycle can amount to \siK, inducing electron-phonon nonequilibrium up to 3 \sips, with the material in solid state for at least 1 \sips. Internal electronic thermalization is assumed, justified by high levels of energy deposition in the vicinity of the threshold which accelerates electronic energy exchange to fs scales Mueller and Rethfeld (2013). In this range, calculations are carried out with the plane-wave code Abinit Gonze et al. (2009), in the frame of the density functional theory Hohenberg and Kohn (1964); Kohn and Sham (1965) extended to finite electronic temperatures Mermin (1965). The generalized gradient approximation Perdew et al. (1996) is employed to model exchange and correlation energies, and projector augmented-waves atomic data Torrent et al. (2008) account for the effects of nuclei and core electrons. A 54 atoms supercell of body centered cubic (bcc) W is considered, with 5556 valence electronic configuration; 4 electrons are neglected as their effect is weak at the considered here Bévillon et al. (2014). We first perform ab initio molecular dynamics simulations in the isokinetic ensemble at room temperature, with \siK during 2 \si\pico\second. This calculation provides an average thermodynamic equilibrium from which ionic configurations are extracted, standing for representative states of the W lattice at ambient conditions. Then electronic structures are computed at of , and \siK. They serve as a basis to evaluate optical properties in solid phase at these levels of electronic excitation.

Iii Results

We first focus on the evolution of the electronic density of states (DOS) with electronic temperatures in the presence of a cold, ambient lattice, with calculated DOS profiles provided in Fig. 1(c). If finite ionic temperature induces a certain smoothing of the features compared to calculations at = 0 \siK Bévillon et al. (2014) due to a loss of degeneracy arising from atom oscillations around their high symmetry position, a highly-structured band remains. The DOS shape is remarkably stable against electronic heating with a maximal block shift of 0.15 \sieV at \siK, indicative of a stiff electronic structure. This relates to the roughly symmetric profile of the DOS on both sides of the electronic chemical potential . The high density of empty electronic states on the right side of the Fermi level collects the excited electrons from the left-sided filled electronic states, leading to a weak dependence of , contrary to most of transition metals Lin et al. (2008); Bévillon et al. (2014). The location of the chemical potential within a mid-range pseudo-gap between high density of filled and empty electronic states determines the non-plasmonic behavior in the 1-5 \sieV range, i.e. for visible photon energies bridging the gap. The increase of determines however a slight augmentation of the number of electrons from low-lying part of orbitals, implying a moderately strengthen localization of the charge density, noted in increasing Hartree energies Bévillon et al. (2014). The main effect resumes to a Fermi broadening within the DOS. The impact of the occupation probability is discussed below.

Figure 1: (Color online) (a) Typical field-perpendicular surface periodic nanostructures at quasi-wavelength periodicity induced by 800 \sinm 50 \sifs laser pulses on W. (b) Electron (dashed red) and lattice (solid black) temperature evolutions for W irradiated by a 50 \sifs laser pulse. Dotted line indicates the standard vaporization limit. (c) DOS of bcc W computed at \siK and its evolution with . Dashed lines indicate the Fermi levels and dark colored areas show occupied electronic states mainly impacted by 800 \sinm photons.

Relying on the as determined electronic structures, the subsequent optical properties are obtained from an average on three ionic configurations. The real part of the frequency-dependent optical conductivity is obtained within the Kubo-Greenwood (KG) formalism Mazevet et al. (2010):


where electronic transitions from to states are integrated over the reciprocal space for each photon energy , accounting for the Fermi-Dirac occupations and the eigenenergies of the electronic states . represents the velocity operator. is the volume of the cell while corresponds to the three spatial dimensions. The imaginary part of the frequency-dependent conductivity is obtained using the Kramers-Kronig (KK) relation, , where is the principal value of the integral. Frequency-dependent permittivities and optical indices can be derived.

Optical properties follow electronic structure evolutions and large excursions up to plasmonic states are argued below. Fig.  2 shows the computed frequency-dependent optical conductivities and optical indices as a function of the electronic temperature. A good agreement is found between theoretical values obtained at \siK and the reflectivity measurements of Weaver Weaver et al. (1975), confirming a realistic description of the W electronic structure. is an implicit measure of optical absorption and its spectral behavior can be inferred based on the profile of the energy bands calculated in Fig. 1(c). For the low case (dotted blue line), at photon energies below 0.5 \sieV, the intraband part dominates, resulting from electronic transitions inside 6 bands. This contribution rapidly decays as the photon energy increases. On the other hand, interband transitions originating from the partially filled sub-bands become gradually more important Romaniello et al. (2006). From 0.5 to 5.1 \sieV, photon-driven electronic transitions access an increasingly larger DOS domain () centered on , resulting in a stepwise build-up of mapping the local DOS. This trend can be seen as the wing slope of a resonant behavior around the 5.1 \sieV peak given by the particular electronic DOS splitting around the Fermi level and the finite width of the sidebands. The conductivity finally decreases once main -bands peaks have been included and diluted into the continuously increasing electronic transition phase-space. From the KK relation, relies on the overall profile. Conceptually, this integral can be separated in two parts depending on the value of with respect to the reference value . For , the integral is negative and reverse signs for higher . Accordingly, the magnitude of depends on the profile of the real conductivity mainly around . A quasi-symmetric profile of tends to balance positive and negative components of the integral and provide low values for . On the contrary, an asymmetric profile emphasizes the respective sign components of the integral, depending on the trend of asymmetry (left or right-turned), determining positive or negative values of the imaginary conductivity. For W, the positive slope of profile from 1 to 5.1 \sieV with values ranging from to \siS cm^-1 leads to a negative at ambient conditions. A spectral view on indicates an anomalous-like dispersive behavior related to the absorption resonances.

Figure 2: (Color online) Real (a) and imaginary (b) part of the frequency-dependent optical conductivity; real (c) and imaginary (d) part of the optical indices. Colored curves stand for the electronic temperatures of \siK, \siK and \siK and the squares represent the experimental data for non-excited W Weaver et al. (1975).

The profiles of optical conductivities in Fig. 2(a,b) and optical indices in Fig. 2(c,d) significantly change with the electronic temperature, requiring an introspection in the corresponding excitation-driven electronic effects. If the observed changes in optical properties are not a consequence of DOS variation due to its stability against heating, the electronic temperature affects the degree of filling. Thus the optical evolution is the direct consequence of a broaden Fermi-Dirac charge redistribution, making more states available for photon-induced transitions. With the increase of , the optical transitions concern an increasing -centered interval mainly corresponding to [, ] Hopkins et al. (2008), illustrated in Fig. 1(c) for a photon energy of 1.55 \sieV. The consequence is manyfold, observable in the which maps the spectral absorption. Firstly this produces a broadening of available transition phase-space for the various photon energies. This translates into an increase of the intraband part, balanced by a decrease in the interband domain (qualitatively similar to a clockwise turn), damping the 5.1 \sieV peak. The subsequent asymmetric change of slope in with determines the increase of in the 1-5 \sieV (as the dispersive behavior across the resonance flattens) and a passage in the positive values domain for a significant part of the spectral domain. The situation becomes more clear in the evolution of the optical indices. At 1.55 \sieV (800 \sinm), relevant for the LIPSS, optical indices are strongly affected by the heating of the electronic system, with at \siK reaching at \siK. Thus, in the near infrared and low frequency visible part of the spectrum, the real part of the index goes down and the imaginary part augments.

Iv Experimental confirmation

The evolution was confirmed by time-resolved pump-probe ultrafast ellipsometry on laser-excited W surfaces. The transient optical properties upon ultrafast (120 fs) laser irradiation were probed at 1.55 eV photon energy using a two-angle one color time-resolved ellipsometry method following the technique proposed in Ref. Roeser et al. (2003). The static properties of the non-excited surface were first evaluated ex-situ using a commercial ellipsometer (Uvisel, Horiba Jobin Yvon) and the results give for massive W materials (Goodfellow purity, mechanically polished). Alongside massive W, foils (Goodfellow 0.3 mm thick, polished at 0.1 mRa -purity ) were equally used as reference. The dynamic reflectivity changes were subsequently interrogated on massive thick targets by p-polarized 120 fs, 800 nm low energy non-perturbing probe laser pulses at 27.1  and 65.8  incidence angles. The probe pulses were time-synchronized with fs accuracy with the exciting pump pulse of equally 120 fs 800 nm, arriving at normal incidence on the W surface. Two photodiode detectors were used in imaging geometries with respect to the surface. The probed zone is significantly smaller than the spatial extent of the excited region. The exciting fluences were chosen slightly below the ablation threshold.

Figure 3: (Color online) Example of dynamic time-resolved reflectivity traces at the two probe angles (27.1  and 65.8 ) at incident pump peak fluence of 0.12 J/cm. Inset: () contour plots corresponding to measured reflectivities at the two given angles. The intersection point represents a uniquely determined () pair satisfying simultaneously the two reflectivity conditions. Non-excited values obtained from ellipsometric measurements on bulk and foil samples as well as literature data Rakić et al. (1998) are given as references.

The swift optical activity on massive W samples is underlined by strong reflectivity changes, with a reflectivity snapshot example for an input peak fluence of 0.12 J/cm, just below damage threshold being shown in the Fig. 3 (a). The time-profile of the reflectivity transients maps the heating/cooling cycle of the electronic system and the associated redistribution in the electronic occupation around the chemical potential with . The measured maximum values of the transient reflectivity changes occurring just after the peak of the excitation pulse were then depicted in terms of corresponding () values in the () optical phase-space. They represent uniquely-determined () pairs obtained by inverting Fresnel formulas at the given angles. The result is presented in Fig. 3 (b). The intersection point of the () contour plots corresponding to two angle-resolved measured reflectivities were used to extract the corresponding () pair, allowing thus access to the evolution of optical indices. The result is , where resulting optical indices indicate slight decrease and increase in above the experimental value of its dispersive part. Note that these correspond to a macroscopic state averaged over a region set by the optical penetration depth of 18 nm, with inhomogeneous temperature distribution. The accuracy of the measurement is affected by the roughness and local planarity of the surface and care was taken to minimize the errors. The optical evolution has strong impact on the possibility to excite surface plasmon, with the fulfilment of the required optical conditions.

Figure 4: (Color online) Real part of the effective refractive indices () in case of air-tungsten interface as a function of . The symbol line stands for experimental data. Inset: variation of plasmon wavelength as a function of laser wavelength in a spectral domain ranging from 0.9 to 2.3 \sieV.

For air-material interfaces the condition for surface plasmon existence reduces to , a condition fulfilled in the conditions of Fig. 3, marking thus the ultrafast plasmonic activation at fluencies in the close vicinity of the damage threshold.

V Discussion

Surface plasmon periodicity as a function of laser wavelength is given by , where is the real part of the effective refractive index Pitarke et al. (2007). Calculated is plotted in Fig. 4 and the absence of data indicates non-existence domains of surface plasmons. With the increase of , one can note the expansion of the existence domain in the red photon energy region. The temperature-induced broadening of the electronic transition domain determines thus a plasmonic switch at visible optical frequencies. It appears that, upon electronic excitation, the light-induced onset of plasmonic character can sustain an origin based on optical resonances for LIPSS at 800 \sinm even though room temperature optical indices indicate non-plasmonic properties. As expected for air-metal interfaces, remains close to one, especially at low photon energy, leading to slightly inferior to the laser wavelength (inset of Fig. 4).

From the expression of the dielectric permittivity the existence condition can be expressed more directly in terms of imaginary conductivity (and implicitly on real permittivity) with . To clarify processes leading to the increase of the existence domain, we propose a simplifying approach. The imaginary conductivity is tentatively split into intra and interband components as depicted in Fig. 5(a,b). We first compute optical properties for a degenerate electronic system at \siK and , and \siK. This disregards ionic temperature and phonon effects, assuming they assist mostly the intraband component via momentum conservation conditions. Conceptually this is justified in a classical view by the temperature dependence of damping frequencies. Accordingly, the intraband contribution vanishes and (Fig. 5(b)). The intraband part at \siK is then extracted by subtracting the as-determined -insensitive interband part from the total value of the imaginary conductivity (Fig. 2(b)). In the visible spectral range, the intraband part rapidly increases with the rise of and saturates at \siK. An example of this behavior at 1.55 \sieV is given in the inset. At the opposite, the interband part shows a more complex behavior, with negative values of in the 0 to 5 \sieV energy interval that leads to negative values of the total imaginary conductivity, explaining the non-plasmonic nature of this metal. At higher energies, a resonance-like dispersive shape induced by the 5.1 \sieV peak of is clearly visible (Fig. 5(b)). By weakening the peak of , Fermi broadening also flattens the shape of around the resonance and gradually reduces its negative component, progressively switching on plasmonic properties of W. The increase is not yet saturated at \siK giving the possibility of a stronger lift and a subsequent extension of the plasmon existence domain for higher electronic temperatures. This highlights the preponderant role of -electron-driven interband transitions in the optical response at high .

Figure 5: (Color online) Intra and interband contribution to the imaginary conductivity as a function of . Inset: Local evolution of at 1.55 \sieV.

The electronic evolution described above is related to the fast achievement of the non-equilibrium electron-lattice phase. However, W is a strong coupling material and lattice effects may be rapidly generating along the electronic relaxation. Performing simulations at different lattice temperature values we observe that a ionic temperature effect is indeed observable, increasing slightly the plasmon existence domain. This is attributed to a loosening of the atomic order initially responsible for the material non-plasmonic nature. However the effect is of secondary importance compared to the charge redistribution induced by the electronic temperature within the band structure. We conclude that lattice heating, albeit its influence on atomic order, does not severely impact the calculated electronic structure on the relevant timescales, maintaining a dominant electronic drive for the process.

Vi Conclusion

In conclusion, electron temperature dependent ab initio MD-KG calculations of solid state W indicate large duty-cycle optical tuning upon ultrafast laser irradiation and potential excitation of propagating collective electronic motion for an initially non-plasmonic state. We demonstrate that the evolution of optical properties with produces, via the necessary optical conditions, an extension of the predictable existence domain of surface plasmon in the visible range, rendering possible a transient plasmonic phase and a potential plasmonic involvement in LIPSS. The necessary condition for optical indices was confirmed by time-resolved ellipsometry on excited W surfaces. The dynamic evolution mechanism is related to a redistribution of localized -electrons across a chemical potential located in a -band pseudo-gap. Since the DOS is not distorted by electronic heating, the changes of plasmon properties, indicated here by corresponding changes of optical conductivities, are principally due to Fermi broadening within a structured -block, extending the transition space for visible frequencies. By depopulating low-lying electronic states in favor of high electronic states, quasi-resonant transitions from regions of high DOS are diluted in a continuum of transitions. The dissimilar behaviors of intra and interband absorption events mark thus the evolution of the optical conductivity towards fulfilling resonant conditions. Similar phenomena may occur in other metals exhibiting non-plasmonic characteristics Rakić et al. (1998), especially Cr and Mo, as they crystallize in a similar structure. Stronger changes of optical properties Garrelie et al. (2011) are to be expected in case of transition and noble metals where the electronic structure varies substantially with electronic temperature. All these effects have implications for optical tunability and ultrafast switching of plasmonic properties extending beyond the domain of laser nanostructuring and validate concepts of structure engineering for metallic materials.

Vii acknowledgments

We thank N. Faure and M. Torrent for experimental and computing support. This work was supported by ANR project DYLIPSS (ANR-12-IS04-0002-01) and by LABEX MANUTECH-SISE (ANR-10-LABX-0075) of the Université de Lyon, within the ANR program ”Investissements d’Avenir” (ANR-11-IDEX-0007). Calculations used resources from GENCI (project gen7041).


  1. M. P. Desjarlais, J. D. Kress,  and L. A. Collins, “Electrical conductivity for warm, dense aluminum plasmas and liquids,” Phys. Rev. E 66, 025401 (2002).
  2. Z. Chen, B. Holst, S. E. Kirkwood, V. Sametoglu, et al., “Evolution of ac Conductivity in Nonequilibrium Warm Dense Gold,” Phys. Rev. Lett. 110, 135001 (2013).
  3. H. E. Elsayed-Ali, T. B. Norris, M. A. Pessot,  and G. A. Mourou, “Time-resolved observation of electron-phonon relaxation in copper,” Phys. Rev. Lett. 58, 1212 (1987).
  4. R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto,  and G. L. Eesley, ‘‘Femtosecond studies of nonequilibrium electronic processes in metals,” Phys. Rev. Lett. 58, 1680 (1987).
  5. V. Recoules, J. Clérouin, G. Zérah, P. M. Anglade,  and S. Mazevet, “Effect of Intense Laser Irradiation on the Lattice Stability of Semiconductors and Metals,” Phys. Rev. Lett. 96, 055503 (2006).
  6. Z. Lin, L. V. Zhigilei,  and V. Celli, ‘‘Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008).
  7. Y. V. Petrov, N. Inogamov,  and K. Migdal, “Thermal conductivity and the electron-ion heat transfer coefficient in condensed media with a strongly excited electron subsystem,” JETP letters 97, 20 (2013).
  8. B. Y. Mueller and B. Rethfeld, “Relaxation dynamics in laser-excited metals under nonequilibrium conditions,” Phys. Rev. B 87, 035139 (2013).
  9. E. Bévillon, J. P. Colombier, V. Recoules,  and R. Stoian, “Free-electron properties of metals under ultrafast laser-induced electron-phonon nonequilibrium: A first-principles study,” Phys. Rev. B 89, 115117 (2014).
  10. K. F. MacDonald, Z. L. Sámson, M. I. Stockman,  and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photon. 3, 55 (2009).
  11. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen,  and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707 (2010).
  12. A. Hessel and A. A. Oliner, “A New Theory of Wood’s Anomalies on Optical Gratings,” Appl. Opt. 4, 1275 (1965).
  13. M. Birnbaum, “Semiconductor Surface Damage Produced by Ruby Lasers,” J. Appl. Phys. 36, 3688 (1965).
  14. V. Zorba, E. Stratakis, M. Barberoglou, E. Spanakis, P. Tzanetakis, S. H. Anastasiadis,  and C. Fotakis, “Biomimetic Artificial Surfaces Quantitatively Reproduce the Water Repellency of a Lotus Leaf,” Adv. Mater. 20, 4049 (2008).
  15. B. Dusser, Z. Sagan, H. Soder, N. Faure, J.-P. Colombier, M. Jourlin,  and E. Audouard, “Controlled nanostructrures formation by ultra fast laser pulses for color marking,” Optics express 18, 2913 (2010).
  16. J. Zhang, M. Gecevičius, M. Beresna,  and P. G. Kazansky, “Seemingly Unlimited Lifetime Data Storage in Nanostructured Glass,” Phys. Rev. Lett. 112, 033901 (2014).
  17. B. Öktem, I. Pavlov, S. Ilday, H. Kalaycıoğlu, et al., “Nonlinear laser lithography for indefinitely large-area nanostructuring with femtosecond pulses,” Nat. Photon. 7, 897 (2013).
  18. J. E. Sipe, J. F. Young, J. S. Preston,  and H. M. van Driel, “Laser-induced periodic surface structure. I. Theory,” Phys. Rev. B 27, 1141 (1983).
  19. A. Y. Vorobyev and C. Guo, “Femtosecond laser-induced periodic surface structure formation on tungsten,” Journal of Applied Physics 104, 063523 (2008).
  20. J.-P. Colombier, P. Combis, E. Audouard,  and R. Stoian, “Guiding heat in laser ablation of metals on ultrafast timescales: an adaptive modeling approach on aluminum,” New Journal of Physics 14, 013039 (2012).
  21. X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, et al., “ABINIT: First-principles approach to material and nanosystem properties,” Computer Physics Communications 180, 2582 (2009).
  22. P. Hohenberg and W. Kohn, “Inhomogeneous Electron Gas,” Phys. Rev. 136, B864 (1964).
  23. W. Kohn and L. J. Sham, “Self-Consistent Equations Including Exchange and Correlation Effects,” Phys. Rev. 140, A1133 (1965).
  24. N. D. Mermin, “Thermal Properties of the Inhomogeneous Electron Gas,” Phys. Rev. 137, A1441 (1965).
  25. J. P. Perdew, K. Burke,  and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Phys. Rev. Lett. 77, 3865 (1996).
  26. M. Torrent, F. Jollet, F. Bottin, G. Zérah,  and X. Gonze, “Implementation of the projector augmented-wave method in the ABINIT code: Application to the study of iron under pressure,” Comput. Mater. Sci. 42, 337 (2008).
  27. S. Mazevet, M. Torrent, V. Recoules,  and F. Jollet, “Calculations of the transport properties within the PAW formalism,” High Energy Density Physics 6, 84 (2010).
  28. J. H. Weaver, C. G. Olson,  and D. W. Lynch, “Optical properties of crystalline tungsten,” Phys. Rev. B 12, 1293 (1975).
  29. P. Romaniello, P. L. de Boeij, F. Carbone,  and D. van der Marel, “Optical properties of bcc transition metals in the range 0-40 eV,” Phys. Rev. B 73, 075115 (2006).
  30. P. E. Hopkins, J. C. Duda, J. L. Salaway, R. N. and. Smoyer,  and P. M. Norris, “Effects of Intra- and Interband Transitions on Electron-phonon Coupling and Electron Heat Capacity after Short-pulsed Laser Heating,” Nanosc. Microsc. Therm. 12, 320 (2008).
  31. C. A. D. Roeser, A. M.-T. Kim, J. P. Callan, L. Huang, E. N. Glezer, Y. Siegal,  and E. Mazur, “Femtosecond time-resolved dielectric function measurements by dual-angle reflectometry,” Rev. Sci. Instrum. 74, 3413 (2003).
  32. A. D. Rakić, A. B. Djurišić, J. M. Elazar,  and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271 (1998).
  33. J. M. Pitarke, V. M. Silkin, E. V. Chulkov,  and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1 (2007).
  34. F. Garrelie, J.-P. Colombier, F. Pigeon, S. Tonchev, et al., “Evidence of surface plasmon resonance in ultrafast laser-induced ripples,” Opt. Express 19, 9035 (2011).
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