MICROMACHINING OF GLASS WITH SHORT NS-PULSES AND HIGHLY REPETITIVE FS-LASER PULSES

Paper # 403

U. Loeschner, S. Mauersberger, R. Ebert, H. Exner, J. Schille, P. Regenfuss, L. Hartwig

Hochschule Mittweida – University of Applied Sciences

Technikumplatz 17, 09648 Mittweida (Germany)

Abstract

In this paper first results on 3d laser cutting of glasses as a technology for rapid tooling, obtained at the laser institute of the University of Applied Sciences Mitt-weida, are presented. The investigations were carried out with a short pulse Nd:YVO4 slab laser from Edge-wave (Aachen) and a high repetition rate femtosecond laser of Clark-MXR Inc. Michigan. In the experiments the laser beam was focussed onto the sample with both a stationary aspheric lens and a laser scanner with an f-theta-objective combined with a high precision xyz-axis stage.

The technique utilizes nonlinear absorption effects to induce local heating, followed by stress generation and finally micro defect formation inside the transparent bulk material. Several side effects have to be consid-ered in machining of transparent materials, for exam-ple, nonlinear processes like self focussing and the focal shift.

In the beginning for various glasses the dependence of the micro defect formation on the process parameters were investigated in detail - possibilities and limits are discussed. The development of strategies of applicable arrangements of micro defects to produce fracture lines, planes and shells enclosing the required compo-nent are object of the investigations in order to produce 3d parts. These components created with the presented technology are consisting of bulk material - the key benefit in comparison to laser sintered parts.

Introduction

Using high intensity laser pulses for locally confined permanent modifications inside transparent materials, like changes in the refractive index, are possible by nonlinear absorption mechanisms. Thus optical com-ponents with tailored functions, like micro lenses, Fresnel lenses, gratings, waveguides, couplers, switches, up to complex three-dimensional integrated optical devices, can be generated inside transparent bulk materials [1-5].

There are four processes involved in the interaction of laser radiation with a solid: photon-electron-inter-action, electron-electron-interaction, electron-phonon-interaction, and phonon-phonon-interaction. First the electromagnetic field transfers its optical energy to electrons during several femtoseconds. Electron-electron interaction takes place on a femtosecond to picosecond time scale, electron-phonon interaction ranges from picoseconds to nanoseconds depending on the atomic bonds. The phonon system relaxation takes nanoseconds up to microseconds [6-8].

Most of the glass materials are transparent to infrared (IR) laser radiation, that means the photon energy is less than the band gap of the material, so the linear single photon absorption process cannot take place. If the material is exposed to high intensity laser pulses the probability of nonlinear absorption mechanisms increases. There are two mechanisms involved to gen-erate free electrons: tunnel ionization due to the high field strength and multi-photon ionization as a result of multi-photon absorption. These electrons can absorb energy of other photons and thereby they will be accel-erated. By transferring their energy to electrons in the valence band via collisions these free electrons are able to generate more free electrons by impact ionization. The described mechanism results in a snowballed in-crease of the density of free carriers, also called ava-lanche ionization. By the interaction of thermalized electrons with the phonon system of the solid melting and boiling of the material is initiated. If the energy input into the material is sufficient plasma formation sets in and material damage can occur.

By irradiating transparent materials with high intensi-ties several nonlinear effects have to be considered like self focusing, the most important effect. Self focusing occurs above a critical laser pulse power which is for-mulated for a Gaussian pulse by

( ) InnInnn32λπ1.22

P 2020

20

cr ⋅+=⋅⋅⋅⋅

= (1)

where λ0 is the laser wavelength and n0 and n2 are the respective linear and nonlinear indices of refraction of the propagation medium [9,10]. In fused silica, for instance, the critical power amounts to 3 MW at a wavelength of 1064 nm.

In this paper first results in 3d laser cutting of glasses via laser induced micro defects using high intensity short nanosecond (ns) and ultrashort femtosecond (fs) laser pulses are reported. At the beginning detailed investigations were conducted to gain information about the dependence of micro defect formation on the laser parameters pulse length, pulse energy, and the irradiation regime. With this background strategies for suitable arrangements of micro defects separating the required component from the bulk material are dis-cussed. Finally first 3d parts are presented.

Experimental Details

In the investigations two laser systems differing in their laser pulse length were used: a short pulse Nd:YVO4 laser from Edgewave and an ultrashort pulse laser from Clark MXR Inc. Laser parameters of both types are listed in detail in table 1.

As a special feature in the internal beam path of the fs-laser an acousto-optic modulator for very fast beam switching is integrated allowing for an exact controlla-ble interaction of laser activity and sample movement.

The optical system consists of separated attenuators for each laser, turning mirrors, and a focussing unit con-taining a laser scanner, a mount for stationary objec-tives, and an off-axis camera for exact positioning of the sample. The entire focussing unit can be moved in the z-direction allowing the precise adjustment of the focal plane on the sample surface or inside the mate-rial. In the experiments both, an f-theta-objective with a 56 mm focal length and a stationary focussing aspheric lens with a 15 mm focal length, were used. The sample can be fixed on a high precision xy-positioning stage realizing exact positioning and

movement of the sample relative to the incident laser beam.

The optical properties of the materials used in the study are presented in table 2. BK9 is a boron-crown glass, free of streaks, bubbles, and stress, mainly used for laser engraving. The other glasses, BK7, Lithosil, and B270, are commercial optical materials produced by Schott AG.

Results and Discussion

Short-pulse ns-laser

As already mentioned, in transparent materials near infrared laser radiation cannot be absorbed by a linear single-photon process because the band gap is much larger than the photon energy, except for a minor num-ber of free electrons due to impurities and defects that allow single-photon absorption. To initiate multi-photon absorption in transparent materials with a band gap larger than 4.5 eV by laser radiation with a wave-length of 1.064 µm - which corresponds to a photon energy of 1.16 eV - at least a four-photon excitation is necessary. The probability of multi-photon absorption strongly depends on the intensity of the laser radiation – two-photon absorption sets in at several MW/cm², three- and more-photon absorption requires intensities in the GW/cm² and TW/cm² range.

Using a short pulse ns-laser source with the fundamen-tal wavelength (1064 nm) in connection with the f-theta objective defects could be obtained in BK 9 glass at pulse energies above 1 mJ. The applied intensity of the laser radiation of 29 GW/cm² agrees with the re-quired intensity range for four-photon absorption. As can be seen in fig.1 the produced defects consist each of a set of radiant cracks with a dark centre represent-ing the original position of the laser focus within the material. The course of the interaction of ns-laser

Table 1: Laser parameters

ns-laser fs-laser

wavelength 1064/ 532 nm 1030 nm (central)

min. pulse length 6 ns 250 fs (sech²)

max. repeti-tion rate 30 kHz 25 MHz

max. pulse energy 2.2 mJ 8 µJ

Table 2: Optical properties of the investigated mate-rials [10-18]

BK9 BK7 Lithosil B270

band gap [eV]

~4.7 4.7 9 4.5

refractive in-dex n0 (1060 nm)

1.5 1.51 1.45 1.51

nonl. refract. index n2 [10-16 cm² W-1]

? 3.45 3 3.4

pulses with the solid could be explained as follows: first free electrons will be generated by multi-photon absorption, further on impact ionization results in an avalanche ionization process which, while the laser pulse and therefore the photon absorption still contin-ues, lead to a strong increase in “free” electrons.

Thermalized electrons transfer their energy to the lat-tice which causes a permanent heating followed by melting and boiling of the material in combination with plasma formation as long as the laser pulse lasts.

Fig.2: cross-polarized microscope image of a defect in BK9 glass

The plasma expands explosively from the focal region of the laser spot into the surrounding material and causes stress and crack formation. In the focal region less dense material remains together with void forma-tion. In fig.2 the cross-polarized microscope image demonstrates pronounced stress formation around the focal region.

The minimal lateral extension of the cracks from a single defect achieved in BK 9 glass with optimized parameters is around 150 µm (fig.1). The shape of the defects along the axis of the incident laser beam (axial direction) is more channel-like with an approximate length of 300 µm. Within the same focal plane the ax-ial position of these “channels” varies up to 200 µm.

With increased pulse energy the defect dimensions are growing too. Smallest defect dimensions can be achieved with a pulse energy of 1.2 mJ. At this pulse energy level defect generation is not very reproducible because of the stochastic nature of multi-photon ab-sorption. With increasing pulse energy and therefore higher intensities the probability of multi-photon ab-sorption rises and defect generation becomes more reproducible as can be seen in fig.3.

In order to cut the material by means of laser induced defects it is necessary to arrange defects suitably in lines, planes or shells. Starting at pulse distances of 200 µm down to 80 µm planes filled with constant lateral pulse distances were produced first in BK9 glass. As seen in fig.4 left, at pulse distances of 200 µm defects do not overlap. Reducing the pulse distance the defect overlap increases. Below 80 µm distance it is no more possible to produce discrete de-fects but a single volume of disintegrated material arises from a number of pulses which extends beyond the limits of the irradiated zone (fig.4 right). A lateral pulse distance of 130 µm, that means with a slight de-fect overlap, seems to be optimal. Therefore excessive overlap during the acceleration and deceleration phases of a laser beam track should be avoided.

Fig 1: single defect dimensions in BK9 glass

Fig.3: defect generation left) 1.2 mJ pulse energy, right) 1.8 mJ

165

µm

140 µm

100 µm

150 µm 150 µm

Using these results the investigations were extended to the glasses BK7, B270, and Lithosil.

BK7 glass is very similar to BK9 glass that was al-ready investigated. As expected it shows the same de-fect behaviour like BK9 glass regarding the pulse en-ergy. Also the lateral as well as the axial dimensions are equal to defects in BK9 glass. Machining of B270 glass with short ns-laser pulses leads also to results comparable with ones achieved in BK9 and BK7 glass. In contrast to these results in Lithosil considerably more pulse energy is needed to generate defects. Even at the highest available pulse energy of 2.2 mJ defect generation cannot be guaranteed. Because of the larger band gap by a factor of two compared to the other glasses it is obvious that the number of photons has to be doubled also from 4 to 8 to initiate multi-photon absorption. With higher pulse energy this effect can be counterbalanced.

The results of the experiments that were conducted with the second harmonic wavelength (532 nm) of the Nd:YVO4 laser source and the 56 mm f-theta objective reveal that the lateral diameter of defects in BK9 could be halved to 70 µm at a pulse energy of 0.26 mJ com-pared to the process with 1064 nm. Above a threshold pulse energy of approximately 0.2 mJ defect genera-tion is reproducible due to the doubled photon energy. Therefore half of the number of photons are necessary to overcome the band gap - at comparable intensities the two-photon absorption process becomes more probable than the four-photon absorption process needed for the regime with 1064 nm.

Additionally the defect length in axial direction could be halved to 150 µm in contrast to the fundamental wavelength. Also the axial defect position vary by less than 50 µm.

Latest investigations performed by means of an aspheric lens with 15 mm focal length for laser beam focussing of the fundamental wavelength 1064 nm

resulting in a smaller focus diameter. So the intensity of the laser radiation rises nearly one order of magni-tude up to 200 GW/cm² at 1 mJ pulse energy. Repeat-ing the experiments mentioned above with the aspheric lens defects can be generated reliably at 1 mJ pulse energy because the rise of the intensity of the laser radiation will be accompanied by an increasing prob-ability of the multi-photon process leading to a more controlled defect generation. Furthermore with de-creasing pulse energy, the lateral defect dimension in BK9 drops down to 70 µm at 0.2 mJ pulse energy (fig.5). Below this energy level defect generation be-comes not reproducible. Characterizing the defect for-mation in axial direction the channel-like shape re-mains, but the length will be reduced to 100 µm and the axial position differs less than 20 µm.

Using these results in order to produce first simple 3d parts (cuboids) a suitable irradiating strategy was de-veloped. Starting at the bottom of the part a layer by layer irradiation regime was realized leading to a shell consisting of defects which encloses the part to be cre-ated. To release the 3d part easily from the glass bulk material additional well-arranged cut outs are inserted.

The cuboids generated with 532 nm using the f-theta objective with 56 mm focal length and 1064 nm using the aspheric lens are of best quality as can be seen in fig 6 and 8, which corresponds with small defect di-mensions. The walls are free of cracks and show a typical structure obtained after splitting off of material. Edges appear sharply. To characterize the surface qual-ity of the walls roughness measurements were con-

Fig.4: defect arrangement left) with 200 µm pulse distance i.e. no defect overlap, right) with 80 µm pulse distance with uncontrollable defect formation

Fig.5: defect arrangement with 150 µm pulse distance (0.2 mJ pulse energy)

200 µm200 µm

150 µm

Fig.6: cuboid in BK9 glass (parameters: wavelength 532 nm, f-theta objective f=56 mm, pulse energy 0.26 mJ, lateral pulse distance 75 µm, axial pulse distance 200 µm): a) optical microscope image of the cuboid, b) SEM micrograph of one corner

Fig.7: 2D surface profile plot of a wall of the cuboid shown in fig.6

Fig.8: cuboid in BK9 glass (parameters: wavelength 1064 nm, asphere f=15 mm, pulse energy 0.2 mJ, lateral pulse distance 75 µm, axial pulse distance 100 µm): a) optical microscope image of the cuboid, b) SEM micrograph of one corner

Fig.9: 2D surface profile plot of a wall of the cuboid shown in fig.8

0.0

-7.91.0

-16.9-25.8-34.7-43.6

9.918.827.7[µm]

2.39.9

-5.4-13.0-20.6-28.2

17.525.132.7[µm]

0.0

500 µm

200 µm

1 mm

200 µm b)

a)

b)

a)

Ra = 3.2 µm Rmax = 17.7 µm

1000

1000

x [µm]

y [µm]

Ra = 2.5 µmRmax = 11.6 µm

500

500 y [µm]

x [µm]

ducted with a confocal point sensor µScan from NanoFokus AG. In fig. 7 and 9 surface profile plots and roughness values of the cuboids from fig.6 and 8 respectively are presented. The comparison of the results created with both wavelengths show that the cuboid machined with the aspheric lens and 1064 nm appears smoother, according to the average and maximum roughness values, than the other one processed with the f-theta objective and 532 nm.

Ultrashort pulse fs-laser

In a first approach fs-laser radiation with a pulse en-ergy of 3.3 µJ and a pulse length of 250 fs was focus-sed inside a block of BK 9 glass. During the irradiation in the focal region inside the material a 0.5 mm broad light blue shining channel along the laser beam path could be observed. As reported in several publications [1,10] the shining channel is attributed to filament formation due to nonlinear effects causing laser in-duced structural modifications inside the transparent material. At a pulse length of 450 fs and a laser wave-length of 248 nm in [1] three types of structural modi-

fications strongly depending on the pulse energy ob-served in fused silica are distinguished: at a low num-ber of pulses and pulse energies less than 2 µJ (type A) isotropic change of the refractive index is predominant. If the energy level exceeds 2 µJ in combination with an increasing number of pulses (type B) formation of bi-refringent microstructures sets in because the modifi-cation of the refractive index becomes anisotropic. At pulse energies above 150 µJ and a high number of pulses type C is active characterized by cracks and

voids associated with stress formation in the surround-ing material. According to this classification the ap-plied pulse energy in the experiments belongs to type B. Additionally as mentioned above the self focussing effect must be taken into account. The applied laser peak power of around 9 MW exceeds the critical power of self focussing (for BK-glass approximately 2.4 MW) by a factor larger than three, so the highly intensive Gaussian-distributed laser beam causes a refractive index gradient throughout its cross section in the material leading to a spatial contraction of the beam combined with a strong rise of intensities up to 1013W/cm², sufficient to generate free electrons through multi-photon processes. The free electrons reduce the refractive index and counterbalance the self focussing effect so a narrow channel is formed guiding the laser radiation.

In fig.10 an optical microscope image of an arrange-ment of filaments with 10 µm distance to each other is shown. Detailed investigations reveal that the filament length depends on the pulse energy and the total num-ber of pulses in the same way as discussed in [1].

As a side effect, filament arrangements can act as an optical grating. By irradiating filament arrangements with a monochromatic light source, diffraction patterns can be generated. Fig. 11 contains both a photo of the diffraction pattern and the calculated intensity distribu-tion. The measured and the calculated patterns agree very well.

Fig.10: side view of a filament arrangement (between the dotted lines), parameters: pulse energy 3.4 µJ, rep. Rate 500 kHz, pulse length 250 fs, filament length 350 µm

Fig.11: diffraction pattern (10 µm pitch i.e. groove density p=100 mm-1, 300 grooves total) on a screen and calculated intensity distribution at 532 nm wave-length

100 µm

0

0,5

1

-80 -60 -40 -20 0 20 40 60 80

screen coordinate [mm]

rel.

Inte

nsity

Regarding the generation of defects it can be con-cluded: with the chosen parameters no single defect formation inside the transparent material occurs. Throughout the whole range of adjustable laser pa-rameters (pulse length 250 fs - 3 ps, pulse energy up to 8 µJ, pulse repetition rate 200 kHz - 1.8 MHz) only filament formation can be observed. This is in agree-ment with the discussion in [1] regarding the pulse energy levels mentioned above. Neither have addi-tional tests with a CPA laser system delivering high pulse energies up to 0.8 mJ at low repetition rates and comparable pulse lengths between 180 fs and 3 ps been successful. With increasing pulse energy only strong filament formation occurs. These results cannot be explained at the moment. There are two aspects that have to be taken into account: first in the experiments reported in [1] a significant shorter wavelength was used that favours the multi-photon absorption process. Secondly the intensity of laser radiation applied to the material was probably higher because of the reflection objective (NA 0.4 x 25, focal length 8 mm) that was used for a tight focussing of the laser beam.

Up to now in the experiments laser radiation at 1030 nm as well as at 780 nm wavelength only modifies the material - single defect generation cannot be realized. However, if the laser pulses have a strong overlap, i.e. a very short pulse distance, at certain laser parameters imbricative material damage occurs in the laser focal region inside the bulk glass. Strong pulse overlap means that already modified material will be irradiated several times so that a changed absorption process can

be assumed. What happens in detail cannot be under-stood completely at the moment. The described effect in combination with pulse repetition rates starting at 500 kHz and with pulse energies of 3.7 µJ and more lead to defect morphologies that are entirely different from the ones achieved with short nanosecond pulses (compare fig.12 and fig.3).

Obviously material damage does not occur at pulse lengths below 700 fs at 500 kHz pulse repetition rate and 500 fs at 1.8 MHz pulse repetition rate. Several conclusions can be derived from the achieved results: at the specified pulse length of 1.5 ps and pulse energy of 7 µJ there exists a pulse repetition rate dependant threshold of a maximum pulse distance to generate material damage, e.g. 0.7 µm at 500 kHz and 1 µm at 1.8 MHz. If the pulse distance falls below a laser pa-rameter dependant threshold material damage becomes uncontrollable and extends beyond the irradiated area. At a given pulse length of 1.5 ps and pulse distance of 0.5 µm the pulse energy necessary for material de-

Fig.12: material damage inside BK9 glass (parame-ters: pulse energy 7.4 µJ, pulse repetition rate 500 kHz, pulse length 1.5 ps, lateral pulse distance 0.7 µm)

Fig.13: cuboid in BK9 glass (parameters: wavelength 1030 nm, f-theta objective f=56 mm, pulse energy 3 µJ, lateral pulse distance 0.5 µm, axial pulse dis-tance 150 µm): a) optical microscope image of the cuboid, b) SEM micrograph of one corner

100 µm

a)

1 mm

b) 200 µm

struction is reduced at higher pulse repetition rates, e.g. 5.6 µJ at 500 kHz and 3.7 µJ at 1.8 MHz.

Because there are four parameters - pulse energy, pulse repetition rate, pulse length, and pulse distance - more detailed investigations are necessary to control the la-ser-material interaction, to specify these results, and to learn more about dependencies of material damage from process parameters.

Analogue to the investigations with short nanosecond pulses 3d parts (cuboids) could be created with adapted process parameters. In fig. 13 and 14 a cuboid proc-essed with optimum parameters and the corresponding

surface profile plot are shown. By comparing the qual-ity with the optimum results obtained with short nano-second pulses it can be observed that the surface roughness of this specimen is three times higher.

Conclusions

In this paper first results on laser micromachining of various glasses with short ns-laser pulses and highly repetitive fs-laser pulses are presented. Irradiating the material with short nanosecond pulses above a material specific i.e. band gap specific pulse energy level single micro defect formation sets in. Because of the stochas-tic nature of the multi-photon absorption process defect generation at the fundamental wavelength becomes more reproducible at increasing intensities achieved either with increased pulse energy or smaller focal spots. Using the second harmonic wavelength defect formation is reproducible above a pulse energy thresh-old much lower than that at the fundamental wave-length because of the higher photon energy and there-

fore the halved number of photons that are necessary for the multi-photon absorption process. The smallest defect dimensions of 70 µm in lateral direction and 100 µm in axial direction were achieved using an aspheric lens of 15 mm focal length at the fundamental wavelength 1064 nm and with an f-theta objective of 56 mm focal length at the second harmonic wavelength 532 nm. Comparing the quality of the generated 3d parts it can be observed that the cuboid machined with the aspheric lens at the fundamental wavelength has the best quality and is characterized by sharp edges, crack-free walls and also low roughness values.

As a result of material modification inside the glass by focussed near IR fs-laser radiation, filament formation was observed. Upon variation of the pulse energy and pulse length over a wide range no single defect forma-tion could be achieved. Merely, with strong overlap-ping laser pulses (pulse distance < 1 µm) at certain laser parameters imbricative material damage was ob-tained inside the bulk glass. Using this effect a cuboid could be produced. It shows a higher roughness than the specimens produced with nanosecond pulses.

Looking ahead defect formation with nanosecond laser pulses and controlled material damage with fs-laser pulses will be improved in order to realize complex 3d parts and to downscale the 3d part size.

Acknowledgement

The authors gratefully acknowledge financial support of the present work by the Bundesministerium für Bildung und Forschung (project number 03IP506). Our thanks go to Prof. Frank Mueller at Hochschule Mitt-weida (FH) dep. MB/FWT for expert SEM recordings.

References

[1] Papazoglou, D.G., Zergioti, I., Tzortzakis, S., Sgouros, G., Maravelias, G., Christopoulos, S., Fo-takis, C.; Sub-picosecond ultraviolet laser filamenta-tion-induced bulk modifications in fused silica; Appl. Phys. A 81, (2005), p.241–244

[2] Davies, K.M., Miura, K., Sugimoto, N., Hirao, K.; Writing waveguides in glass with a femtosecond laser, Opt. Lett. 21, (1996), p.1729

[3] Glezer, E.N., Milosavljevic, M., Huang, L., Finlay, R.J., Her, T.-H., Callan, J.P., Mazur, E.; Three-dimensional optical storage inside transparent mate-rials, Opt. Lett. 24, (1996), p.2023

Fig.14: 2D surface profile plot of a wall of the cuboid shown in fig.6

-2.215.0

-19.5-36.7-53.9-71.1

32.249.466.6[µm]

0.0

Ra = 8.3 µm Rmax = 41.7 µm

1000

1000

x [µm]

y [µm]

[4] Bricchi, E., Mills, J.D., Kazansky, P., Klappauf, B., Baumberg, J.; Birefringent Fresnel zone plates in silica fabricated by femtosecond laser machining, Opt. Lett. 27, (2002), p.2200-2202

[5] Nolte, S., Will, M., Bughoff, J., Tuennermann, A.; Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics, Appl. Phys. A 77, (2003), p.109-112

[6] Horn, A.; Zeitaufgelöste Analyse der Wechselwir-kung von ultrakurz gepulster Laserstrahlung mit Die-lektrika; German PhD Thesis, Rheinisch-Westfaelische Technische Hochschule Aachen, (2003)

[7] Will, M.; Ultrakurzpulsinduzierte Brechzahlmodi-fikationen in transparenten Festkörpern; German PhD Thesis, F.-Schiller-Universität Jena, 2004

[8] Stuart, B.C., Feit, M.D., Herman, S., Rubenchik, A.M., Shore, B.W., Perry, M.D.; Optical ablation by high-power short-pulse lasers, Vol. 13, No. 2, Febru-ary, (1996), J. Opt. Soc. Am. B, p. 459

[9] Marburger, J.H.; Prog. Quantum Electr. 4, 35 (1975)

[10] Boyd, R.W.; Nonlinear Optics (Academic Press, San Diego, 2003)

[11] Gopal, R., Deepak, V., Sivaramakrishnan, S.; Systematic study of spatiotemporal dynamics of in-tense femtosecond laser pulses in BK-7 glass; PRA-MANA Journal of physics, Indian Academy of Sci-ences, Vol. 68, No. 4 April 2007, p. 547-569

[12] Streltsov, A.M., Jinendra, K.R., Gaeta, A.L.; Femtosecond autocorrelation measurements based on two-photon conductivity in fused silica, Optics Letters, Vol.23, No. 10, 1998, p.798-800

[13] Schott datasheets of glass issue: 28.02.2008

[14] Schott datasheet of B270 glass issue: 23.06.2004

[15] Menzel, R.; Photonics, Springer Verlag Berlin 2001

[16] Aitchison, J.S., Silberberg, Y., Weiner, A.M., Leaird, D.E., Oliver, M.K. , Jackel, J. L., Vogel, E.M., Smith, P.; Spatial optical solitons in planar glass wa-veguides; J. Opt. Soc. Am. B/Vol. 8, No. 6/June 1991, p. 1290-1297

[17] Rayner, D.M., Naumov, A., Corkum, P.G.; Ul-trashort pulse non-linear optical absorption in trans-parent media, Optics Express, Vol.13, No. 9, 2005, p.3208-3217

[18] Glass catalogue of Praezisions Glas & Optik GmbH 06/2005, http://www.pgo-online.com.