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The origin of high-spatial-frequency laser-induced periodic surface structures (HSFL) driven by incident ultrafast laser fields, with their ability to achieve structure resolutions below λ/2, is often obscured by the overlap with regular ripples patterns at quasi-wavelength periodicities. We experimentally demonstrate here employing defined surface topographies that these structures are intrinsically related to surface roughness in the nano-scale domain. Using Zr-based bulk metallic glass (Zr-BMG) and its crystalline alloy (Zr-CA) counterpart formed by thermal annealing from its glassy precursor, we prepared surfaces showing either smooth appearances on thermoplastic BMG or high-density nano-protuberances from randomly distributed embedded nano-crystallites with average sizes below 200 nm on the recrystallized alloy. Upon ultrashort pulse irradiation employing linearly polarized 50 fs, 800 nm laser pulses, the surfaces show a range of nanoscale organized features. The change of topology was then followed under multiple pulse irradiation at fluences around and below the single pulse threshold. While the former material (Zr-BMG) shows a specific high quality arrangement of standard ripples around the laser wavelength, the latter (Zr-CA) demonstrates strong predisposition to form high spatial frequency rippled structures (HSFL). We discuss electromagnetic scenarios assisting their formation based on near-field interaction between particles and field-enhancement leading to structure linear growth. Finite-difference-time-domain simulations outline individual and collective effects of nanoparticles on electromagnetic energy modulation and the feedback processes in the formation of HSFL structures with correlation to regular ripples (LSFL).
© 2016 Optical Society of America
1. Introduction
The question of the formation of anisotropic regular structures (the so-called laser-induced periodic surface structures –LIPSS) on materials irradiated by light fields of isotropic and uniform energy distribution is a key issue in controlling laser structuring processes below the diffractive limit [1]. Often related to a polarization state, these structures respond to a vectorial anisotropy of the beam [2, 3]. This particularity fueled present formation scenarios based on light scattering and interference processes driven by incoming and scattered waves with evanescent components in the vicinity of the surface, but other scenarios are equally considered; from plasmonic responses [4] to self-organization of laser excited and destabilized matter [5]. It is however probable that structured electromagnetic field distributions at the surface are the driving contributions in ripple formation, with subsequent effects of the morphology deriving from the particular thermal and mechanical dynamics of the system [6].
A particular type of ripples is represented by a periodic arrangement below λ/2 (with λ the incident light wavelength), called high-spatial-frequency laser-induced periodic surface structures (HSFL) [7], and we will focus on HSFL in this work. Typical interference phenomena involving incident and surface scattered waves mediated by the material optical indices show mainly spatial periods close to the incident wavelength and results in the common LIPSS (low-spatial-frequency LIPSS –LSFL) [2]. Thus the formation mechanisms of ripples of smaller periodicities imply more complex light interaction scenarios, involving both local and non-local light-assisted processes. We show here that the appearance of high-frequency LIPSS is inherently related to the presence of nano-scaled rough surface topographies, confirming a scenario anticipated in the reference [8] where HSFL periodicities were, function of the complex dielectric constant, connected in different proportions to interference and scattering. The dielectric function defines the weight of interactions between the incident light and the scattered fields or the superposition of diffuse fields which originate from the scattering of the incoming light by a nano-scaled surface topography. To this end, and focusing on a metallic case, we have chosen a Zr-based alloy material in two structural states: thermoplastic metallic glass state [9] with optically smooth surfaces and rigid crystalline state with inherently defined nano-topography [10,11]. Formed by annealing of the glassy material, the later shows typically the development on Zr-rich nano-crystallites either embedded in the matrix or randomly protruding the surface. Upon irradiation, the topography imprints thus distinct classes of ripples on the two materials, with high frequency patterns on the nano-rough surface. The interaction of light with the topographical surfaces is then analyzed by solving the Maxwell equations at the interface using finite-difference-time-domain (FDTD) approaches. We show collective and individual light effects relying on mutual interaction of particles seen as secondary light sources and structure growth driven by anisotropic light-enhancement. We then pinpoint the potential role of the thermomechanical properties on the morphology of the structures. The manuscript discusses thus recipes for tuning surface topographies and results of FDTD simulations on individual or collective nano-roughness features leading to variability in periodicity and topography.
2. Experiment
2.1 Materials
Zr-based superalloy is in particular conditions a glass-making material showing disordered atomic-scale structure [11]. Formed from supercooled liquids, it is characterized by a lack of crystallites, grain boundaries and dislocations in the material structure. Here we focus on Zr-BMG of Zr41.2Ti13.8Cu12.5Ni10Be25.5 (at%) composition which demonstrates thermoplasticity, becoming moldable at temperatures above the glass transition temperature Tg = 623 K [11]. Single-side polished Zr-BMG samples with a diameter of 8 mm and a thickness of 3 mm were used in the experiment. Zr-BMG samples were produced by arc melting under purified Ar atmosphere and dropping into a copper mold. After cutting, polishing was done by diamond paste and alumina powder with grit size down to 0.1 µm. The amorphous structures of the Zr-BMG samples were confirmed by electron backscatter diffraction (EBSD). Upon heating above crystallization temperature Tx = 705 K the material produces crystalline phases with different structural arrangements (tetragonal Zr2Cu phase, Laves MgZn2 phase, tetragonal Zr2Ni phase) depending on pressure and annealing time [10,11]. As compared to the glass state, the crystalline phase shows typically increased hardness and brittleness, without a significant variation in density. In our case Zr-crystalline alloy (Zr-CA) was obtained by annealing Zr-BMG at 800 K for 50 h in order to produce stable crystalline phases.
2.2 Surface topology analysis
The first striking element comes from the inspection of the surface topography for the two materials. The surface topologies of the Zr-BMG and Zr-CA samples were analyzed using scanning electron microscopy (Zeiss Supra55 FEG-SEM). Figure 1 presents SEM images of pristine Zr-BMG and Zr-CA surfaces with the following characteristics. Zr-BMG surface has a flat smooth aspect with low residual roughness (a defect hole is shown in Fig. 1(a) as a reference). A roughness value around Ra = 7 nm was measured by means of atomic force microscopy. The annealing treatment had nonetheless as strong influence on the CA, as we observe a range of high-density random-distributed nanoparticles with the size smaller than 200 nm on Zr-CA surface (see Fig. 1(b)). The measured mean roughness lies around Ra = 40 nm. These are intrinsically related to the process of crystallization, generating thus a surface with nano-protuberances with the size smaller than 200 nm in a random distribution.
Fig. 1 SEM images of (a) Zr-BMG surface and (b) Zr-CA surface. The presence of nano-particulates and protuberances is visible for the crystalline alloy surface and is a product of the annealing procedure. Inset: EDX analysis of nano-crystallites.
The nanoparticles on the Zr-CA surface are most probably products of the crystallization process. Energy dispersive X-ray spectrometry (EDX) analysis of the chemical composition (inset in Fig. 1(b)) indicates that the main elements composing the nanoparticles are Zr and Cu indicating potential nano-particulates of Zr2Cu crystalline phase in the Zr-CA. The two different topographies will have a strong influence on the formation of LIPSS.
2.3 Surface laser irradiation
A regenerative Ti:sapphire oscillator-amplifier system at a central wavelength of 800 nm with pulse duration of 50 fs and repetition rate of 1 kHz was used to perform the experiments. Before and after laser irradiation, Zr-BMG and Zr-CA samples were cleaned ultrasonically in ethanol for 5 min. The linearly polarized Gaussian laser beam was focused by a focusing lens of f = 100 mm focal distance, down to a spot with the diameter of 26 μm (1/e2 intensity) on the surface at the focus plane. The laser fluence was adjusted by using the combination of a waveplate and a polarizer. The number of pulses is controlled by a synchronized laser shutter. The sample was mounted on a computer-controlled XYZ translation stage and the irradiated zone was observed in real time by a magnifying imaging system and projected on a CCD monitor. All experiments were performed in an ambient atmosphere with the sample surface perpendicular to the laser beam. Microscopy techniques were applied to characterize the irradiation results.
2.4 Surface periodic structuring
We follow below the structural arrangements upon the irradiation with ultrashort laser pulses on two surfaces of different topographies, the flat smooth BMG and that randomly nano-rough CA surface. We used two sets of fluence and variable doses, encompassing thus a range of formation conditions. According to the experiments, the single-pulse ablation threshold of Zr-BMG is Fth = 0.3 J/cm2, and the single-pulse ablation threshold of Zr-CA is Fth = 0.15 J/cm2. In that concerns the effect with multipulse irradiation, the spot dimensional analysis points to a more effective incubation effect in case of Zr-BMG. Figure 2 summarizes the results and shows the SEM images of Zr-BMG and Zr-CA surfaces after irradiation at the fluence F = 0.38 J/cm2 and F = 0.15 J/cm2 with a variable number of linearly polarized pulses. A range of LSFL and HSFL structures on BMG and CA are discussed below.
Fig. 2 SEM images of BMG (a, c) and CA (b, d) sample surfaces after irradiation with linearly polarized laser pulses at the fluence F = 0.38 J/cm2 (a, b) and F = 0.15 J/cm2 (c, d). Magnified zones for CA topographies are shown in the insets as well as EBSD structural evaluations of BMG surfaces for amorphous and crystalline phases. A low number of pulses was used for the higher fluence value (N = 1, 2, 4) while a higher number of pulses (N = 20, 50, 100) was used for the low fluence case. An example for a higher fluence F = 0.6 J/cm2 at N = 4 is given in the inset in (a). The polarization direction of the laser beam is indicated with a double-headed arrow. LSFL denotes LSFL ripples formed typically perpendicular to the laser polarization direction. HSFL represents high-spatial-frequency ripples parallel to the laser polarization direction in this case. The 2D Fourier-transformation (FT) representations of LIPSS at N = 4 pulses are given for BMG and CA cases in (a,b), indicating the development of LSFL and HSFL and their specific spatial periodicities in the spatial-frequency space (K-space).
The inspection of irradiation results on surface show primarily the following visual aspects. For these fluence ranges and for Zr-BMG (see Figs. 2(a) and 2(c)), we observe the net formation of LSFL patterns perpendicular to the laser polarization direction. Their evolution depends on the fluence and dose, however LSFL defines the main periodic arrangement obtained for ultrashort pulse irradiated BMG, with a characteristic high definition of the features. At higher fluences the probable increase in melt depth would flatten the ripples contrast within the spot (see inset in Fig. 2(a)). In most cases the resulting structural phase stays amorphous, with some isolated nano-crystalline domains at high number of pulses, as verified using EBSD monitoring the presence of Kikushi lines in the EBSD images [12].
In contrast, the CA case shows a more complex situation (see Figs. 2(b) and 2(d)), with a mix of patterns combining both LSFL perpendicular to the laser polarization direction and HSFL oriented parallel to the polarization direction, i.e. to the laser field. Following their dynamic evolution with the number of pulses we observe that, for the higher fluence, the first pulse irradiation forms a dense ensemble of nano-protuberances related to the initial distribution of nano-crystallites creating discontinuities in the surface topology. With the increase in the number of pulses, starting with the second one, linear elongations of the structures are observed, forming gradually the HSFL pattern. The typical periodicities of the two patterns as deduced from the 2D Fourier transformation (FT) representations (examples in Fig. 2 insets) are centered at 740 nm for the BMG case (LSFL), and 708 nm (LSFL) and 384 nm (HSFL) for the CA in the conditions indicated in Fig. 2. Nevertheless we note a large broadening in the period values for HSFL along its central value.
Comparing the results we may deduce that the formation of HSFL ripples on Zr-CA is strongly related to the specific nano-structured surface of Zr-CA with a high density of nanoparticles, while LSFL generation can be related to an initial roughness as well as to a laser-induced evolving topology on both surfaces in terms of laser-induced additional roughness and corrugation. We discuss below the consequences of the high density nano-roughness on structured distribution of field in the vicinity of the surface. We then indicate potential consequences related to the specific thermal and hydrodynamic characteristics of the two materials.
3. The effect of the nanoparticles on electromagnetic energy modulation
The electromagnetic solutions of the field distribution are strongly influenced by the surface state [13–16]. We have seen that in the Zr-CA case we have an initial inherent high-density nano-scaled roughness, while on both BMG and CA, subsequent laser exposure in the vicinity of the threshold will add new topology features, from localized centers for phase transition [17] to ordered corrugation and larger features. We estimate that the energy distribution following the exposure of rough surfaces is driven by local effects determined by single-nanoparticle scattering and by multiple-nanoparticles collective inter-coupling scattering effects. The effect on LSFL being largely discussed [13, 15, 16] and implying stationary structured field distributions involving interference effects between scattered and incident fields on surfaces corrugations, we concentrate here of fine HSFL structures oriented parallel to the field and linked to the nanoscale characteristic dimension of roughness. Note that in general the concept of HSFL involves a range of periodicities and orientations for the given structures [7, 8, 16].
In order to investigate the role of the nanoparticle on Zr-CA surface, the electromagnetic energy modulation induced by single nano-protuberance on a flat surface is calculated by 3D FDTD simulations that can simulate light propagation, scattering and diffraction phenomena by solving Maxwell equations numerically [18]. The method is used to compute the inhomogeneous electric field distribution on the surface (XOY plane) for an electromagnetic beam propagating along Z axis. Perfectly matched layer method was used as absorbing boundary condition. The surface is irradiated at normal incidence in air with linearly polarized laser pulses of 50 fs duration (FWHM) at 800 nm central wavelength. From ellipsometry measurements, the refractive index of Zr-CA is ñ = 2.59 + 3.30i under 800 nm light irradiation. Zr-CA flat surface with an hemisphere with the diameter of 100 nm placed in the surface center is built as the surface model. The incident plane wave propagates along the Z axis. The associated electric field E is defined with 800 nm wavelength and a polarization direction set along the X axis. The amplitude of electric field in incident plane wave is fixed to 1 V/m.
We will first focus on the response of a single nanoparticle-like topological feature. The energy distribution pattern induced by a single nano-protuberance is given in Fig. 3 for the case of a ϕ100-nm hemisphere on flat Zr-CA surface. Figure 3(a) gives the time-averaged E2 distribution at the surface equivalent to a stationary structured energy pattern. This shows that a main channel in the energy modulation comes from the near-field enhancement at the edge of the nano-protuberance. At the same time, at larger distance, field modulation is observed, driven by scattering patterns and interference with the incident fields. The Fourier transform analysis (see Fig. 3(b)) shows two main components in the spatial wave-vectors space (K = 2π/λ with λ = 800 nm), a component oriented along the KX axis (and thus corresponding to modulations perpendicular to the polarization axis) and a higher spatial frequency component along the KY axis (with modulations parallel to the polarization direction). These are consistent with our previous research work [8].
Fig. 3 Energy distribution patterns around a nanoscale topological feature of a ϕ = 100 nm hemisphere on flat Zr-CA surface. (a) Total energy distribution pattern derived from time-averaged E2 with (b) its Fourier transform (FT). (c) Insights into the X-component of energy distribution derived from time-averaged EX2 with (d) its FT. Note that the laser polarization direction is set along the X axis. Identical colorbars are used for (b) and (d). K0 = 2π/λ.
In order to analyze the origin of these modulations, we have verified the EX2 component (equivalent to a scalar energy value corresponding to the resulting field component in the vicinity of the surface containing the incident polarization) in Figs. 3(c) and 3(d). The interferential pattern shows similar amplitude and distributions as the total field, with a difference related to the higher frequency component along KY (see Fig. 3(d)). We conclude that the higher spatial frequency component (present in the total field distribution) has a mixed origin, scattering in a characteristic pattern and potential interferential interactions along the polarization direction. The field patterns generated by a single nanoscale topological feature will be amplified and reordered in the case of an ensemble of particles.
Figure 4 represents modulated energy patterns resulting from structured stationary fields distribution in the case of a high density ensemble of nanoparticles (500 nanoparticles with the same size of 40 nm × 40 nm × 40 nm (length × width × height) are distributed randomly on the flat surface with the size of 25 μm × 25 μm). Figure 4(a) is the time-averaged E2 distribution at the surface, with its Fourier transformation given in Fig. 4(b). As in the case of randomly distributed nanoparticles, the real space and K-space analyses in Fig. 4 show periodic spatial features with their vector aligned on KX (structures perpendicular to the field). Their K/K0 value of about 1.25 (corresponding to λ/1.25) relates the features to LSFL originating from interference between scattered and incident fields. The features along KY with higher spatial frequencies in the HSFL range have a dual nature, originating in both interference and scattering with a strong inter-particle coupling and mutual coherent interactions. We therefore relate spatial features in the HSFL band to both coherent interactions with the incident field and interparticle scattering interactions without involving a modulating interaction with the incident field. However, though an electromagnetic (EM) approach satisfies the dimensional analysis, one problem related to the EM interpretation is that the contrasts typically associated to HSFL are significantly smaller than those of LSFL, suggesting a lower probability of formation, somehow in contradiction with the experimental results. These effects depend on the particle size and we therefore take into account the near-field interaction around the nanoparticle.
Fig. 4 Energy distribution patterns for an ensemble of nanoscale topological features of randomly distributed nanoparticles on flat Zr-CA surface. (a) Total energy distribution pattern derived from time-averaged E2 with (b) its Fourier transform (FT). Note that laser polarization direction is along the X axis. K0 = 2π/λ.
4. Feedback between nanostructure and electromagnetic field
4.1 Electromagnetic field enhancement
A complementary analysis of the field interaction with a single nanoscale topography feature shows a singular feature of the structured field in the near-range of the nanoparticle. A localized field enhancement with poles aligned along the polarization direction becomes visible already in Fig. 3(a). The field enhancement factor depends on the geometry and the size of the nano features. Figure 5(a) puts into the evidence of this effect by resuming the dimensional influence of nanoparticles with the different sizes of ϕ = 100 nm, ϕ = 200 nm, ϕ = 400 nm and ϕ = 800 nm on energy redistribution. Observing the time-averaged E2 distribution along the X axis (at Y = 0) in Fig. 5(b), we note both a near-field enhancement and an increase of modulation on a larger scale coming from the interference between the incident and the scattered wave. The modulation contrast maximizes when the particle size approaches the incident wavelength suggesting an increase in the scattering efficiency while the field enhancement stays high for subwavelength sizes. We conclude that for nanoparticles with the size similar to those observed on the Zr-CA surface, the near-field enhancement may play a role in the electromagnetic energy modulation. At the same time, as for the bigger size of nanoparticles, the interference between scattered wave and incident laser becomes stronger. This becomes a driving factor in forming the LSFL ripples perpendicular to the laser polarization direction.
Fig. 5 (a) Time-averaged E2 distribution on the surface (XOY plane) induced by a hemisphere of different diameters: ϕ = 100 nm, ϕ = 200 nm, ϕ = 400 nm, ϕ = 800 nm; (b) Time-averaged E2 distribution along Y = 0 axis induced by a hemisphere with different sections: ϕ = 100 nm, ϕ = 200 nm, ϕ = 400 nm, ϕ = 800 nm. (c) Time-averaged E2 distribution on the XOY plane induced by four hemispheres of ϕ = 100 nm as a function of the number of pulses. Top: a first incident pulse, middle: elongated structures interact with a second pulse, bottom; more elongated ripple in interaction with a forth pulse. The ripple domains are indicated by the pink color. The polarization direction of the incident planewave is along the X axis.
The field enhancement in the near-field range leads to energy localization at the sides and thus to thermal gradients. Considering the material motion along this direction driven by the thermal gradients in thermocapillary convection [19], we foresee an anisotropic growth for the nano-features along the polarization direction. Assuming that the growth covers the region of field-enhancement, we can observe now a feedback mechanism developing with the increase of the number of pulses.
The experimental results depicted in the inset of Fig. 2(b) shows already a gradual evolution from spherical to elongated forms with N varying from 1 to 4. Already after the 2nd pulse, high frequency short regular structures form along the direction of laser polarization from an ensemble of many nanoparticles (see Fig. 2(b)). After N = 4 pulses, the pattern of HSFL becomes fully visible. This supports a hypothesis of HSFL feature being influenced by the feedback process between the surface nanostructures and laser pulses.
We have tried to simulate the effect by considering a topological effect of the near-field enhancement. The effect is visualized in the following 3D-FDTD simulations assuming a Zr-CA flat surface with some same hemispheres on surface, built as the surface model, and the results are given in Fig. 5(c).The diameter of the hemispheres is set to 100 nm. The results show the time-averaged E2 distribution on XOY plane with the incoming pulses on a variable topology. Near-field enhancement determines energy modulation and the maximum energy is distributed at the edge of hemisphere along the X axis, consistent with the polarization direction of incident plane wave. It is presumed that the feature grows at first in the region absorbing maximum energy, so the initial nano-particle becomes longer along the X axis after first laser pulse, forming one short ripple. This is related to material flow and assumes that the ablation threshold is not achieved in the enhancement region. According to the maximum energy distribution in the case of N = 1 pulse in Fig. 5(c), the next short nanostructure model is built in the second step of the FDTD simulation. In the same simulation conditions, after the second pulse, the time-averaged E2 distribution on XOY plane elongates furthermore, as shown in the case of N = 2 pulses in Fig. 5(c). Maximum energy gets localized at the two ends of the initial short ripple, contributing to additional enlargement along the X axis. This is also confirmed after subsequent irradiation as shown in the case of N = 4 pulses in Fig. 5(c). This process can thus lead to the development of elongated structures where the period is first given by the initial distribution of nanoparticles, determining an evolution in scattering. The scenario can be applied for the case of many random distributed nanoparticles on Zr-CA surface, contributing to the formation of initial HSFL ripples. Thus, the feedback process that become apparent in the simulations in Fig. 5(c) can lead to a polarization-assisted anisotropic grow of the structures in directions parallel to the polarization direction.
The whole process has equally an influence on the LSFL, as scattering depends on the size of the scatterers. As sizes of initial nanoparticles and short ripples enlarge gradually with increasing number of laser pulses, the contrast of energy modulation originating in the coherent interaction between the incoming field and the scattered waves increases (shown in Figs. 5(a) and 5(b)), contributing to the enhancement of LSFL ripples perpendicular to laser polarization direction. The pulse-dependent size effect of surface nanostructures seems consistent with the LIPSS evolution in the experiment in Fig. 2(b), in which HSFL ripples form in the first several pulses, then LSFL ripples form in the following pulses with bigger size of surface nanostructures. The evolutions of both HSFL and LSFL ripples with the increasing pulses are discussed in the following.
4.2 Feedback between the laser pulses and the rough surface including the near-field induced elongation of nanoparticles
Similar to Fig. 5(c), the feedback relating in a dynamic manner the incoming laser pulses and an evolving rough surface with nanoparticles that are subject to the near-field induced elongation effect is simulated by the FDTD method. In the simulation, the initial rough surface model is represented by a flat surface incorporating an ensemble of nanoparticles (500 nanoparticles with the same size of 100 nm × 100 nm × 50 nm (length × width × height) that are distributed randomly on the flat surface with the overall size of 10 μm × 10 μm). The polarization direction of the incoming laser pulses is aligned along the X axis. After the rough surface is irradiated by subsequent laser pulse, the elongation of each nanoparticle along the polarization direction is assumed to occur according to the near-field energy distribution discussed before, leading to the evolution of the surface topography. For the next pulse, the surface model of the new topographies is used in the simulation, leading to new features of energy modulation. The simulation results are shown in Fig. 6, representing the effects of the feedback between laser pulses and the rough topographies involving the near-field induced elongation. Figures 6(a)–6(d) depict respectively the time-averaged E2 distributions at the pulse numbers of N = 1, 2, 3, 4, while the corresponding Fourier transformations are shown in Figs. 6(e)–6(h), pointing out an intricate evolution of energy distribution. As the interparticle distance is becoming comparable to the gradual elongation of single particles, narrow HSFL-like lines are becoming apparent via particle interconnection along the X axis (see Fig. 6(d) and 6(h)). The mutual influence between topology and field becomes equally visible in the enforcement of LSFL with the number of pulses, in the conditions where the sole topography evolution was related to particle elongation and interconnection. This indicates a reinforced correlation between scattering and particulates geometries.
Fig. 6 Time-averaged E2 distribution for an ensemble of randomly-distributed nanoparticles subject to near-field induced elongation for a number of pulses of (a) N = 1, (b) N = 2, (c) N = 3, (d) N = 4. The corresponding Fourier transformations are respectively given in (e, f, g, h). The polarization direction of the incident planewave is along the X axis. K0 = 2π/λ.
4.3 The role of thermodynamics
The scenario presented above includes only electromagnetic effects. However, besides the nanoscale roughness, Zr-BMG and Zr-CA present opposite thermodynamic features, notably a thermoplastic character for Zr-BMG and a more brittle character with sharp thermodynamic transition points for Zr-CA. The thermoplastic moldable character of Zr-BMG is presumably responsible for the quality arrangement and morphology of LSFL. The HSFL morphology on Zr-CA depends on the input energy and ranges from droplet-like forms to inner-structure texturing, suggesting equally a dewetting mechanisms. This shows a strong inter-relation between field and thermodynamic issues in building a comprehensive scenario for ripple formation.
5. Conclusion
We argued by experiments and simulations that a type of high-spatial-frequency LIPSS parallel to laser polarization direction is intrinsically related to the presence of nano-scaled roughness on surfaces. Using prepared surfaces ranging from flat surfaces on Zr-based bulk metallic glasses (Zr-BMG) to the nano-scale rough surfaces containing a high density of nano-crystallites on Zr crystalline alloys (Zr-CA), microscopy analyses, and electromagnetic FDTD simulations, we observed the preferential formation of HSFL on rough Zr-CA surfaces (as compared to LSFL on flat thermoplastic Zr-BMG surfaces). By analyzing single and multiple particle scattering features we proposed scenarios for HSFL formation relying on individual anisotropic near-field enhancement processes and collective mixed scattering and interference effects driven by the incident field and inter-particle coupling. The near-field enhancement becomes important for particles sizes in the range of 200-400 nm (but also works effectively for smaller sizes approaching the sub-100 nm roughness value) and can drive anisotropic structure growth along the polarization direction, giving thus an essential feedback base. We discussed the potential situation where local feedback-driven effects and collective scattering concur to a topology-related evolution of HSFL. Equally, scattering and coherent interaction with the incident field contribute to LSFL formation. The specific thermomechanical properties add an additional dimension to the ripple formation process.
Acknowledgments
The authors acknowledge the financial support from China Scholarship Council in Chinese high-level public university post-graduate project and National Natural Science Foundation of China (No. 61378019 and No. 61223007). This work was also supported by French ANR project DYLIPSS (ANR-12-IS04-0002-01).The authors equally acknowledge École nationale supérieure des mines de Saint-Étienne in France for the assistance in EBSD measurements.
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