s.l. chin et al- interference of transverse rings in multifilamentation of powerful femtosecond...

8/3/2019 S.L. Chin et al- Interference of transverse rings in multifilamentation of powerful femtosecond laser pulses in air

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Interference of transverse rings in multifilamentation

of powerful femtosecond laser pulses in air

S.L. China, S. Petita, W. Liua, A. Iwasakia, M.-C. Nadeaua, V.P. Kandidovb,O.G. Kosarevab,*, K.Yu. Andrianovb

a

Centre dOptique, Photonique, et Laser (COPL) and Dept. de Physique, de G

eenie Physique et dOptique,Universitee Laval, Que., Canada G1K 7P4

b Physics Department, International Laser Center, Moscow State University, Moscow 119899, Russia

Received 30 January 2002; received in revised form 28 June 2002; accepted 16 July 2002

Abstract

We observe multiple filaments and interference of their ring structures in the propagation of 14 mJ, 45 fs infrared

laser pulse in air. We suggest a simple physical model describing the formation and the interference of rings as the result

of superposition of the background field of the whole beam and the fields that diverge from the filaments due to the

defocusing in the laser-produced plasma. The size and the number of maxima in the interference pattern depend on the

position of the filament formation along the direction of propagation. The simulated picture of the ring structure in-

terference is in qualitative agreement with the one obtained from the experiment. 2002 Elsevier Science B.V. All

rights reserved.

PACS: 42.25.Hz; 42.65.Jx; 42.65.Re; 52.35.Mw; 32.80.Fb

Keywords: Interference; Multiple filamentation; Self-focusing; Photoionization

1. Introduction

Filamentation of powerful femtosecond laserpulses in air is now a subject of intense experi-

mental and theoretical study. In the first experi-

ments [13] pulses generated by Ti:sapphire laser

amplification systems were used with the duration

150230 fs and peak power 550 GW. In these

experiments part of the pulse energy was concen-

trated in the narrow near-axis region with the di-

ameter of the order of 100 lm and stayed localized

there for propagation distances of several tens ofmeters. Filamentation was accompanied by the

conical emission with continuum spectrum in the

range 500800 nm [2,4]. Later [5] it was found that

a white-light continuum generated in air by 2-TW

35 fs laser pulses at 800 nm extends at least from

300 nm to 4.5 lm. Generation of wideband spec-

tral continuum is of considerable current interest

in view of potential LIDAR applications [6,7].

Filamentation of powerful femtosecond la-

ser pulses arises because of the joint effect of

15 September 2002

Optics Communications 210 (2002) 329341

www.elsevier.com/locate/optcom

* Corresponding author. Fax: +709-59-393-113.

E-mail address: [email protected] (O.G. Kosar-

eva).

0030-4018/02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved.

P II: S0 0 3 0 -4 0 1 8 (0 2 )0 1 8 0 8 -4
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self-focusing due to Kerr nonlinearity of air and

defocusing in the laser-produced plasma. In the

course of propagation the intensity increase due to

self-focusing is replaced by strong aberrationaldefocusing as soon as the ionization threshold of

air is achieved. As a result, dynamic ring structure

in the transverse intensity distribution is created.

Formation of a ring structure in the propagation

of intense subpicosecond laser pulses in gases was

for the first time reported in [8], where 0.9 ps and

90 fs pulses with the wavelength 620 nm were fo-

cused in xenon gas at a pressure of 50 Torr. At the

output of the gas cell a beam profile with the ring

created due to the ionization was observed. The

disintegration of transverse intensity distribution

into multiple rings was observed in the conditions

of resonant interaction of a picosecond pulse with

Ba and Cs vapor [9]. A detailed experimental and

theoretical study of ring structure created in the

course of filamentation was performed in [10]. In

this experiment 320 and 350 fs pulses with the

energy 75 and 85 mJ, respectively, were used. A

beam with a diameter of 1 cm was focused by a

lens with a focal length of 150 cm. For the regis-

tration of transverse fluence distribution a silicate

glass plate was inserted at various positions in the

vicinity of the geometrical focus. The damagepattern created by the laser pulse on the glass plate

showed formation of multiple concentric rings

surrounding a wide near-axis part of the beam.

The observation of rings in the filamentation of

focused ultraviolet pulses (k 248 nm) with theduration 450 fs, incident energy 2 mJ and focusing

length of the lens 9.5 m was performed in [11,12].

The appearance of ring patterns could be seen in

the burn spots of the laser beam on UV photo-

graphic paper recorded at various distances along

the propagation direction. It was found in thesimulations [12] that at the stage of the filament

formation the rings were merging inward to the

beam center. After the filament formation the

rings were travelling outward in agreement with

the observations in the infrared pulse filamenta-

tion [10].

Theoretical investigation of transverse ring

formation in the propagation of powerful femto-

and picosecond laser pulses in gases was discussed

in several publications. The author of [13] calcu-

lated the map of spectral blueshift in the transverse

intensity rings of the pulse focused in argon at

atmospheric pressure. Peak vacuum intensity of

the pulse was 1015

10

16

W=cm2

. In these condi-tions a local intensity minimum arises at the

trailing part of the pulse due to the defocusing in

the laser-produced plasma [14]. As the gas pressure

increases up to 5 atm the contribution of plasma to

the nonlinear refraction of the pulse increases. As

a result multiple rings are formed in the transverse

section of the pulse. In [15] it is demonstrated that

multiple ring formation results from spatio-tem-

poral instability of the radiation in the conditions

of self-focusing and nontransient defocusing in the

laser-produced plasma. The reason for dynamic

instability is shown to be in the temporal depen-

dence of the medium nonlinear response, i.e., dis-

persion of the nonlinearity.

Formation of rings in the course of filamenta-

tion of infrared pulses in air was numerically

studied in [10,16,17]. In [16] it was shown that

formation of rings in the transverse section of the

beam is caused by the temporal growth of the

negative contribution to the refractive index on

the beam axis. This negative contribution is asso-

ciated with a growing number of free electrons on

the beam axis. The ring structure in the transversefluence distribution was obtained in [17] without

consideration of the group velocity dispersion in

air. In [18,19] it was demonstrated that group ve-

locity dispersion essentially affects the spatio-tem-

poral transformation of the pulse in the course of

filamentation. Due to dispersion, the intensity

growth caused by self-focusing slows down and

plasma-induced defocusing occurs at lower inten-

sity on the beam axis. A close relation between the

spatial rings in the intensity distribution and the

conical emission accompanying filamentation hasbeen studied in [19] in details. It was demonstrated

that the spatio-temporal gradients of the phase of

the electric field complex amplitude cause strong

broadening of the frequency-angular spectrum of

the pulse and the generation of supercontinuum

conical emission.

In view of possible LIDAR applications of

white light continuum, filamentation of pulses with

terawatt peak power is of considerable current

interest. Such peak power is several hundred times

330 S.L. Chin et al. / Optics Communications 210 (2002) 329341


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higher than the critical power for self-focusing in

air of the pulse with 800 nm laser wavelength.

Therefore, multiple filaments are produced.

Breakup of high power laser beam into multiplefilaments results from modulational instability of

the light field in the Kerr medium. In [20] at the

initial stage of propagation the increase of the

spatial nonuniformity in the beam intensity profile

was observed. However, not all nonuniformities

developed into the filaments. Initial stage of fila-

mentation in the presence of large-scale perturba-

tions in the beam profile has been experimentally

and theoretically studied in [21]. For femtosecond

pulses propagating in air with peak power lying

between 5 and 25 critical powers for self-focusing a

breakup of the beam into two spots due to mod-

ulational instability was observed. Later in the

propagation the two spots coalesced into one

central lobe and a single filament was formed.

Dynamics of multifilamentation process of the

pulse with initial spatial modulation of the electric

field was numerically studied in [22]. A spatio-

temporal picture of multifilamentation reproduces

initial beam breakup due to modulational insta-

bility, regularization of collapsing filaments via

plasma defocusing, recurrement and merging of

filaments in the course of propagation. These col-lapse events lead to the formation of optical tur-

bulence. The dominant regularizing mechanism of

this process is defocusing in the laser-produced

plasma. Formation of filaments in the conditions

of natural atmospheric turbulence was studied in

[23]. Refractive index fluctuations in the turbulent

air were shown to be the seed for the development

of modulational instability in the laser pulse with

peak power larger than the critical power for self-

focusing. As a result, filaments in the turbulent air

experience random wandering in the plane per-pendicular to the propagation direction.

In this paper we study the formation of several

filaments in the pulse with essentially nonmono-

tonic distribution of fluence in the transverse sec-

tion. We have observed experimentally and

confirmed this observation numerically that fila-

ments are created at different distances from the

laser system output. We present the results on the

observation of ring structures arising from several

filaments produced by 0.3 TW laser pulse at

800 nm. The interference of transverse rings cre-

ated by two closely spaced filaments is registered

and a simple physical model is suggested that

clearly explains the observed phenomenon.

2. Experimental setup and initial beam characteris-

tics

The experiment was performed with a brand

new commercial (Spectra Physics) Ti:sapphire

chirped-pulse-amplification laser system that is

able to emit three beams simultaneously. We used

the most powerful channel of this laser system that

consists of a MaiTai oscillator, stretcher, regen-

erative amplifier, pulse slicer, four pass amplifier

with 16 mm sapphire rod and vacuum compressor.

The output pulse was at 800 nm with the duration

45 fs FWHM and maximum energy 130 mJ. The

repetition rate was 10 Hz. The energy of the pulse

was controlled by a half-wave plate and a polarizer

located before the amplifier. The pulses with the

energy in the range 740 mJ (with the corre-

sponding peak powers 0.150.8 TW) were studied.

The laser system at the time of this experiment was

not yet optimized, hence the double spot spatial

distribution was created in the pulse. This was justthe right condition to investigate the multiple fil-

aments and their interference.

The beam was sent into a long hallway by

means of alignment optics and a periscope (Fig. 1).

In order to decrease the influence of turbulence

and self-focusing before launching the pulse into

the hallway, the propagation path was arranged

inside a stainless steel pipeline with a length of

about 10 m and a diameter of about 20 cm. The

optical pipeline was constructed from separate

sections. The pipeline was thoroughly cleanedchemically; and was linked directly onto the vac-

uum compressor. The output CaF2 window was

12.5 cm in diameter and 1 cm thick. The whole

system (vacuum compressor and pipeline) was first

pumped down by an oil free mechanical pump. It

was then filled up with He up to 1 atmospheric

pressure.

After coming out from the stainless steel pipe-

line and the periscope, the beam was directed

through connected sections of carton pipes of

S.L. Chin et al. / Optics Communications 210 (2002) 329341 331


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about 20 cm in diameter in order to minimize air

turbulence. The total length of the carton pipes

was about 96 m while the bulk of our measurement

was done at 87 m.

Fluence distribution in the transverse beam

section was reproduced on the screen and imaged

onto a CCD camera with a dynamic range of 256

grades. Neutral density filters were used in order to

measure the fluence distribution in different ran-

ges: in the filament, where the fluence takes its

maximum, or in the beam background, where the

fluence is several orders of magnitude lower than

in the filament. Before each series of measurementsthe transverse beam size was calibrated with a

scale grid that was put on the screen and imaged

onto the CCD camera.

The initial beam shape was elliptical and its

transverse size at e1 fluence level was 2.0 cm inone dimension and 1.5 cm in the other dimension.

Spatial distribution of fluence Fx;y was essen-tially nonunimodal and this nonunimodal struc-

ture was not a function of the pulse energy.

Typical distributions Fx;y for the pulses with theenergy 550 mJ are shown in Fig. 2. Fluence dis-tribution Fx;y can be divided into two large-scale spatial regions 1 and 2 with their own max-

ima maxfF1g and maxfF2g, respectively. In orderto see the fluence distribution in these two regions

better we show the cross-section of the fluence

distribution Fc along the line CC0 for each pulseenergy under discussion. The line CC0 joints twomaxima max{F1} and max{F2}. The line DD

0,which is perpendicular to the line CC0 and crossesit in the local minimum between the maxima

Fig. 1. Scheme of the experiment. 1 laser system, 2 steel pipeline with a length of about 10 m, 3 output window to the hallway,

4,5 periscope mirrors, 6 carton pipes with 20 cm diameter, 7 registration screen, 8 CCD camera, 9 computer.

Fig. 2. Experimentally measured transverse fluence distribu-

tions Fx;y and fluence profiles Fc along the line CC0 at thelaser system output z 0. The distributions Fx;y and Fcare normalized to the maximum of fluence in the output beam

z 0. Characteristic spatial regions with the two local max-ima of fluence distribution are marked by the numbers 1 and 2.

The ratio W1;2=W shows relative amount of energy in these re-

gions.

332 S.L. Chin et al. / Optics Communications 210 (2002) 329341


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max{F1} and max{F2}, can be considered as the

boundary between the regions 1 and 2.

The values of the maxima max{F1} and

max{F2} are close to each other and the differencebetween them does not exceed 1015% of the

largest maximum. However, the amount of energy

in the regions 1 and 2 is essentially different. To

define the relative amount of energy W1=W orW2=W contained in each region we used the fol-lowing estimate:

W1;2

WRR1;2

Fx;ydxdyR1Fx;ydxdy

; 1

where R1;2 are the subareas in the transverse beam

section separated by the line DD0 and Wis the totalenergy. For the series of measurements performedfor different laser energies W1=W 0:60:7;W2=W 0:30:4.

In addition to large-scale fluctuations in the

laser energy, the size of which corresponds to the

regions 1 and 2, each region contains small-scale

fluctuations (Fig. 2, cross sections along the line

CC0). Small-scale structure in the distribution

Fx;y varied from shot to shot. However, thegeometric position of the regions 1 and 2 remained

unchanged. Therefore, for the pulses with the same

total energy the picture of the filament formationdepended only on the ratio between W1 and W2.

3. Filament formation

Measurements of fluence Fx;y were per-formed at different laser energies W at a distance

z 87 m defined by the length of the cartonpipeline. Typical fluence distributions and fluence

cross-section Fc are shown in Fig. 3.For an energy ofW 7 mJ spatial localizationof energy due to Kerr self-focusing in the regions

1 and 2 only starts to develop at a distance of

measurements (Fig. 3(a)). In the 10 mJ pulse self-

focusing leads to the formation of two maxima

with high fluence value (Fig. 3(b)). The first re-

gion contains more energy and self-focuses into

the maximum that is higher and narrower than

the maximum created in the second region. This

Fig. 3. Experimentally measured transverse fluence distributions Fx;y and fluence profiles Fc for different input laser pulse en-ergies: (a) 7, (b) 10, (c) 14 mJ. Propagation distance z 87 m. The distributions Fx;y and Fc are normalized to the maximumof fluence obtained at z 87 m for the corresponding pulse energy.

S.L. Chin et al. / Optics Communications 210 (2002) 329341 333


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is the evidence for the fact that in the region 1 we

have a developed filament at a distance of 87 m

while in region 2 the filament development is still

underway. For an energy of W 14 mJ the dis-tribution of fluence reveals two narrow and in-tense maxima that correspond to the two

developed filaments (Fig. 3(c)). The peak value of

fluence, the width, and the amount of energy are

nearly the same for both filaments. Stabilization

of the parameters for the developed filaments is

associated with the defocusing of the radiation in

the laser-produced plasma. This phenomenon of

intensity clamping in the course of filamentation

was recently considered in gases [24,25] and

condensed matter [26].

The redistribution of fluence at z 87 m shownin Fig. 3 demonstrates the process of successive

formation of filaments. Their development may be

considered independently in each of the regions 1

and 2. Indeed, the value of the peak power P1;2 in

each region can be calculated from the amount of

energy W1;2 under the assumption of Gaussian

pulse shape

Et E0 exp t2=2s20; 2

where s0 is half of the pulse duration at e1 in-

tensity level. According to Eq. (2) the peak poweris P1=2 W1=2=

ffiffiffip

ps0. For the pulse duration of

45 fs FWHM the value s0 is equal to 27 fs. If the

total energy of the pulse is 7 mJ then P1 % 90100GW in the first region and P2 % 4060 GW in thesecond region. The values P1 and P2 exceed the

critical power for self-focusing in air Pcr. To find

the starting position of the filament, we, accord-

ing to the moving focus model [27], consider the

self-focusing distance for the central slice of the

pulse [28]

znf1;2 0:367ka21;2

P1;2=Pcr1=2 0:852; 3

where a1;2 is the radius of the regions 1, 2, re-

spectively, estimated at e1 level of the measuredfluence distribution and Pcr is the effective value ofthe critical power for self-focusing. The moving

focus model, which gives us the nonlinear focus

position (3), is well established only in the initial

stage of the filament formation. After the filament

is formed, the nonlinear refraction in the plasma

takes place and we cannot apply Eq. (3) for the

description of filamentation at z> znf.The value Pcr is defined by the third-order

nonlinearity of neutral air molecules that has in-stant electronic contribution and delayed contri-

bution due to the stimulated Raman scattering on

rotational transitions of oxygen and nitrogen

molecules. The time of the delayed cubic nonlinear

response is of the order of 1013 s and is compa-rable to the pulse duration. Therefore, the effective

critical power Pcr depends on the interaction timebetween the pulse and air.

The nonlinear contribution to the refractive

index in air Dnnl can be written in the form [18]:

Dnnlt 12n2 Etj j28

s.l. chin et al- interference of transverse rings in multifilamentation of powerful femtosecond...

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