We ascertain by measuring the surface topography of a cleaved sample in which damage lines have been written in volume by scanning with a femtosecond laser, that matter shearing occur along the laser track with alternating sign (scissor or chiral effect). We note that the shearing in the head of the laser tracks change its sign with the change in scanning direction (pen effect or non reciprocal writing). We also show that nano-structures in the head are nano-shearing, with all the same sign whatever the direction of writing may be. We suggest that symmetries revealed by the shearing mimic the laser induced electron plasma density structures and inform on their unusual symmetries induced by the laser beam structures.
©2008 Optical Society of America
The commercialization of moderate size femtosecond lasers, has given scientists an impetus by providing easy access to high peak fluence (≈100 TW/cm2). The nature of light-matter interaction with an ultra short pulse is entirely different from that with longer (nano or picosecond) pulse durations . Specifically, it is easier to make 3D modifications with femtosecond lasers and in a wide variety of transparent materials. Recently, many possibilities in transparent insulating materials appear: oxidation or reduction of transition metal dopant in glasses , refractive index change including a strong birefringence , nano-crystal mastering [4, 5], induction of chirality , non-reciprocal writing [6, 7]. In addition, no other technique has the potential to realize 3D multi-component photonic devices fabricated in one single step in a variety of transparent materials. These specificities enable the development of a new generation of powerful components for micro-optics, telecommunications, optical data storage, imaging, biophotonic and so more . It is thus necessary to improve our understanding on the femtosecond laser-matter interaction, on the resulting properties, on damage and on the methods to master and exploit them efficiently.
Previously, at a microscopic scale, we have shown that strain fields are produced in silica glass in which laser damage lines have been written by means of femtosecond laser . In this paper, we analyze further the dependence of the laser induced strain field with the writing direction and we investigate the strain field inside the laser tracks themselves for finding information about the origin of matter deformation.
2. Experimental details
The experimental procedure is already described in Ref.  precisely. We recall here only a few details. We used plates of pure silica glass (synthetic fused silica Herasil) of 500 µm thick and 20 mm in diameter. Considering that the propagation vector k⃗ is along z⃗ direction, the beam was focused 250 µm below the entry surface. The sample was moved along a direction perpendicular (let us say x⃑) to the laser beam either in one direction or in the other, thereby tracing continuous lines. The polarization lied either along y, (perpendicular to the beam and the sample displacement) or along x, (parallel to the sample displacement). The beam power was varied from Pmax=220 mW (1.1 µJ/pulse, repetition rate 200 kHz) down to 26 mW (0.13 µJ/pulse. The spacing between lines was 50 µm. For closer distance, there is an overlap of the photo-induced effects between neighboring lines.
After writing the lines, the sample was cleaved after scratching linearly its surface with a diamond pen. The topography of the cleaved faces (crossing the written lines) was then observed using a phase shift interferometric microscope (PSI) and an atomic force microscope (AFM) in tapping mode. The recorded topographies resulting from the surface stress relaxation are coded in wrong colors: bright corresponds to high and dark to low surface level. Both faces of the cleaved samples were observed in order to confirm the complementarity of the glass relaxation. Lastly, by convention, we consider that a line in space has one orientation and can be scanned in two directions.
3. Laser track symmetries
Figure 1(a) shows the surface topography of a cleaved sample edge in which 4 lines were previously written alternatively downward and upward. The laser polarization was set perpendicular to the propagation axis and scanning orientation. The laser writing conditions are shown in the Figure caption. It is worth noticing that similar topographies have been obtained for pulse energy between 0.23 and 1.1 µJ/pulse.
The color scale allows showing an alternate succession of yellow and brown (bright and dark) regions on each side of the laser track showing respectively upward and downward surface relaxation. The periodicity along the laser tracks seems to vary but clearly the color appears reversed at the head and not at the tail of the tracks when laser scanning direction is reversed as we already mentioned in Ref. . Therefore, it is possible in our experiments to differentiate the direction of writing by comparing head and tail of the laser tracks i.e. the writing is non-reciprocal. This is unusual feature at a microscopic scale and in centrosymmetric medium.
Indeed, in a non-centrosymmetric medium, modification of the material can differ for light propagating in opposite directions. For example, non-centrosymmetric photorefractive crystals exhibit a non-reciprocal character (e.g. non reciprocal transmission) as is discussed in Ref. . That is, one can obtain non symmetrical energy exchange of counter propagating light beams, depending upon the orientation of the optical axis of the crystal (e.g., BaTiO3, KNbO3:Mn). Chiral media have also been found to exhibit non-reciprocal  phenomena as a result of their lack of centrosymmetry. Recently, W. Yang et al.  demonstrate that when the direction of the femtosecond laser beam propagation is reversed from the +z to −z direction, the corresponding structures written in LiNbO3 crystal change. It was the first evidence of a new optical phenomenon of non-reciprocal photosensitivity. Here we demonstrate that when scanning the femtosecond laser beam along the +x and −x directions, the structures (i.e. laser tracks) written within pure SiO2 are partly mirrored. This is the first evidence of non-reciprocal photosensitivity in centrosymetric medium.
The change of color from one side to the other side of the laser track indicates a shearing at the micrometer range (as it can be seen on the profile in Fig. 1(b)). If one takes into account the laser propagation, this means an action like with a scissor on a paper sheet or a chiral action (the shearing) resulting in a chiral effect (the shear strain). We published earlier that the strain distribution displayed by the surface topography of the cleaved sample exhibits a chiral structure but with several point of chiralities like in an organic chain . If we take, as example, the organic compound CR1R2R3-CR4R5R6 where Ri are radicals linked to carbon atoms C, this chain contains two chiral centers: the carbon atoms. According to the relative electronic properties of the radicals, there are four possible chiral symmetries. If we use the R and S notation (rectus and sinister), they are configurations RR, RS, SS and SR that they are derived from each other by simple radical permutations on one carbon. By analogy, we observe in our experiment only SR and RR-like configurations (the head changes but not the tail of the laser tracks). More specifically in our case, there are a series of shearing between the head and the tail. Parts of them are reversed with the direction of writing and the other part is not. This leads us to think that we can consider that this effect is composed by an insensitive part Sy to the direction of writing and a part ASy reversing with it. Therefore, the laser track topography image (Im) for upward (up) and downward (down) writing can be expressed as follows:
For separating the symmetry contributions, we have tentatively performed image subtraction and addition on the basis of the following equations deduced simply by inverting equation (1):
For performing this operation, we have shifted the topography image on its copy from left to right in order to superimpose laser tracks written in opposite direction. The results are shown in Fig. 2. It is clear that the sum picture Fig. 2(a) reveals the part of the topography which is independent of the writing direction (all laser tracks appear to be the same) and that the difference picture Fig. 2(b) displays the part which is dependent on the writing direction (the contrast of two neighboring lines are symmetric in a mirror containing the propagation axis and the scanning orientation). We can see again that the two kinds of topography of laser tracks are chiral but only one type is on Fig. 2(a) (e.g. like R on the second carbon atom of the chain on our previous analogy) whereas the two symmetric types appears on Fig. 2(b) (like R and S on the first carbon of the analogous chain). As a matter of fact, we can note that the part independent of the writing direction is located on the tail of the laser track but the dependent one is detected, in fact, all along the laser tracks. This was not obvious in Fig.1.
4. Inside the laser tracks
Now, achieving a topography profile across the heads of the laser tracks shown in Fig. 1(a), we obtain Fig. 1(b). As we can see, the laser tracks, which are about a few µm wide in the head and almost 1 µm wide in the tail, appear as a rapid variation of the topography i.e. as a discontinuity. This is described extensively in Ref.  and we have shown that the discontinuity changes its sign along the laser track. The first idea is thus to investigate the glass structure inside the laser tracks in order to determine the origin of these discontinuities, eventually. However, phase shift interferometer microscope (with an objective of x40) is limited to a spatial resolution of 0.55 µm and a maximum measurable slope of 22.5°. The resolution is thus not enough to see such details.
For better investigating the structure of the laser tracks at the nanometer scale, we have thus performed AFM measurements. They have been achieved in tapping mode. Results are reported in Fig. 3 including profiles across track. (We have checked that we find again with this method the same results than with the PSI when an overlap is possible.) Figure 3 shows the head (focal region) of two laser tracks written in opposite direction. We can see a series of dashes on the images that appears to be nano-discontinuities, surprisingly. On the profiles, the white arrows indicate these discontinuities. They correspond to shearing like we observed at micrometer scale but here they are at the nanometer-scale. Their character is R for all we can see in this Fig. We have not detected some shearing having other sign in our experiments (if the laser is virtually going to your eye, the matter displacement is upward on your left and downward on the right).
Such nanostructures have been revealed in Scanning electron microscope (SEM) by Shimotsuma et al. . They obtained contrasted nano-gratings in back-scattered electron imaging corresponding to electrons density contrast. Chemical analysis by Auger spectroscopy revealed that it corresponds to oxygen content and specific density changes . Then, Kazansky group [12–15] found intensity modulation of nano-gratings following the laser propagation axis (z axis) mainly in the head of the laser track. Bricchi et al.  show that modulation appears above an energy of 0.2 µJ/pulse for NA=0.55 and 150fs pulse duration. Here also, we detect such a modulation in our experiment. Those extraordinary structures have been confirmed by Hnatovsky et al. [16, 17]. But they show in their case that they are plane nanocracks .
To sum up, in conditions similar to the authors detecting nano-gratings, nano-plan or nano-cracks, we point out nano-shear-planes with the shearing perpendicular to the laser polarization. They exhibit the same chirality sign (R). They do not change sign with scanning direction whereas the micro-shearing detected out of the laser tracks do. More specifically, we cannot say that accumulation of nano-shearing yield micro-shearing. Their origin is thus not the same. Other investigations are currently in progress to see if they change with some other laser parameters.
The appearance of spontaneous periodic surface structures or ripples has been frequently observed during the illumination of solid surfaces with a uniform laser beam of sufficient intensity. These are usually called laser-induced periodic structures (LIPS). This LIPS formation was first observed by Birnbaum  on various semiconductor surfaces. Since then, LIPS have been produced on the surface of a variety of materials including semiconductors, metals, and dielectrics [19–23]; using Cw, nanosecond, picosecond as well as femtosecond lasers [19–23] sources operating over a wide range of wavelengths ~0.17–10.6 µm. Usually, LIPS show a regular groove structure oriented perpendicularly to the polarization of the incident light. There are also to make a difference between LIPS of low and high spatial frequency. The first ones are due to diffraction of the lens used for focusing the beam , occur above the surface ablation threshold  and exhibit a periodicity close to the laser wavelength. The second ones exhibit a sub-wavelength periodicity (λ/n for normal incidence ) and are triggered by random surface nano-irregularities only after several pulses and might be resulting of a coupling between surface Plasmon and electro-magnetic wave. The spacing is roughly λ for semiconductors and metals, whereas those observed on wide bandgap dielectrics are spaced at λ/n for normal incidence [24, 25].
Recently similar nanostructures have been revealed in volume of silica glass using femtosecond lasers (due to multiphoton absorption regime) and especially in the head of the laser tracks . The grating pattern is also oriented perpendicular to the direction of the laser polarization as for surface LIPS. Their spacing was found to be around is around λ/2n and depend slightly on the pulse energy, and the number of laser pulses . A further common feature of these nanostructures is that the periodicity is shown to be clearly dependent of a memory effect by Wagner et al.  for surface ripples and Hnatovsky et al.  in volume. They show the request of pulse superimposition for the nanostructures appearance, the period of which is stable whatever the speed of laser scanning . We think they have the same origin: a plasma density structure subsequently imprinted in the matter.
In this paper, we reveal nano-discontinuities on the topography of a cleaved sample produced by the interaction of the femtosecond laser within the pure silica glass. They are of the same kind of the ones already seen at a micrometer scale in Ref.  and recalled here. They correspond to shearing of the glass like it can be done by a scissor on a paper sheet. Scissor is obviously a chiral tool but this is not so obvious for a linearly polarized laser light. On the other hand, glass is isotropic and so achiral, the experimental geometry is also achiral although anisotropic following the direction of scanning. Furthermore, we show that one part of the micro-shearing series is dependent on the direction of laser scanning whereas another part is not. The first part allows distinguishing the direction of writing like we can do with a pen (i.e. non reciprocal writing). This suggests that the laser beam is not cylinder symmetric. The second part has been found not only independent of writing direction (but not of writing orientation) but also of laser polarization, or of pulse energy within some bounds. The origin of these chiral interactions is under investigation.
Our observations are different from the ones from Kazansky team although probably in relation with them. This group confirmed recently [7, 28] (what we reported in our paper in 2003 ) that the direction of the displacement of the laser in silica can be distinguished. However, we arrived at this conclusion by observing the strain relaxation and they did the same by observing optical properties. Furthermore, we note the same physical effect but reversing with the direction of scanning whereas Kazansky team reports different physical effect (different texture) according to the direction of scanning. Symmetry properties are thus different. These authors lead to the conclusion that the laser beam is asymmetric (arising from a spatially asymmetric phase distribution in the beam cross-section and related wave front tilt). On our side, we reach also to similar conclusion but from different pathway.
For better understanding, we can use Fig. 4. When the beam exhibits at least a π-symmetry according to the propagation axis, scanning the laser beam in one or another direction has the same effect as a π rotation symmetry (according to the propagation axis). In this case, traces may look like a welding row but the shearing will not be different when the scan direction is changed as this one is invariant by π rotation symmetry. In contrast, when laser beam exhibits an up-down asymmetry according to the scanning direction, the aspect of the trace can be different (represented by the color of the row in Fig. 4). However, as shearing changes its sign with the writing direction, we can conclude that this asymmetry is an anti-symmetry following mirror symmetry with the mirror plane containing propagation axis and perpendicular to the scanning axis. Furthermore, as we observe the same shearing but reversed with the writing direction, whereas Kazansky team observed different processes, we can suggest that the symmetry we probe are not the same: asymmetry for him, anti-symmetry for us. These are not contradictory because the orientation of the beam according to the writing direction maybe not the same. This point is currently under study by varying the laser beam structure.
These structures, written in the glass, are obviously related to electron plasma density structure. For instance, concerning the tail of the laser tracks, the stability of the shearing for any polarization of the laser, indicates that the plasma density structures in the laser track tail are not dependent on the laser polarization at this location contrarily to what it stands in the focus. The laser scanning line orientation defines the shearing (but not the direction of the scanned line), while the plasma structure (“modulation”) is defined by seeding like it is mentioned e.g. in Ref. . The process, giving rise to such asymmetric structure in the tail, independent of the laser polarization, remains at the moment an opened question without performing complex calculation of the plasma density.
But these effects are the printing of structures existing in the electron plasma. It is the printing of the plasma density explaining in such a way the perpendicularity of the nano-planes to the laser polarization  (this point has been already suggested by Kazansky et al. in several papers). Here, we have to extend the structuring of the plasma along the propagation direction. We can suggest that the sign of the micro-shearing alternating along the propagation axis for both components (mirror and π symmetry) is correlated to non-linear optical mixing. As a matter of fact, the periodicity of the shearing is of order of 10–15 µm like the phase mismatch between ω and 3ω in silica i.e. 17 µm.
We show by measuring the surface topography of edges of a cleaved sample in which lines have been written by scanning a femtosecond laser, that micro-shearing occurs along the laser track with an alternating sign along the propagation axis. We call this the scissor effect that gives rise to chiral structures. We show, firstly, that the shearing in the head is dependent on the direction of laser scanning. They change sign with the change of scanning direction. We term this a pen effect. It is a non reciprocal writing process. Secondly, we show that nano-structures in the focus are nano-shearing all of the same sign and are thus uncorrelated with the previous micro-shearing. Thirdly, the micro-shearing in the tail of the laser tracks is only defined by the laser scanning orientation and not by the direction of scanning.
These results reveal that the interaction of the laser with matter can either be sensitive or insensitive to the laser scanning direction. In particular if we change direction of scanning, the effect changes sign or does not. The effects depicted here are compatible with the ones shown in  although different, these authors pointing out different physical processes according to scanning orientation. Finally, the analysis is continuing to understand the origin of the “homochirality” of the tail of the laser track and to better analyze the influence of the laser beam structure.
We are indebted to E. Lepleu from Scientec Company, for performing AFM measurements with great precision. We are grateful to Lab. Optique Appliquée at Ecole Polytechnique (Pr. Mysyrowicz group) for the original writing with the femtosecond laser.
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