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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 7908–7915
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Control of laser filamentation in fused silica by a periodic microlens array

Acner Camino, Zuoqiang Hao, Xu Liu, and Jingquan Lin  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 7908-7915 (2013)
http://dx.doi.org/10.1364/OE.21.007908


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Abstract

Deterministic wavelength-dependent multifilamentation is controlled in fused silica by adjusting the diffraction pattern generated by a loosely focusing 2D periodic lens array. By simply translating the sample along the propagation axis the number and distribution of filaments can be controlled and are in agreement with the results of linear diffraction simulations. The loose focusing geometry allows for long filaments whose distribution is conserved along their propagation inside the sample. The effect of incident energy and polarization on filament number is also studied. Laser filamentation controlled by a microlens array could be a promising method for easy and fast 3D track writing in transparent materials.

© 2013 OSA

1. Introduction

When ultrashort laser pulses with enough peak power propagate in a nonlinear medium, the interplay between self-focusing, natural diffraction and plasma divergence will give place to a long self-guided structure called filament [1

1. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20(1), 73–75 (1995). [CrossRef] [PubMed]

] that spans for distances longer than the Rayleigh length [2

2. A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22(5), 304–306 (1997). [CrossRef] [PubMed]

]. Its potential applications include the creation of channels for guided transmission of microwave radiation in the atmosphere [3

3. M. Chateauneuf, S. Payeur, J. Dubois, and J.-C. Kieffer, “Microwave guiding in air by a cylindrical filament array waveguide,” Appl. Phys. Lett. 92(9), 091104 (2008). [CrossRef]

5

5. M. Alshershby, J. Q. Lin, and Z. Q. Hao, “Numerical analysis of guiding a microwave radiation using a set of plasma filaments: dielectric waveguide concept,” J. Phys. D Appl. Phys. 45(6), 065102 (2012). [CrossRef]

], the control of lightning in storm clouds [6

6. B. La Fontaine, D. Comtois, C.-Y. Chien, A. Desparois, F. Génin, G. Jarry, T. Johnston, J.-C. Kieffer, F. Martin, R. Mawassi, H. Pépin, F. A. M. Rizk, F. Vidal, C. Potvin, P. Couture, and H. P. Mercure, “Guiding large-scale spark discharges with ultrashort pulse laser filaments,” J. Appl. Phys. 88(2), 610–615 (2000). [CrossRef]

, 7

7. N. L. Alexandrov, E. M. Bazeljan, N. A. Bogatov, A. M. Kiselev, A. N. Stepanov, B. A. Tikhomirov, and A. B. Tikhomirov, “Nonlinear effects of propagation of intense femtosecond laser radiation in atmosphere,” Proc. Int. Conf. on ‘High-power laser beams’ HPLB-2006 (N. Novgorod-Yaroslavl, 3–8 July) 107, (2006).

] or increasing the speed of techniques available for the fabrication of two- and three-dimensional photonic devices inside a glass [8

8. A. Saliminia, N. T. Nguyen, M.-C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003). [CrossRef]

11

11. O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006). [CrossRef]

].

Control of the multiple filamentation (MF), consequently, allows for a considerable speed up of the above mentioned fabrication process. However, it is widely known that by increasing the laser power the beam eventually undergoes a break-up into multiple narrow filaments that are spatially distributed according to random noise in the beam profile. The success of parallel writing by using MF depends critically on the effective control of the position, the number and the length of the filaments during the total exposition time, which cannot be realized automatically by only increasing laser power. Deterministic MF has been realized through modification of the spatial profile into an elliptical beam [15

15. A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126–1128 (2004). [CrossRef] [PubMed]

, 16

16. D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009). [CrossRef]

], adjustment of the numerical aperture [17

17. Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19(8), 7799–7806 (2011). [CrossRef] [PubMed]

], interference between two replicas of the laser beam [18

18. C. Corsi, A. Tortora, and M. Bellini, “Generation of a variable linear array of phase-coherent supercontinuum sources,” Appl. Phys. B 78(3–4), 299–304 (2004). [CrossRef]

] introduction of a phase mask [19

19. J. P. Bérubé, R. Vallée, M. Bernier, O. Kosareva, N. Panov, V. Kandidov, and S. L. Chin, “Self and forced periodic arrangement of multiple filaments in glass,” Opt. Express 18(3), 1801–1819 (2010). [CrossRef] [PubMed]

, 20

20. P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A 77(1), 013812 (2008). [CrossRef]

] and amplitude modulation with a periodic mesh [11

11. O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006). [CrossRef]

, 21

21. V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B 80(2), 267–275 (2005). [CrossRef]

]. In particular, periodic elements are well known to introduce a diffraction pattern that modulates the MF distribution and varies along the propagation axis [11

11. O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006). [CrossRef]

, 21

21. V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B 80(2), 267–275 (2005). [CrossRef]

23

23. J. Liu, R. Li, Z. Xu, H. Schroder, and S. L. Chin, “Control and organization of multi-filamentation of femtosecond laser pulses in optical media,” J. Korean Phys. Soc. 51(94), 1572–1577 (2007). [CrossRef]

]. Several studies [24

24. S. Minardi, A. Varanavicius, P. Di Trapani, and A. Piskarskas, “A compact, multipixel parametric light source,” Opt. Commun. 224(4-6), 301–307 (2003). [CrossRef]

26

26. K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett. 86(2), 021105 (2005). [CrossRef]

] have chosen an array of microlenses to generate MF in solids and liquids. This is an attractive optical element that both provides a high-efficiency collection of light [27

27. M. Taghizadeh, P. Blair, K. Balluder, A. Waddie, P. Rudman, and N. Ross, “Design and fabrication of diffractive elements for laser material processing applications,” Opt. Lasers Eng. 34(4-6), 289–307 (2000). [CrossRef]

] and generates diffraction patterns typical of periodic components, which enable the formation of many filaments per lenslet. Liu et al. [23

23. J. Liu, R. Li, Z. Xu, H. Schroder, and S. L. Chin, “Control and organization of multi-filamentation of femtosecond laser pulses in optical media,” J. Korean Phys. Soc. 51(94), 1572–1577 (2007). [CrossRef]

] observed that an amplitude mesh is preferable over a microlens array because of the strong divergence ultimately introduced by the lenslets to the beam. In our experiment parallel MF is realized outside the focal region by controlling the transverse energy modulation induced by a microlens array. We overcome the disadvantage pointed out by [23

23. J. Liu, R. Li, Z. Xu, H. Schroder, and S. L. Chin, “Control and organization of multi-filamentation of femtosecond laser pulses in optical media,” J. Korean Phys. Soc. 51(94), 1572–1577 (2007). [CrossRef]

] by means of a loosely focusing geometry and obtain MF patterns of comparative length and filaments number. We also demonstrate a strong dependence of the MF distribution on the incident wavelength and sample-to-lens distance as well as a direct effect of pulse energy and polarization on the number of filaments.

2. Experimental setup

A schematic of our setup is sketched in Fig. 1
Fig. 1 Sketch of the experimental setup. F, filter; WP, quarter-wave plate; PM, power meter; MLA, multilens array; FSB, fused silica block; L, imaging lens; S, screen. The inset Fig. is a representation of the commercial microlens array utilized.
. The laser source is a commercial system (Libra, Coherent Inc.), consisting of the pulses from a Ti: Sapphire oscillator, amplified through a CPA system that provides linearly polarized 50-fs pulses centered on 800 nm, at a 1 kHz repetition rate The laser power instability from shot to shot is less than 0.3%. By using a beam splitter and optical density filters, we can control the input at fundamental frequency to a maximum of 480 µJ per pulse. An iris opened 11 mm is placed before the focusing element. We have adjusted a quarter-wave plate for nearly circular polarization and used a switching mount to easily change the incident polarization. A BBO crystal and a color filter can be added to generate the second harmonic and filter out the fundamental light. A quarter-wave plate for 400 nm light was also used in order to change the polarization of the second harmonic into circular.

The focusing element is a commercial 10 × 10 mm array of fused silica parabolic plano-convex microlenses of focal 218.3 mm and pitch 1.015 mm arranged in a square geometry (Edmund Optics, part number #64-487). The radius of curvature of the single lenslets that form the element is 100 mm as provided by manufacturer, and the thickness of the element is 1.20 mm. Controlled MF is achieved inside a 20-mm-long fused silica sample mounted in a translation stage that enables us to control its distance from the lens array. The operating laser energy and focusing geometry were chosen in order to avoid permanent modifications in the sample. Behind the silica, by using an f = 50.8 mm lens (L) we image the MF pattern on a white screen located at a distance of 5.02 m from the microlens array, and take pictures of it using a digital camera. Such lens L can be moved in the direction of the z-axis to select the filamentation pattern in different transversal planes along the filaments propagation inside silica.

3. Results and discussion

When a microlens array is used to modulate the MF distribution in a solid sample placed in the focal region, a single filament per lenslet is formed [25

25. W. Watanabe, Y. Masuda, H. Arimoto, and K. Itoh, “Coherent Array of White-Light Continuum Generated by Microlens Array,” Opt. Rev. 6(3), 167–172 (1999). [CrossRef]

]. In Fig. 2
Fig. 2 Typical MF patterns formed by (a) 800-nm and (b) 400-nm laser pulses when the sample is placed in the focal region.
we show two typical transverse profiles of the fundamental and second harmonic imaged on the screen by lens L1 respectively. Observe that although the array contains a total of 100 lenslets, due to the Gaussian profile of the beam only the central ones carry enough power to generate a filament.

However, this is not always the case, and many filaments per lenslet can be generated if the sample is moved away from the focal region. Figure 3
Fig. 3 Filament patterns at different laser propagation distances inside the fused silica block formed from incidence of fundamental (a-e) and second harmonic laser (e-h). The images are taken at (a, e) 10 mm, (b, f) 12 mm, (c, g) 15 mm and (d, h) 18 mm from the front surface of the sample respectively.
represents four typical cross-sectional pictures of the MF distributions at different propagation distances inside the fused silica, when the sample was placed before the focus, at a fixed distance of z = 144 mm from the lens array. The pulse energy was set to 315 μJ for the IR pulse and 80 μJ for the second harmonic, which correspond to about the same multiple of the critical power for self-focusing in fused silica. Figures 3(a)3(d) correspond to incident fundamental frequency and Figs. 3(e)3(h) to incidence of the second harmonic. In both cases each of the four patterns imaged on the screen were obtained by carefully moving the imaging lens L along the z-axis to select the desired object plane inside the 20-mm fused silica block. For a better intelligibility, only the 9 central filament regions were selected and the distance between their centers is equal to the pitch of the lens array, which is about 1 mm.

For both wavelengths we observe the formation of several filaments per lenslet in different distributions. The filaments propagate for a long distance inside the silica, preserving their pattern until the end of the sample. The nonlinearity of the medium is the dominating mechanism once the beam enters the sample, allowing the MF pattern to be conserved, although the effect of linear diffraction continues to affect the beam along its subsequent propagation. The images corresponding to fundamental laser [Figs. 3(a)3(d)] depict formation of three filaments per lenslet, where the central one carries most of the energy. However, at the same sample position, the filament distribution formed by the second harmonic is totally different [Figs. 3(e)3(h)], manifesting four filaments per lenslet. The reason for such dissimilarity between the two MF distributions is the wavelength-dependence of the diffraction pattern induced by the microlens array on the entrance face of the sample. Such diffraction is what determines in which positions intense spots will favor nonlinear buildup and therefore filament formation.

It is known that the energy distribution of the incident laser pulse on the entrance face of the sample determines the positions where filaments appear [11

11. O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006). [CrossRef]

, 17

17. Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19(8), 7799–7806 (2011). [CrossRef] [PubMed]

23

23. J. Liu, R. Li, Z. Xu, H. Schroder, and S. L. Chin, “Control and organization of multi-filamentation of femtosecond laser pulses in optical media,” J. Korean Phys. Soc. 51(94), 1572–1577 (2007). [CrossRef]

]. By adjusting the distance of the sample from the focusing element, the MF can be modified into completely different distributions. We have imaged the MF patterns at three different lens-to-sample distances as shown in Fig. 4
Fig. 4 MF dependence on the relative position of the sample. Filament patterns from the fundamental laser case are depicted on (a-b) while patterns from the second harmonic case in (c-e). Images (a) and (c) correspond to sample position z = 144 mm, image (d) to z = 164 mm and images (b) and (e) to z = 180 mm.
. The pulse energy of 480 μJ and 110 μJ for fundamental and second harmonic are used respectively. Figures 4 (a)4(b) shows the patterns corresponding to the fundamental laser case while Figs. 4(c)4(e) corresponds to the second harmonic case. Notice how changing the position of the sample from z = 144 mm [Fig. 4(a)] to z = 180 mm [Fig. 4(b)] leads to a drastic transformation of the distribution and number of filaments obtained from fundamental laser light. Filament patterns from incidence of second harmonic also suffer a radical modification when the sample is moved from 144 mm [Fig. 4(c)] to 180 mm [Fig. 4(e)]. However, it can be seen that in the case of second harmonic the filaments formed are more stable and better organized than those appearing from diffraction of the fundamental laser frequency. In addition, as seen from the Fig. 4, the filaments obtained from incidence of second harmonic appear smaller (diameter in the range of 45 – 50 μm) than those formed by the fundamental laser (diameter in the range of 50 – 90 μm).

In order to provide an explanation to this effect, we have performed simulations of the diffraction-pattern’s evolution along the z-axis for three different wavelengths, which allow us to predict the diffraction that determines the MF distributions and contrast them to the experimental results. The simulation was carried out using the ray tracing software Zemax, considering a 10-mm Gaussian beam that passes through a lens array which has the same configuration with that in our experiments, and propagates through the same distance used in our experiments without including nonlinear effects. It was performed for 800-nm, 400-nm and 248-nm light at 5 different sample positions. The results are shown in Fig. 5
Fig. 5 Zemax simulations of the diffraction pattern at the entrance face of the sample for three different wavelengths at five different sample positions. Images (a-e) represent the central spot for 800-nm, (f-j) for 400 nm and (k-o) for 248 nm. Columns from left to right represent sample position at respectively z = 144 mm, 155 mm, 164 mm, 172 mm and the rightmost at 180 mm.
, in which each image represents a 1 × 1mm diffraction pattern at the entrance face of the sample. The first row of images in Fig. 5 represent the evolution of the pattern that corresponds to incidence of fundamental light when the sample is moved from position z = 144 mm [Fig. 5(a)] to position z = 180 mm [Fig. 5(e)]. Figures 5(f)5(j) and 5(k)5(o) represent the evolution over the same region for the wavelengths 400 nm and 248 nm respectively.

The simulations depicted in Fig. 5 confirm that the experimental MF distributions shown in Figs. 3 and 4 are indeed determined by the diffraction patterns on the entrance face of the sample. We observe that diffraction from second harmonic [Figs. 5(f)5(j)] provides intensity patterns that benefit the appearance of more filaments in better organized structures compared to diffraction from fundamental light [Figs. 5(a)5(e)], in agreement with the experimental results shown in Fig. 4. Also, for all wavelengths the diffraction at distances closer to the lens array (not shown) forms patterns where the energy is distributed over a higher number of intense spots within a bigger area, preventing the diffraction pattern from generating filaments when the sample is too far from the focus. Several studies [11

11. O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006). [CrossRef]

, 21

21. V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B 80(2), 267–275 (2005). [CrossRef]

] have attributed the characteristic patterns induced by meshes, gratings and arrays to the Talbot effect [28

28. M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 39–46, (June 2001).

], which states that such distributions are interference patterns appearing from overlapping copies of the periodic element. Talbot theory predicts modifications and periodic revivals of the resulting pattern as the sample is moved to different fractions of a distance ZT [28

28. M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 39–46, (June 2001).

]
ZT=Λ2λ,
(1)
called the Talbot length, whereΛis here the pitch of the microlens array. Since the Talbot length is dependent on the wavelength, a fixed position in the z-axis represents different fractions of ZT for each of the three cases shown in Fig. 5. As a consequence, the evolution of the diffraction pattern along the z-axis is characterized by more drastic changes when the wavelength is shorter. This allows a more effective control of the MF distribution by reducing the laser wavelength.

Another important feature of the pattern’s evolution is that for all wavelengths the spot size tends to be smaller as the sample approaches the geometric focus of the microlenses. Interestingly, this fact causes that the patterns in Figs. 5(l), 5(n) and 5(o) that correspond to diffraction of 248 nm light are miniaturized versions of those in Figs. 5 (f), 5(h) and 5(i) that correspond to diffraction of light at 400 nm. Such reproduction of the same structure in a smaller scale suggests that by properly tuning the input wavelength and sample position, the distance between individual filaments formed by each lenslet can be regulated. The condensation of the pattern when the sample approaches the focus can lead to filament interaction that originates chaotic distributions like the one appearing in Fig. 4(b) and reduce the filament length.

Besides, some other variables that enable control of the filament number in the MF pattern are the pulse energy and polarization. In Fig. 4(c), where the energy of the second harmonic pulses is higher than that in Figs. 3(e)3(h), we observe more filaments, although both cases correspond to the same wavelength at the same sample position. However, observe that the fundamental structure of the pattern was not notably affected by the energy. A very clear picture of this effect is shown in Fig. 6
Fig. 6 Effect of input energy on the number of filaments formed per lenslet. Pictures (a–d) represent respectively energies of 250 µJ, 300 µJ, 370 µJ and 480 µJ.
where we irradiate with four different pulse energies fundamental 800-nm pulses on the sample fixed at z = 144 mm. Notice that more filaments corresponding to the position of the higher order diffraction of laser beam appear when the incident energy is increased.

In the experiment we rotated laser polarization from linear polarization (LP) to circular polarization (CP). The filament pattern is as shown in Fig. 7
Fig. 7 Effect of laser polarization in the number of filaments formed per lenslet. Picture (a) represents LP and (b) CP.
, which is obtained for 800-nm input pulses of 481 µJ at z = 144 mm. It is found that a MF pattern with a higher number of filaments is obtained under the incidence of LP pulses than that of CP pulses. This is mainly because the critical power for circular polarization (CP) is greater than that for linear polarization (LP) [29

29. G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89(1), 013901 (2002). [CrossRef] [PubMed]

]. Figures 6 and 7 confirm the fundamental structure of the pattern is independent from laser energy and polarization, whose effect is only a stronger or weaker completion of the diffraction pattern per lenslet that induces the filaments.

4. Conclusions

We have shown deterministic control of multifilamentation induced by the diffraction pattern from an array of microlenses by changing the incident wavelength and the sample’s position with respect to the focusing element. By simply moving the sample along the z-axis, different diffraction patterns at its entrance face modulate the MF distribution, which is preserved along its nonlinear propagation. Energy and polarization have shown to influence the total number of filaments but not the fundamental structure of the pattern. By choosing a phase mask and a loose focusing geometry (f-number = 215 for each lenslet) we achieve both high efficiency and long filaments in controllable distributions. Diffraction of second harmonic light proved to enable in general more organized filament patterns per lenslet than those from incidence of fundamental light. There is a growing interest in studying higher photon energy sources for applications of filamentation in glass [30

30. A. Saliminia, J. P. Bérubé, and R. Vallée, “Refractive index-modified structures in glass written by 266nm fs laser pulses,” Opt. Express 20(25), 27410–27419 (2012). [CrossRef] [PubMed]

, 31

31. D. Papazoglou, I. Zergioti, S. G. Sgouros, G. Maravelias, S. Christopoulos, and C. Fotakis, “Sub-picosecond ultraviolet laser filamentation-induced bulk modifications in fused silica,” Appl. Phys., A Mater. Sci. Process. 81(2), 241–244 (2005). [CrossRef]

], so the superiority of blue and UV filaments proved in experiments and suggested by simulations is opportune in terms of their characteristics in the processes of index modification and track writing in transparent media.

Acknowledgments

This project was supported by 973 program (2013CB922404), National Natural Science Foundation of China under Grant Nos. 11074027, 61178022, 11274053 and 11211120156; Funds from Sci. &Tech. Dept of Jilin Province, Grant No. 20111812. Research Fund for the Doctoral Program of Higher Education of China (No. 20112216120006, 20122216120009)

References and links

1.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20(1), 73–75 (1995). [CrossRef] [PubMed]

2.

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22(5), 304–306 (1997). [CrossRef] [PubMed]

3.

M. Chateauneuf, S. Payeur, J. Dubois, and J.-C. Kieffer, “Microwave guiding in air by a cylindrical filament array waveguide,” Appl. Phys. Lett. 92(9), 091104 (2008). [CrossRef]

4.

M. Alshershby, Z. Q. Hao, and J. Q. Lin, “Guiding microwave radiation using laser-induced filaments: the hollow conducting waveguide concept,” J. Phys. D Appl. Phys. 45(26), 265401 (2012). [CrossRef]

5.

M. Alshershby, J. Q. Lin, and Z. Q. Hao, “Numerical analysis of guiding a microwave radiation using a set of plasma filaments: dielectric waveguide concept,” J. Phys. D Appl. Phys. 45(6), 065102 (2012). [CrossRef]

6.

B. La Fontaine, D. Comtois, C.-Y. Chien, A. Desparois, F. Génin, G. Jarry, T. Johnston, J.-C. Kieffer, F. Martin, R. Mawassi, H. Pépin, F. A. M. Rizk, F. Vidal, C. Potvin, P. Couture, and H. P. Mercure, “Guiding large-scale spark discharges with ultrashort pulse laser filaments,” J. Appl. Phys. 88(2), 610–615 (2000). [CrossRef]

7.

N. L. Alexandrov, E. M. Bazeljan, N. A. Bogatov, A. M. Kiselev, A. N. Stepanov, B. A. Tikhomirov, and A. B. Tikhomirov, “Nonlinear effects of propagation of intense femtosecond laser radiation in atmosphere,” Proc. Int. Conf. on ‘High-power laser beams’ HPLB-2006 (N. Novgorod-Yaroslavl, 3–8 July) 107, (2006).

8.

A. Saliminia, N. T. Nguyen, M.-C. Nadeau, S. Petit, S. L. Chin, and R. Vallée, “Writing optical waveguides in fused silica using 1 kHz femtosecond infrared pulses,” J. Appl. Phys. 93(7), 3724 (2003). [CrossRef]

9.

H. Chen, X. Chen, Y. Xia, D. Liu, Y. Li, and Q. Gong, “Beam coupling in 2×2 waveguide arrays in fused silica fabricated by femtosecond laser pulses,” Opt. Express 15(9), 5445–5450 (2007). [CrossRef] [PubMed]

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11.

O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun. 267(2), 511–523 (2006). [CrossRef]

12.

L. Shah, A. Y. Arai, S. M. Eaton, and P. R. Herman, “Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate,” Opt. Express 13(6), 1999–2006 (2005). [CrossRef] [PubMed]

13.

V. Kudriašov, E. Gaižauskas, and V. Sirutkaitis, “Birefringent modifications induced by femtosecond filaments in optical glass,” Appl. Phys., A Mater. Sci. Process. 93(2), 571–576 (2008). [CrossRef]

14.

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett. 26(1), 19–21 (2001). [CrossRef] [PubMed]

15.

A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126–1128 (2004). [CrossRef] [PubMed]

16.

D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009). [CrossRef]

17.

Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19(8), 7799–7806 (2011). [CrossRef] [PubMed]

18.

C. Corsi, A. Tortora, and M. Bellini, “Generation of a variable linear array of phase-coherent supercontinuum sources,” Appl. Phys. B 78(3–4), 299–304 (2004). [CrossRef]

19.

J. P. Bérubé, R. Vallée, M. Bernier, O. Kosareva, N. Panov, V. Kandidov, and S. L. Chin, “Self and forced periodic arrangement of multiple filaments in glass,” Opt. Express 18(3), 1801–1819 (2010). [CrossRef] [PubMed]

20.

P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A 77(1), 013812 (2008). [CrossRef]

21.

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B 80(2), 267–275 (2005). [CrossRef]

22.

H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004). [CrossRef] [PubMed]

23.

J. Liu, R. Li, Z. Xu, H. Schroder, and S. L. Chin, “Control and organization of multi-filamentation of femtosecond laser pulses in optical media,” J. Korean Phys. Soc. 51(94), 1572–1577 (2007). [CrossRef]

24.

S. Minardi, A. Varanavicius, P. Di Trapani, and A. Piskarskas, “A compact, multipixel parametric light source,” Opt. Commun. 224(4-6), 301–307 (2003). [CrossRef]

25.

W. Watanabe, Y. Masuda, H. Arimoto, and K. Itoh, “Coherent Array of White-Light Continuum Generated by Microlens Array,” Opt. Rev. 6(3), 167–172 (1999). [CrossRef]

26.

K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett. 86(2), 021105 (2005). [CrossRef]

27.

M. Taghizadeh, P. Blair, K. Balluder, A. Waddie, P. Rudman, and N. Ross, “Design and fabrication of diffractive elements for laser material processing applications,” Opt. Lasers Eng. 34(4-6), 289–307 (2000). [CrossRef]

28.

M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 39–46, (June 2001).

29.

G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89(1), 013901 (2002). [CrossRef] [PubMed]

30.

A. Saliminia, J. P. Bérubé, and R. Vallée, “Refractive index-modified structures in glass written by 266nm fs laser pulses,” Opt. Express 20(25), 27410–27419 (2012). [CrossRef] [PubMed]

31.

D. Papazoglou, I. Zergioti, S. G. Sgouros, G. Maravelias, S. Christopoulos, and C. Fotakis, “Sub-picosecond ultraviolet laser filamentation-induced bulk modifications in fused silica,” Appl. Phys., A Mater. Sci. Process. 81(2), 241–244 (2005). [CrossRef]

OCIS Codes
(110.5100) Imaging systems : Phased-array imaging systems
(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter
(320.2250) Ultrafast optics : Femtosecond phenomena

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 28, 2013
Revised Manuscript: March 9, 2013
Manuscript Accepted: March 11, 2013
Published: March 25, 2013

Citation
Acner Camino, Zuoqiang Hao, Xu Liu, and Jingquan Lin, "Control of laser filamentation in fused silica by a periodic microlens array," Opt. Express 21, 7908-7915 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-7908


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References

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  2. A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett.22(5), 304–306 (1997). [CrossRef] [PubMed]
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  11. O. G. Kosareva, T. Nguyen, N. A. Panov, W. Liu, A. Saliminia, V. P. Kandidov, N. Akozbek, M. Scalora, R. Vallee, and S. L. Chin, “Array of femtosecond plasma channels in fused silica,” Opt. Commun.267(2), 511–523 (2006). [CrossRef]
  12. L. Shah, A. Y. Arai, S. M. Eaton, and P. R. Herman, “Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate,” Opt. Express13(6), 1999–2006 (2005). [CrossRef] [PubMed]
  13. V. Kudriašov, E. Gaižauskas, and V. Sirutkaitis, “Birefringent modifications induced by femtosecond filaments in optical glass,” Appl. Phys., A Mater. Sci. Process.93(2), 571–576 (2008). [CrossRef]
  14. K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, “In situ observation of photoinduced refractive-index changes in filaments formed in glasses by femtosecond laser pulses,” Opt. Lett.26(1), 19–21 (2001). [CrossRef] [PubMed]
  15. A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett.29(10), 1126–1128 (2004). [CrossRef] [PubMed]
  16. D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A79(3), 033843 (2009). [CrossRef]
  17. Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express19(8), 7799–7806 (2011). [CrossRef] [PubMed]
  18. C. Corsi, A. Tortora, and M. Bellini, “Generation of a variable linear array of phase-coherent supercontinuum sources,” Appl. Phys. B78(3–4), 299–304 (2004). [CrossRef]
  19. J. P. Bérubé, R. Vallée, M. Bernier, O. Kosareva, N. Panov, V. Kandidov, and S. L. Chin, “Self and forced periodic arrangement of multiple filaments in glass,” Opt. Express18(3), 1801–1819 (2010). [CrossRef] [PubMed]
  20. P. Rohwetter, M. Queißer, K. Stelmaszczyk, M. Fechner, and L. Wöste, “Laser multiple filamentation control in air using a smooth phase mask,” Phys. Rev. A77(1), 013812 (2008). [CrossRef]
  21. V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B80(2), 267–275 (2005). [CrossRef]
  22. H. Schroeder, J. Liu, and S. L. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express12(20), 4768–4774 (2004). [CrossRef] [PubMed]
  23. J. Liu, R. Li, Z. Xu, H. Schroder, and S. L. Chin, “Control and organization of multi-filamentation of femtosecond laser pulses in optical media,” J. Korean Phys. Soc.51(94), 1572–1577 (2007). [CrossRef]
  24. S. Minardi, A. Varanavicius, P. Di Trapani, and A. Piskarskas, “A compact, multipixel parametric light source,” Opt. Commun.224(4-6), 301–307 (2003). [CrossRef]
  25. W. Watanabe, Y. Masuda, H. Arimoto, and K. Itoh, “Coherent Array of White-Light Continuum Generated by Microlens Array,” Opt. Rev.6(3), 167–172 (1999). [CrossRef]
  26. K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett.86(2), 021105 (2005). [CrossRef]
  27. M. Taghizadeh, P. Blair, K. Balluder, A. Waddie, P. Rudman, and N. Ross, “Design and fabrication of diffractive elements for laser material processing applications,” Opt. Lasers Eng.34(4-6), 289–307 (2000). [CrossRef]
  28. M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 39–46, (June 2001).
  29. G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett.89(1), 013901 (2002). [CrossRef] [PubMed]
  30. A. Saliminia, J. P. Bérubé, and R. Vallée, “Refractive index-modified structures in glass written by 266nm fs laser pulses,” Opt. Express20(25), 27410–27419 (2012). [CrossRef] [PubMed]
  31. D. Papazoglou, I. Zergioti, S. G. Sgouros, G. Maravelias, S. Christopoulos, and C. Fotakis, “Sub-picosecond ultraviolet laser filamentation-induced bulk modifications in fused silica,” Appl. Phys., A Mater. Sci. Process.81(2), 241–244 (2005). [CrossRef]

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