Dynamic behavior of postfilamentation Raman pulses

Jean-François Daigle,1,* Tie-Jun Wang,1 Sima Hosseini,1 Shuai Yuan,1

Gilles Roy,2 and See Leang Chin1

1Centre d’Optique, Photonique et Laser (COPL) et Département de physique, de génie physique et d’optique,Université Laval, Québec, Québec G1V 0A6, Canada

2Defence Research and Development Canada-Valcartier, Québec, Québec G3J 1X5, Canada

*Corresponding author: jfdaigle2@yahoo.ca

Received 2 June 2011; accepted 8 August 2011;posted 21 September 2011 (Doc. ID 148539); published 16 November 2011

We report on the postfilamentation behavior of a Stokes pulse created from intense and collimatedultrashort pulses propagating in air. A systematic analysis of the pulse propagation revealed thatthe redshifted Raman pulse produced during filamentation had a larger divergence than the postfila-mentation intense pump pulse. Also, the analysis of the far-field Stokes transverse ring revealed thatthe intensity in this ionization-free light channel is still sufficiently high to induce stimulated Ramanscattering after ionization had ended. This behavior further extends the potential of filamentation toremotely induce third-order nonlinearities. © 2011 Optical Society of AmericaOCIS codes: 010.1300, 260.5950, 190.5940.

1. Introduction

Filamentation [1–6] of ultrashort pulses in air re-sults from a dynamic interplay between two opposingnonlinear contributions: self-focusing attributed tothe intensity-dependent refractive index and defo-cusing induced by the self-generated plasma. Inair, filaments produced from collimated pulses whosepower is larger than the critical power [7] can extendover hundreds of meters [8] and, for laser pulses cen-tered at 800nm, maintain a clamped intensity [9,10]that is about 5 × 1013 W=cm2. Depending on the initi-al pulse conditions, after the intensity had droppedbelow the ionization threshold (∼1013 W=cm2), an in-tense, low divergence light channel was observed foreven longer distances [11,12].

Similar to optical fibers, filaments are self-inducedstructures where light can be confined at extremelyhigh intensities over extended distances. These areideal conditions for efficient nonlinear energy conver-sion and, at filament-level intensities, air becomes ahighly active nonlinear medium. For example, dur-ing filamentation, laser pulses undergo spectral

modifications induced by self-phase modulation,four-wave mixing [13,14], and stimulated Ramanscattering (SRS) [15,16]. Even though the first twoeffects are related to the anharmonic response ofthe bound electrons while SRS involves the ex-citation of molecular rotational states (mainly N2and O2 in air), these are all nonlinear intensity-dependent mechanisms. As a consequence, nonlinearself-focusing can enhance the Raman process by in-creasing the on-axis intensity.

The spectral modifications induced by SRS arecharacterized by the scattering of laser energy atthe fundamental frequency into multiple Stokesand anti-Stokes frequencies. This mechanism is de-scribed by a three-level nonresonant molecular pro-cess between a nonpopulated higher energy virtualstate and two lower energy rotational/vibrationalstates. Under the impulsive excitation of the laser,the molecules are almost instantaneously alignedand start to rotate at a speed that depends on thetorque applied on the individual molecules. As a re-sult, delayed molecular alignments are observed[17]. For femtosecond pulses, only the initial molecu-lar alignment has a contribution because the secondalignment time (quarter revival) occurs for N2 ap-proximately 2:1ps after the pulse excitation. In air,

0003-6935/11/336234-05$15.00/0© 2011 Optical Society of America

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the characteristic instantaneous full alignment timeis approximately 80 fs. Because of the dispersiveproperties of air, SRS emissions can propagate atlarge angles with respect to the propagation axis. Ina Raman-active liquid, those large angle emissionsallowed the observation of an X-wave pattern inthe Stokes’ angular-spectral distribution [18].

For very long pulse durations (>10 ps), the transi-ent effects linked to the delayed response are negli-gible and the Raman gain is mainly governed by theintensity of the pump pulse. However, as the pulseduration is decreased, the Raman gain continuouslygrows due to the pulse’s increasing spectral width,which excites larger and larger molecular rotationalstates. As a result, long pulses induce narrow spec-tral lines centered at the Stokes and anti-Stokes fre-quencies, while short and spectrally broad pulsesproduce a “quasi-continuum” of Raman frequencies[16]. This enhancement continues until the laserpulse becomes shorter than the rotational period(<2:1ps in air) of the molecules where a drastic de-crease of the Raman gain is observed [15].

Even though the Raman gain should be very weak,strong SRS amplification of Stokes frequencies hasbeen observed for femtosecond pulses during fila-mentation in air [19]. In fact, even if the Ramancontribution is small, the high intensity inside thefilament core and the long interaction length providegood conditions for near-axis amplification of aStokes pulse with an excellent beam quality. In addi-tion, cascaded self-frequency downshifting of a laserpulse was attributed to SRS during filamentation inair [20].

This work is a direct continuation of the resultsreported in Refs. [12,20]. Indeed, we report on thepostfilamentation behavior of a Raman Stokes pulsecreated from inside the intense and collimatedultrashort filamenting pulse propagating inair. A sys-tematic analysis of the pulse propagation performedafter the end of the filament revealed that the inten-sity in this ionization-free channel is still sufficientlyhigh to induce SRS long after the filament had ended.The Raman pulse wasmainly redshifted with respectto the fundamental beamand had a larger divergencethan the postfilamentation intense pump pulse. Thisresult indicates that even though the postfilamentbeam cannot ionize air, its intensity can still induceappreciable third-order nonlinearities, such as Kerrself-focusing (Refs. [11,12]) and, in this case, SRS.This result further extends the potential of laserfilamentation to be used as a remote, broadbandatmospheric lamp [21].

2. Experimental Methods and Results

Collimated transform limited laser pulses(5mJ=45 fs), emitted at a 10Hz repetition rate froma typical Ti:sapphire amplifier, were launched in a25m long corridor. The laser pulses were initially el-liptical in shape and characterized with 3:6mm and2:5mm transverse diameters at full width at half-maximum (FWHM). The initial pulse conditions

ensured that a stable single filament occurred at al-most every laser shot. The evolution of the laserpulses was characterized along the propagation axisusing a mobile experimental unit.

The experimental unit is presented in Fig. 1. Firstof all, the number of free electrons produced alongthe filament was characterized by measuring the in-tensity of the N2 fluorescence with a photomultipliertube (PMT) together with a UG11 filter. For each po-sition, the N2 fluorescence was imaged, with a one-to-one magnification, onto the surface of the PMT suchthat a 5mm long section of the filament limited bythe diameter of the sensitive surface was detected.The spectra were measured using an ocean opticfiber spectrometer coupled to an integration sphere.A 2:0mm diameter iris ensured that mainly theintense filament/postfilament core went into thesphere. We call these the on-axis spectra. In order tolimit the nonlinearities on the solid surfaces andavoid damaging the material, only a weak reflectionfrom the front surface of a bulk fused silica wedgewas used to perform the measurement. Finally, thebeam patterns were measured with a CCD camerausing bandpass filters centered at 800nm (BP800)and 850nm (BP850) to observe either the behaviorof the pulse’s fundamental wave or that of theStokes-shifted frequencies. BP800 and BP850 eachhad a 10nm transmission bandwidth. In this case,the wedge’s front surface reflection was incident ontoa spectrally flat white diffuser. The CCD camera

Fig. 1. (Color online) Experimental unit that was moved alongthe beam. At each position, three measurements were performed.The weak reflection from a bulk fused silica wedge is directed to anintegration sphere (IS) connected to a fiber spectrometer. A 2:0mmdiameter iris (PH) was inserted before IS to measure the filament/hot spot spectrum. IS and PH were then removed and W’s frontsurface reflection was directed to a spectrally flat diffuser. ACCD camera imaged the scattered beam pattern for variousspectral windows (bandpass filters, BP). Finally, the wedge wasremoved and N2 fluorescence was imaged onto the sensitive sur-face of a photomultiplier tube (PMT) with a fused silica lens(f 2 ¼ 6 cm). A UG11 filter and a 800nm dielectric mirror ensuredthat the detected signal was attributed to N2 fluorescence.

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measured the scattered patterns of the pulses; appro-priate neutral density (ND) filters were used to avoidsaturation of the detector. These measurements wereperformed at every 50 cm along the 25m propagationlength.

In order to discriminate the shifted Stokes fre-quencies, let us first take a look at Fig. 2, whichshows the on-axis spectra, in linear (a) and logarith-mic (b) scales. The propagation starts at the compres-sor’s output (black) with the spectrum centered atλ0 ¼ 803nm with a 22nm spectral width at FWHM.As mentioned earlier, the Raman effect can scattershifted photons at large angles with respect to thepropagation axis. However, with femtosecond pulsesduring filamentation, mainly axial or near axial scat-tered photons can be amplified via SRS such that theeffect of their divergence can only be observed nearthe beam axis in the far field [16]. This is why theselected spectra were measured after the filamenthad ended. To learn more about the spectral evolu-tion of femtosecond laser pulses during filamentationin air, please refer to Refs. [1,16,19,20].

Near the end of the filament (14:8m from thecompressor, red), the on-axis spectra exhibited amoderate amplification accompanied by strong mod-ulations on the blue side of λ0. The modulations in-dicate that this type of spectral broadening wasmainly attributed to the interaction of the pulse’strailing edge with the plasma formed at the peakof the pulse. On the other hand, the spectral intensityfor wavelengths larger than λ0 presented strong axialenhancement with almost no modulations. Thison-axis intensity enhancement is the consequenceof self-focusing of the laser pulse while the spectralbroadening toward longer wavelengths is domi-nantly attributed to SRS. When we look at thatspectrum, we can immediately draw a line [dotted,Fig. 2(a)] between the two regimes and this limit ispositioned at exactly λ0. This is a direct consequenceof group-velocity dispersion in air where the longerwavelengths propagate faster. Therefore, the shorter

wavelengths diffract/refract on the plasma behindthe leading edge. Interestingly, from 14.8 to 19:3m(blue), the on-axis spectrum continues to evolve to-ward longer wavelengths even if the filament hadended almost 5m before. Meanwhile, the λ < λ0 spec-tral region remained almost constant. This suggeststhat SRS could still play an important role duringpostfilamentation propagation.

However, between 19.3 and 24:3m (green), thespectral intensity for λ > λ0 suffered a drastic deple-tion. As it will be discussed in the following para-graphs, this drastic signal depletion was caused bythe emission of the transverse ring and the largerdivergence of the Raman pulse. However, the axialintensity is still much higher than what it used tobe at the compressor’s output.

This is clearly shown in Fig. 3, which presentsbeam patterns measured along the propagation axis.The top row corresponds to pictures captured usingBP800 and the bottom row, BP850. The latter filterwas selected to observe the behavior of the Stokesfrequencies with limited contamination from the fun-damental pulse. We should emphasize that otherStokes frequencies could have different characteris-tics (emission angle, energy), this spectral rangearound 850nm is only used to show the overallbehavior of the SRS pulse. For each picture, the dis-tance from the compressor and the transmission ofthe combined ND and BP filters are indicated onthe top left corner.

The pictures measured at 800nm are almost iden-tical to those presented in Ref. [12] because similarlaser pulses (same laser, same conditions, differentdays) were used. They show the evolution of thepulse from the beginning of filamentation (8:8m)to the postfilamentation ionization-free regime(> 15m). On the other hand, the Stoke-shifted pulsepresented a beam profile of excellent quality attrib-uted to the self-cleaning process [19] that occurredduring filamentation. However, the far-field diver-gence of the hot spot at 850nm was significantly

Fig. 2. (Color online) On-axis spectra measured using a fiber spectrometer coupled to an integration sphere. A 2:5mm diameter pinholeensured that only the filament/postfilament hot spot entered the sphere. Spectra are presented for different positions in (a) linear and (b)logarithmic scales.

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larger such that the core diameter was already2:6mm FWHM at 28:3m (compared to 1:6mm for800nm). Because of the increasing filter transmis-sion, a concentric ring could be observed startingfrom 18m when using BP850. The formation of thisring is partly responsible of the Stokes-shifted fre-quencies’ axial depletion observed in Fig. 2. As wewill see, the effects of linear dispersion on SRS areresponsible for its formation [15] and this subject willbe discussed in the following section.

The hot spot diameter, measured from the picturestaken using BP800 (black circles) and BP850 (bluesquares), is plotted as a function of distance in Fig. 4.As an indication, themolecularN2 fluorescence inten-sity (red triangles) is also plotted as a function of dis-tance showing a filament staring at 9:5m and endingnear 14:5m. This figure reveals that the divergenceof the Raman pulse is 0:15� 0:1mrad, while that ofthe postfilament ionization-free channel is 0:03�0:1mrad. This explains the spectral depletion of theStokes wavelengths observed in Fig. 1 beyond 20m.

3. Postfilamentation SRS

It is now clear that a laser filament formed from fem-tosecond pulses can produce a Stokes pulse via SRS[19,20]. However, to the best of our knowledge, thereis no evidence as to, whether or not, the postfilamentlight channels can induce SRS. The divergence angleof the concentric ring observed using BP850, in Fig. 3,provides information related to the laser intensityrequired to produce that ring.

As reported by Peñano et al. [15], the scatteredangle of the Stokes pulse via SRS from intense laserpulses can be described by the following approxi-mate, analytical expression, which relates the angleof perfect phase matching θ0 to the pump laserintensity I0:

cos θ0 ≈ 1 −

β2ðω2R þ Γ2

2Þ2k0

−

ðnK þ nRÞn0

�ω2R þ Γ2

2

ω20

�I0:

θ0 corresponds to the angle where two pump, oneStokes, and one anti-Stokes photons are totallyphased matched [18]. This angular region is charac-terized by a zero Raman gain, i.e., it is located some-where in the solid angle located between the ring andthe central spot. In this relation, k0 is the wave vec-tor, n0 is themedium’s linear index of refraction, ω0 isthe angular frequency, β2 is the group-velocity disper-sion parameter, ωR is the molecular rotational fre-quency, and Γ2 is the dipole dephasing rate. nKand nR are the nonlinear contributions to the indexof refraction attributed to the Kerr and rotationalRaman effects, respectively. Because of Raman’sdelayed response, in the short pulse limit, nR→0.

In air, with 800nm laser pulses, we haveβ2 ¼ 2:2 × 10−31 s2=cm, Γ2 ¼ 1:3 × 1013 s−1, ωR ¼16 × 1012 s−1, and nK ¼ 3 × 10−19 cm2=W [16]. Nowassuming that this ring was formed in the intensefilament core, where we would expect an intensityneighboring I0 ¼ 5 × 1013 W=cm2, the perfect phasematching angle would be θ0 ¼ 4:88. However, basedon our measurement, this angle is approximatelyθ0 ¼ 0:27� 0:02mrad such that the high intensityinside the filament core could not be responsiblefor this ring. The Raman ring emitted at those largeangles during filamentation was not detected due tothe strong attenuation provided by the neutral den-sity filters located in front of the CCD.

Fig. 3. (Color online) Beam patterns measured along the propagation direction using a CCD camera protected with bandpass filterscentered at 800nm (top row) and 850nm (bottom row).

Fig. 4. (Color online) Hot spot diametersFWHMplotted as a func-tion of the distance from the compressor. The black circles show thedata measured using BP800 and the blue squares, the data ob-tainedwithBP850.The red triangles correspondto the fluorescencesignal intensity measured along the beam with a PMT. The corre-sponding scale is on the right-hand side of the figure.

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An angle θ0 comparable to the measured data canbe obtained with laser intensities I0≈2 × 1011 W=cm2,which gives θ0 ¼ 0:29mrad. This is not too far fromthe intensity of the postfilamentation ionization-freechannels measured in Refs. [11,12]. This resultwould imply that the intensity inside those channelsis sufficiently high to induce SRS and amplifiesStokes frequencies. Indeed, assuming a linear diver-gence of this ring (it is linear based on our observa-tion), its origin can be traced back to 15–17m afterthe compressor, 2m after ionization had ended.Based on the results presented in Fig. 2, this typeof postfilamentation SRS amplification still occurred∼5m after the filament ended.

4. Conclusion

In this paper, we reported on the postfilamentationdynamics of a redshifted Raman pulse producedvia SRS. This Stokes pulse presented an excellentbeam profile, attributed to the self-cleaning processoccurring during filamentation. Because SRS canamplify photons that propagate at large angles withrespect to the propagation axis, the Raman pulse di-verged almost 4 times faster than the postfilamentintense light channel. This behavior was observedin both the measured on-axis spectra and the beampatterns measured at 850nm.

Furthermore, an analysis of the transverse Ramanring divergence revealed that the intensity in thepostfilament light channels is sufficiently high tofurther amplify a Stokes pulse via SRS. This newlydiscovered property extends the potential of filamen-tation nonlinear optics [22] to produce broadbandlaser pulses. Indeed, intense postfilamentation chan-nels were observed km after the laser source, thusproviding a very long nonlinear interaction zone.

We acknowledge the support from the NaturalSciences and Engineering Research Council, DefenseResearch and Development in Canada–Valcartier,the Canadian Institute for Photonic Innovation,the Canadian Foundation for Innovation, Fonds Qué-bécois de Recherche pour la Nature et la Technologie,and the Canadian Research Chair. We would alsolike to thank Dr. Francis Théberge for fruitfuldiscussions.

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