Extension of filament propagation in water with Bessel-Gaussian beamsG. Kaya, N. Kaya, M. Sayrac, Y. Boran, J. Strohaber, A. A. Kolomenskii, M. Amani, and H. A. Schuessler Citation: AIP Advances 6, 035001 (2016); doi: 10.1063/1.4943397 View online: http://dx.doi.org/10.1063/1.4943397 View Table of Contents: http://scitation.aip.org/content/aip/journal/adva/6/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Plasmonic formation mechanism of periodic 100-nm-structures upon femtosecond laser irradiation of siliconin water J. Appl. Phys. 116, 074902 (2014); 10.1063/1.4887808 Lasing action in water vapor induced by ultrashort laser filamentation Appl. Phys. Lett. 102, 224102 (2013); 10.1063/1.4809585 Generation of extreme ultraviolet radiation with a Bessel–Gaussian beam Appl. Phys. Lett. 95, 131114 (2009); 10.1063/1.3240404 Short pulsed laser machining: How short is short enough? J. Laser Appl. 11, 268 (1999); 10.2351/1.521902 Construction of a subpicosecond double-beam laser photolysis system utilizing a femtosecond Ti:sapphireoscillator and three Ti:sapphire amplifiers (a regenerative amplifier and two double passed linear amplifiers),and measurements of the transient absorption spectra by a pump-probe method Rev. Sci. Instrum. 68, 4364 (1997); 10.1063/1.1148398

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Extension of filament propagation in waterwith Bessel-Gaussian beams

G. Kaya,1 N. Kaya,1,2,a M. Sayrac,1 Y. Boran,1 J. Strohaber,1,3

A. A. Kolomenskii,1 M. Amani,2 and H. A. Schuessler1,21Department of Physics, Texas A&M University, College Station, Texas 77843, USA2Science and Petroleum, Texas A&M University at Qatar, Doha 23874, Qatar3Department of Physics, Florida A&M University, Tallahassee, Florida 32307, USA

(Received 22 October 2015; accepted 22 February 2016; published online 2 March 2016)

We experimentally studied intense femtosecond pulse filamentation and propaga-tion in water for Bessel-Gaussian beams with different numbers of radial modallobes. The transverse modes of the incident Bessel-Gaussian beam were createdfrom a Gaussian beam of a Ti:sapphire laser system by using computer generatedhologram techniques. We found that filament propagation length increased withincreasing number of lobes under the conditions of the same peak intensity, pulseduration, and the size of the central peak of the incident beam, suggesting thatthe radial modal lobes may serve as an energy reservoir for the filaments formedby the central intensity peak. C 2016 Author(s). All article content, except whereotherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4943397]

I. INTRODUCTION

Filamentation by femtosecond laser radiation,1 propagating in nonlinear media, facilitates anumber of applications, including remote sensing,2 attosecond physics,3,4 and lightning control.5

In such settings, extended filaments are desirable, and various techniques aiming to prolong theirlength have been explored.6,7 The substantial extension of optical filaments continues to attractconsiderable interest and much still remains to be understood.8 Commonly, filamentation is consid-ered to be a result of a dynamic balance of the Kerr self-focusing of an intense beam and the defo-cusing involving the self-generated weak plasma and the effect of free electrons.9 It is of interest toinvestigate how different incident laser transverse modes affect filament propagation dynamics.

The linear propagation of Bessel beams that exhibits a suppressed diffraction during propaga-tion attracted considerable attention.10 The studies of nonlinear Bessel beams has also revealed apossibility for the existence of localized and stationary solutions.11–13 A possible scenario wherefilaments appear because of spontaneous beam reshaping into a conical wave was investigatedby suggesting an interpretation of femtosecond pulse filamentation not related to the effect ofself-generated weak plasma.14 The survival of filaments transmitted through clouds15 was explainedby a dynamic energy balance between the formed quasi-solitonic structure and the surroundinglaser photon bath, which acts as an energy reservoir. The self-reconstruction properties of filamentsand their extension were also explained in terms of the energy reservoir surrounding filaments.16

Nonlinear dynamics of pulsed Bessel beams17–19 and possible applications20–22 were also investi-gated.

Ideal Bessel beams are known to be diffraction-free when they propagate in vacuum.23 Al-though these beams do not exist, the use of approximate or quasi-Bessel beams has long beensuggested in diverse areas of optical physics, since such beams maintain long propagation lengthsin optical media by virtue of the strongly suppressed diffraction of their central lobe.24 When aBessel beam is compared to a Gaussian beam with the same diameter of the central peak, it shows

aElectronic mail: necati@physics.tamu.edu

2158-3226/2016/6(3)/035001/7 6, 035001-1 ©Author(s) 2016.

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a remarkable resistance to diffraction in the linear propagation regime.25 Recent theoretical studieson filamentation dynamics in Ar gas of intense femtosecond beams with different transverse modeshave shown that the cross-sectional profile of the laser beam in Bessel modes remains undistorted26

during propagation, and the outer part of the Bessel beam serves as an energy reservoir for thefilament that is formed around the central portion of the beam.27 In addition, Scheller and colleagueshave experimentally shown that the propagation of a femtosecond laser filament in air can besubstantially extended by an appropriate use of a surrounding auxiliary dressing beam, continuouslysupplying energy to the filament.28

In most of the related works, a conical lens called axicon is employed to generate a quasi-Bessel beam which is not collimated, and this makes the data analysis and interpretation morecomplicated. However, with that approach it was not possible to investigate the effect of the numberof lateral lobes of a Bessel beam on the propagation of filaments, either. We formed a collimatedBessel-Gaussian beam with arbitrary number of lateral lobes by using a spatial light modulator(SLM) and a computer generated hologram (CGH) technique. This novel and universal approachenables the formation of arbitrary beam modes and is ideally suited for the main goal of this study,namely to investigate the influence of the mode structure of the Bessel beams on the formationand propagation of filaments. In order to study the influence of the mode structure of the incidentBessel-Gaussian beams on their propagation we experimentally investigate filament propagationdynamics in water of intense femtosecond pulses with Bessel-Gaussian beam profiles and differentnumbers of radial modal lobes under the condition of similar peak intensities, pulse durations, anddiameters of the central peak of the beams. The choice of water as a nonlinear medium is dictatedby its broad use and the fact that in liquids the Kerr nonlinearity is about three orders of magnitudelarger than in gases,29 therefore the nonlinear effects develop on a shorter distance and require lesslaser power, which fits well our experimental conditions.

II. EXPERIMENTAL DETAILS, RESULTS AND DISCUSSION

The profile of an ideal Bessel beam is described by a zero-order Bessel function of the first kindwhich has a narrow main lobe surrounded by a decaying set of “side-lobe” rings.23 In our setup, thecreated transverse Bessel-Gaussian beams can be described by the following spatial distribution ofthe field amplitude: EBG (r, z = 0, t = 0) = E0J0 (αr) e−(β r )2, where E0 is the peak amplitude, and J0

is the zero order Bessel function. The constants α and β are chosen in such a way as to make thecentral peak of the transverse mode create filaments, whereas the radial lobes have intensities toolow to produce filamention.

The input beam patterns were created from an initial Gaussian beam of a Ti:sapphire lasersystem (pulse duration of ∼50 fs, central wavelength of 800 nm, and an output energy of 1 mJ perpulse at a 1 kHz repetition rate) by using computer generated-holograms30 displayed on a liquidcrystal spatial light modulator (Hamamatsu LCOS-SLM X10468-2). The SLM had a resolution of800x600 pixels (16 mm x 12 mm), and a maximum reflectivity of >95% for radiation between750 nm and 850 nm. Figure 1 shows an illustration of the experimental setup used. The laser beamilluminates the SLM with a phase-amplitude encoded hologram set by a computer to produce adesired optical beam in the 1st diffraction order. Such grayscale computer-generated hologramsfor Bessel-Gaussian beams, prepared with a MATLAB code, were displayed on the LCD of theSLM via a digital visual interface connection. An illustration of the computer-generated hologramused to produce a Bessel-Gaussian beam in the first diffraction order is shown in the inset ofFig. 1. We note that the SLM creates a quasi-Bessel amplitude-phase distribution that togetherwith the Gaussian distribution of the incident beam produces a Bessel-Gaussian beam, which has alimited cross section and a finite number of lobes. With all optical losses, including losses from theSLM, which employs off-axis holography to generate the beam modes, the incident power of theBessel-Gaussian beam mode with a 300 µm diameter at FWHM in the central Gaussian counterpartat the entrance of the cell was measured as 55 mW. Consequently, for the repetition rate of our lasersystem (1 kHz) and the pulse duration (∼50 fs), we obtained an input peak power of ∼1.1 GW perpulse for the central lobe of the Bessel-Gaussian beam.

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FIG. 1. Experimental setup: SLM, spatial light modulator; SP, syringe pump; GC, glass cell with an optical window; FG, flatglass; IR-F, infrared filter (which can be complimented by a neutral density filter) to measure the incident beam; PM, powermeter; SM, spectrometer. The image next to the SLM is an example hologram used to create a Bessel-Gaussian beam. Theimage on the right shows a Bessel-Gaussian beam with filaments in the central part; it was taken with a color CCD camerausing necessary filters and attenuators.

When the initial power in the produced optical beam exceeds the critical value for the opticalmedium, nonlinear optical self-focusing effect becomes important. Condensed transparent materialsserve as efficient media for producing femtosecond filaments, which are sustained by the dynamicbalance of Kerr self-focusing and defocusing due to plasma generation combined with energylosses resulting from nonlinear effects.31,32 The chromatic dispersion and self-steepening can bealso important factors able to modify the pulse spectrum and intensity.33 To assess the influence ofthe group velocity dispersion (GVD) in water on the beam dynamics we estimated the dispersionlength Ld = τ2/(∂2k/∂2ω) ≈ 5 cm with τ = 50 fs and GVD = (∂2k/∂2ω) = 2.5 × 104 fs2/m.34 Sincethis length is significantly longer than the self-focusing length ∼2cm for the central peak of theincident beam, the dispersion should play comparatively minor role at our conditions. Also othernonlinear processes (like multiphoton absorption14) can contribute to balancing the nonlinear effectsfor filament stabilization until the energy of the pulse is depleted.

The peak power of the central lobe of the Bessel-Gaussian beams incident on the water sur-face was adjusted to a much larger value than the critical power for self-focusing in water, assuringthe filament formation in water within the water cell, as was observed previously.35–37 Indeed, hotspots in the central part of the beam corresponding to filament formation were directly observed inour experiments, while the radial lobes had intensities too low to produce a filament as seen in theimage of the inset of Fig. 1. We note that at the higher beam powers, which were avoided in ourexperiments, once the regime of multi-filamentation is reached, the beam energy quickly depletes,and filaments die out, since each filament dissipates energy at a similar rate. In addition to avoidingany undesirable beam break-up into multiple filaments, much care was also taken to ensure that theproduced beams had central peaks with similar peak intensities, pulse durations, and beam diameters.The peak intensity and diameter were determined from the measurements with a power meter inter-changed with a CCD camera; the measurements with the latter required additional neutral-densityfilters in front of it. We kept the distance between the SLM and the glass cell as short as possible tominimize the chromatic distortions due to diffraction gratings on the SLM.38 The beams were passedthrough a 13 cm-long glass cell, which was arranged vertically allowing us to measure the powerand spectrum as a function of the propagation distance by changing the water level in the cell with

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FIG. 2. Experimentally created modes of the incident Bessel-Gaussian beam registered with the CCD camera: (a) the centralpeak of the beam with no lobes and (b-h) the central peak with different number of additional radial lobes.

a programmable infuse/withdraw syringe pump (Harvard PHD 2000). A mechanical iris was usedto select the central peak of the beam. An optical flat was positioned after the cell to reflect a smallportion of the beam into the spectrometer. Spectral measurements were performed as a function ofthe propagation distance by collecting the radiation at the exit of the cell and analysing it with anOcean Optics USB-2000 spectrometer. Simultaneously, laser power measurements were taken usinga photodiode power meter head (Ophir PD300-IR) with a spectral range within 700-1800 nm. Inorder to measure the beam power after the water cell, a long-pass glass filter (RG-780) was placed infront of the power meter to filter out white-light. A LabVIEW code was used to control the infusingand withdrawing of water via a syringe pump and to acquire the values from the power meter and thespectrometer.

To understand the propagation of Bessel-Gaussian beams of different mode structure, we inves-tigated their propagation dynamics by varying the number of radial lobes. Figure 2 depicts theexperimentally created modes of the incident Bessel-Gaussian beam registered with the CCD cam-era. Figure 3 shows the comparison of the distributions of the laser intensity in the central part ofthe beams registered at different propagation distances for a beam with only the central lobe andfor a Bessel-Gaussian beam, which has also 7 radial lobes. The distributions were measured with amonochromatic CCD camera and the generated white-light was filtered out by using RG-780 filter.The self-focusing effect took place near the entrance of the beam into the cell, and the changesof the beams with different number of radial lobes with the propagation distance in water wereobserved. The filaments formed by the incident beam with only the central peak exhibit faster decayas the pulse propagates than the filaments formed by the incident Bessel-Gaussian beam with radiallobes.

We also performed power and spectral measurements for only the central peak of Bessel-Gaussian beams with different number of radial lobes. The FWHM diameter of 300 µm of thecentral peak of the Bessel-Gaussian beam was selected by the mechanical iris positioned after thewater cell in front of the power meter or spectrometer for spectral measurements. The spectraldistributions measured as a function of the propagation distance are shown in Fig. 4(a). The effectof increasing number of radial lobes can be seen by an increase in the propagation distance of thecentral filament-containing peak of the beam. The increments of this increase are most noticeable,when 1, 2 or 3 lobes are added.

In Fig. 4(b), we show the infrared power measured for only the central peak of Bessel-Gaussianbeams with different number of radial lobes as a function of the propagation distance. With eachadditional radial lobe we observe the trend of an increasing power delivered to a given propagationdistance. At intermediate distances 6-9 cm the beams with multiple lobes (>2) show a significantly

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FIG. 3. Measured IR distributions of the laser intensity (shown with false colors) of the beams at different propagationdistances z: (a) a beam with only the central lobe is used and (b) a Bessel-Gaussian beam with the central and 7 radial lobeswas produced at the entrance of the cell. The sharp intensity peaks, corresponding to formed filaments are clearly visible.These peaks are sustained for longer distances for the Bessel-Gaussian beam with radial lobes (case (b)).

slower rate of the power decrease compared to the beams with small number of lobes (1-2). Atlarger distances (>6cm) the delivered power decreases faster, and while the beams with multiplelobes show increased power decay rate, they maintain a higher power, as compared to the beamswith smaller number of lobes.

The trend of a filament elongation was recently demonstrated experimentally by using dressedbeams, where the central Gaussian beam is surrounded by an auxiliary dressing beam, which iswider and has a lower intensity.28 Since a Bessel-like beam, which has an annular structure, pos-sesses an inward energy flux towards its optical axis,39 it is expected to be well suited to replenishthe filament core, as is confirmed by our measurements. Also, when we compare our results withrecent theoretical studies on filamentation of femtosecond beams with different transverse modesin Ar gas,26,27 we see a similar effect that the central filament-containing core in a Bessel-Gaussianbeam mode with lateral lobes is sustained for a longer propagation distance (compared to a beamwith only the central peak or a Gaussian beam). By extending the outer part of a Bessel-Gaussianbeam we have shown how addition of radial lobes helps to maintain the energy in the central peak,thus demonstrating that this outer part serves as an energy reservoir for the filaments formed in thecentral portion of the beam.

FIG. 4. Spectra (a) and average IR power (b) of the central peak of the Bessel-Gaussian beams with different number ofradial lobes measured as a function of the propagation distance.

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III. CONCLUSION

We have studied the influence of the beam mode structure of intense femtosecond laser pulseson the filament propagation length in water. With the computer-generated hologram technique anda spatial light modulator we were able to create collimated Bessel-Gaussian beam modes with theouter part consisting of different number of radial lobes and investigated how the extension of thisouter part helps to sustain the filaments in the central part of the beam during the propagation pro-cess. We have found that by increasing the number of outer radial lobes of Bessel-Gaussian beams(provided that the characteristics of the central part of the beam, such as the peak intensity, pulseduration, and beam diameter stay the same) contributes to maintaining the central intensity peakwith filaments, and thus these additional lobes serve as energy reservoir for the central portion of thebeam. Our findings demonstrate the high potential of Bessel-Gaussian beams for various nonlinearoptics applications involving the extended propagation of filaments formed by ultrafast pulses in aKerr medium.

ACKNOWLEDGMENTS

This publication was made possible by the NPRP award [NPRP 5-994-1-172] from the QatarNational Research Fund (a member of The Qatar Foundation). The authors would also like toexpress their appreciation to Robert A. Welch Foundation (Grant No. A1546) as well as Turkey’sMinistry of National Education. The statements made herein are solely the responsibility of theauthors.1 A. Couairon and A. Mysyrowicz, Physics Reports-Review Section of Physics Letters 441, 47 (2007).2 H. L. Xu and S. L. Chin, Sensors (Basel) 11, 32 (2011).3 F. Krausz and M. Ivanov, Reviews of Modern Physics 81, 163 (2009).4 E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D.

T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, Science 320, 1614 (2008).5 R. Ackermann, G. Méchain, G. Méjean, R. Bourayou, M. Rodriguez, K. Stelmaszczyk, J. Kasparian, J. Yu, E. Salmon, S.

Tzortzakis, Y. B. André, J. F. Bourrillon, L. Tamin, J. P. Cascelli, C. Campo, C. Davoise, A. Mysyrowicz, R. Sauerbrey, L.Wöste, and J. P. Wolf, Applied Physics B 82, 561 (2006).

6 P. Polynkin, M. Kolesik, A. Roberts, D. Faccio, P. Di Trapani, and J. Moloney, Optics Express 16, 15733 (2008).7 S. Akturk, B. Zhou, M. Franco, A. Couairon, and A. Mysyrowicz, Optics Communications 282, 129 (2009).8 A. Schweinsberg, J. Kuper, and R. W. Boyd, Physical Review A 84, 053837 (2011).9 A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, Optics Letters 20, 73 (1995).

10 H. E. Hernández-Figueroa, M. Zamboni-Rached, and E. Recami, Localized Waves (Wiley, 2007).11 M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, Physical Review Letters 93, 153902 (2004).12 P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, Physical Review

Letters 99, 223902 (2007).13 M. A. Porras and P. Di Trapani, Physical Review E 69, 066606 (2004).14 A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, Physical Review Letters 92, 253903 (2004).15 F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, Applied Physics Letters 83, 213 (2003).16 A. Dubietis, E. Kucinskas, G. Tamošauskas, E. Gaižauskas, M. A. Porras, and P. Di Trapani, Optics Letters 29, 2893 (2004).17 P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, Physical Review A 77, 043814 (2008).18 P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, Physical Review E 73,

056612 (2006).19 P. Polesana, D. Faccio, P. D. Trapani, A. Dubietis, A. Piskarskas, A. Couairon, and M. A. Porras, Optics Express 13, 6160

(2005).20 M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, Applied Physics Letters

97, 081102 (2010).21 M. K. Bhuyan, F. Courvoisier, H. S. Phing, O. Jedrkiewicz, S. Recchia, P. Di Trapani, and J. M. Dudley, The European

Physical Journal Special Topics 199, 101 (2011).22 M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, Optics Express 18,

566 (2010).23 J. Durnin, J. J. Miceli, and J. H. Eberly, Physical Review Letters 58, 1499 (1987).24 F. O. Fahrbach, P. Simon, and A. Rohrbach, Nature Photonics 4, 780 (2010).25 J. Durnin, J. H. Eberly, and J. J. Miceli, Optics Letters 13, 79 (1988).26 Z. Song, Z. Zhang, and T. Nakajima, Optics Express 17, 12217 (2009).27 Z. Song and T. Nakajima, Optics Express 18, 12923 (2010).28 M. Scheller, M. S. Mills, M. A. Miri, W. B. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides,

Nature Photonics 8, 297 (2014).29 J. H. Marburger, Progress in Quantum Electronics 4(Part 1), 35 (1975).30 J. Strohaber, G. Kaya, N. Kaya, N. Hart, A. A. Kolomenskii, G. G. Paulus, and H. A. Schuessler, Optics Express 19, 14321

(2011).

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. IP: 128.194.151.233 On: Wed, 09 Mar 2016

17:04:51

035001-7 Kaya et al. AIP Advances 6, 035001 (2016)

31 A. Penzkofer, A. Seilmeier, and W. Kaiser, Optics Communications 14, 363 (1975).32 S. L. Chin, W. Liu, F. Théberge, Q. Luo, S. A. Hosseini, V. P. Kandidov, O. G. Kosareva, N. Aközbek, A. Becker, and H.

Schroeder, Progress in Ultrafast Intense Laser Science III (Springer, Berlin Heidelberg, 2008), Vol. 89, p. 243.33 S. Skupin and L. Bergé, Physica D: Nonlinear Phenomena 220, 14 (2006).34 Y. Coello, B. Xu, T. L. Miller, V. V. Lozovoy, and M. Dantus, Applied Optics 46, 8394 (2007).35 A. Brodeur and S. L. Chin, Journal of the Optical Society of America B 16, 637 (1999).36 N. Kaya, J. Strohaber, A. A. Kolomenskii, G. Kaya, H. Schroeder, and H. A. Schuessler, Optics Express 20, 13337 (2012).37 A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, Physical Review A 89,

033809 (2014).38 J. Strohaber, T. D. Scarborough, and C. J. G. J. Uiterwaal, Applied Optics 46, 8583 (2007).39 G. Steinmeyer and C. Bree, Nature Photonics 8, 271 (2014).

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