Results of the experimental study of filamentation of terawatt femtosecond pulses of a Ti:Sapphire laser along an atmospheric path 106 m long using different spatial focusing and pulse power are presented. The control of filamentation region position and length by means of changing the initial laser beam focusing is shown to be highly effective. Dependencies are derived of filamentation region position and length on the initial degree of focusing, pulse power, and the number of filaments along the filamentation region. The obtained data on the filamentation region length and the number of filaments are compared with the results of our previous experiments and data from other authors

Apeksimov, Dmitrij V.

Iglakova, Anastasiya N.

Kabanov, Andrej M.

Kuchinskaya, Olesya I.

Matvienko, Gennadij G.

Oshlakov, Viktor K.

Petrov, Aleksej V.

Zemlyanov, Alexander A.

Atmospheric and Oceanic Optics

English

D. V. Apeksimov

A. A. Zemlyanov

A. N. Iglakova

A. M. Kabanov

O. I. Kuchinskaya

G. G. Matvienko

V. K. Oshlakov

A. V. Petrov

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Filamentation of terawatt laser pulses along hundred-meter atmospheric paths

Tomsk State University Repository

ISSN 10248560, Atmospheric and Oceanic Optics, 2015, Vol. 28, No. 4, pp. 372–375. © Pleiades Publishing, Ltd., 2015.Original Russian Text © D.V. Apeksimov, A.A. Zemlyanov, A.N. Iglakova, A.M. Kabanov, O.I. Kuchinskaya, G.G. Matvienko, V.K. Oshlakov, A.V. Petrov, 2015, published in OptikaAtmosfery i Okeana.372INTRODUCTIONFormation of a region of multiple filamentation ata preset distance (hundreds and thousands meters)from a source is an urgent problem for femtosecondatmospheric optics, including both sensing tasks andtransmission of light fields of extremely high intensities. To control the filamentation region (FR) position, there are several main methods: variation in thelaser pulse power, spatial and temporal focusing, variation in the initial transverse profile of beam intensity,including adaptive control [1].In this work, we consider results of the experimental study of spatial parameters of a multiple filamentation region along a 100m path controllable throughout the whole length, when the FR position and lengthare controlled with the use of variable initial spatialfocusing and a change in the pulse energy. The experimental layout is shown in Fig. 1. A mirror Galileantelescope is used as a focusing element.Figure 1a shows the filamentation of a femtosecondpulse along the path. A glow is in the red spectral range.A blackandwhite photograph of rings on the screen atthe path end is shown in Fig. 1b. On the screen, the ringcolor changes from red in the beam center to blue at thebeam periphery, which points to the filamentation alongthe path. Figure 1c shows scorches on the photosensitive paper after the filaments.FR measurement results are shown in Figs. 2 and 3for the cases of controlling the distance to the filamentation beginning using the initial spatial focusing(Fig. 2) and pulse energy (Fig. 3). It is seen than anincrease in the telescope base within a range of several centimeters (sharper focus) allows moving thefilamentation beginning and the FR along the whole100m path. Varying the pulse energy and, hence, thepower, we can vary the FR position; however, anincrease in the source–FR space is accompanied bya significant increase in the number of filaments inthis case (Fig. 4). Figure 3 also shows the dependenceof the filamentation beginning distance calculated bythe Marburger equation [2] for nonlinear focusing: where  is the Rayleigh length, r0 is thebeam radius;  is the dimensionless pulsepower, P0 is the pulse power,  is theselffocusing critical power (Pcr = 3.2 GW for air andλ = 800 nm), n0 is the refractive index of the medium,and n2 is the nonlinear refractive index.It is seen that experimental and calculated valuesagree well in the region of low pulse energies (powers),where the number of filaments in a beam is small.As the power increases, that is, under multiple filamentation, the coordinates of filamentation beginningmeasured are significantly smaller than the calculatedones, i.e., filaments are formed earlier than is forecast−= η − − 1 2 2 1 20.734    0.852   0.021[( ) ]9 ,n RF L20RL r= π λcr0P Pη =cr20 23.77 8P n n= λ πFilamentation of Terawatt Laser Pulsesalong HundredMeter Atmospheric PathsD. V. Apeksimov, A. A. Zemlyanov, A. N. Iglakova, A. M. Kabanov, O. I. Kuchinskaya, G. G. Matvienko, V. K. Oshlakov, and A. V. PetrovV.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, pl. Akademika Zueva 1, Tomsk, 634055 Russiaemail: apeximov@iao.ru, zaa@iao.ru, ian@iao.ru, kam@iao.ru, koi@iao.ru, mgg@iao.ru, ovk@iao.ru, pav@iao.ruReceived January 21, 2015Abstract—Results of the experimental study of filamentation of terawatt femtosecond pulses of a Ti:Sapphirelaser along an atmospheric path 106 m long using different spatial focusing and pulse power are presented.The control of filamentation region position and length by means of changing the initial laser beam focusingis shown to be highly effective. Dependencies are derived of filamentation region position and length on theinitial degree of focusing, pulse power, and the number of filaments along the filamentation region. Theobtained data on the filamentation region length and the number of filaments are compared with the resultsof our previous experiments and data from other authors.Keywords: laser radiation, filamentation, femtosecond pulse, liquid, spectrumDOI: 10.1134/S102485601504003XOPTICAL INSTRUMENTATIONATMOSPHERIC AND OCEANIC OPTICS  Vol. 28  No. 4  2015FILAMENTATION OF TERAWATT LASER PULSES 373by a model. This might well be connected with the factthat the Marburger equation is not applicable to thewhole beam, but for some its regions where a single filament is formed.Measurements of the number of filaments in a laserbeam crosssection have shown that it is inhomogeneous along the FR length. There are several filamentsat the beginning of the FR, the number increases up toabout two tens to the FR center, and then decreasesagain (see Fig. 4).The dependence of the maximal number of filaments on the relative pulse power is shown in Fig. 5.The increase in the number of filaments in a beamobserved agrees with our previous data [3, 4] and datafrom other authors [5–7].10 cm(a) (b) (c)2 mm100 m11 5 2014100 m6 m12345678910 111213141516Fig. 1. Experimental layout: Ti:Sapphire laser (1) (pulse length t = 30 fs, pulse energy E < 80 mJ, P < 2.5 TW, wavelength λ =800 nm, pulse frequency ν = 10 Hz, beam diameter at the level e–2 d = 2.5 cm (after telescope d = 5 cm); rotating plates (2, 3,9, and 10), pulse length meter (4) (autocorrelator), Galilean telescope (5), defocusing mirror F1 = –50 cm (6), focusing mirrorF2 = 100 cm (7), variable telescope base (intermirror space b = 50 cm corresponds to a collimated beam) (8), OPHIRII pulsepower meter (11), CCD arrays, photo cameras, and video cameras (12 and 15), movable screen for recording the FR position (13),FR (14), fixed screen at the path end (16); (a) laser beam along the path (filamentation at the beginning of the path); (b) beamstructure on the screen at the path end; (c) smallscale beam structure on the movable screen in the FR along the path (in theheterochromatic structure center).1801601401201008040200Beginning56555350 5251 54Distance, mTelescope base, cm20060EndFR lengthExtrapolationFig. 2. Coordinates of the FR beginning, end, and lengthversus the telescope base (telescope focal length).1401201008040200 8070403010 50Distance, mPulse energy, mJ60103050709011013020 60BeginningEndFR lengthCalculated beginning(Marburger equation)Fig. 3. Coordinates of the FR beginning, end, and lengthof a collimated beam versus the laser pulse energy.374ATMOSPHERIC AND OCEANIC OPTICS  Vol. 28  No. 4  2015APEKSIMOV et al.Analyzing the results of this work and our previousdata [8–11] on the FR length, one can see (Fig. 6) thatsharper focusing results in FR shortening. An increasein the pulse power at a preset numerical aperture of thebeam (NA = r0/F, where F is the length of the geometrical beam) results in an increase in the FR length.Thus, the results of the experiments performedshow the efficiency of the control of the position of amultiple filamentation region several tens of meterslong when using the initial spatial beam focusing along100m atmospheric paths with tens of filaments in abeam crosssection, localized at centimeter areas.ACKNOWLEDGMENTSThe work was supported by the Russian Foundationfor Basic Research (project no. 142802023 ofi_m).REFERENCES1. Yu. E. Geints, A. A. Zemlyanov, A. M. Kabanov, andG. G. Matvienko, Nonlinear Femtosecond AtmosphericOptics, Ed. by A.A. Zemlyanov (Publishing House ofIAO SB RAS, Tomsk, 2010) [in Russian].2. J. H. Marburger, “Selffocusing: Theory,” Prog. Quant.Electr. 4, Part 1, 35–110 (1975).3. D. V. Apeksimov, Yu. E. Geints, A. A. Zemlyanov,A. M. Kabanov, G. G. Matvienko, and A. N. Stepanov,“Filamentation of nonGaussian laser beams withdifferent geometric divergence along an atmosphericpath,” Atmos. Ocean. Opt. 26 (3), 171–177 (2013).4. Yu. E. Geints, A. A. Zemlyanov, A. M. Kabanov,G. G. Matvienko, and A. N. Stepanov, “Experimentalstudy of filamentation of highpower ultrashort laserpulses with initial angular divergence in air,” QuantumElectron. 43 (4), 350–355 (2013).5. P. Béjot, L. Bonacina, J. Extermann, M. Moret,J.P. Wolf, R. Ackermann, N. Lascoux, R. Salame,E. Salmon, J. Kasparian, L. Berge, S. Champeaux,C. Guet, N. Blanchot, O. Bonville, A. Boscheron,P. Canal, M. Castaldi, O. Hartmann, C. Lepage,L. Marmande, E. Mazataud, G. Mennerat, L. Patissou, V. Prevot, D. Raffestin, and J. Ribolzi, “32 TWatmospheric whitelight laser,” App. Phys. Lett. 90(15), 1511061–1511064 (2007).6. A. Couairon and A. Myzyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441 (2–4),47–189 (2007).7. J.F. Daigle, O. Kosareva, N. Panov, T.J. Wang,S. Hosseini, S. Yuan, G. Roy, and S. L. Chin, “Formation and evolution of intense, postfilamentation, ion100 80604020Number of filamentsDistance, m15520Fig. 4. Number of filaments in a beam crosssection alongthe atmospheric path for a collimated beam with pulseenergy of 82 mJ.1001011000010 100 1000Number of filamentsP0/Pcr1000Fig. 5. Number of filaments versus the relative pulse power.Dots correspond to data [3, 4], empty circles, to data [5–7],and the asterisk shows data of this work.10.10.010.011E–5 1E–4 1E–3FR length, mNA10010 GW [8–10]101E–330 GW [8–10]100 GW [11]TWFig. 6. Experimental data from works [8–11] and this work(empty circles) on the length of the multiple filamentationregion in air versus the numerical beam aperture for different pulse power.ATMOSPHERIC AND OCEANIC OPTICS  Vol. 28  No. 4  2015FILAMENTATION OF TERAWATT LASER PULSES 375izationfree low divergence beams,” Opt. Commun. 284(2–4), 47–189 (2011).8. Yu. E. Geints, S. S. Golik, A. A. Zemlyanov,A. M. Kabanov, and G. G. Matvienko, “Influence ofthe laser beam size on the length of a filament formedby highpower femtosecond laser radiation in air,”Quantum Electron. 44 (5), 489–497 (2014).9. D. V. Apeximov, E. E. Bykova, Yu. E. Geints, A. A. Zemlyanov, A. M. Kabanov, G. G. Matvienko, V. K. Oshlakov, A. V. Petrov, O. A. Bukin, A. A. Ilyin, E. B. Sokolova,and S. S. Golik, “Filamentation of a focused Ti:Sapphirelaser pulse at two harmonics in air,” Plasma Phys.Rep. 39 (13), 1074–1081 (2013).10. D. V. Apeksimov, O. A. Bukin, E. E. Bykova,Yu. E. Geints, S. S. Golik, A. A. Zemlyanov, A. M. Kabanov, and G. G. Matvienko, “Filamentation length ofhighpower sharply focused femtosecond laser radiation in air. Effect of light beam size,” Atmos. Ocean.Opt. 26 (6), 539–544 (2013).11. D. V. Apeksimov, O. A. Bukin, S. S. Golik, A. A. Zemlyanov, A. M. Kabanov, O. I. Kuchinskaya, G. G. Matvienko, V. K. Oshlakov, A. V. Petrov, E. B. Sokolova,and E. E. Khoroshaeva, “Spatial characteristics of thefilamentation region of gigawatt laser pulses at theirvarious focusing along an atmospheric path,” Opt.Atmos. Okeana 27 (12), 1042–1046 (2014).Translated by O. Ponomareva

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Filamentation of terawatt laser pulses along hundred-meter atmospheric paths

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