Nanoscale confinement of energy deposition in glass by double ultrafast Bessel pulses
Jesus del Hoyo, Remi Meyer, Luca Furfaro, Francois Courvoisier
NNanoscale confinement of energy deposition in glass by double ultrafast Bessel pulses
Jesus del Hoyo , ,Remi Meyer ,Luca Furfaro ,Francois Courvoisier , ∗ FEMTO-ST institute, Univ. Bourgogne Franche-Comt´e, CNRS,15B avenue des Montboucons, 25030, Besanc¸on Cedex, France Applied Optics Complutense Group, Optics Department,Universidad Complutense de Madrid, Facultad de Ciencias Fisicas,Plaza de las Ciencias, 1, Madrid, 28040, Spain ∗ Corresponding author [email protected] is a post-peer-review, pre-copyedit version of an article published inNanophotonics (De Gruyter). The final authenticated version is available online at:https://doi.org/10.1515/nanoph-2020-0457
Ultrafast laser pulses spatially shaped as Bessel beams in dielectrics create high aspect ratio plasma channelswhose relaxation can lead to the formation of nanochannels. We report a strong enhancement of the nanochanneldrilling efficiency with illumination by double pulses separated by a delay between 10 to 500 ps. This enablesthe formation of nanochannels with diameters down to 100 nm. Experimental absorption measurements demon-strate that the increase of drilling efficiency is due to an increase of the confinement of the energy deposition.Nanochannel formation corresponds to a drastic change in absorption of the second pulse demonstrating theoccurrence of a phase change produced by the first pulse. This creates a highly absorbing long-living state. Ourmeasurements show that it is compatible with the semi-metallization of warm dense glass which takes placewithin a timescale of <
10 ps after the first laser pulse illumination.
INTRODUCTION
Transparent dielectrics are ubiquitous in modern technol-ogy, but their structuring at the nanometric scale is a difficulttask. The main advantage of ultrafast laser-based process-ing techniques is the capability of structuring the material inthree dimensions as well as processing elongated straight [1]or curved [2] voids in single shot. This is possible becauseof the nonlinearity of the energy deposition process. It allowsfor a very precise control and versatility of the manufacturingprocess.The formation of high aspect ratio voids with diametersin the 100’s nanometers range using only a single ultrafastlaser pulse is particularly useful for the creation of nanopho-tonic crystals and Bragg gratings[1, 3] or for glass cutting, inthe framework of so called ”stealth-dicing” technique [4–10]which enables cutting glass using laser illumination speedsexceeding tens of centimetres per second.Drilling of high aspect ratio nanochannels is made par-ticularly controllable when using zeroth-order Bessel beams[1, 9–13]. for sufficiently high focusing angles, Kerr effectis negligible and energy absorption occurs mainly in the cen-tral lobe. Although the mechanism leading to void channel formation in transparent dielectrics after the energy deposi-tion stage is still an open question, [14–16], our problematichere is that depending on the material and illumination geom-etry, limitations arise on the maximal and minimal nanochan-nel diameters that can be processed with Bessel beams. Thisis exemplified in Fig.1(a). It shows Scanning Electron Mi-croscopy (SEM) images of nanochannels processed in SchottD263 glass with single femtosecond pulses. The pulse energyrange over which a nanochannel can be opened is very lim-ited. Increasing the pulse energy did not lead to an increase ofthe channel diameter above ∼
300 nm, in contrast with a rela-tively similar glass, Corning 0211 where nanochannels couldbe processed with diameters from 200 to 800 nm [1] with atwice shorter Bessel beam length.Here, we investigate how double pulses can solve this is-sue. Surface ablation by double Gaussian pulses convention-ally sees a decrease of the ablation efficiency. This has mainlybeen attributed to a reduction of nonlinear ionization due tothe intensity decrease when splitting the pulse in two, as wellas to a screening effect from the plasma [17–21]. In contrast,the case of in-volume material excitation, at fluences lowerthan the ablation threshold, shows stronger modifications offused silica (index of refraction, nanogratings formation) with a r X i v : . [ phy s i c s . op ti c s ] F e b FIG. 1. SEM images of channels drilled using single pulses (a) and double pulses (b). The insets correspond to a zoom in the images. Thediameter of the channels is shown in the insets. The energy indicated corresponds to the total energy. double pulses in comparison with single pulses of identicaltotal energy, for inter-pulse delay typically on the order of 10-100 ps [22–27]. The stronger modifications were attributed toan increase of the total deposited energy because of a higherabsorption of the second pulse by the material softened af-ter the first pulse. The first pulse generates a plasma of free-electrons and holes or ions that decays into self-trapped exci-tons and color centers. Those defects increase the absorptionefficiency of the second pulse.In this article, we report that splitting the pulse energyin two equal energy pulses allows for drastically increasingthe nanochannel formation efficiency. Nanochannels with ∼
100 nm diameters can be reliably processed, and we canincrease by a factor two the maximal channel diameter com-pared to single shot case. We have studied the evolution ofthe channel morphology with inter-pulse delay and have char-acterized the evolution of absorption as a function of delayand energy. The overall absorption is slightly less for the dou-ble pulse case than for the single pulse one. But our resultsdemonstrate for the first time that pulse splitting with a de-lay in the 100-500 ps allows for enhancing the confinement ofenergy deposition.An analysis of the evolution of the second pulse absorp-tion in time reveals two different dynamics respectively forsub- and above threshold for nanochannel drilling. Whileat the lowest energies, the absorption dynamics follows thedecrease conventionally expected by the formation of self-trapped excitons, our results at higher energies,those whichallow nanochannel formation, show a striking new behaviourfor bulk excitation. These are compatible with the genera-tion of warm dense silica within ∼
10 ps after the first pulse,which has a very localized and high absorptivity because ofsemi-metallization. The Bessel beam geometry associated toa pulse burst in the GHz repetition rate regime [28] is thereforeexpected to lead to highly efficient formation of Warm DenseMatter with tabletop experiments, which is important for thefundamental understanding of astrophysical objects [29].
FIG. 2. (Left column): Experimental longitudinal intensity distribu-tion for single and double pulses. (Right column): Correspondingexperimental intensity cross sections. All images are normalized totheir own maximum.
EXPERIMENTAL SETUP
Our experimental setup is based on a 5 kHz ultrafast Ti-sapphire laser source with 800 nm central wavelength. Be-fore beam shaping, the ultrafast pulses were split into equalparts and recombined using a Mach-Zehnder interferometerarrangement. The pulses were independently circularly polar-ized with the same rotation orientation. The inter-pulse delayis controlled using a micrometric motorized translation stageand can be varied up to a maximum of 500 ps. The zero-delaywas characterized using the interference between the pulses.Beam shaping was performed using an axicon with base angle1 ◦ and a telescopic arrangement with magnification ∼
110 togenerate a Bessel beam with a length of ∼ µ m and a coneangle of 26 ◦ in air.A computer-controlled Pockels cell was used for single shotillumination. To avoid any potential cumulative effects due tothe irradiation by the small polarization leakage during thedead time between the sample positioning to a fresh area andthe effective illumination by the high intensity pulses, two ad-ditional fast mechanical shutters were installed with effectiveopening time of ∼ ±
15 fs. We usedrecently cleaved Schott D236 borosilicate glass slides as sam-ple. The sample flatness was ensured to be below 0.1 mrad.Beam characterization was performed using a microscope ob-jective with numerical aperture 0.8, which was combined toa lens to form a telescope with a magnification factor of 56[30]. Figure 2 shows the intensity distribution of the gener-ated beams. We highlight the fact that the high magnification( × µ radwhen translating the mirrors to change the inter-pulse delayfrom 0 to 100 ps. This deviation is enough to prevent theaccurate superposition of the central lobes of the two Besselbeams. The bottom panel in Fig. 2 shows the perfect beamsuperposition, which was corrected for each inter-pulse delay.The samples were characterized first using conventionaloptical microscopy with through-illumination using a mi-croscope objective equipped with a variable correction col-lar. This was followed by Focused Ion Beam (FIB) millingwhere a careful procedure was developed to avoid modify-ing the laser processed structures as in reference [31]. Thisallows side-imaging the nanochannels by scanning electronmicroscopy (SEM).In a second step, we conducted absorption measurementsof the single pump pulse or of the double pump one. Pulseabsorption was characterized using the ratio of the signals be-tween two photodiodes positioned before and after the sample.The photodiodes were large photodiodes (100 mm ) to ensurethe whole beam was collected. The reference photodiode wasplaced after a 10% splitter before the first telescope. After thesample, the beam was collimated by a microscope objectivewith numerical aperture 0.8 and the far-field was imaged ontothe second photodiode. The acquisition was performed in sin-gle shot using an oscilloscope. The linearity of the acquisitionwas specifically ensured over the whole energy range investi-gated. For the absorption measurements, the Bessel beam wasfully enclosed within the sample thickness, and the samplewas also translated so that each shot illuminates an undam-aged area.Because of the Bessel beam conical structure, reflection andtransmission on the plasma are indistinguishable. Both trans-mitted and reflected beams are directed in the forward direc-tion with the same angle with respect to the optical axis. Theoverall absorption A is therefore complementary to the mea-sured transmission: A = 1 − E/E , where E and E are the energies collected after the sample with the Bessel beamrespectively placed inside and outside of the glass sample.Therefore, the Fresnel losses are eliminated from the absorp-tion curves. The experiment was repeated 50 times with thesame parameters and the results were averaged. RESULTS
Figure 1(a) shows SEM images of Schott D263 glass sam-ples after single pulse irradiation. We observe that channelsof diameters ∼
200 and 300 nm are drilled for energies of re-spectively 3 and 5.2 µ J. However, further increase of the pulseenergy does not lead to channel opening but instead to a den-sity modification. This modification extends over a diameterwhich increases with pulse energy. We infer that at the high-est energies shown here, a plasma is formed over a too widediameter, which limits the thermodynamical gradients neededto generate microexplosions and void formation.We repeated the same experiment for double pulses withinter-pulse delay of 500 ps and the results are shown in Fig.1(b). We readily observe that the morphology of the channelsis relatively similar to the single pulse case, except that, now,nanochannels are opened in all cases. The produced channelswidth extends from ∼
100 to more than 700 nm. This is amuch wider processing window than in the single pulse case.The small inhomogeneities along the channels are attributedto the intensity inhomogeneities of the beam as can be seenfrom Figure 2 [32].We will now investigate the influence of the inter-pulse de-lay. For this, we show in Fig. 3 images of nanochannels un-der optical microscopy with five inter-pulse delays. For eachcase, the drilling experiment has been repeated several times,so as to evaluate the repeatability of the laser-induced materialmodification. In the figure we show two images of channelsobtained in identical conditions. We note that the distancebetween two channels is 20 µ m to avoid any influence of amaterial modification by a previous pulse on the next modifi-cations. Under our optical characterization system, voids withdiameter (cid:39)
400 nm appear deep black.Delays below the pulse duration produce results that varyvery significantly from shot to shot (not shown). A possibleexplanation is that the phase between the two pulses cannotbe controlled with sufficient accuracy to maintain the sameinterference state from shot to shot. Strong shot to shot vari-ations were similarly observed in the absorption experimentsas described below.For inter-pulse delays from 1 ps and up to 500 ps, irradia-tions produced channels over the full tested range of energies(2 - 16.5 µ J total energy), in high contrast with the single pulsecase. This is confirmed from SEM measurements. For inter-pulse delays between 0.2 to ∼
10 ps, a transition occurs wherethe channels appear wider, more uniform along their lengthand more reproducible on a shot to shot basis. For delays of10 ps and above, the structures show a higher degree of unifor-mity and repeatability. We noted that the optimum depends on
FIG. 3. Optical microscopy images of several channels producedusing double pulses for a total energy of 5 µ J. Two channels in eachimage were obtained with the same parameters. The images of eachchannel have been cropped and stitched together to save figure space.FIG. 4. Channel diameter measured on SEM images for modifica-tions made using single and double pulses with inter-pulse delays of1, 10 and 500 ps, at a depth of 5 µ m below the surface of the out-put facet. Filled dots correspond to the formation of a void channel,while circles correspond to refractive index modification. Dashedlines correspond to B-spline interpolation. The horizontal axis cor-responds to the total energy in all cases. the total pulse energy. In the case where the inter-pulse delaywas of several tens of ms, i.e. when the excitation by the firstpulse has fully relaxed before the second pulse arrives (notedas ∞ in the figure), the structures are much more faint andless regular. This indicates the state reached at 500 ps is notidentical to state reached after the complete relaxation.Noticeably, the marks of thermal effects are highly reducedon the optical microscopy images and on the SEM images ofFig. 1(b) in comparison with what is conventionally observedwith picosecond illumination in glass [33] or in sapphire [31],or in comparison with illumination via a second pulse withnanosecond duration or more [34, 35]. We infer that the ther-modynamical pathways (ionization dynamics, pressure, tem-perature...) are different between the case of double femtosec-ond pulses excitation and the case of illumination by picosec-ond pulses.Figure 4 quantitatively compares the evolution of the chan- nel diameter with the total input pulse energy for single pulsesand three delays. The measurements have been performedusing SEM images of the channel cross-sections, after FIBmilling. The black markers show the evolution of the diam-eter of the modification produced in the single shot regime.The error bar on the measurement is due to the accuracy ofFIB milling between two SEM images and is ∼
40 nm. Voidsare shown with black disks, density modifications with thecircles. The three other lines show the results for inter-pulsedelays of 1, 10 and 500 ps. We first notice that for the threecases in double pulse regime, the evolution is approximatelythe same, with a quasi-linear increase with pulse energy. Thisfollows the same trend as shown originally in reference [1].At the lowest energies, the longest delays produce the small-est diameters. This variation can be attributed to a decay of thematerial excitation by the first pulse. For a delay of 1 ps, atenergies above 8 µ J, we observe a fluctuation of the diameter.This variation can be attributed to the strong phase transitionthat we describe in the next section, which occurs over a scaleof 1-10 ps depending on the deposited energy.The differences between single and double pulses is notice-able. First, double pulses allow reaching extremely small di-ameters down the ∼
100 nm, i.e. nearly eight times lower thanthe laser wavelength. For the glass used here (Schott D263),the maximal diameter reached with double pulses is almostthree times higher than in the single pulse case. These resultssuggest that wider channels could be produced using higherpulse energies. We expect that the maximal channel diameterachievable will depend on the inter-pulse delay.
PULSE ABSORPTION
A priori, two origins can explain a higher drilling efficiencywith double pulses than with single ones. This can be dueto a higher overall absorption of energy or to the absorp-tion of a possibly smaller amount of energy but on a signif-icantly smaller diameter (the length of the modifications re-mains constant between single and double pulse illumination).We demonstrate here that it is the second case.Figure 5(a) shows the total absorption for single and dou-ble pulses as a function of the total input pulse energy. It canbe seen that the absorption is overall similar in all cases, thus,splitting the pulse does not lead to a higher absorption. Theabsorption is in fact higher for the single pulse case (blackcurve), particularly for energies in the range 2-4 µ J, where theslope is the highest and which also correspond to the thresh-old energy for channel drilling. Therefore, the highest drillingefficiency observed at 500 ps inter pulse delay does not cor-respond to a higher absorption. The higher absorption mea-sured for the single pulse case can be attributed to a higher ef-ficiency for the multiphoton and tunnel ionization processes.Those might take place either out of the central lobe of theBessel beam or within this central lobe, but on a wider areathan in the double pulse case. We conclude that the enhancedefficiency for void channel opening originates from a higher
FIG. 5. Absorption measurements of single and double pulses. (a)Total absorption of double pulses. (b) Absorption of the first and thesecond pulse. In (a) and (b), the dashed lines show the value of thestandard deviation over 100 shots.FIG. 6. Second pulse absorption as a function of the inter-pulse de-lay, for different individual pulse energies. For reference, we indicatewith square markers the absorption of the first pulse. Dashed linescorrespond to B-spline interpolation. The error bars correspond toone standard deviation. density of deposited energy.The absorption of the second pulse can be straightforwardlyderived from the overall absorption by subtracting the singlepulse contribution. Figure 5(b) shows the absorption of thefirst and second pulses, shown as a function of the individual pulse energy (we recall that first and second pulses have thesame energy). Above an individual pulse energy of ∼ µ J, thesecond pulse absorption drastically increases with a step-likecurve, reaching absorption above 0.6, and well above the firstpulse absorption at this energy. This is followed by a smootherincrease, for energies greater that 2 µ J. We note that the step inabsorption occurs for an energy which nearly corresponds tothe threshold for nanochannel drilling (2 µ J total energy). Theabrupt change in absorption shows that an important transitionis crossed when the energy of the first pulse is sufficientlyhigh. We will see below that this transition corresponds to theformation of warm dense matter.To obtain a better view of the evolution of absorption intime, we plot in Fig. 6 the evolution of the second pulseabsorption as a function of the inter-pulse delay for a set ofrepresentative energies. Square markers show the first pulseabsorption as a reference, for the same pulse energy.For the lowest individual pulse energies, typically below1 µ J ( i.e below threshold for nanochannel drilling in doublepulse regime) the absorption effectively decreases with theinter-pulse delay (red and blue curves). This is consistent withthe decay times of self-trapped excitons (STEs), which are onthe order of 30 and 300 ps [36]. The higher absorption of thesecond pulse in comparison with the first can be attributed inthis case to the formation of STEs which have a much higherionization cross-section than glass because of their intermedi-ate position in the bandgap. The evolution of the second pulseabsorption with time at low pulse energies explain the dynam-ics observed by Wang et al using Bessel beams in fused silicain double pulse configuration: after chemical etching of themodifications inscribed, channel length highly increased fordelays in the pulse separation window 1-50 ps and decreasedfor longer delays [25].In contrast, at energies above the threshold for channeldrilling (it e.g. green and purple curves for 1.5 and 3 µ J), theabsorption curves show only a small decrease with delay upto 10 ps and then stay nearly constant with time. We also notethat the curves with different delays are nearly identical withinthe fluctuations in Fig. 5(b) above 1.5 µ J. This indicates that,in the case of nanochannel drilling, a transformation triggeredby the first pulse occurs during 10 ps and reaches a state whichhas a typical lifetime exceeding the nanosecond scale.
DISCUSSION
Our observations are in high agreement with the results byGarcia-Lechuga et al of the measurements of the transient re-flectivity and transmission of the surface of fused silica afterirradiation by high fluence (7 J/cm ) femtosecond pulses [37].A state with absorptivity close to 1 and negligible reflectivitywas characterized to form within the same scale of 1 to 10 ps.This state of matter was inferred by the authors to be a hotblackbody. In our case, the fluence reached for only 1 µ J sin-gle pulse energy exceeds 10 J/cm in the central lobe of theBessel beam because of the extreme focusing angle (withoutaccounting for potential nonlinear losses on the beam path).The fluence range in which we operate is therefore very sim-ilar to the conditions of the work mentioned above. We notethat in our case, the pulse absorption cannot reach 1 becausethe plasma, with typical size of a few 100’s nm, is smaller thanthe diameter of the Bessel beam central spot (660 nm FWHM,1.2 µ m in linear regime), so that the interaction cross sectionbetween the second pulse and the hot cylinder of matter isnecessarily below 1.For an individual pulse energy of 1.5 µ J, at the onset of theplateau of absorption in Figure 5(a), the energy density ab-sorbed within the central lobe is already exceeding 8 MJ/kg,for a diameter of the excited material estimated to (cid:46)
600 nm(order of magnitude of the central lobe FWHM of the Besselbeam). This corresponds to the typical energy density ofWarm Dense Matter in fused silica [38]. Denoeud et al haveexperimentally determined with X-ray absorption near-edgespectroscopy that warm dense glass shows a semi-metallicbehaviour[39]. Engelhorn et al demonstrated that with similarenergy density (10 MJ/kg) as in our experiment, warm densesilicon dioxide reaches an ionic temperature of 5 000 K andan electronic temperature on the order of 30 000 K within aduration of 20 ps [38]. Our results are fully in line with those,including the typical temporal scale of the transformation.Therefore, our results can be explained by the metallizationof glass occurring within a couple tens of picosecond afterthe first pulse. Because of the drastic change in drilling effi-ciency observed between single and double pulses, absorptionof the second pulse must occur within a significantly smallervolume than in the case of a single pulse. We interpret theincrease of reproducibility as originating from a progressiveincrease of the confinement of absorption between 10 and500 ps. The warm dense matter diameter shrinks while itsabsorption is expected to increase. The diameter shrinkage isassociated to some energy loss, which makes, at the lowestenergies, the single pulse slightly more efficient than the dou-ble pulse with 500 ps, but less efficient than with 1 and 10ps delays (see Fig.4). We note that modelling the absorptionproperties of warm dense matter is for now computationallyextremely challenging [29]. The large variability observed atdelays smaller than 10 ps is attributed to the phase change oc-curring during this time.
CONCLUSION
We have demonstrated that double pulse femtosecond illu-mination can drastically enhance the efficiency of nanochan-nel formation in comparison with the single pulse case. Themorphology of the channels shows a negligible heat affectedzone in contrast with conventional illumination with picosec- ond durations. Absorption measurements show that the in-creased void channel formation efficiency can be understoodas a higher confinement of the energy deposition. At energiesbelow the threshold for nanochannel opening, the absorptionof the second pulse decreases with time as can be expectedfrom the formation of self-trapped excitons. At higher ener-gies, where nanochannel formation occurs, our experimentalresults indicate that the first pulse triggers a phase transitionwithin 1-10 ps, and this state has a lifetime exceeding 1 ns.The higher efficiency for void formation is explained bythe swift generation of the semi-metallic state of warm denseglass generated over a diameter significantly smaller than inthe single pulse case, with a diameter typically lower than600 nm. For all delays above 1 ps, channel formation wasobserved in double pulse illumination, and a smoother transi-tion operates between 10 and several hundreds picoseconds.We note that our measurements cannot distinguish betweenthe generation by the first pulse of a cylinder with a uniformdensity of warm dense matter or if a rarefied region at the cen-ter, surrounded by warm dense matter progressively forms ata scale of several 100’s ps. Our results are therefore compati-ble with both expected mechanisms of nanochannel formation[15, 16].Our results have implications both on applied and funda-mental aspects. In the field of nano-machining with ultrafastlaser pulses, the best configuration in the investigated delayrange is for 10-500 ps depending on the energy. This timeinterval falls in the GHz repetition range. Our results canalso explain the enhancement of localized energy depositionin glass using GHz repetition rate sources [28]. The multi-ple pulse configuration, at high total energies, can be used toincrease the maximal void diameters, while at the lowest en-ergies, fine tuning of the void diameter below ∼
100 nm be-comes possible. Further research with GHz sources is neededto evaluate an optimal number of pulses. Our results alsodemonstrate the capability of generating Warm Dense Mat-ter within the bulk of materials by using burst of pulses. Webelieve a similar state can be created within other transparentmaterials such as sapphire. The confinement in the material’sbulk using a nondiffracting Bessel beam increases the confine-ment in comparison with laser impacts on surface. This opensnew routes to create and control high temperature and highpressure states within relatively high volumes, with length upto centimetre scale [10], for tabletop laboratory scale exper-iments to reproduce astrophysical pressure and temperatureconditions.We acknowledge the support and funding from EuropeanResearch Council (ERC) 682032-PULSAR, Region Franche-Comte council, the EIPHI Graduate School (ANR-17-EURE-0002), I-SITE BFC (ANR-15-IDEX-0003), French RENAT-ECH network.Technical assistance by C. Billet, E. Dordor and fruitful dis-cussions with R. Giust are gratefully acknowledged. [1] Bhuyan, M. K. et al.
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