Nano-groove and 3 D fabrication by controlled avalanche using femtosecond laser pulses

We report fabrication of sub-100 nm resolution structures by ablation on the surface of sapphire using femtosecond laser pulses. A single 50-70 nm wide groove was recorded by laser ablation via a controlled ripple formation on the surface. Ripples are created by breakdown due to a sphere-to-plane formation of an ionisation below surface in a similar way as the bulk ripples. Different thresholds for the ripples formed parallel and perpendicular to direction of the laser scan were observed. In a sol-gel photo-polymer SZ2080 and thermo-polymer polydimethylsiloxane, free-standing 3D structures were formed without use of two-photon absorbing photo-sensitizers. Both cases of the surface and bulk structuring were achieved via a controlled avalanche, which dominated ionisation of materials. © 2013 Optical Society of America OCIS codes: (140.3390) Laser materials processing; (220.4000) Microstructure fabrication; (350.3850) Materials processing; (160.1245) Artificially engineered materials. 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Introduction
Direct laser writing with ultra-short sub-1 ps laser pulses can reach resolution of 100 nm in all three dimensions (3D) which is below the diffraction limit and enters space of nanotechnology.Recent in-bulk 3D structuring of photo-polymers showed that various photo-materials can be 3D structured with high resolution close to the light wavelength ∝ λ 0 at tight focusing conditions (NA > 1) with a pulse durations ranging from nanoseconds to femtoseconds and even a continuous wave illumination can be used for 3D photonic crystal fabrication [1][2][3][4].Moreover, despite the pulse duration t p changing over incredible 6 orders of magnitude in the case of pulsed irradiation, the pulse energy E p and the exposure dose is usually within the same order of magnitude [3,4].The 3D structuring initially branded as two-photon polymerization [5,6] now can be achieved via a controlled thermal and avalanche absorption (both are linear processes) at well controlled exposure conditions.The exposure doses used in 3D structuring of polymers are in the range of a therapeutic and not in a surgery regime of live tissue [7], which makes 3D structuring appealing for biologic and medical applications.
Better understanding of 3D laser structuring is still required since changes of the pulse dura- tion over several orders of magnitude in polymerization is not compatible with the multi-photon ionization, however, could be explained by domination of avalanche processes in bond breaking and polymerization [4,8].Indeed, it was already demonstrated that even one photon absorption at tight focusing can deliver 3D polymerization [1].Also, a direct plasma emission (a black body radiation) into the absorption band of polymers at 2-3 µm window was consistent with size scaling of polymerized 3D structures in SU-8 using fs-laser irradiation [9].With an increasing popularity of sol-gel resists, photo-initiators can be easily chosen and mixed with resist for tests of polymerization mechanisms by fs-laser pulses [10,11].It was shown that the highest resolution of 3D structuring is achieved in pure organic-inorganic SZ2080 resist without photo-initiator [8] believed to be essential for a nonlinear absorption [12].Surface laser structuring of dielectrics [13][14][15] and metals [16,17] by ablation and formation of ripples (called also light-induced periodic surface structures) using fs-laser pulses is another active area of research where mechanisms are strongly debated.On surface of metals ripples with sub-wavelength periods are formed apparently via parametric generation of a surface plasmon polariton (SPP) with a back reflection of a scattered wave at a shifted frequency; the energy and momentum conservation reads: ω l = ω 2 +ω SPP and k l = k 2 +k SPP , where ω l and k l are the cyclic frequency and wavevector of the laser wave, subscript 2 is for the scattered color-shifted wave, and SPP is for the surface wave.Moreover, ripples can be formed inside materials [18] -the bulk-ripples -and on the surface with periods dependent on irradiation conditions and material properties (molten flows and instabilities are affecting the final morphology).Since ripples are formed at high electron density of a pre-breakdown and breakdown plasma [19], avalanche processes are essential; we present analysis of avalanche role in surface (ripples) and bulk (polymerization) structuring with ultra-short laser pulses.
Here we show how a controlled avalanche ionisation driven by ultra-short laser pulses can be used for a sub-diffraction-limited structuring by ablation on surfaces and how the laser polymerization can be achieved without use of photo-initiators.Via controlled light interaction with a free electron plasma the dielectric breakdown can be localized within a sub-100 nm crosssection on sapphire surface and polymerization via the electron avalanche can deliver 3D cure of photo-polymers.

Ripples on the surface of sapphire
Ripples [20] on a 400-µm-thick high purity optical grade sapphire were fabricated using an amplified Ti:Sapphire fs-laser system (Spitfire, Spectra Physics Inc.) operating at ν = 1 kHz repetition rate with a pulse duration t p = 150 fs.Second harmonic wavelength at 400 nm was used for surface structuring.Linearly polarized beam was focused on the front surface of sapphire using high numerical aperture NA = 0.7 objective (Mitutoyo Ltd.).Aerotech linear stages positioned the sample with respect to a stationary focal spot.
Set of 30 µm length lines were fabricated at different pulse energies ranging from 23.5 nJ to 45 nJ (after the objective lens) and at different scan speeds (v scan ) in the range 0.7 to 70 µm/s.Distance between pulses d pp = v scan /ν ranged from 0.7 to 70 nm and pulse-to-pulse overlap pp = d f oc /d pp ranged from 1000 to 10 pulses per focal spot, respectively; d f oc = 1.22λ /NA = 0.7 µm is the diameter of the focal spot.Beam was not blanked during acceleration, causing a higher pulse overlap and dose at the ends of lines due to acceleration or deceleration.Figure 1 illustrates geometry of experiments and the mechanism of ripple formation via a sphere-toplane ionisation growth (a) similar as in the bulk of dielectrics [19] (see discussion in Sec. 4).

3D polymerization via avalanche (the one-photon process)
We used organic-inorganic Zr containing SZ2080 (IESL-FORTH) [21] hybrid and polydimethylsiloxane (PDMS: Sylgard 184, Dow Corning) polymers as received, without adding any photo-or thermo-initiators.This allows production of 3D microstructures free from an undesired light absorbtion and cytotoxic ingredients [22].Samples were prepared by a drop casting of resin on a standard 150-µm-thick cover glass.Prebake at 75 • C for 45 min was applied for the SZ2080 sol-gel resist.After laser irradiation, SZ2080 and PDMS samples were submerged into a 4-methyl-2-pentanon bath for 30 min to develop the fabricated structures.
Either no metal coating or a 10 nm of Ag was used for structural inspection by the scanning electron microscope (SEM: Hitachi TM-1000).A 3D polymerization was carried out using fs-laser (Pharos, Light Conversion) delivering 300 fs duration pulses at a 200 kHz repetition rate.Both, fundamental 1030 nm and second harmonic 515 nm irradiation were used for SZ2080 fabrication, while for PDMS was structured at 515 nm wavelength.Objectives with different numerical apertures (NA = 0.95, 1.25, 1.4) were employed for beam focussing and are specified where applies.The polymerization trajectory was controlled using xy-galvanometric scanners (SCANLAB hurrySCAN II 10) and a sample positioning system Aerotech ALS130-100 (x,y-axes) with ALS130-50 (z-axis) linear motion stages ensuring a ∼10 nm positioning precision.A 3DPoli software was used for the control and automation of sample processing [23].Detailed description of the setup can be found elsewhere [24].

Estimation of ionisation rates
The multi-photon absorption and avalanche rates of electron multiplication w mpi and w imp , respectively, are given by [25]: where n ph = ∆Ee/(hω) + 1 is the number of photons required for direct absorption (truncated to an integer) with ∆E being the band-gap of material, h is the Plank's constant, ω = 2πc/λ is the cyclic frequency of light of wavelength λ , e is the electron charge, and c is the speed of light.The electron quiver energy ε osc = e 2 E 2 4mω 2 with the electrical field strength defined by intensity/irradiance, I p , as E = I p /(cε 0 n), where ε 0 is the vacuum permittivity and n is the refractive index of the host material.The electron-ion interaction is governed by the electronphonon momentum exchange rate ν e−ph 6 × 10 14 s −1 [8]; the exact value was not critically important for this qualitative estimation of the mechanisms discussed here.
With the multi-photon absorption and avalanche rates estimated by Eqs. ( 1) and ( 2) it is possible to calculate the rate of free electron generation, hence, the rate free radicals (broken chemical bonds) are created: where n e is free electron density (available only for the avalanche multiplication) and n a is the atom density (available only for the multi-photon ionization).Solution of the Eqs.( 3) is following: This equation allows to follow explicitly temporal evolution of ionisation for the known temporal intensity envelope I(t) [26]; here n e0 is the initial (dark) electron density in material ∼ 10 10 cm −3 .
When second harmonic excitation is used, effects of long ns-background are suppressed which otherwise can significantly alter the avalanche ionization since the avalanche rate scales as ∝ λ 2 (Eqs.( 2)).

Results and Discussion
We show (i) formation of a single groove of ∼ 70 nm (or λ /6) by a controlled laser ablation and (ii) 3D polymerization when a linear light-matter interaction prevails.The results are discussed in the context of the mechanisms which are active topic of research in laser micro-/nano-processing.

Ripples: towards an ultimate resolution
Since the first observation of ripples by Birnbaum in 1965 [20] they attracted a lot of attention both from the pure science and applications in sensing, optical memory, polarisation control, microfluidics and packaging.Most of ripples phenomenology can be accounted for by interaction of incident and scattered fields on the surface [27].However, ripples on surfaces of dielectrics are less well behaved and periods in the range Λ = λ 0 /(2 − 20) have been reported especially for excitation with fs-laser pulses.Most of them scales closely to the empirical Λ = λ 0 /n/2 where n is the refractive index of an unperturbed material [28] and dielectric  permittivity of the ambient medium [29].However, since n is dependent on intensity via strong electronic excitation during the pulse, n(I,t p ), this transient permittivity can imprint ripples of different periods.Laser ablation and ripple formation can be, in fact, tuned to produce a single groove pattern as shown below.

Ripples on sapphire
Lines fabricated by single scan of the laser beam contain several grooves -ripples (Fig. 2(b)) which can then be patterned over larger area by scanning [28].Ripples on surfaces of high melting temperature substrates such as sapphire and SiC showed almost intensity independent period λ 0 /n/2 [28,30].Here we study wide parameter space of the ripple formation (Fig. 2(a)) and a weak, but discernible dependence of the period on a pulse energy (Fig. 3(a)) and overlap between pulses (Fig. 3(b)) was observed.Generation of free electrons (plasma) creates a negative contribution to the refractive index n(I) = n 0 − ∆n (with ∆n > 0) where changes are proportional to the electron density ∆n ∝ n e , hence intensity.This should cause an increase of the ripple period (λ 0 /n(I))/2, the trend observed in experiments (Fig. 3(a)).The ripple period calculated using a refractive index of unaffected sapphire, n 0 = 1.79, is equal to 112 nm, which is close to the measured period values at a low pulse energy and a high pulse overlap.It is important to note that period saturates at certain value ∼160 nm; this is consistent with a dielectric ablation theory [25], which predicts that at the ablation threshold, the free electron number density approaches the atomic number density, hence saturates.The dependence of ripple period on energy was most pronounced for high pulse to pulse overlap, presumably because high number of pulses are required to establish the most stable conditions (e.g, accumulation of point defects in lattice and trapped charges).• At high PP ( PP > 100 ) overlap period dependence on pulse energy is stronger, compare e.g.1000 vs 100PP: At 1000 PP period increases 45%, at 100PP only 17 %, error of period measurement about 10%.

•
At small overlap ( PP < 100) period increase is in the range of error.

•
Period increase saturates at certain energy.

•
Only at lowest energy period is reducing as overlap is increasing.

•
At higher energy period does not depend on overlap (or is slightly increasing), dependence is ~ 10%, in the range of error.
Period dependence on pulse energy and pulse to pulse overlap  500 pp overlap.The dependence of ripple period on the pulse overlap was much weaker as compared to the dependence on the pulse energy.Only a minor period decrease (from 130 to 110 nm) was observed for the overlap between 100 and 500 pp, respectively, at the lowest energy.The full set of pulse-to-pulse overlap values ranged from 10 to 1000 pp and was tested at different energies from the ripple fabrication threshold to few times above it.A similar trend, reduction of the ripple period at a higher pulse overlap, was observed in the bulk [31] and on the surface [32] of a fused silica, however dependence was much stronger.To compare, on the surface of fused silica ripple period reduced about 3 times (from 260 to 80 nm) for a pulse overlap change from 20 to 500 pp (using 45 fs, 800 nm pulses).To explain this difference, material properties are important.Fused silica has a lower refractive index, a lower melting temperature (1600 • C vs 2040 • C for sapphire), has a fictive temperature anomaly, i.e., a denser phase at a higher temperature [33].

Single groove-ripple on sapphire
Figure 4 shows how the ripple formation can be dynamically tuned to a single-groove ablation as exposure dose becomes close to the threshold (by changing the pulse overlap).Figure 1(b) schematically depicts the number of ripple periods Λ 150 nm, which fit into the focal spot at a different intensity cross sections; here the Gaussian intensity profile of 700 nm diameter at a 1/e 2 intensity level is shown, which is the same as used for the fabrication: d f oc = 1.22λ /NA = 700 nm.Both parameters, the pulse overlap and energy have to be optimised for a single groove formation.At the beginning of line scan where overlap of pulses occurs, an initiation of ripple formation was observed.Then, a single groove (ripple) can be made by reducing the overlap or energy of laser pulses.Higher overlap creates more ripples, because preceding pulses creates defects and reduces the ablation threshold, so lower intensity regions of Gaussian distribution can to interact with material and so increase fabrication line width.Assuming the Gaussian intensity envelope, it was estimated that a single groove can be formed, if the maximum pulse intensity is less than ∼10 % above the ablation threshold.Tere, beam width is below 150 nm and two-grooves cannot fit into the spot.It is not difficult to achieve a 10 % pulse energy stability  with current fs-lasers to control such process.In this regime a single groove of a 50 -70 nm diameter is formed.To compare the intensity stability required to achieve a 50 nm diameter groove without ripple formation effect, stability close to 1 % (the Gaussian beam intensity is at a 99 % level at 50 nm diameter) would be required as shown in Fig. 1(b).We demonstrate here, that ripple fabrication is more than a technique for the uniform surface nano-texturing, which has already found many applications, e.g., for surface wettability control [34] and as surfaceenhanced Raman (SERS) substrates [35], but it is also promising as the highest resolution direct laser writing technique.
A single groove has been demonstrated in the case of in-bulk ripples in porous glasses [36] with a single nano-plane crack formed at a close-to-critical irradiance.We show here that a single sub-100-nm-wide groove is recorded on the surface on sapphire (Fig. 4).The dielectric breakdown of the surface can be scanned over the surface making the pattern of a very high resolution res = width/(1.22λ0 /NA) 70 nm/700 nm 10 (one tenth of the diffraction limit at the employed focusing).Hence, similarly to the inscription of radial and azimuthal polarizations [37], the linear polarization can be imprinted as a single sub-diffraction groove.
This observation is consistent with formation of ripples starting in a sub-surface region via plasma sphere-to-plane formation since the sub-critical plasma density is required and it grow towards the surface where it is imprinted by ablation (Fig. 1(a)).The self-organization and quasi-periodicity of ripples occurs via self-organization and pairing of the plasma planes (λ 0 /n)/2 [30] (Fig. 1(b)).Crests of the wave are locations of augmented electron density where the breakdown occurs.Accumulation of the light-induced defects is important for the ripple formation and can be rationalized via a stochastic seeding of the defects where subsequent pulses start ionisation, which evolves into the planes.This mechanism is consistent with formation of the bulk ripples [38,39].

Hysteresis in ripple formation
Finally, an interesting behavior of the ripple formation threshold with orientation parallel ( ) or perpendicular (⊥) to the scan was observed (Fig. 5).There is approximately a 10% difference in the pulse energy threshold and the periods slightly differs Λ ⊥ < Λ .Apparently, the plasma density created for the -ripples is larger than that for ⊥ ones.Larger plasma density is expected from the regions where larger number of structural defects is accumulated, material is preheated, amorphous or noncrystalline regions are created on a crystalline substrate [28].In all of those situations stronger absorption is expected.As pattern of ripples develops, it has nano-features or roughness down to tens of nanometers [35].Anisotropy of temperature diffusivity induced by ripples is important and discussed next.The -ripples facilitate thermal transport along the scan direction and the heat affected zone is expected to advance further along scan as compared with the ⊥-ripples.As a result creation of defects, amorphous regions, etc., is favored in the case of -ripples.This is why plasma density n e is expected to be larger in this case and correspondingly the larger period Λ = λ /(n 0 − ∆n(n e ))/2 is observed.
We have shown earlier by polymerization [40] that nano-structures and nanoparticles can localize temperature and the nano-structured regions are hot for longer since the mean free path of heat carriers (electrons and phonons), l m f p = v t τ becomes smaller, here v t is the thermal velocity of heat carriers, τ is the time between scattering events.This causes a decrease of the thermal conductivity χ = ρv t cl m f p /3, where c is the specific heat, ρ is the density of carriers.Temperature localization due to decrease of temperature diffusivity by 1-2% in the fs-laser structured regions of polymers and sapphire has been demonstrated by direct measurements [41][42][43][44].In those cases, a laser structuring inside the bulk was made at the conditions when bulk-ripples are not formed.
Further studies are required to explore surface plasma formation on dielectrics which create conditions of parametric generation of surface structures similar to the reported in metals [16], where period dependence on pulse energy scales in a similar fashion as shown in Fig. 3(a).In metals ripples with periods corresponding to the surface plasma wave with energy ω p / √ 2 (ω p is the plasma density) are imprinted on surfaces at the dielectric breakdown conditions when the critical plasma density is ω cr ; the ripple period is

3D polymerization: structuring without photo-initiators
We show here 3D polymerization when photo-initiators are not used and estimate ionisation rates according to formulae given in Sec. 3 at different wavelengths and exposure conditions.The detailed experimental conditions are presented in refs.[8,45].The SZ2080 resist without a two-photon absorbing initiator can be 3D structured with high resolution and good structural quality by fs-laser pulses [8].The avalanche rate is several orders of magnitude higher as compared with the multi-photon (4-photon) ionisation in the case of λ l = 1030 nm fs-laser pulses.Photonic crystal structures with log's lateral cross section d 300 nm were fabricated at 1030 nm wavelength and retrieved after a wet-bath development  (Fig. 6(a)).Resolution can be improved by up to 40% using a critical point dryer [46] which prevents a capillary collapse [47].
Two-photon absorption of SZ2080 (without a photo-initiator) at the second harmonic λ l = 515 nm irradiation is expected to be efficient due to λ l = 0.7λ g [8] (λ g is the wavelength of direct absorption).However, at the employed high intensities the avalanche prevailed in 3D polymerization of structures shown in Fig. 6(b); see estimations in Sec.4.3.Polymerization of SZ2080 was performed without use of photo-initiators at 1030 and 515 nm wavelength irradiation.Pulse energy, required for polimerisation was only ∼10 times different, while a larger difference is expected for the nonlinear absorption.To expedite fabrication of micro-optical elements over large areas with sub-1 mm cross sections we use a surface contour definition by laser writing [48], then development, and subsequent uniform UV exposure.This delivers up to a 100 times faster fabrication of simple shapes of micro-optical elements such as lenses and prisms [48].
Laser structuring of bio-compatible polymers with laser direct write is expected to find wide field of applications [45].Scaffolds can be formed in pure SZ2080 (Fig. 7(a)) which are bioincompatible due to absence of photo-initiators.PDMS was also laser structured without use a photo-initiator at throughput higher as reported earlier [49] (see, Fig. 7(b)).Efficient fabrication is required for practical bio-medical applications [7,22,50].We found (Table 1) that avalanche is much more efficient in ionisation and bond opening, which is required for cross-linking of PDMS as compared with a 3-photon ionisation at the used 515 nm irradiation (for rate comparison see Sec. 4.3).

Estimation of multi-photon and avalanche rates
Let us evaluate the values of w mpi and w imp for the used polymerization of undoped PDMS, SZ2080 and in the case of ripple formation on sapphire.For PDMS, a strong absorption starts at λ g 225 nm or J i = 5.5 eV and is considered as a direct absorption transition; in case of SZ2080 λ g 325 nm and λ g 150 nm for sapphire.Estimation of the ionization rates are given next for the typical conditions used in experiments.Surface of sapphire was laser textured by ripples with E p = 35 nJ which corresponds to an average irradiance of I p = E p /(πw 2 0 t p ) 6.11 × 10 13 W/cm 2 for the 3-photon process.The ionisation rates one can find directly from Eqs. ( 1)-( 2): for multi-photon w mpi 10.49 × 10 10 s −1 and w imp 3.84 × 10 13 s −1 for avalanche; refractive index n = 1.7.
In PDMS for the typical E p = 2 nJ at NA = 1.25 focusing the avalanche is even more efficient as compared with sapphire w mpi 3.9 × 10 8 s −1 and w imp 6.4 × 10 12 s −1 ; refractive index n = 1.4.In the most narrow bandgap material SZ2080 at the laser wavelength λ 0 = 515 nm, the ionisation by a two-photon process n ph = 2 is expected according to the favorable λ l = 0.7λ g [8] conditions; refractive index n = 1.45.For the highest resolution structures in SZ2080 obtained with NA = 1.4 objective lens and E p = 16.5 nJ, the intensity I p 8.7 × 10 12 W/cm 2 (for 4-photon process at 1030 nm).Correspondingly, the rates are: w mpi 3.4 × 10 10 s −1 and w imp 8.4 × 10 13 s −1 (Fig. 6(a)).At the 515 nm when two-photon can be efficient and for E p = 1.75 nJ (Fig. 7(a)) the difference between the two ionisation mechanisms becomes slightly smaller: w mpi 3.7 × 10 10 s −1 and w imp 4.4 × 10 12 s −1 .
In all the analysed cases the avalanche is a prevailing ionisation mechanism up to the dielectric breakdown when ν e−ph c/λ (see, Table 1).

Conclusions
We show that avalanche ionisation plays an essential role in surface nano-texturing by ripples and that it can be controlled to achieve ten times higher resolution as compared with the diffraction limit at the used NA = 0.7 focusing.A single 50-75 nm wide groove was fabricated using linear polarization on sapphire surface.This is an example of a controlled avalanche breakdown of the surface.Different thresholds for ripples oriented and ⊥ to the scan direction was found to be ∼ 10% and can be attributed to the temperature diffusivity changes due to nano-texturing.The sphere-to-plane ionisation model can explain formation of ripples as well as the single The 3D photostructuring of of SZ2080 and PDMS polymers without photoinitiators at different focussing conditions is demonstrated.Microlenses and scaffolds were produced as sample structures.This shows a potential to produce optically transparent integrated optical elements as well as bio-compatible scaffolds [50].Though the influence of photo-initiator concentration on a polymerization rate and degree of cross linking has been investigated [51], additional studies on monomer-to-polymer conversion under the avalanche and thermal processes for 3D polymerization requires future studies as it influences mechanical [52] and biological properties [53].Thermal black-body emission of the laser breakdown region can provide an efficient source for direct absorption into vibrational modes of some polymers [9] and enhance polymerization.
The analysed cases of surface ripple formation and 3D polymerization clearly shows an importance of avalanche via linear one-photon absorption and opens pathways for a wellcontrolled laser microfabrication and additive micro-manufacturing of optical elements and bio-compatible structures.

Fig. 1 .
Fig. 1.(a) Plasma breakdown driven by an avalanche in a sub-surface region of a sapphire substrate under tight NA 0.7 focusing.Plasma nano-planes (perpendicular to the laser polarization) are formed in the bulk under the laser irradiation area and grow towards the surface (an incoming beam).(b) Geometry of interaction between subsurface scattered field superimposed with the Gaussian intensity distribution, which was used for focusing.Locations where breakdown plasma are formed marked by ellipsis.Intensity range corresponding to 50 nm diameter groove fabrication by ripple formation (>91 %) and by regular ablation (>99 %) are indicated.The period of surface charge is dependent on the free electron density, n e , which depends on light intensity, I. Top-view projection and the spot size at different intensity cross sections with ripples shown on the right-side (see Sec. 4 for discussion).

Fig. 2 .
Fig. 2. (a) A parameter space for ripple formation: number of pulses per focal spot pp = d f oc /d pp vs. pulse energy E p for 400 nm/150 fs pulses focused using NA = 0.7 objective lens.30 µm long lines with parallel ripples were fabricated for each condition.A colored region indicates ripple formation region, where light-shade color indicates uniform, not damaged ripples, while darker-shade region show where ripples start to deteriorate due to increased ablation; a "+" sign indicates full line fabrication, "-" no fabrication and "•" a partial line fabrication.(b) SEM images of ripples representing different fabrication conditions, numbers link parameters with the SEM images.

Fig. 3 .
Fig. 3. (a) A ripple period dependence on a pulse energy at three different pulse-to-pulse (pp) overlap values: 50, 100 and 1000.At low pulse energy and high pp overlap, period is close to predicted by λ 0 /2n 0 = 112 nm, where n 0 is refractive index for laser unaffected sapphire, value indicated on graphs by dotted line.Period is increasing with energy and saturates at ∼160 nm.Trend is more pronounced for higher pp values.(b) A ripple period dependence on pp overlap at the three different pulse energies: 25, 29 and 45 nJ.Only at the lowest energy period decreases with overlap.Inset shows SEM images linked by numbers with values on (a) and (b) graphs.

Fig. 4 .
Fig. 4. Ripples fabricated on a sapphire substrate by 25 nJ / 150 fs laser pulses at 400 nm wavelength and 500 pp overlap, beam focused using NA = 0.7 objective lens.Sample was scanned at 14 µm/s speed, beam was not blanked during acceleration.(a) 30 µm length line consisting of different number of ripples and extended length of a single ripple.Zoomed-in section (b) show groove width (50-75 nm), (c) transition from 3 to 2 to 1 ripple / groove, diameter of the focal spot (0.7 µm) indicated by circle.

Fig. 5 .
Fig. 5. (a) Probability of the ripple formation at different energies for the parallel ( to the fabrication line) and perpendicular (⊥) ripples.Threshold is about 10 % lower for the parallel ripples.Each dot on the graph was calculated as an average probability from 3 trials; 10 lines were fabricated in each trial.(b) SEM images of the typical -and ⊥-ripples.Polarization direction and ripple period are indicated.