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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 3, Iss. 10 — Oct. 1, 2013
  • pp: 1586–1599
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Asymmetric Orientational Writing in glass with femtosecond laser irradiation

B. Poumellec, M. Lancry, R. Desmarchelier, E. Hervé, F. Brisset, and J.C. Poulin  »View Author Affiliations


Optical Materials Express, Vol. 3, Issue 10, pp. 1586-1599 (2013)
http://dx.doi.org/10.1364/OME.3.001586


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Abstract

We review the question on the origin of the differences observed on various properties when we scan the femtosecond laser beam in an isotropic media (i.e. a glass) in two orientations of a given direction. Publications on refractive index changes, birefringence, nanogratings, stress, bubbles formation and on quill writing effects are analyzed. A new interpretation based on space-charge built from ponderomotive force and stored in the dielectric inducing an asymmetric stress field is proposed.

© 2013 OSA

1. Introduction

Later on, Kazansky et al. [8

8. W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2(2), 99–104 (2008). [CrossRef]

] suggested that the laser beam symmetry is in fact broken due to a Pulse Front Tilt (PFT) that is inherent to such type of ultrashort pulse laser. This produces an effect similar on the quasi-free electrons to a snow-plough through a term occurring in the ponderomotive force i.e. I where I is the intensity of the beam in the focal volume. In the same time, Kazansky called that the “Quill” writing [2

2. P. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett. 90(15), 151120 (2007). [CrossRef]

]. As we can see with the equations below, for short time, the ponderomotive force induced a movement of electrons initially at rest in the direction of I and then an electronic current in the same direction.

Je=nev (assuming that the ions are not moving), net+div(nev)=sourcewell, vt+(v)v=ponderomotiveforcene, the term “sources” account for by multiphoton ionization or tunnelling and/or avalanche ionization and the term “wells” is for electron trapping under self trapped excitons [9

9. M. Lancry, N. Groothoff, B. Poumellec, S. Guizard, N. Fedorov, and J. Canning, “Time-resolved plasma measurements in Ge-doped silica exposed to infrared femtosecond laser,” Phys. Rev. B 84(24), 245103 (2011). [CrossRef]

]. The electronic current induces an electric and a heat current that are generally different in a non-centersymmetric crystal like LiNbO3. This term is invoked for producing asymmetric heating in [8

8. W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2(2), 99–104 (2008). [CrossRef]

]. In that case, a PFT is not necessary, in contrast to what occurs in glasses.

Because the PFT was suggested to be at the root of the symmetry breaking, several groups made efforts to prove it. A first experiment was performed by reversing the beam spatial symmetry by introducing an additional mirror on the optical path and actually they reversed the observation [5

5. W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008). [CrossRef]

]. This proved that the asymmetry originates actually in the beam. But the most clearcut proof has been given by Vitek et al. [10

10. D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express 18(24), 24673–24678 (2010). [CrossRef] [PubMed]

] making a special set-up for controlling the PFT at will. Let us mention here on the way, that they increased the PFT by more than 5 order of magnitude but they do not observed a change of AOW in the same proportion. More recently, Salter et al. [11

11. P. Salter and M. Booth, “Dynamic control of directional asymmetry observed in ultrafast laser direct writing,” Appl. Phys. Lett. 101(14), 141109 (2012). [CrossRef]

, 12

12. P. Salter, R. Simmonds, and M. Booth, “Adaptive control of pulse front tilt, the quill effect, and directional ultrafast laser writing,” in Frontiers in Ultrafast Optics (International Society for Optics and Photonics, 2013), 861111.

] used a SLM (Spatial Light Modulator), a less costly system and more flexible one, for suppressing or reversing the AOW easily by controlling the PFT. They show also that PFT is not necessary for AOW, just an intensity gradient without PFT is able to produce it. Therefore, we can deduce that asymmetry in the plasma density is required for AOW but why it is not observed for any set of laser parameters? For getting an insight on these conditions, as the properties exhibiting AOW are various, let us study them in details.

2. Results

Let us start with the refractive index permanent change [13

13. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996). [CrossRef] [PubMed]

]. As the pulse energy is increased, it is now widely known that above a first energy threshold (T1), the index change is almost isotropic (with only a small birefringent contribution from form stress). Then going on increasing the energy, a second threshold is overcome (T2) and a strong negative birefringence appears [14

14. L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4-6), 279–284 (1999). [CrossRef]

]. These processing windows have been recently reviewed in ref [15

15. B. Poumellec, M. Lancry, A. Chahid-Erraji, and P. Kazansky, “Modification thresholds in femtosecond laser processing of pure silica: review of dependencies on laser parameters [Invited],” Opt. Mater. Express 1(4), 766–782 (2011). [CrossRef]

]. This negative birefringence has been attributed to the appearance of nanostructures also called nanogratings [7

7. E. Bricchi, B. G. Klappauf, and P. G. Kazansky, “Form birefringence and negative index change created by femtosecond direct writing in transparent materials,” Opt. Lett. 29(1), 119–121 (2004). [CrossRef] [PubMed]

]. We can see a nice example of such a nanostructure in Fig. 1
Fig. 1 FEG-SEM, Secondary electrons images of the cross-section of laser tracks written in opposite orientation. The laser parameters were: 0.4 μJ/pulse, 800 nm, 160 fs, 200 kHz, 0.5 NA, 100 μm/s i.e. 2.103 pulses/µm. (b) Cross-section microscope images taken between crossed polarizers with the birefringent lines slow axis oriented at about 30° of the polarizer.
that shows secondary electrons images of laser track cross-section for lines written in opposite orientations. It is series of nanoplanes that we proved to be decomposed silica (i.e. nanoporous silica containing molecular oxygen) [16

16. J. Canning, M. Lancry, K. Cook, A. Weickman, F. Brisset, and B. Poumellec, “Anatomy of a femtosecond laser processed silica waveguide [Invited],” Opt. Mater. Express 1(5), 998–1008 (2011). [CrossRef]

, 17

17. M. Lancry, B. Poumellec, J. Canning, K. Cook, J. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser & Photonics Reviews . In Press.

]. This has been confirmed recently in Ref [18

18. S. Richter, A. Plech, M. Steinert, M. Heinrich, S. Doering, F. Zimmermann, U. Peschel, E. B. Kley, A. Tünnermann, and S. Nolte, “On the fundamental structure of femtosecond laser‐induced nanogratings,” Laser & Photonics Reviews 6(6), 787–792 (2012). [CrossRef]

]. They are sometimes well organized like with Fig. 1, sometimes more disordered (especially at higher pulse energy [19

19. C. Hnatovsky, R. Taylor, E. Simova, P. Rajeev, D. Rayner, V. Bhardwaj, and P. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process. 84(1-2), 47–61 (2006). [CrossRef]

]).

We have decided to study the retardance (proportional to the birefringence) and the nanostructures systematically in order to check if they are correlated. In first, we detected that changing the sense of writing for the configuration used in Fig. 1 i.e. Xy (writing horizontal i.e. X, laser polarization vertical i.e. y), the length of the laser tracks and thus the length of the volume containing the nanostructures varies. On the contrary, the number of nanoplanes transversally remains the same. Looking the birefringence at the cross section of the sample by transmission between crossed polarizers correlate to the observed change on the nanostructures.

Quantitatively, the retardance changes from 110nm ( + X scanning) to 150nm (-X scanning) for perpendicular configuration (see Fig. 2(b)
Fig. 2 Plot of the quantitative phase Δφ (left side) and retardation (right side) with respect to writing velocity in left-to-right ( + X) direction (blue squares) and right-to-left (-X) direction (black squares). The pulse energy was varied from 0.05 up to 1.1 μJ/pulse. (a) parallel polarization quoted Xx; (b) perpendicular polarization quoted Xy. T1 and T2 thresholds are shown by arrows. The other laser parameters were: 800 nm, 160 fs, 200 kHz, 0.5 NA, 100 μm/s i.e. 2.103 pulses/µm.
). This seems to be smaller than the value that we can expect from Fig. 1 as the retardance is proportional to the length, the number of nanoplanes and increases with the refractive index difference between the matter within the nanoplanes (i.e. nanoporous silica) and the matter between them, but one has also to take into consideration the size of the probe beam used for performing the measurement with respect to the laser track width. That is why, in order to minimize any misinterpretation, we used QPM (Quantitative Phase Measurements) and Abrio (Quantitative retardance measurements) for performing a correct correlation between retardance and nanostructures, by varying the laser parameters. We first measured the profiles of phase, retardance and slow axis orientation (this will be reported extensively in another paper). From this database, we were able to plot the Fig. 2 including the phase change and the retardance for the two orientations ( + X and –X) for two different configurations i.e. Xx and Xy. As it is well known, we see on the phase curve that whatever the configuration (but not for the same energy range), there is an increase of the average index change (above T1 threshold) followed by a strong decrease above T2 threshold. It is important to note that the phase and thus the azimuthal average index exhibit an orientational asymmetry. It is larger on Xx than on Xy configuration.

Asymmetry is also detected on retardance profiles across the lines as shown in Fig. 3
Fig. 3 Plot of the retardance profile with respect to writing velocity in left-to-right ( + X) direction (blue squares) and right-to-left (-X) direction (pink squares). (a) Perpendicular configuration quoted Xy, (b) parallel configuration quoted Xx. The laser parameters were: 0.4 μJ/pulse, 800 nm, 160 fs, 200 kHz, 0.5 NA, 100 μm/s i.e. 2.103 pulses/µm.
. This has been mentioned previously by Beresna et al. [20

20. M. Beresna and P. G. Kazansky, “Polarization diffraction grating produced by femtosecond laser nanostructuring in glass,” Opt. Lett. 35(10), 1662–1664 (2010). [CrossRef] [PubMed]

]. The authors observed retardance amplitude that is larger on one edge of the line when they write in one sense or the other one but they did not quantify it. In Fig. 3, we see that for Xy configuration (Left plot), the magnitude of the retardance changes on the sense of writing whereas for Xx configuration (Right plot), the retardance does not change in magnitude but is transversally asymmetric.

We can now correlate these asymmetries according to the laser pulse energy (Fig. 4
Fig. 4 (Left) Plot of retardance according to the laser pulse energy with respect to writing velocity in left-to-right ( + X) direction (blue squares) and right-to-left (-X) direction (pink squares). The pulse energy was varied from 0.025 up to 1 μJ/pulse. The laser polarization was perpendicular Xy. The other laser parameters were: 1030 nm, 300 fs, 100 kHz, 0.5 NA, 500 μm/s i.e. 200 pulses/µm. (Right) FEG-SEM, Secondary electrons images of the cross-section of laser tracks for writing laser polarization perpendicular to the scanning direction.
). We see in this figure that no AOW appears on retardance for low energies but for higher energy around 0.7 μJ. With the writing conditions used here, the difference with the sense of writing is quite spectacular (jumping from 100 down to 40 nm) and can have a negative impact on the writing technology, clearly. Trying to see what are the corresponding changes on nanostructures, we cleaved the sample and observed the cross section using SEM as shown at the right side of Fig. 4. When no AOW is detected on retardance, there is nevertheless a transversal asymmetry on the nanostructures that reverses under the sense of writing. We can deduce that it is an antisymmetric orientational writing. Increasing pulse energies, leads to the increase not only of the length of the nanostructures but also of the number of nanoplanes. At 0.6 μJ, whereas no AOW is detected on retardance, there is already a dissymmetry on the number of nanoplanes.

Nevertheless, in another sample, varying the energy, we were able to correlate the retardance and the nanograting length whatever the configuration may be. This is shown in Fig. 5
Fig. 5 Plot of retardance according to the nanogratings length (in the z propagation direction). The pulse energy was varied from 0.4 up to 1.2 μJ/pulse. The laser polarization was perpendicular Xy. The other laser parameters were: 800 nm, 160 fs, 200 kHz, 0.6 NA, 200 μm/s.
. The quality of the linear fit leads us to consider that the retardance is proportional to the nanostructure length (i.e. in the z propagation direction). As we have seen in Fig. 4 that the number of nanoplanes (i.e. laser track width) increases also with increasing energy in the low energy range, this indicates that the retardance is also proportional to the number of nanoplanes within the probe volume.

On the other hand, the effect of the repetition rate on the energy threshold for the appearance of the AOW seems relatively weak varying only from 0.5 μJ to 0.8μJ when the repetition rate is decreased from 500 kHz down to 5 kHz but with a speed of hundred’s μm/s. On the contrary, the sensitivity of AOW energy threshold is much larger for a repetition rate of 1 kHz when the scanning speed is increased from 10 to 1500 μm/s (blue curve in Fig. 7
Fig. 7 (Left) Plot of the AOW threshold pulse energy according to the pulse to pulse overlap ratio. The overlap ratio between two consecutive pulses is defined by 1-v/(f.D), where v is the scanning speed, f the repetition rate and D the beam diameter at the focus. The repetition rate was varied from 1kHz up to 500kHz and the scanning speed from 10 up to 1500μm/s. The other laser parameters were: 1030 nm, 300 fs, 0.5 NA, parallel polarization Xx. (Right) The laser parameters were 800nm, 130fs, 1kHz, 0.6NA.
on the left). This leads to consider that the relevant parameter is the number of pulses per μm or the overlap ratio between pulses i.e. 1-v/(f.D), where v is the scanning speed, f the repetition rate and D the beam diameter at the focus. Results plotted in Fig. 6 shows that even with an overlap ratio as low as 0.5, it is still possible to observe AOW for pulse energy larger than 1.8 μJ with the laser condition that we used here.

We have mentioned at the beginning that AOW is not only observed on the refractive index change but also on residual stress field due to irradiation. This phenomenon has been extensively described in two papers [1

1. B. Poumellec, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Femtosecond laser irradiation stress induced in pure silica,” Opt. Express 11(9), 1070–1079 (2003). [CrossRef] [PubMed]

, 22

22. B. Poumellec, M. Lancry, J. C. Poulin, and S. Ani-Joseph, “Non reciprocal writing and chirality in femtosecond laser irradiated silica,” Opt. Express 16(22), 18354–18361 (2008). [CrossRef] [PubMed]

]. We have just to recall here that it is a complex effect when the pulse energy falls in the domain where the nanostructures are formed in pure silica (above T2 threshold). In that case, one possibility for explaining the observed AFM topography shown in Fig. 8
Fig. 8 (Left) Two laser traces written in opposite directions ( + X and –X) seen in AFM after cleaving the sample. The contrast is topographic. The laser is coming from the bottom. The laser parameters were: 0.23 μJ/pulse, 800 nm, 160 fs, 200 kHz, 0.5 NA, 100 μm/s i.e. 2.103 pulses/µm. The laser polarization was perpendicular to the scanning direction. (Right) FEG-SEM, Secondary electrons images of the cross-section of the same laser tracks written in opposite directions.
may be a shear solicitation which direction is along the direction of writing. Taking into account the direction of propagation of the laser light, shearing is like a scissor and reveals a chiral action. There are two kinds of shearings: one with a given chiral type and the mirrored one. What we observe, looking at the cross section of the laser tracks, is that there are successive shearings of opposite sign along the laser track. The most striking feature is that shearing around the focal volume is sensitive to the orientation of writing and to the laser polarization direction. It can reverse with the orientation or just change in amplitude. On the contrary, shearing close to the filament, is not sensitive to the orientation of writing nor to the laser polarization direction.

As a matter of fact, we observe it in soda lime silicate [23

23. C. Fan, B. Poumellec, H. Zeng, R. Desmarchelier, B. Bourguignon, G. Chen, and M. Lancry, “Gold Nanoparticles Reshaped by Ultrafast Laser Irradiation Inside a Silica-Based Glass, Studied Through Optical Properties,” J. Phys. Chem. C 116(4), 2647–2655 (2012). [CrossRef]

], in Li2O-Nb2O5-SiO2 [24

24. C. Fan, B. Poumellec, H. Zeng, M. Lancry, W. Yang, B. Bourguignon, and G. Chen, “Directional Writing Dependence of Birefringence in Multicomponent Silica-based Glasses with Ultrashort Laser Irradiation,” J. Laser Micro Nanoen 6(2), 158–163 (2011). [CrossRef]

]. Other authors reported AOW in alumino-borate [4

4. P. G. Kazansky and M. Beresna, “Quill and Nonreciprocal Ultrafast Laser Writing,” in Femtosecond Laser Micromachining (Springer, 2012), pp. 127–151.

, 5

5. W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008). [CrossRef]

], and in chalcogenide glasses [3

3. M. Gecevičius, M. Beresna, J. Zhang, W. Yang, H. Takebe, and P. G. Kazansky, “Extraordinary anisotropy of ultrafast laser writing in glass,” Opt. Express 21(4), 3959–3968 (2013). [CrossRef] [PubMed]

]. Let us report what we have observed in Li2O-Nb2O5-SiO2 glasses (see Fig. 9
Fig. 9 (Upper part) Plot of the retardation with respect to writing velocity in + Y direction (black triangles) and -Y direction (red dots): (a) parallel polarization Yy; (b) perpendicular polarization Yx. (Bottom part) Plot of the retardation with respect to writing velocity in + X direction (red dots) and -X direction (black triangles): (c) perpendicular polarization Xy; (d) parallel polarization Xx. The other laser parameters were: 2.3 μJ/pulse, 800 nm, 120 fs, 10 kHz, 0.5 NA.
). The measurements of the retardance in this kind of glasses is shown in Fig. 9 for four possible configurations of writing direction and polarization varying the scanning speed from 10 μm/s up to 500 μm/s. From each of them, the sense of writing has been investigated. As we can see, AOW is detected for three of them, vanishing for large speed, whereas the retardance is not decreasing. This confirms that the overlap should be larger than a certain value to observe AOW as we saw in Fig. 7. On the contrary, the average retardance value is weakly dependent on the scanning speed as shown in Fig. 6 which was for a pure silica glass. A surprising feature in Fig. 9 is the absence of AOW for the configuration Yy. The idea that AOW is determined by only the PFT would lead to say that it was detected for any laser configuration, not perpendicular to the PFT [4

4. P. G. Kazansky and M. Beresna, “Quill and Nonreciprocal Ultrafast Laser Writing,” in Femtosecond Laser Micromachining (Springer, 2012), pp. 127–151.

, 25

25. P. G. Kazansky, Y. Shimotsuma, M. Sakakura, M. Beresna, M. Gecevičius, Y. Svirko, S. Akturk, J. Qiu, K. Miura, and K. Hirao, “Photosensitivity control of an isotropic medium through polarization of light pulses with tilted intensity front,” Opt. Express 19(21), 20657–20664 (2011). [CrossRef] [PubMed]

]. This would imply that if no AOW appears for Yy, there should be no AOW also on Yx but this is actually not the case. Clearly, the laser polarization plays a role in the phenomenon. In addition, we measured the PFT and found it is oriented 36° anticlockwise in the xy plane and 0.064° out of the z axis for a 5mm wide beam (i.e. before focusing). The explanation of our results is thus not straightforward with the theory available. Lastly, it is worth mentioning that birefringence is produced in this sample by stress field.

A decisive experiment on that point is the one from Salter et al. in 2012 [11

11. P. Salter and M. Booth, “Dynamic control of directional asymmetry observed in ultrafast laser direct writing,” Appl. Phys. Lett. 101(14), 141109 (2012). [CrossRef]

, 12

12. P. Salter, R. Simmonds, and M. Booth, “Adaptive control of pulse front tilt, the quill effect, and directional ultrafast laser writing,” in Frontiers in Ultrafast Optics (International Society for Optics and Photonics, 2013), 861111.

]. These authors using a SLM (spatial light modulator) produced on one hand PFT of different sign and observed a reversal of AOW but they built also a transversally asymmetric intensity gradient without PFT and produced the same effect in fused silica showing that the gradient intensity is at the basis of the process.

3. Tentative mechanism

Our proposal for symmetry breaking will be therefore based on the above review and results. In the condition that we used for inducing permanent refractive index change, the plasma is formed by multiphoton ionization (or by tunneling) in a few 10’s of fs above an energy threshold and in the same time it is heated by multiphoton absorption of the excited electrons in the conduction bands. If impact ionization plays a role in the excitation for higher energy density, it does not change the view. One hundred femtosecond later, a part of the excited electrons couple with the phonons and stabilize under Self Trapped Excitons (STE) below the bottom of the conduction band [9

9. M. Lancry, N. Groothoff, B. Poumellec, S. Guizard, N. Fedorov, and J. Canning, “Time-resolved plasma measurements in Ge-doped silica exposed to infrared femtosecond laser,” Phys. Rev. B 84(24), 245103 (2011). [CrossRef]

, 29

29. S. Mao, F. Quéré, S. Guizard, X. Mao, R. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004). [CrossRef]

]. Notice that STE formation is specific to some glassy materials like silica and doped-silica but not all of them. In the first part of this process, electrons are mobile and moves under the ponderomotive force as described by Bethune [30

30. D. Bethune, “Optical second-harmonic generation in atomic vapors with focused beams,” Phys. Rev. A 23(6), 3139–3151 (1981). [CrossRef]

]. The plasma becomes transversally asymmetric (Bethune discussed the timescale for such process and the conditions are actually fulfilled in our case). Since STE’s are almost immobile, they will “record” the non-uniformity of the plasma spatial distribution that will survive after the pulse will be exhausted. Then, STE’s relaxe (their lifetime is less than a few 100’s ps at room temperature) and a space charge is definitely stored in the matter (this space charge is a separated charge of opposite sign, it is globally neutral). However, we can note that in the same time, the matter temperature increases in a few 10’s ps and will decrease down to room temperature by thermal diffusion at the scale of one μs. With the typical pulse energy and the repetition rate that we used (below 500 kHz), pulses are thus completely separated and there is no heat accumulation from pulse to pulse. The space charge in a hot matter can deform the matter thanks to the opposite charge attraction. Nevertheless, the time is not long enough, considering the atomic mobility to completely erase the space charge by ionic migration or plastic deformation. When the matter has returned to room temperature, it contained therefore a space charge, a plastically deformed matter and a stress field due to residual electrostatic force and modification of mechanical properties due to the irradiation (in particular fictive temperature [31

31. M. Lancry, E. Régnier, and B. Poumellec, “Fictive temperature in silica-based glasses and its application to optical fiber manufacturing,” Prog. Mater. Sci. 57(1), 63–94 (2012). [CrossRef]

] that increases after laser irradiation [15

15. B. Poumellec, M. Lancry, A. Chahid-Erraji, and P. Kazansky, “Modification thresholds in femtosecond laser processing of pure silica: review of dependencies on laser parameters [Invited],” Opt. Mater. Express 1(4), 766–782 (2011). [CrossRef]

]).

fe=(Pe)E+PetB=ε0χfe(E22+(EB)t+nenetEB)wherePe=ε0χfeEwithε0χfe=nee2mω2.

The first term of the last part of the equation is sensitive to the pulse front tilt, it pushes the electrons forward in front and on the edge of the side of the pulse (see Fig. 10a). The second and the third terms are oriented by the Poynting vector; they act partly in the opposite orientation of the first term with the same strength. They push the electrons back to the PFT but they are not sensitive to the PFT. In strong converging regime, they tend to decrease the electron density at the center of the focal volume. The first term in E2has also a similar effect, more efficient but it introduces a dissymmetry when PFT is not zero. In conclusion, in the absence of a PFT, the electrons are just pushed out from the center whereas with a PFT, they are pushed more on one side. As shown by Bethune [30

30. D. Bethune, “Optical second-harmonic generation in atomic vapors with focused beams,” Phys. Rev. A 23(6), 3139–3151 (1981). [CrossRef]

], this creates a DC field but here without center of symmetry (see Fig. 10b). Lifetime of the electrons may be smaller than the pulse duration and part of them are trapped under STE’s (typically within 150fs in silica or doped-silica) [9

9. M. Lancry, N. Groothoff, B. Poumellec, S. Guizard, N. Fedorov, and J. Canning, “Time-resolved plasma measurements in Ge-doped silica exposed to infrared femtosecond laser,” Phys. Rev. B 84(24), 245103 (2011). [CrossRef]

, 32

32. M. Lancry, N. Groothoff, S. Guizard, W. Yang, B. Poumellec, P. Kazansky, and J. Canning, “Femtosecond laser direct processing in wet and dry silica glass,” J. Non-Cryst. Solids 355(18-21), 1057–1061 (2009). [CrossRef]

, 33

33. F. Quéré, S. Guizard, and P. Martin, “Time-resolved study of laser-induced breakdown in dielectrics,” EPL 56(1), 138–144 (2001) (Europhysics Letters). [CrossRef]

]. A large part of them is readily re-ionized but this does not erase the DC field. A small part of the STE’s relaxe over a few 100’s ps under charged point defects that contribute to record the electric field into the glass network. Also as the pulse ends, the glass temperature increases. Glass distorts but does not screen the electric field completely because melting is not achieved (time at high temperature is too short). When glass has cooled down again, it contains an electric field, a free of stress deformation (or strain) field and a residual stress field.

In the ponderomotive expression considered until now (when light is on), the laser polarization does not play a role whereas the experiment clearly points out an effect. For getting back in the mechanism a laser polarization effect, we have to relax part of the assumption made until now. The first one can be to consider the appearance of a contribution of the static field in the ponderomotive expression but this does not introduce an effect, the plasma polarization remaining linear. The second possibility is that plasma polarization is no more linear in E at the laser frequency. The first non-linear contribution at the laser frequency may be from third order polarization. In isotropic media like plasma is, in the dipolar approximation, we can write PNL3D=ε0χeff(3d)|E|2E i.e. a term parallel to the laser polarization that is just modifying χfe and does not introduce term sensitive to laser polarization in the ponderomotive force. In the quadrupolar approximation, we have:
PNL3Q=ε0χeff,1(3q)|E|2Bt+ε0χeff,2(3q)(E)|E|2
(1)
On the contrary to dipolar contribution, this term introduces component dependent on the laser polarization. This is also the case if we relax the third assumption i.e. the electron plasma speed is not negligible. In that case, terms we have to considered is given for example by Maugin [34

34. G. A. Maugin, Continuum Mechanics of Electromagnetic Solids, Applied Mathematics and Mechanics (North-Holland Amsterdam, 1988), Vol. 33.

]. We have:
(P.)(vB)+curl(Pv)B+div(P).vB+(×B)(vP).
(2)
It is a bit cumbersome but it can be shown that these terms introduce mostly forces perpendicular to E2 and toB. They deviate all the direction of the plasma density gradient according to the laser polarization. Rough computation of their amplitude considering that average speed allows the electron to cross the beam radius during the pulse duration, shows that they are of comparable order of magnitude when compared to the ponderomotive force at zero speed in our conditions. These two last contributions are thus important for explaining the laser polarization effect in AOW. The larger effect is when the laser polarization lies in the rotation plan of the PFT, increasing its effect.

4. Conclusion

After reviewing the publications together with new results that show AOW on refractive index changes, birefringence, nanogratings, stress, bubble formation, their analyses suggest a new interpretation based on a space-charge built from ponderomotive force and stored in the dielectric inducing an asymmetric stress field. With such mechanism, we are able to explain most of the observations. Additional experiments are nevertheless required for establishing definitely the existence of the space charge and the spatial distribution of the stress field. Even though, we do not explain everything at the moment like the shearing inversion on scanning orientation inversion but we are working on considering the spatial distribution of the ponderomotive force that appears when plasma electron speed is not neglected.

Acknowledgments

This work has been performed in the frame of FLAG (Femtosecond Laser Application in Glasses) consortium project with the support of several organisations: the Agence Nationale pour la Recherche (ANR-09-BLAN-0172-01), the RTRA Triangle de la Physique (Réseau Thématique de Recherche Avancée, 2008-056T), the Essonne administrative Department (ASTRE2007), the Ministry of the Foreign Affairs (PHC Alliance) and FP7-PEOPLE-IRSES e-FLAG 247635.

References and links

1.

B. Poumellec, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Femtosecond laser irradiation stress induced in pure silica,” Opt. Express 11(9), 1070–1079 (2003). [CrossRef] [PubMed]

2.

P. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett. 90(15), 151120 (2007). [CrossRef]

3.

M. Gecevičius, M. Beresna, J. Zhang, W. Yang, H. Takebe, and P. G. Kazansky, “Extraordinary anisotropy of ultrafast laser writing in glass,” Opt. Express 21(4), 3959–3968 (2013). [CrossRef] [PubMed]

4.

P. G. Kazansky and M. Beresna, “Quill and Nonreciprocal Ultrafast Laser Writing,” in Femtosecond Laser Micromachining (Springer, 2012), pp. 127–151.

5.

W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett. 93(17), 171109 (2008). [CrossRef]

6.

Y. Bellouard and M. O. Hongler, “Femtosecond-laser generation of self-organized bubble patterns in fused silica,” Opt. Express 19(7), 6807–6821 (2011). [CrossRef] [PubMed]

7.

E. Bricchi, B. G. Klappauf, and P. G. Kazansky, “Form birefringence and negative index change created by femtosecond direct writing in transparent materials,” Opt. Lett. 29(1), 119–121 (2004). [CrossRef] [PubMed]

8.

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2(2), 99–104 (2008). [CrossRef]

9.

M. Lancry, N. Groothoff, B. Poumellec, S. Guizard, N. Fedorov, and J. Canning, “Time-resolved plasma measurements in Ge-doped silica exposed to infrared femtosecond laser,” Phys. Rev. B 84(24), 245103 (2011). [CrossRef]

10.

D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express 18(24), 24673–24678 (2010). [CrossRef] [PubMed]

11.

P. Salter and M. Booth, “Dynamic control of directional asymmetry observed in ultrafast laser direct writing,” Appl. Phys. Lett. 101(14), 141109 (2012). [CrossRef]

12.

P. Salter, R. Simmonds, and M. Booth, “Adaptive control of pulse front tilt, the quill effect, and directional ultrafast laser writing,” in Frontiers in Ultrafast Optics (International Society for Optics and Photonics, 2013), 861111.

13.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21(21), 1729–1731 (1996). [CrossRef] [PubMed]

14.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4-6), 279–284 (1999). [CrossRef]

15.

B. Poumellec, M. Lancry, A. Chahid-Erraji, and P. Kazansky, “Modification thresholds in femtosecond laser processing of pure silica: review of dependencies on laser parameters [Invited],” Opt. Mater. Express 1(4), 766–782 (2011). [CrossRef]

16.

J. Canning, M. Lancry, K. Cook, A. Weickman, F. Brisset, and B. Poumellec, “Anatomy of a femtosecond laser processed silica waveguide [Invited],” Opt. Mater. Express 1(5), 998–1008 (2011). [CrossRef]

17.

M. Lancry, B. Poumellec, J. Canning, K. Cook, J. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser & Photonics Reviews . In Press.

18.

S. Richter, A. Plech, M. Steinert, M. Heinrich, S. Doering, F. Zimmermann, U. Peschel, E. B. Kley, A. Tünnermann, and S. Nolte, “On the fundamental structure of femtosecond laser‐induced nanogratings,” Laser & Photonics Reviews 6(6), 787–792 (2012). [CrossRef]

19.

C. Hnatovsky, R. Taylor, E. Simova, P. Rajeev, D. Rayner, V. Bhardwaj, and P. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process. 84(1-2), 47–61 (2006). [CrossRef]

20.

M. Beresna and P. G. Kazansky, “Polarization diffraction grating produced by femtosecond laser nanostructuring in glass,” Opt. Lett. 35(10), 1662–1664 (2010). [CrossRef] [PubMed]

21.

S. Richter, M. Heinrich, S. Döring, A. Tünnermann, S. Nolte, and U. Peschel, “Nanogratings in fused silica: Formation, control, and applications,” J. Laser Appl. 24(4), 042008 (2012). [CrossRef]

22.

B. Poumellec, M. Lancry, J. C. Poulin, and S. Ani-Joseph, “Non reciprocal writing and chirality in femtosecond laser irradiated silica,” Opt. Express 16(22), 18354–18361 (2008). [CrossRef] [PubMed]

23.

C. Fan, B. Poumellec, H. Zeng, R. Desmarchelier, B. Bourguignon, G. Chen, and M. Lancry, “Gold Nanoparticles Reshaped by Ultrafast Laser Irradiation Inside a Silica-Based Glass, Studied Through Optical Properties,” J. Phys. Chem. C 116(4), 2647–2655 (2012). [CrossRef]

24.

C. Fan, B. Poumellec, H. Zeng, M. Lancry, W. Yang, B. Bourguignon, and G. Chen, “Directional Writing Dependence of Birefringence in Multicomponent Silica-based Glasses with Ultrashort Laser Irradiation,” J. Laser Micro Nanoen 6(2), 158–163 (2011). [CrossRef]

25.

P. G. Kazansky, Y. Shimotsuma, M. Sakakura, M. Beresna, M. Gecevičius, Y. Svirko, S. Akturk, J. Qiu, K. Miura, and K. Hirao, “Photosensitivity control of an isotropic medium through polarization of light pulses with tilted intensity front,” Opt. Express 19(21), 20657–20664 (2011). [CrossRef] [PubMed]

26.

S. Matsuo, Y. Umeda, T. Tomita, and S. Hashimoto, “Laser-Scanning Direction Effect in Femtosecond Laser-Assisted Etching,” Journal of Laser Micro Nanoengineering 8(1), 35–38 (2013). [CrossRef]

27.

C. L. Sones, S. Mailis, W. S. Brocklesby, R. W. Eason, and J. R. Owen, “Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations,” J. Mater. Chem. 12(2), 295–298 (2002). [CrossRef]

28.

J. Choi, M. Bellec, A. Royon, K. Bourhis, G. Papon, T. Cardinal, L. Canioni, and M. Richardson, “Three-dimensional direct femtosecond laser writing of second-order nonlinearities in glass,” Opt. Lett. 37(6), 1029–1031 (2012). [CrossRef] [PubMed]

29.

S. Mao, F. Quéré, S. Guizard, X. Mao, R. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004). [CrossRef]

30.

D. Bethune, “Optical second-harmonic generation in atomic vapors with focused beams,” Phys. Rev. A 23(6), 3139–3151 (1981). [CrossRef]

31.

M. Lancry, E. Régnier, and B. Poumellec, “Fictive temperature in silica-based glasses and its application to optical fiber manufacturing,” Prog. Mater. Sci. 57(1), 63–94 (2012). [CrossRef]

32.

M. Lancry, N. Groothoff, S. Guizard, W. Yang, B. Poumellec, P. Kazansky, and J. Canning, “Femtosecond laser direct processing in wet and dry silica glass,” J. Non-Cryst. Solids 355(18-21), 1057–1061 (2009). [CrossRef]

33.

F. Quéré, S. Guizard, and P. Martin, “Time-resolved study of laser-induced breakdown in dielectrics,” EPL 56(1), 138–144 (2001) (Europhysics Letters). [CrossRef]

34.

G. A. Maugin, Continuum Mechanics of Electromagnetic Solids, Applied Mathematics and Mechanics (North-Holland Amsterdam, 1988), Vol. 33.

OCIS Codes
(160.6030) Materials : Silica
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors
(350.3450) Other areas of optics : Laser-induced chemistry

ToC Category:
Laser Materials Processing

History
Original Manuscript: May 31, 2013
Revised Manuscript: August 1, 2013
Manuscript Accepted: August 21, 2013
Published: September 3, 2013

Virtual Issues
Ultrafast Laser Modification of Materials (2013) Optical Materials Express

Citation
B. Poumellec, M. Lancry, R. Desmarchelier, E. Hervé, F. Brisset, and J.C. Poulin, "Asymmetric Orientational Writing in glass with femtosecond laser irradiation," Opt. Mater. Express 3, 1586-1599 (2013)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-3-10-1586


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References

  1. B. Poumellec, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Femtosecond laser irradiation stress induced in pure silica,” Opt. Express11(9), 1070–1079 (2003). [CrossRef] [PubMed]
  2. P. Kazansky, W. Yang, E. Bricchi, J. Bovatsek, A. Arai, Y. Shimotsuma, K. Miura, and K. Hirao, ““Quill” writing with ultrashort light pulses in transparent materials,” Appl. Phys. Lett.90(15), 151120 (2007). [CrossRef]
  3. M. Gecevičius, M. Beresna, J. Zhang, W. Yang, H. Takebe, and P. G. Kazansky, “Extraordinary anisotropy of ultrafast laser writing in glass,” Opt. Express21(4), 3959–3968 (2013). [CrossRef] [PubMed]
  4. P. G. Kazansky and M. Beresna, “Quill and Nonreciprocal Ultrafast Laser Writing,” in Femtosecond Laser Micromachining (Springer, 2012), pp. 127–151.
  5. W. Yang, P. G. Kazansky, Y. Shimotsuma, M. Sakakura, K. Miura, and K. Hirao, “Ultrashort-pulse laser calligraphy,” Appl. Phys. Lett.93(17), 171109 (2008). [CrossRef]
  6. Y. Bellouard and M. O. Hongler, “Femtosecond-laser generation of self-organized bubble patterns in fused silica,” Opt. Express19(7), 6807–6821 (2011). [CrossRef] [PubMed]
  7. E. Bricchi, B. G. Klappauf, and P. G. Kazansky, “Form birefringence and negative index change created by femtosecond direct writing in transparent materials,” Opt. Lett.29(1), 119–121 (2004). [CrossRef] [PubMed]
  8. W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics2(2), 99–104 (2008). [CrossRef]
  9. M. Lancry, N. Groothoff, B. Poumellec, S. Guizard, N. Fedorov, and J. Canning, “Time-resolved plasma measurements in Ge-doped silica exposed to infrared femtosecond laser,” Phys. Rev. B84(24), 245103 (2011). [CrossRef]
  10. D. N. Vitek, E. Block, Y. Bellouard, D. E. Adams, S. Backus, D. Kleinfeld, C. G. Durfee, and J. A. Squier, “Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials,” Opt. Express18(24), 24673–24678 (2010). [CrossRef] [PubMed]
  11. P. Salter and M. Booth, “Dynamic control of directional asymmetry observed in ultrafast laser direct writing,” Appl. Phys. Lett.101(14), 141109 (2012). [CrossRef]
  12. P. Salter, R. Simmonds, and M. Booth, “Adaptive control of pulse front tilt, the quill effect, and directional ultrafast laser writing,” in Frontiers in Ultrafast Optics (International Society for Optics and Photonics, 2013), 861111.
  13. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett.21(21), 1729–1731 (1996). [CrossRef] [PubMed]
  14. L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun.171(4-6), 279–284 (1999). [CrossRef]
  15. B. Poumellec, M. Lancry, A. Chahid-Erraji, and P. Kazansky, “Modification thresholds in femtosecond laser processing of pure silica: review of dependencies on laser parameters [Invited],” Opt. Mater. Express1(4), 766–782 (2011). [CrossRef]
  16. J. Canning, M. Lancry, K. Cook, A. Weickman, F. Brisset, and B. Poumellec, “Anatomy of a femtosecond laser processed silica waveguide [Invited],” Opt. Mater. Express1(5), 998–1008 (2011). [CrossRef]
  17. M. Lancry, B. Poumellec, J. Canning, K. Cook, J. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser & Photonics Reviews. In Press.
  18. S. Richter, A. Plech, M. Steinert, M. Heinrich, S. Doering, F. Zimmermann, U. Peschel, E. B. Kley, A. Tünnermann, and S. Nolte, “On the fundamental structure of femtosecond laser‐induced nanogratings,” Laser & Photonics Reviews6(6), 787–792 (2012). [CrossRef]
  19. C. Hnatovsky, R. Taylor, E. Simova, P. Rajeev, D. Rayner, V. Bhardwaj, and P. Corkum, “Fabrication of microchannels in glass using focused femtosecond laser radiation and selective chemical etching,” Appl. Phys., A Mater. Sci. Process.84(1-2), 47–61 (2006). [CrossRef]
  20. M. Beresna and P. G. Kazansky, “Polarization diffraction grating produced by femtosecond laser nanostructuring in glass,” Opt. Lett.35(10), 1662–1664 (2010). [CrossRef] [PubMed]
  21. S. Richter, M. Heinrich, S. Döring, A. Tünnermann, S. Nolte, and U. Peschel, “Nanogratings in fused silica: Formation, control, and applications,” J. Laser Appl.24(4), 042008 (2012). [CrossRef]
  22. B. Poumellec, M. Lancry, J. C. Poulin, and S. Ani-Joseph, “Non reciprocal writing and chirality in femtosecond laser irradiated silica,” Opt. Express16(22), 18354–18361 (2008). [CrossRef] [PubMed]
  23. C. Fan, B. Poumellec, H. Zeng, R. Desmarchelier, B. Bourguignon, G. Chen, and M. Lancry, “Gold Nanoparticles Reshaped by Ultrafast Laser Irradiation Inside a Silica-Based Glass, Studied Through Optical Properties,” J. Phys. Chem. C116(4), 2647–2655 (2012). [CrossRef]
  24. C. Fan, B. Poumellec, H. Zeng, M. Lancry, W. Yang, B. Bourguignon, and G. Chen, “Directional Writing Dependence of Birefringence in Multicomponent Silica-based Glasses with Ultrashort Laser Irradiation,” J. Laser Micro Nanoen6(2), 158–163 (2011). [CrossRef]
  25. P. G. Kazansky, Y. Shimotsuma, M. Sakakura, M. Beresna, M. Gecevičius, Y. Svirko, S. Akturk, J. Qiu, K. Miura, and K. Hirao, “Photosensitivity control of an isotropic medium through polarization of light pulses with tilted intensity front,” Opt. Express19(21), 20657–20664 (2011). [CrossRef] [PubMed]
  26. S. Matsuo, Y. Umeda, T. Tomita, and S. Hashimoto, “Laser-Scanning Direction Effect in Femtosecond Laser-Assisted Etching,” Journal of Laser Micro Nanoengineering8(1), 35–38 (2013). [CrossRef]
  27. C. L. Sones, S. Mailis, W. S. Brocklesby, R. W. Eason, and J. R. Owen, “Differential etch rates in z-cut LiNbO3 for variable HF/HNO3 concentrations,” J. Mater. Chem.12(2), 295–298 (2002). [CrossRef]
  28. J. Choi, M. Bellec, A. Royon, K. Bourhis, G. Papon, T. Cardinal, L. Canioni, and M. Richardson, “Three-dimensional direct femtosecond laser writing of second-order nonlinearities in glass,” Opt. Lett.37(6), 1029–1031 (2012). [CrossRef] [PubMed]
  29. S. Mao, F. Quéré, S. Guizard, X. Mao, R. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process.79, 1695–1709 (2004). [CrossRef]
  30. D. Bethune, “Optical second-harmonic generation in atomic vapors with focused beams,” Phys. Rev. A23(6), 3139–3151 (1981). [CrossRef]
  31. M. Lancry, E. Régnier, and B. Poumellec, “Fictive temperature in silica-based glasses and its application to optical fiber manufacturing,” Prog. Mater. Sci.57(1), 63–94 (2012). [CrossRef]
  32. M. Lancry, N. Groothoff, S. Guizard, W. Yang, B. Poumellec, P. Kazansky, and J. Canning, “Femtosecond laser direct processing in wet and dry silica glass,” J. Non-Cryst. Solids355(18-21), 1057–1061 (2009). [CrossRef]
  33. F. Quéré, S. Guizard, and P. Martin, “Time-resolved study of laser-induced breakdown in dielectrics,” EPL56(1), 138–144 (2001) (Europhysics Letters). [CrossRef]
  34. G. A. Maugin, Continuum Mechanics of Electromagnetic Solids, Applied Mathematics and Mechanics (North-Holland Amsterdam, 1988), Vol. 33.

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