Supercontinuum conical emission accompanying filamentation of a femtosecond laserpulse in fused quartz

E. O. Smetaninaa� and A. E. Dormidonov

M. V. Lomonosov Moscow State University, Moscow

V. O. Kompanets

Spectroscopy Institute, Russian Academy of Sciences, Troitsk, Moscow Oblast�Submitted April 13, 2010�Opticheski� Zhurnal 77, 75–77 �July 2010�

The frequency-angular spectrum of the supercontinuum accompanying the filamentation offemtosecond laser pulses in KU-1 fused quartz at various wavelengths has been experimentallyand numerically investigated. The splitting effect of divergent conical-emission radiation of thesupercontinuum into discrete rings when the radiation is refocused is compared for variouswavelengths. © 2010 Optical Society of America.

INTRODUCTION

When a femtosecond laser pulse undergoes filamenta-tion, superbroadening of its frequency and angular spectrumoccurs, and so-called supercontinuum conical emission �CE�is formed.1,2 The formation of supercontinuum CE accompa-nying the filamentation of a femtosecond pulse at a wave-length of 800 nm in fused quartz was considered in Ref. 3.To explain the general trends of the formation of thefrequency–angular spectrum of a femtosecond pulse, this pa-per presents the results of a study of the formation of super-continuum CE accompanying filamentation of the pulses inquartz at a wavelength of 1300 nm. The results are comparedwith those shown in Ref. 3 for radiation with a wavelengthof 800 nm.

LABORATORY EXPERIMENT AND NUMERICAL MODELLING

Supercontinuum CE was investigated on the femtosec-ond spectroscopic test stand of the TsKP IS RAN. The ex-periments were carried out with pulses at a wavelength of1300 nm and width 60 ps at a repetition rate of 1 kHz andwith an energy of up to 5 �J. To obtain CE, femtosecondradiation was focused by a long-focus quartz lens onto thesurface of the sample. The beam diameter was 70 �m at itsinput face. The luminous filaments and plasma channelswere recorded through the side face of the sample, using adigital camera with an exposure time of 20 sec. A whitescreen was placed 20 cm from the output face and used toobserve the supercontinuum CE, whose image was recordedby a digital reflex camera.

The supercontinuum CE and the threads of the filamentsin the sample were investigated as the pulse energy was var-ied from 2 to 5 �J. When the pulse energy is more than3 �J, an orange spot is formed at the center of the screen,and this is evidence of an improvement of the supercon-tinuum spectrum, since the central wavelength lies outsidethe visible region. In the energy range 3.5–4 �J, coloredrings appear around the central spot, whose radius monotoni-cally increases as the frequency shift increases into the anti-Stokes region relative to the central wavelength of the pulse�Fig. 1a�. The divergence angle for the short-wavelength re-

463 J. Opt. Technol. 77 �7�, July 2010 1070-9762/2010/070

gion of the spectrum is about 5°. One plasma channel thatextends 1.5–2 mm �Fig. 1e, top� is formed inside the sampleat a distance of 10 mm from the input face. When the energyis increased to 4.8 �J, a second plasma channel, located onthe axis of the filament at a distance of 1.5 mm behind thefirst, appears after the first plasma channel �Fig. 1f, top�. Thespectrum of concentric rings of the CE, which is continuousin angle, splits into discrete rings �Fig. 1b�. The dependenceof the radius of the colored rings on their wavelength, char-acteristic of the CE, is conserved in this case. The process offorming the CE at 1300 nm as the energy of the pulses in-

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FIG. 1. Pulse energy: 3.8 �J �left column� and 4.8 �J �right column�. �a�and �b� are photographs of conical emission, �c� and �d� show the angulardependence of the spectral components Sh

����� /S0 on a logarithmic scale,calculated for the following wavelength intervals: 600–730 nm �solidcurves�, 580–600 nm �dashed curves�, and 480–560 nm �dot-dash curves�,and �e� and �f� are the plasma channels recorded by a camera through theside face of the sample. The dependence of the electron concentration Ne�z�along the axis of the plasma channel, obtained by calculation, is shownunder the photographs.

463463-02$15.00 © 2010 Optical Society of America

creases qualitatively coincides with the process of formingthe CE of the pulses at 800 nm.3 When the energy of thepulses is more than 5 �J, a speckle diagram is formed on thescreen.

The CE was theoretically studied, using a model of thefilamentation of the femtosecond laser pulse in condensedmedia and software that makes it possible to numericallymodel the generation of the supercontinuum when there isfilamentation of radiation of different wavelengths. Thegiven model, along with diffraction and nonlinear-optical in-teraction of femtosecond radiation with the medium, fullytakes into account the material dispersion in quartz in accor-dance with the Sellmeier formula. As a result of numericallymodelling the filamentation of the femtosecond laser pulsesunder the conditions of our experiment, the free-electron dis-tributions Ne�r ,z� in the plasma channels �Figs. 1e and 1f,bottom� and the frequency–angular spectra S�� ,�� of thepulses �Fig. 2� were obtained. The calculated parameters ofthe plasma channels, their extent, and the location in thevolume of the medium coincide with those recorded in ex-periment �Figs. 1e and 1f�.

The frequency–angular spectrum of the pulse at1300 nm, lying in the zero-dispersion region of the groupvelocity in quartz, has a characteristic fish shape �Fig. 2a�,while the spectrum of the pulse at 800 nm, lying in thenormal-dispersion region of the group velocity in quartz, is asuperposition of X and fish shapes �Fig. 2b�. As a result ofthe refocusing of the pulses, their frequency–angular spectraacquire a clearly expressed modulation, and this corresponds

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FIG. 2. Numerically obtained spectra of the pulses: �a� spectrum of a pulseat 1300 nm after refocusing, �b� spectrum of a pulse at 800 nm afterrefocusing.

464 J. Opt. Technol. 77 �7�, July 2010

to the appearance of the discrete CE rings observed in ex-periment.

For a clear comparison of the numerical and experimen-tal results, Figs. 1c and 1d show the angular dependences ofthe spectral components, calculated for a number of wave-length intervals ��1−�2� in the visible region of the spec-trum, taking into account the spectral sensitivity of the digi-tal camera. For a small pulse energy �3.8 �J�, there is oneside maximum for each separate wavelength interval �Fig.1c�, and this corresponds to the continuous CE rainbow rings�Fig. 1a�. The maximum of the green line at �=4° corre-sponds to the external green ring recorded in experiment.With a pulse energy of 4.8 �J �Fig. 1d�, the angular distri-bution of the red spectral component shows several clearlyexpressed side maxima, corresponding to the discrete red CErings �Fig. 1c�.

CONCLUSIONS

The frequency–angular spectrum of a femtosecond pulseat 1300 nm with filamentation in fused quartz has been stud-ied experimentally and numerically for the first time. It fol-lows from an analysis of the results of studies of the filamen-tation of the pulses at 1300 nm and 800 nm that the angularsplitting effect of the CE rings is independent of wavelengthand is the result of the interference of radiation from a se-quence of extended coherent sources formed as a result ofthe refocusing of the pulse.

This work was carried out with the support of a grant ofthe Russian Foundation for Basic Research No. 08-02-00517-a.

a�Email: jannes-2002@yandex.ru

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2V. P. Kandidov, S. A. Shlenov, and O. G. Kosareva, “Filamentation ofhigh-power femtosecond laser radiation,” Kvantovaya Elektron. �Moscow�39�3�, 205 �2009�. �Quantum Electron. 39, 205 �2009��.

3A. E. Dormidonov, V. O. Kompanets, V. P. Kandidov, and S. V. Chekalin,“Discrete conical emission rings observed upon filamentation of a femto-second laser pulse in quartz,” Kvantovaya Elektron. �Moscow� 39, No. 7,

653 �2009� �Quantum Electron. 39, 653 �2009��.

464Smetanina et al.