3D Raman bullet formed under filamentation of femtosecond laserpulses in air and nitrogen

Daria Uryupina • Nikolay Panov • Maria Kurilova •

Anna Mazhorova • Roman Volkov •

Stepan Gorgutsa • Olga Kosareva • Andrei Savel’ev

Received: 14 June 2012 / Revised: 24 September 2012 / Published online: 29 November 2012

� Springer-Verlag Berlin Heidelberg 2012

Abstract Complex experimental study of spectral, spatial

and temporal behaviors of the IR shifted component observed

under filamentation of the collimated femtosecond laser beam

(80 GW, 50 fs, 805 nm) in molecular gases showed that this

component behaves like a Raman soliton. Namely, it is con-

fined in all domains: (a) it propagates within the filament core,

(b) it has a stable duration of 30 fs along the filament, and (c) its

spectrum shifts as a whole from 820 to 870 nm on the distance

of 2 m from the filament start. A simple model explaining the

origin of anomalous group velocity dispersion in the plasma

channel of a filament is suggested.

1 Introduction

Filaments created during propagation of an ultrashort laser

pulse in gases and solids have gained increasing attention in

the last years. A lot of application areas are widely

discussed nowadays ranging from atmospheric optics to

photonic micro-devices formation and generation of a few-

cycle optical and THz pulses [1–5]. The filamentation

phenomenon is intrinsically non-linear process arising due

to the interplay between Kerr self-focusing and plasma

induced de-focusing of a laser beam. That means that the

filament itself has high non-linear susceptibility. Since light

intensity inside a filament core goes beyond 10 TW/cm2

and the filament length is much longer than the Rayleigh

length, different non-linear optical processes gain high

efficiency. This was approved in numerous experiments on

white light generation [6], four-wave mixing [7, 8], coher-

ent Raman scattering [9], third harmonic production [10],

THz emission [11, 12], probe pulse polarization rotation

[13, 14], and other phenomena.

Most of these experiments dealt with changes in a

radiation spectrum (including new spectral components

generation and/or their angular distribution). Recently it

was shown that spectral broadening might be accompanied

by pulse self-compression in noble gases, and a few cycle

pulses were obtained from the filament created by the

800 nm, 30–50 fs, 3–5 mJ laser pulse [15–18]. The central

wavelength of the compressed pulse was nearly the same as

of the initial pulse creating the filament.

The other behavior was observed in the air and some

other molecular gases: red shifted spectral component grows

up under filamentation of 800 nm femtosecond laser pulses

[9, 19, 20]. In [19] this phenomenon was explained by the

self-phase modulation. In [9] it was shown that this com-

ponent propagates after the filament termination as a slightly

divergent smooth beam in the same direction as the initial

laser beam. The spectrum of IR-shifted component moves

also with the distance from the filament start toward longer

wavelengths, while its spectral shape remains nearly

unchanged [9]. In [9] the new red shifted component was

D. Uryupina � N. Panov � M. Kurilova � A. Mazhorova �R. Volkov � S. Gorgutsa � O. Kosareva � A. Savel’ev (&)

International Laser Center and Faculty of Physics,

Lomonosov Moscow State University, Leninskie Gory,

Moscow 11991, Russia

e-mail: abst@physics.msu.ru

N. Panov

e-mail: napanov@ilc.edu.ru

Present Address:A. Mazhorova

Ecole Polytechnique de Montreal, Genie Physique,

Montreal, QC H3C 3A7, Canada

Present Address:S. Gorgutsa

Institut National de la Recherche Scientifique-EMT,

Varennes, QC J3X 1S2, Canada

123

Appl. Phys. B (2013) 110:123–130

DOI 10.1007/s00340-012-5261-9

explained by the rotational Raman process, but numerical

simulations failed to reproduce the experimentally observed

data. Such a behavior looks almost like as in the case of self-

shifted Raman soliton in usual [21] and photonic [22] fibers

with broadband anomalous GVD, but the medium inside a

filament has normal group velocity dispersion (GVD) near

800 nm. Hence, the mechanisms of formation of this com-

ponent remained unclear and investigations of its temporal

and spatial properties could shed a light on its origin.

Our study presents a thorough experimental character-

ization of the Raman-shifted component in spectral, spatial

and temporal domains. We explored pre-collimated beam

geometry to trace the Raman shifted component behavior

at long distances. For the first time we showed that this

component has a soliton-like structure being confined in

3D inside a filament core. We also suggest a simple model

of refraction in a filament pointing at the origin of the

anomalous GVD in its plasma channel.

2 Experimental arrangement and techniques

The scheme of our experimental setup is shown in Fig. 1.

A single filament was created by the laser pulse delivered

by a Ti:Sapphire laser system with the central wavelength

805 nm, pulse duration 55 fs, spectral width of 23 nm,

energy per pulse up to 10 mJ, and repetition rate of 10 Hz.

The beam splitter formed two beams with pulse energies of

4.5 and 3.5 mJ. The first beam creates a single filament,

while the second beam serves as a reference for the SPI-

DER temporal profile measurements. Peak power of the

first beam (almost 80 GW) exceeded well the critical self-

focusing threshold (Pcr *5 GW for femtosecond filamen-

tation in air, argon or nitrogen [23]), but was still below

than the onset of multi-filamentation. This was also due to

arbitrary poor M2 = 1.7 parameter of our radiation [24].

A telescope consisting of the plane-convex lens (focal

length 4.52 m) and the convex mirror (focal length 1 m)

reduced the 4.5 mJ beam diameter to 1.3 mm FWHM to

generate arbitrary short (2–3 m in length) single filament.

The collimated laser beam entered the evacuated tube,

which had a variable length (from 2 to 4 m) and was filled

with air, nitrogen or argon. The tube had 0.6 mm thick input

and output quartz glass windows. The tube was equipped

with an exchangeable movable aperture with the diameter

d of 300–1,000 lm positioned at any desired place along

the filament. The moveable aperture stopped the filament at

the desired position by cutting off certain energy from the

background reservoir [25] and simultaneously selected the

central part of the filament [18]. The beam became diver-

gent after the aperture thus preventing damage to the output

window by the radiation.

Spectral phase and duration of the output pulse were

measured using the SPIDER technique [18, 26, 27]. Energy

passed through the aperture was assessed by placing the

wedge in the beam immediately after the output window of

the tube and measuring the attenuated energy of the

reflected pulse by the pyroelectric detector. The energy

measurement setup was calibrated at peak powers of the

initial beam well below the self-focusing threshold and

without aperture inside the tube. The same wedge was used

to measure a spectrum of the output radiation by the Solar

S150-II spectrometer.

3 Experimental results

Figure 2a presents typical single-shot spectra of radiation

passed through apertures with different diameter d. An

aperture was positioned at the distance L *140 cm from the

point at which the filament appeared (hereafter all the dis-

tances are counted out from this position). Measurements

Fig. 1 Experimental set up (see description in the text)

124 D. Uryupina et al.

123

were made in air at a pressure of 1 atm. The spectrum

obtained with the widest aperture (d = 1 mm, black line in

the Fig. 2a) consists of the two distinct components. The first

component is the fundamental one broadened up to *40 nm

(mostly to the longer wavelength side). The next component

is red shifted to 870 nm and has the spectral FWHM of

15–20 nm. Note that the very different spectra (with huge

wing on the short wavelength side) were observed under fil-

amentation of loosely focused [9] or collimated [18] laser

beam in argon. This also supports that the IR shifted com-

ponent appears due to rotational Raman process, which is

possible for the molecular gases, but does not exist for the

noble ones.

The aperture with d = 500 lm (blue line in the Fig. 2a)

cuts off the fundamental component leaving the red-shifted

one nearly unchanged. The spectrum preserves if the

aperture with d = 300 lm was placed into the beam (see

Fig. 2a, red line). Hence, it follows from our measurements

that the observed Raman component propagates inside the

thin filament core, while the fundamental radiation occu-

pies the outer part of the filament. In particular, this

explains results published in [9], where authors observed

that Raman shifted component forms the high spatial

quality low divergent beam propagating in the same

direction as the fundamental one.

The same changes in the spectrum with aperture size were

observed at distances L ranging from 10 to 200 cm (the latter

value was close to the point where the filament stops due to

energy leakage), i.e., if the aperture size was below 500 lm

the spectrum generally contains only the red-shifted com-

ponent. This component undergoes the monotonic spectral

shift with an increase in the distance L (see Fig. 2b). Our

findings coincide with data obtained with the loosely focused

laser beam [9], but spatial filtering using aperture allows us to

view the Raman component more clearly. It is interesting to

note that this component existed already at the very beginning

of the filament and was not observable if the spectrometer is

placed immediately after the convex mirror. Hence, the

Raman component is formed during the filament formation

due to phase self-modulation and rotational Raman processes

and experienced monotonic spectral red shift for the longer

distances. This was confirmed recently in the numerical

experiment [28].

Even more complicated behavior was observed if nitro-

gen was used instead of air (Fig. 3, d = 500 lm). Data

obtained at L = 70–80 cm shows that much more energy

750 800 850 900

0,5

1,0

d =1000 μmd =500 μmd =300 μm

λ, nm

S, a.u.

(a) (b)

750 800 850 900

0,5

1,0

L =10 cmL =40 cmL =70 cmL =100 cmL =180 cm

λ. nm

S, a.u.

Fig. 2 Spectra of radiation

under filamentation in the air

(pressure 1 atm) obtained at the

distance L = 140 cm using

apertures with different

diameter d (a) and at different

distances L using aperture with

d = 500 lm (b)

800 850 900

0,5

1,0

80 cm 110 cm 180 cm

S, a.u

λ, nm800 850 900

0,5

1,0 80 cm 150 cm 210 cm

S, a.u

λ, nm

(a) (b)Fig. 3 Spectra of radiation

under filamentation in nitrogen

obtained at different distances

L at pressure 1 atm (a) and

0.5 atm (b) using aperture with

d = 500 lm

3D Raman bullet formed under filamentation of femtosecond laser pulses 125

123

preserved at the fundamental frequency in the latter case

(compare red curves in Figs. 2b, 3a). This can be due to the

lower non-linearity of the nitrogen gas as compared with the

air because of the molecular oxygen impact [19]. The sec-

ond red-shifted component appears in the nitrogen at arbi-

trary long distances when the first component shifted from

its original spectral position quite far (see the blue curve for

L = 110 cm in Fig. 3a). Spectral amplitude of the first

component gradually decreases along the filament, while

the spectral amplitude of the second component increases.

Moreover, the third component arises at L = 180 cm (black

curve in Fig. 3a). At the same time, the amount of energy at

the fundamental frequency decreases with L.

The case of the nitrogen gas appearance of numerous

Raman shifted components can be explained by the re-

focusing phenomenon [1–5]: radiation in the reservoir

undergoes multiple re-focusing events along the filament

propagation. This leads to the non-monotonic behavior of

such quantities as plasma channel diameter, peak intensity

of radiation, etc. Hence, the Raman shifted component

forms at each refocusing event provided intensity near the

fundamental frequency is high enough. This is true for the

case of the nitrogen gas but not with air. The first re-

focusing event appears at L *100 cm at the experimental

conditions quite close to our [18], while the distance to the

second one from the first focusing point is much smaller.

Hence, the origin of multiple spectral maxima in nitrogen

indeed can be due to consecutive re-focusing events.

Figure 4 presents the amount W of energy passed

through the aperture (d = 500 lm, L = 140 cm) in

dependence on the nitrogen gas pressure. This energy was

*1 mJ at pressures below 0.5 atm (the transmittivity

t = 0.22 ± 0.05 corresponds to the transmittivity t *0.2

of the same aperture for the collimated beam without self-

focusing). The transmittivity increases steadily with

pressure and equals *0.65 ± 0.15 (W *2.5–3 mJ) at the

pressure of 1 atm. One could conclude that the red-shifted

Raman component takes nearly half of the energy of the

initial lase pulse, taking into account data in Fig. 2a.

In Fig. 3b we show spectra obtained at the nitrogen gas

pressure of 0.5 atm corresponding to the filamentation

‘‘threshold’’ (see Fig. 4). These spectra contain the red-

shifted component, but it does not experience further

spectral shifting with the distance L. This again points at

the fact that initially the Raman component appears during

the filament formation, while spectral self-shifting comes

into play during propagation of this component in the fil-

ament created by the fundamental radiation (see also the

green curve corresponding to the L = 10 cm in Fig. 2b).

We also measured temporal shape of the Raman shifted

component using the SPIDER technique. The SPIDER set up

provides for additional spatial filtering and eliminates radia-

tion coming not from the filament core [18]. This allows us to

use the 700 lm aperture for measuring temporal structure at

different points along the filament (larger aperture makes

SPIDER measurements easier lowering simultaneously

problems associated with the beam pointing instability). The

SPIDER signal was very stable in our experimental condi-

tions. Typical single-shot data obtained at the L = 140 cm is

presented in Fig. 5a. One can see that the Raman component

is confined in time having a duration slightly less than the

duration of the initial laser pulse. Moreover, this pulse has no

chirp, and its spectral and temporal phases are nearly flat.

The high quality of the pulse is well demonstrated by

Fig. 5b, which represents the time–frequency diagram of

the pulse calculated from the SPIDER data using the PG

FROG algorithm [29]. We revealed that the temporal shape

of the Raman component is nearly the same for any dis-

tance L up to the end of the filament (see Fig. 6).

4 Discussion and estimates

Let us now consider how the spectrally and temporally

confined, IR-shifted light bullet could appear during the

filamentation. The commonly used equation governing

changes in spatial, temporal and spectral properties of

radiation inside a femtosecond filament is [30, 31]:

2ik0

oE

oz¼ T�1D?E � k0 k00

o2E

os2þ DE

� �

þ 2k20 TDnk þ T�1Dnp

� �E � ik0aE; ð1Þ

where E is an envelope of the electric field, z is a

propagation coordinate, k0 is a wave number at the carrying

frequency x0 corresponding to the central wavelength k0,

s is a time in a coordinate system propagating with a group

velocity, T ¼ 1� i=x0o=os, k00 is a second-order

Fig. 4 The dependence of the energy W passed through the aperture

with d = 500 lm of the nitrogen pressure P. Initial pulse energy

4.5 mJ, L = 140 cm

126 D. Uryupina et al.

123

dispersion coefficient at x0, D is a high-order dispersion

operator, Dnk and Dnp are Kerr and plasma nonlinearities, ais a multiphoton absorption coefficient. Air and nitrogen

are molecular gases, therefore Dnk contains both

instantaneous electronic and inertial Raman responses:

Dnk ¼n2

4

Eðx; y; z; sÞj j2þ

Zs

�1

Hðs� s0ÞX2

� exp �Cðs� s0Þ2

� �sin Kðs� s0Þð Þ

KEðx; y; z; s0Þj j2ds0Þ;

ð2Þ

where n2 is the Kerr coefficient of the gas at x0,

K2 = X2 – C2/4 (for the air at normal conditions

X = 20.6 THz, U = 26 THz) and H(s) is the Heaviside

step function.

The code, solving Eq. (1), was extensively used in our

previous studies, including filament formation, pulse self-

compression, polarization rotation, etc. [14, 18, 24, 31].

Unfortunately, the current state of this code is not appro-

priate to shed light onto the problem under consideration.

This mainly is due to the fact that group velocity dispersion

k00 and other dispersion coefficients (in the operator D) are

fixed in the code, i.e., not affected by fast changes to the

filament index of refraction due to plasma generation.

Formation of a soliton in a Kerr medium, including

formation of a Raman soliton-like structures [22], is pos-

sible only if this medium has anomalous GVD [21]. At the

same time, the air and nitrogen gas have the normal dis-

persion in the optical range [32], hence soliton-like struc-

tures cannot be formed in these media.

Changes in the GVD could come from various nonlinear

processes in a filament. The total index of refraction of the

filament can be written in the following form:

nðxÞ ¼ 1þ Aþ Bx2 þ n2ðxÞIðxÞ �2pe2Ne

mex2þ nHOKEðxÞ;

ð3Þ

where me and e are electron mass and charge respectively,

Ne is the concentration of a free electrons, x is the radiation

frequency, I is the laser pulse spectral intensity, and

A = 2.73 9 10-4, B = 5.79 9 10-37 c2 for the air under

normal conditions [32]. First three terms in (3) describe the

index of refraction of the air, the fourth one comes from the

Kerr impact, the next term is the filament plasma response

within the Drude model, while the last one is due to the

high-order Kerr effect (HOKE, [33]). The most reasonable

physical mechanism of the HOKE under filamentation is

the impact of highly excited atoms due to the multi-photon

resonant absorption in the Rydberg states [34]. In [33] the

term nHOKE was written as the expansion of powers of the

intensity I in temporal domain. However, wave functions

of the Rydberg states are very broad in space and one needs

-100 -50 0 50 100

0,5

1,0

time, fs

A, a.u.

~30fs

(a) (b)Fig. 5 The typical temporal

envelope of the Raman

component retrieved from the

SPIDER data (a) and the time–

frequency diagram retrieved

from the SPIDER data using the

PG FROG representation (b).

Nitrogen pressure 1 atm,

d = 700 lm, L = 140 cm

80 120 160 200 2400

10

20

30

40

50 τ, fs

L, cm

Fig. 6 The dependence of the FWHM duration s of the Raman

component of the distance L. Nitrogen pressure 1 atm, d = 700 lm

3D Raman bullet formed under filamentation of femtosecond laser pulses 127

123

nonperturbative methods of their analysis instead. The

susceptibility per one electron for the Rydberg states has

nearly the same absolute value and frequency dependence

as the susceptibility of a free electron [35]. Hence one can

rewrite (3) as

nðxÞ � 1þ Aþ Bx2 þ n2ðxÞIðxÞ

� 2pe2Ne

mex21þ aðxÞNR

Ne

� �ð4Þ

where NR stands for the concentration of atoms in a Ryd-

berg state, and aðxÞ � 1 is a slowly varying function of the

frequency x [35].

The GVD k00ðxÞ (kðxÞ ¼ xnðxÞ=c) inside a filament is:

k00ðxÞ ¼ o2k

ox2� 6Bx� 4pe2Ne

mex31þ aðxÞNR

Ne

� �ð5Þ

Here we took into account that n2ðxÞ dependency is

slow [36], while spectral power density of the pulse

envelope amounts at frequencies 10–100 times lower than

the frequency x0, and one can neglect normal Kerr impact

to the GVD. This can be applied for a few cycle pulses and/

or in the case of the leading front sharpening due to a non-

linear dispersion [37]. The ratio NR/Ne varies in time and

strongly depends on the laser field strength, so the issue of

HOKE-to-plasma impact on filamentation is widely

discussed nowadays [33, 38–40]. In the recent numerical

study [41] it was shown (by direct solving the 3D

Shrodinger equation for the Xe atom with an ionization

potential of 12.13 eV in a strong laser field) that for

intensities above 20 TW/cm2 the ionization probability

surpasses few times the excitation one. Thus, we can putNR

Ne� 1 in (5), and neglect the HOKE impact below. Note,

that the HOKE-induced anomalous GVD can be essential

at the pulse front and/or at the plasma filament periphery.

Since k00ðx! 0Þ ! �1 and k00ðx! þ1Þ ! þ1 the

equation k00ðxÞ ¼ 0 has a solution corresponding to the

non-zero electron concentration NRe at which the GVD

inside the filament equals zero at a given frequency x:

NRe ðxÞ ¼

3Bmex4

2pe2: ð6Þ

If k00ðxÞ ¼ 0 is satisfied at the frequency

nonperturbative x0, the GVD is anomalous for all

x\ x0. Consequently, the relation (6) determines the

key condition in the Raman soliton formation inside the

filament. Figure 7 presents the dependence of k00ðx0Þinside the filament on the concentration Ne. The shaded

area corresponds to the area of anomalous GVD. Estimates

show that NRe = 3.26 9 1016 cm-3 at k0 = 800 nm (air

under normal conditions).

Experimental determination of the electron concentra-

tion inside the plasma channel of the filament is intensively

investigated but a difficult task, because diameter of the

plasma channel is small, below 100 lm, and the electron

concentration rapidly changes at the leading front of the

laser pulse. Besides this concentration is still low for the

easy implementation of commonly used plasma physics

methods. Different indirect methods were used for this

goal, including optical interferometry [42, 43] and in-line

holography [44], THz probing [43], plasma fluorescence

[45], and secondary electrical discharges [46]. Experi-

mental conditions (focal distance and numerical aperture,

gas composition, contamination and humidity, etc.) and

methods used (in particular, spatial and temporal averaging

of data) have the prominent impact on the inferred prop-

erties of the plasma channel. In the most cases, the

experiments provide with averaged over time and space

values for the electron concentration ranging from 1015 to a

few times 1017 cm-3. Electron concentrations above 3 9

1016 cm-3 were reported even if the filament is launched

by the loosely focused laser beam [44, 45].

Fig. 7 The dependence of the second-order dispersion coefficient

inside the filament k00 of the free electrons concentration Ne (at

k = 800 nm). The shaded area corresponds to the anomalous GVD

where Raman soliton is possible

750 800 850 900 950

0,5

1,0L = 10 cmL = 100 cmL = 180 cm

S, a.u.

λ, nm

Fig. 8 Simulated spectra of radiation in the filament core obtained at

different distances L (air at a pressure of 1 atm with k00 = –22 fs2/m)

128 D. Uryupina et al.

123

Consequently, the above-mentioned conditions for the

formation of anomalous GVD inside the plasma channel of

the filament can be satisfied at the back front of the laser

pulse, and at Ne = 6 9 1016 cm-3 the GVD k00 = –22 fs2/

m (instead of k00 = 16 fs2/m for the air under normal con-

ditions). To confirm that a Raman soliton could be formed

inside the filament we made numerical simulation using the

1D variant of the Eq. (1) with k00 = –22 fs2/m and other

parameters taken for the air under normal conditions. Data

presented in the Fig. 8 clearly supports this idea (see also

experimental data in the Fig. 2b). Additional approval of

the condition (6) comes from the data plotted in Fig. 3 for

the nitrogen gas at pressures of 1 and 0.5 atm. Indeed, the

condition (6) fails at the lower pressure since the filament

does not form and electron concentration is relatively low.

This explains why we saw the red-shifted component in

this case, but it did not experience further spectral shifting.

5 Conclusions

Thus, our study confirmed the importance of more complex

description of the filamentation process, especially if col-

limated beams are used to produce long filaments in an

open air. It also opens up new possibilities for efficient

generation of collimated ultrashort pulses in IR and visible

bands.

The experimental study of the spectral, spatial and

temporal behavior of the IR shifted component observed

under filamentation of the collimated femtosecond laser

beam in molecular gases showed that this component

behaves like a 3D light bullet:

(1) it propagates within the filament plasma core,

(2) it has a stable duration of 30 fs along the filament, and

(3) its spectrum shifts as a whole from 820 to 870 nm

along the filament.

This ‘‘soliton-like’’ light bullet can gain up to 30–50 %

of the energy of the fundamental pulse. It is formed during

the filament formation but its spectral shift starts if the

pressure is above the certain threshold (0.7–0.8 atm for the

nitrogen gas). We observed this 3D light bullet in the air

and nitrogen gas at different pressures, but nothing was

observed with argon gas. This supports the idea that the

bullet is formed due to the rotational Raman process. The

type of molecular gas used to launch the filament is also

important: depending on its non-linearity, ionization

threshold, etc. few shifting spectral components could be

formed (in nitrogen gas three spectral components were

observed separated by 20–30 nm).

Properties of the 3D light bullet are almost like as of the

well-known self-shifted Raman soliton in optical fibers. It

is impossible to describe such a soliton-like structure

formation within the framework of the simplified com-

monly used model of the filamentation process with fixed

GVD coefficient. The key equation of this approach

describes a filament based on the fundamental generaliza-

tion of the slowly varying amplitude method [47] and is

built for the field envelope. It does not describe changes in

the GVD due to plasma and Kerr impacts. The frequency

dependence in plasma current may be taken into account in

the forward Maxwell equation [48] or unidirectional pulse

propagation equation [49]. A thorough simulation of the

3D Raman light bullet formation is underway in our group.

Acknowledgments The authors wish to thank prof. L. Berge for

fruitful discussions. This work was partially supported by the Russian

Foundation for Basic Research (Grants #12-02-01368-a, #11-02-

12061-ofi-m-2011, #12-02-31341-mol-a, #12-02-33029-mol-a-ved),

the Council of the President of the Russian Federation for Support of

Young Scientists (No. 5996.2012.2) and Leading Scientific Schools

(No. 6897.2012.2), Ministry of Education and Science of Russian

Federation (Grant #8393). N.P. also acknowledges support from the

Dynasty Foundation.

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