Filamentation of femtosecond laser pulses governed ... - OSA Publishing

Ionin et al.

Vol. 30, No. 8 / August 2013 / J. Opt. Soc. Am. B

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Filamentation of femtosecond laser pulses governed by variable wavefront distortions via a deformable mirror A. A. Ionin,1,5 N. G. Iroshnikov,2,3 O. G. Kosareva,2,6 A. V. Larichev,2,3 D. V. Mokrousova,1,4 N. A. Panov,2 L. V. Seleznev,1 D. V. Sinitsyn,1 and E. S. Sunchugasheva1,4 1

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy prospect, Moscow, Russian Federation 2 International Laser Center and Physics Faculty, Lomonosov Moscow State University, 1 Leninskie gory, Moscow, Russian Federation 3 Institute on Laser and Information Technologies of RAS, 1 Svyatoozerskaya St., Shatura, Moscow Region, Russian Federation 4 Moscow Institute of Physics and Technology, 9 Institutskiy Pereulok, Dolgoprudny, Moscow Region, Russian Federation 5 e-mail: [email protected] 6 e-mail: [email protected] Received April 25, 2013; revised June 24, 2013; accepted June 28, 2013; posted July 2, 2013 (Doc. ID 189362); published July 24, 2013 Filamentation of focused UV and IR femtosecond laser pulses and plasma channel formation governed by variable wavefront distortions was experimentally and numerically studied. A deformable mirror was used to control the plasma channel length by introducing a spherical aberration into the initial transverse spatial distribution of a femtosecond laser pulse. An at least double increase of the plasma channel length was observed with increasing deformation of the mirror. Numerical calculations show that the hat-like phase shape of the aberration ensures that the energy of the initial laser pulse remains confined for a longer distance within the limited transverse size of the filament. © 2013 Optical Society of America OCIS codes: (080.1010) Aberrations (global); (120.5060) Phase modulation; (140.7090) Ultrafast lasers; (190.3270) Kerr effect; (190.7110) Ultrafast nonlinear optics; (190.5530) Pulse propagation and temporal solitons. http://dx.doi.org/10.1364/JOSAB.30.002257

1. INTRODUCTION Propagation of an ultrashort laser pulse with a peak power higher than the critical power for self-focusing in the air initiates its energy localization and leads to filament formation. The filamentation phenomenon [1–5] is associated with the nonlinear-optical interaction of ultrashort laser radiation with the medium. The major physical effects are self-focusing [6] and optical-field-induced ionization [7]. The combined action of these effects leads to the formation of long plasma channels. These plasma channels can serve for a number of applications, including lightning protection systems [8–10] and triggering and guiding electric discharge [11–17]. Ultraviolet (UV) laser radiation is of great interest, since the multiphoton ionization probability is essentially higher than that for infrared (IR) radiation [18]. A series of experiments was conducted using a Ti:sapphire/KrF laser system that is able to amplify subpicosecond UV pulses up to ∼1 J energy [15,16,19,20]. This system was used for triggering and guiding electric discharge, including triggering and guiding the discharge by a train of subpicosecond UV pulses [14–17]. Triggering and guiding electric discharge requires a certain length of the plasma channel produced due to filamentation. Several approaches have been used to increase the filament length. Introduction of a negative chirp into the initial pulse 0740-3224/13/082257-06$15.00/0

was applied to atmospheric long-distance femtosecond pulse propagation [21–23]. Another way to control the filament length is to influence the distribution of either the intensity or the phase of the initial laser beam. A variable-diameter iris can be adjusted in the beam path in such a way that a stabilized bunch of multiple filaments is produced and sustains the plasma channel over a much longer distance [24,25] than irregularly spaced hot spots. It was shown in [26] that a diaphragm of different shape (triangular, circle, segmented) can control filament position and length. Control of multiple filaments can also be achieved by producing well-controlled phase aberrations in the input beam. One example of efficient phase control is using a conical lens, or an axicon. Axicon focusing leads to a long and homogeneous plasma channel [27,28]. Among the disadvantages of this method is high energy leakage out of the filament due to the nature of the Bessel beam produced by the axicon lens [27]. In addition, the filament starts very close to the top of the axicon lens, and it is quite difficult to deliver the filament and plasma channel to the remote location. Another way of applying phase control is to use a deformable mirror [29], with which an order of magnitude increase in the fluorescence signal irradiated by the plasma channel was observed at a distance of 120 m from the mirror. The advantage of using a deformable mirror © 2013 Optical Society of America

J. Opt. Soc. Am. B / Vol. 30, No. 8 / August 2013

Ionin et al.

instead of regular transmission optics is avoiding self-phase modulation and self-focusing in optical materials. Also, the type and strength of wavefront deformation of the input laser beam can be varied with such a mirror. It should be noted that before now adaptive optics has been used in experiments with filaments either for focusing a femtosecond laser beam or for eliminating its aberrations [29–31]. To our knowledge there have been no publications related to introducing, into the laser beam, wavefront controllable aberrations aimed at governing filaments and accompanying plasma channels. Our objective in this paper is to experimentally and numerically study filamentation of focused femtosecond laser pulses governed by variable wavefront distortions, including spherical aberrations introduced by a deformable mirror. The plasma channel length of the laser radiation is demonstrated to be elongated with the increase of the mirror deformation. The numerical simulations are in a good agreement with the experimental data. The simulations are aimed at understanding how the phase shape introduced by the mirror deformation leads to the increase of the filament and plasma channel length.

2. EXPERIMENT The experimental setup consisted of a Ti:sapphire laser facility with a central wavelength of 744 nm and a pulse duration of 100 fs. The output laser pulse was directed to a third-harmonic generator made of KDP/BBO crystals. The third-harmonic UV pulse (248 nm) passed through the electron-beam KrF laser amplifier and spatial filter (see details in [14–17,20]). The beam was widened up to 5 cm in diameter, collimated, and directed to a wavefront correction system. The system consisted of two basic elements—the wavefront sensor with a matching telescope, and the unimorph deformable mirror with high UV reflection. The sensor was developed according to a Shack– Hartmann scheme and had an image sensor without protective glass to extend the spectral range to the UV region, down to the wavelength of ∼200 nm. The lens raster of the sensor was fabricated from fused silica with a step of 30 μm. The telescope was also made of fused silica with a specially designed objective to minimize spherical and coma aberrations. The telescope had a magnification factor of ∼10× and a working aperture of 60 mm. The deformable mirror was manufactured through the unimorph technology with a hexagonal arrangement of 59 controlling electrodes. The adaptive optical system was optimized to be used with a UV femtosecond laser pulse with a central wavelength of 248 nm. The laser pulse was focused by the quartz lens with the focal distance of 1 m. The far-field spatial distribution of the laser pulse, attenuated down to 3 μJ, was distorted because of the long (several tens of meters) path through the air and optical windows of the KrF laser amplifier and spatial filter [Fig. 1(a)]. When the wavefront correction system was introduced into the beam, the low-order aberrations were eliminated, and the far-field pattern was improved [Fig. 1(b)]. The dynamic range of the deformable mirror allowed us to add some artificial spherical aberrations. In the course of measurements the phase along the radial direction of the beam was changing according to the Zernike polynomial: p φr k 56r∕a0 4 − 6r∕a0 2 1 × AZ ;

(1)

Fig. 1. Far-field images of the UV pulse (248 nm) passed through the air, e-beam KrF laser amplifier, and spatial filter (a) without and (b) with wavefront correction. The image area is 600 μm × 600 μm.

where e−1 beam diameter 2a0 was 5 cm in the experiment and the amplitude of the mirror deformations AZ was varied from 0 to 0.18 μm (Fig. 2). The first series of experiments was conducted with UV pulses with a laser energy of about 0.2 mJ at a pulse duration of 100 fs. The radiation was focused with the lens, and the laser beam profile was registered with a CCD matrix Spiricon SP620 at different distances from the geometrical focus position. The beam diameter was determined for each of the registered images (Fig. 3). Even though the peak power of the UV laser pulse exceeded the critical power of ∼0.1 GW by an order of magnitude, only a single filament was formed in the experiment. The confined propagation is characterized by the length along which the transverse beam size remains relatively constant. The plasma diameter obtained in our experiment is within the typical range of 20–100 μm published

Fig. 2. Transverse spatial profile of the phase deformations φx; y, 2a0 5 cm

Filament diameter, µm

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filament length with spherical aberration

87.5

spherical aberration without aberrations

75.0 62.5 50.0 37.5 25.0 -40

filament length without spherical aberration

-30

-20

-10

0

10

20

30

Shift from the geometrical focus position, mm

Fig. 3. Beam diameter measured by CCD camera at 248 nm for different distances from the geometrical focus position corresponding to 0 mm. The horizontal dotted line shows the level of 55 μm, while the two horizontal arrows indicate the filament extension with (squares) and without (circles) spherical aberrations.

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in the literature [32,33]. As a criterion of the confined propagation regime we choose the characteristic hot spot diameter below or equal to 55 μm, above which the width of the filament formed without spherical aberrations starts to increase more rapidly and confined propagation no longer exists. The longitudinal distance along which the filament diameter remains less than the characteristic diameter is indicated by the dashed horizontal line in Fig. 3. Note that the length of the filament produced by the beam with spherical aberrations is almost twice as long as the filament length created by the beam without aberrations (compare the two horizontal arrows in Fig. 3). The second series of experiments was carried out with IR laser pulses centered at 744 nm. After the compressor the laser beam was expanded with the off-axis telescope up to a diameter of 30 mm. Afterward the radiation was sent to the wavefront correction system (Fig. 4). After the wavefront corrections and introduction of additional spherical aberrations, the radiation was focused into the air by means of the lens with a focal distance of 70 cm. The laser energy was 2 mJ, which was controlled by an energy meter situated directly behind the lens. For all the laser shots only a single filament was experimentally observed, even though the IR laser pulse peak power (more than 20 GW) was about three times the critical one used in our calculations (see below). Thus, there was no multifilamentation in the experiment. A single femtosecond filament started in front of the geometrical focus of the lens. The extended plasma channel accompanying the filament was visualized from the side by means of the CCD matrix (Spiricon SP620). A remarkable increase of the filament length with the increasing amplitude of the spherical aberration was observed (Fig. 5). (The geometrical focus is not shown in the figure because introduction of the spherical aberration resulted in a small change of the focus distance in the experiment).

3. NUMERICAL SIMULATIONS AND DISCUSSION Numerical simulations of the pulse propagation in the air have been performed based on the slowly evolving wave approximation [1]. The equation for the slowly varying light field amplitude Er; z; τ in the case of cylindrical symmetry, which we can assume because of the experimental fact of a single filament formation, is given by 2ik0

∞ X ∂E kn ∂n E Tˆ −1 Δ⊥ E − k0 ∂Z in n! ∂τn n2

ˆ ˆ −1 2k20 TΔn k T Δnp E − ik0 αr; τE;

(2)

where τ t − z∕vg is the pulse time, Z is the propagation distance, Δ⊥ r −1 ∂∕∂rr∂∕∂r is the transversal Laplacian

Fig. 4 Experimental setup for introducing spherical aberrations into the laser beam profile.

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(b)

(c)

Fig. 5 Side images of plasma channels for different spherical aberrations of amplitude AZ introduced by the deformable mirror. (a) AZ 0, (b) AZ 0.1 μm, and (c) AZ 0.18 μm. The image longitudinal size is 35 mm. The vertical dashed lines indicate the brightest part of the channels with the length of 12 mm. The laser pulse is directed from the right-hand side.

describing diffraction, ω0 and k0 are the laser central frequency and the corresponding wavenumber, and νg is the group velocity corresponding to the frequency ω0 . The second term on the right-hand side of Eq. (2) describes material dispersion including the second and the higher orders (kn is the dispersion coefficient of the nth order). The values Δnk and Δnn in the third term on the right-hand side of Eq. (2) represent Kerr and plasma nonlinearities, respectively. The function αr; τ is responsible for the ionization energy loss in the air. Operator T 1 i∕ω0 ∂∕∂τ describes self-steepening [1]. In the simulations the critical power for self-focusing in the air was taken as P cr ≈ 10 GW for a 45 fs laser pulse with the wavelength 744 nm propagating in atmospheric pressure air according to the experiment. This magnitude of the critical power of self-focusing in air corresponds to its direct measurement for a laser pulse with ∼50 fs duration [34]. The experimental results [35] obtained for femtosecond radiation with similar duration and low quality of spatial mode are in good agreement with [34]. The self-consistent plasma production was taken into account through the contribution to the refractive index, the real part of which is represented by Δnp r; z; τ −

2πe2 N e : me ω20

(3)

Here me and e are electron mass and charge, respectively, and N e is the free-electron density, which is calculated according to the rate equations with the ionization probability of nitrogen or oxygen molecules taken from [7]. In the simulations the initial pulse is Gaussian with the wavefront φr [Eq. (1)], corresponding to the spherical aberration introduced by the deformable mirror in the experiment: 2 r τ2 k r2 Er;z 0;τ E 0 exp − 2 − 2 × exp i 0 iφr : (4) 2F 2a0 2τ0 The beam radius is a0 1.2 mm, the half-pulse duration is τ0 27 fs, and the pulse energy is 1.5 mJ. The geometrical focusing distance is F 226 cm. The beam radius a0 in the simulations was smaller than in the experiment in order to preserve good spatiotemporal resolution on the 3D-plus-time grid. In the simulation we used the same ratio Az ∕k0 a20 of the mirror deformation amplitude AZ to the diffraction length k0 a20 as was used in the experiment. Therefore, the absolute values of the mirror deformation amplitude AZsim will be smaller in the simulations than in the experiment AZexp . At the

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Fig. 6. Elongation of simulated femtosecond filaments. The amplitude of the wavefront deformations corresponds to (a) AZ 0, (b) AZ 0.1 μm, and (c) AZ 0.18 μm.

same time, the ratio AZsim ∕k0 a20sim AZ exp ∕k0 a20 exp remains unchanged when we simulate the filament with spherical aberrations in the initial wavefront. The simulations show that in the linear regime the spherical aberration leads to the elongation of the focal zone by a factor of 1.5 with the beam wavefront distortion corresponding to AZ 0.15 μm as compared to the case without distortion. Self-focusing and filamentation enhance the elongation effect. Both experimentally registered and simulated filaments reveal more than double plasma channel length increase with the increase of the spherical aberration amplitude AZ from 0 to 0.15 μm (compare panels (a) and (c) in Figs. 5 and 6). The structure of the simulated channels is in good qualitative agreement with the experiment. Indeed, without spherical aberrations the channel is comparatively bright and short [Figs. 5(a) and 6(a)]. The arrows [Fig. 5(a)] and the white contour line [Fig. 6(a)] define the intense fluence region at 0.1 of the maximum fluence value. With the increase of the spherical aberration amplitude the length of this selected region is preserved and the overall channel length increases by a factor of at least 2 [Figs. 5(b), 5(c) and 6(b),6(c)]. Comparison between the experimentally obtained and calculated channel dynamics shows that numerical simulations reproduce filamentation controlled by the spherical aberrations in an adequate way (Fig. 6). The loose geometrical focusing chosen in the simulations allows us to further reveal the effect of wavefront deformation on the channel shape, which is not straightforward in the experiment. The detailed structure of the channels is shown by the contours of equal fluence in Figs. 7(a) and 7(b). Without spherical aberrations the radiation diverges out of the channel at a larger angle than in the case with the spherical aberration [compare Figs. 7(a) and 7(b)]. The local minima or the “brim” of the hat-like phase of the spherical aberration (Fig. 2) keep the radiation within a limited transverse area for a longer distance [Fig. 7(b)] than without the aberration [Fig. 7(a)]. Quantitatively, the change of the filament channel properties in the presence of spherical aberrations is characterized by the amount of energy outgoing from the channel [Fig. 7 (c)]. The two curves in Fig. 7(c) show how much energy is outside the round-shaped near-axis area with the radius equal

Fig. 7. Contour maps of the simulated filament channels obtained (a) without the wavefront distortions and (b) with the maximum wavefront distortion, which corresponds to AZ 0.18 μm. The interval between the lowest and the nearest contours is 0.0025 J∕cm2 ; all the other contour intervals are 0.005 J∕cm2 . (c) Energy leaking out from the channel region in the case of the maximum AZ 0.18 μm wavefront deformation (stars) and without the wavefront deformations (circles).

to the initial beam radius a0 . If there are no spherical aberrations in the beam phase, than the energy pulsations in the channel are very high, up to 80% [Fig. 7(c), circles] of the total beam energy. At the beginning of the propagation all the energy flows inside the area with the initial beam radius a0 ; then 80% of the beam energy flows outside this area. The critical effect of spherical aberration introduced into the beam is the decrease in both the energy flowing inside the near-axis area and the energy flowing outside [Fig. 7(c), stars]. The energy variation in the near-axis area decreases to 35% of the total beam energy. This energy variation decrease quantitatively demonstrates that the spherical aberration leads to the decrease in the energy outflow from the filament. If the outflow decreases, then the filament can be sustained for longer distance. That is why we observe filament elongation in the presence of spherical aberrations in the laser beam profile.

4. CONCLUSIONS Filamentation of focused UV and IR femtosecond laser pulses and plasma channel formation governed by variable wavefront distortions was experimentally and numerically studied. A deformable mirror was used to control the plasma channel length by introducing a spherical aberration into the initial transverse spatial distribution of a femtosecond laser pulse.

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At least a double increase of the plasma channel length was observed with increasing deformation of the mirror. Numerical calculations show that the hat-like phase shape of the aberration ensures that the energy of the initial laser pulse remains confined for a longer distance within the limited transverse size of the filament.

ACKNOWLDEGMENTS We acknowledge support from the Russian Foundation for Basic Research (grants 11-02-12061-оfi-m, 11-02-01100, 1202-01368, 12-02-31341, 12-02-33029), EOARD Project 097007 going through ISTC Partner Project 4073 P, the LPI Educational-Scientific Complex, the Council of the President of the RF for Support of Young Scientists (5996.2012.2), Leading Scientist Schools (6897.2012.2), and the Ministry of Education and Science of the RF (8393), Dynasty Foundation.

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