Ultrafast light-matter interaction in transparent medium

Ultrafast light-matter interaction in transparent medium

The ultrafast interaction between high power laser light and plasma has been studied theoretically. The theoretical simulations are based on the nonlinear Schrödinger equation taking into account group velocity dispersion, diffraction, self-focusing and multiphoton absorption. The plasma is forme...

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Datum:2012
1. Verfasser: Korovin, A.V.
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Veröffentlicht: Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2012
Schriftenreihe:Semiconductor Physics Quantum Electronics & Optoelectronics
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/118269
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spelling nasplib_isofts_kiev_ua-123456789-1182692025-06-03T16:28:47Z Ultrafast light-matter interaction in transparent medium Korovin, A.V. The ultrafast interaction between high power laser light and plasma has been studied theoretically. The theoretical simulations are based on the nonlinear Schrödinger equation taking into account group velocity dispersion, diffraction, self-focusing and multiphoton absorption. The plasma is formed during propagation of femtosecond laser pulse with high input power in transparent medium due to multiphoton ionization process. The induced plasma results in light scattering with formation of multiple cones. It was found that plasma forms cone region that is inverse to cones appearing from scattering of electromagnetic field. The Fourier transformation of temporal-spatial dependences of plasma density demonstrates formation of quasi-periodic structure for plasma waves. The author gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft (priority programme 1327 “Optically induced sub-100 nm structures for biomedical and technological applications”). 2012 Article Ultrafast light-matter interaction in transparent medium / A.V. Korovin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 1. — С. 48-54. — Бібліогр.: 21 назв. — англ. 1560-8034 PACS 42.50.Ct https://nasplib.isofts.kiev.ua/handle/123456789/118269 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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description The ultrafast interaction between high power laser light and plasma has been studied theoretically. The theoretical simulations are based on the nonlinear Schrödinger equation taking into account group velocity dispersion, diffraction, self-focusing and multiphoton absorption. The plasma is formed during propagation of femtosecond laser pulse with high input power in transparent medium due to multiphoton ionization process. The induced plasma results in light scattering with formation of multiple cones. It was found that plasma forms cone region that is inverse to cones appearing from scattering of electromagnetic field. The Fourier transformation of temporal-spatial dependences of plasma density demonstrates formation of quasi-periodic structure for plasma waves.
format Article
author Korovin, A.V.
spellingShingle Korovin, A.V.
Ultrafast light-matter interaction in transparent medium
Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet Korovin, A.V.
author_sort Korovin, A.V.
title Ultrafast light-matter interaction in transparent medium
title_short Ultrafast light-matter interaction in transparent medium
title_full Ultrafast light-matter interaction in transparent medium
title_fullStr Ultrafast light-matter interaction in transparent medium
title_full_unstemmed Ultrafast light-matter interaction in transparent medium
title_sort ultrafast light-matter interaction in transparent medium
publisher Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate 2012
url https://nasplib.isofts.kiev.ua/handle/123456789/118269
citation_txt Ultrafast light-matter interaction in transparent medium / A.V. Korovin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 1. — С. 48-54. — Бібліогр.: 21 назв. — англ.
series Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv AT korovinav ultrafastlightmatterinteractionintransparentmedium
first_indexed 2025-12-01T21:45:00Z
last_indexed 2025-12-01T21:45:00Z
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fulltext Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 48-54. © 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 48 PACS 42.50.Ct Ultrafast light-matter interaction in transparent medium Alexander V. Korovin V. Lashkaryov Institute for Semiconductor Physics, NAS of Ukraine, 03028 Kyiv, Ukraine E-mail: korovin@isp.kiev.ua Abstract. The ultrafast interaction between high power laser light and plasma has been studied theoretically. The theoretical simulations are based on the nonlinear Schrödinger equation taking into account group velocity dispersion, diffraction, self-focusing and multiphoton absorption. The plasma is formed during propagation of femtosecond laser pulse with high input power in transparent medium due to multiphoton ionization process. The induced plasma results in light scattering with formation of multiple cones. It was found that plasma forms cone region that is inverse to cones appearing from scattering of electromagnetic field. The Fourier transformation of temporal-spatial dependences of plasma density demonstrates formation of quasi-periodic structure for plasma waves. Keywords: light-matter interaction, ultra-short laser pulse, multiphoton process, transparent medium. Manuscript received 15.12.11; revised version received 05.01.12; accepted for publication 26.01.12; published online 29.03.12. 1. Introduction In recent decades, extra high peak power laser pulses allowing to obtain the extreme intensity of the electromagnetic field in the focus of an ultra-short laser pulses have led to a variety of new applications as well as atmospheric analysis and remote sensing of molecules [1], supercontinuum generation [2, 3], precise scalpels for delicate eye surgery [4], driving sources for table-top particle accelerators [5], etc. Also, one of the most promising applications of ultrafast lasers is a femtosecond-laser processing of transparent materials such as glasses [6], crystals [7], and polymers [8]. This versatile method allows obtaining arbitrary three- dimensional microstructures using a highly focused femtosecond laser beam through a local change in refractive index of the host material. So, integrated optical components can be directly inscribed into the bulk of transparent materials by translating the sample. In fused silica, different regimes of structural changes can be observed [6] depending mainly on the energy carried by the incident individual laser pulses. At low energies, a homogeneous refractive index increase occurs due to the rapid melting and quenching of the glass. In contrast, at high pulse energies microexplosions create permanent voids in the focal volume. Interestingly, at intermediate energies, birefringent index changes are induced. It has been shown that the anisotropy is caused by self-organized structures with subwavelength periodicity, the so-called nanogratings [9] that are oriented perpendicular to the polarization of the writing beam [10]. Since their discovery, much attention has been given to use nanogratings for the fabrication of microfluidic channels [11]. The control of propagation dynamics, both spatial and temporal, is crucial in these applications. This necessitates a complete understanding of the physical processes that govern the spatio-temporal dynamics of the intense ultra-short pulse in the medium. The theoretical description of laser-induced refractive index changes in the interaction of high-intensity laser pulses with plasma was considered by many authors [12-15]. The spontaneous breakup of highly elliptical laser beams into one- and two-dimensional arrays of light filaments was studied in fused silica [16], where the multiple filamentation process is initiated by random intensity Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 48-54. © 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 49 modulation across the beam “amplitude noise”. Besides, formation of filamentation was studied at propagation of 1-ps laser pulses in scattering medium (aqueous suspension of 2-μm polystyrene microspheres) where scattering was introduced through a stochastic diffusion and diffraction term [17]. At present, it is reasonable to say that understanding the interplay of various physical processes over the extensive range of various parameters like input power, pulse width, wavelength and repetition rate is far from complete. This is largely due to the fact that experimental conditions vary widely and models used are not always comprehensive. Thus, the physics of this problem needs further study. In this paper, the numerical simulations of propagation of ultra-short laser pulse in a transparent medium are presented. The theoretical model of ultrafast light-matter interaction is based on the nonlinear Schrödinger equation with taking into account the group velocity dispersion, diffraction, self-focusing and multiphoton absorption as well as continuity equation for the plasma density. Modelling ultra-fast light-matter interaction was performed in 3D space with the spatio- temporal Fourier transformation of electric field and plasma density for transverse (relatively to laser pulse propagation direction) coordinate. This spatio-temporal Fourier transformation gives us information about light- matter interaction because the peculiarities in such transformation correspond to dispersion curves for quasi-particles appearing at interaction between plasmons and photons. Also, this transformation allows us to observe formation of periodic or quasi-periodic structures. The paper is organized as follows. After introduction, in Section 2 the fundamentals for theoretical description of ultrafast light-matter interaction were made. In Section 3, the numerical results and discussions for simulation of ultra-short laser pulse propagation in transparent medium (fused silica) are presented. The final conclusions are presented in Section 4. 2. Fundamentals Modelling light interaction with matter in nonlinear regime could be performed using Maxwell equations with induced current when taking into account optical Kerr effect as well as multiphoton and avalanche ionization. The Maxwell equations in SI units could be read      t t t t , , , RJ RD RHR     ,     t t t    , , RB RER ,    tt ,, RRDR  ,   0,  tRBR , (1) where the designations are commonly used. In the case of isotropic media, relation between electric displacement and electric field if taking into account the optical Kerr effect can be written in the time domain as follows            ttdtttgtt DEEE     23 . (2) where ε is the permittivity for linear response and χ(3) is the third-order nonlinear susceptibility,        tgttg Raman  1 with      tUtetg t Raman 12 2 2 1 2 2 2 1 sin2      . Neglecting the Raman response ( 1 ), Eq. (2) can be rewritten as follows          tttt DEEE  23 . (3) 2.1. Multiphoton and avalanche ionization The evolution equation for the electron density reads [14]   ri PI E U EW t        22 . (4) where τr is the electron recombination time,  is the coefficient of absorption due to inverse bremsstrahlung that follows from the Drude model, and it could be written as 22 0 00 22 0 0 0 2 0 2 0 2 0 11 c c atc c e k n ek           , (5) where k0 = n00/c = 2/ and 0 are the wave number and frequency of the carrier wave, respectively, and n0 is the medium refractive index in the case of linear response, ρat = ε0µe (n00/e)2 – initial electron density in the valence band, µe – reduced electron mass, c – momentum transfer collision time. For usual materials, plasma absorption is a decreasing function while plasma defocusing is an increasing function of c. Thus, the collision time characterizes a balance between plasma absorption and plasma defocusing. For the high-intense light propagating through dielectric media with photon energy lower than the energy gap in media, the multiphoton ionization gives its contribution to free-electron generation, involving transitions from the valence band to the conduction one through the gap potential. For relatively weak fields, the multiphoton ionization rate from Keldysh’s theory for p- photon ionization can be approximated by [15]   )(   at p pPI IIW , (6) where p is the multiphoton (for p-photons) ionization cross section. Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 48-54. © 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 50 The current density for avalanche and multiphoton (p-photons) ionization in frequency domain takes the following form       EEEj 12  p atipU . (7) So, the absorbed photons or plasma density generation rates are defined from Eq. (7) in the following form     . ReRe 2 2 p atp ii UU G        E E Ej      (8) 2.2. Initial conditions To obtain ultra-intense laser pulse, high focusing is needed. We describe focusing the laser pulse by using linearly polarized Gaussian-like beams. So, the initial electric field for laser pulse propagating along z-axis could be presented in the following form [18]       .. 2 exp /1 € , 2 0 cc ziz kr tkzi zzi tE tE RR                       e r , (9) where  2 00 /1)( zzwzw  is the characteristic transverse size of the beam in z-position and w0 is the beam waist,  /2 00 wnz is the Rayleigh range (2z0 is the confocal parameter and    1 0/1  zzif is the curvature of the wave at the distance z from the linear focus), 0ziz  is the complex radius of curvature and    ptt  hsec or     2exp ptt  is the temporal pulse shape with the temporal half-width, p. The typical numerical apertures and beam waists measured with a low intensity femtosecond laser at 800 nm for various objectives could be found in [14]. The input laser power is pinin EP  /2 , so the light intensity could be read as 2 0 2 0 2 wPE in  . Generally, the focal spot could be approximated by plane wave while outside of focal spot the spherical harmonics give best approximation. More accurate formula for linearly polarized Gaussian-like beams takes the following form [19] in the case of diffraction angle satisfying the condition 1/2/ 0000  kwzw           , , 2 0 / / 0 2 0 22 22    Oe gefEzrE tzzrkzi zwr x        (10)   0,  zrE y , (11)      3 0 0 0 ,,  OzrE w x fizrE xz   , (12) where 00 2 00 /2/  wkwz – depth of focus in the Rayleigh’s range,    0hsec tg – temporal pulse shape, tkz  – phase, p0 – characteristic pulse width. 2.3. Nonlinear Schrödinger equation In the framework of paraxial equation approximation, the electric field,  tzyxE ,,, , of the pulse propagating along the +z-direction is presented using the envelope function in the form       ..,,,,,, 00 ccetzyxEtzyxE tzki   , (13) where  tzyx ,,,E is the pulse envelope. For the cases of the slowly-varying envelope approximation, the propagation equation for the pulse envelope can be reduced to the nonlinear Schrödinger (NLS) equation from the wave equation using the well-known arguments [12, 14, 15]. The NLS equation could be extended to include the effects of ionization and the effects of the influence of electron plasma on the pulse envelope and takes the form     .E E E UEW i EE t i c in E yxt i k i t E t Ei z E iPI c 2 2 0 2 0 0 2 2 2 2 2 00 3 3 32 2 2 2 1 1 2 1 1 2 2                                                (14) Usually, E is normalized in the way when 2E equals to the intensity of the pulse in W/cm2. The terms with coefficients β2 and β3 take into account second- and third-order group velocity dispersions (GVD), respectively. The first-order GVD term is vanished for the case of frame of reference moving with the group velocity of the pulse. The subsequent term in the left- hand side is the space-time focusing term in which the transverse Laplacian leads to familiar diffraction effects. The fourth term accounts for third-order nonlinear effects due to the intensity dependent refractive index n2. Self-focusing in space and self-phase modulation (SPM) in time are direct consequences of this term [14, 15, 20]. The partial time derivative in the term causes self- steepening, which leads to the formation of a shock front in the pulse envelope. While SPM is responsible for symmetric broadening of the pulse spectrum, self- steepening causes an asymmetry in the spectrum [20]. The studies of Chiron et al.[12], Couairon et al. [14] and Kumagai et al. [15] justify retaining only the transverse Laplacian in the space-time focusing term for longer pulse widths, 100 fs or longer, when it is of interest to study only the spatio-temporal dynamics for Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 48-54. © 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 51 pulses that are not in the few cycle limit. For the same reason, we can ignore the third-order GVD, self- steepening and Raman response. So, Eq. (14) can be simplified to the following form     .E E UEW EiEEkin E yxk i t Ei z E iPI c 2 2 0 2 02 2 2 2 2 0 2 2 2 2 1 1 2 22                       (15). 3. Numerical results and discussions For simulations, we use the Gaussian pulse laser beam with the operation wavelength equal to 800 nm ( 1 0 fs355.2  ) and duration  = 150 fs. In this case, deviation of the frequency is about   = 13 fs10667.6  (following to the uncertainty relation) that is 0.283% from 0. So, we can neglect dispersion in optical constants due to slow frequency dependence in this spectral region. In calculations, we use parameters that are typical for propagation of a high-intense laser pulse in fused silica (FS), and they are presented in Table. Table. Parameters used in simulations of the propagating ultra-short laser pulse in fused silica. The spatial distribution of the electric field intensity and plasma density are presented in Fig. 1 for various input laser energies. The calculations were made in 3D space using Eqs. (1) and (4) for data from Table. At each step in the z-direction, the electric field envelope is determined from Eq. (1) using the split-step Fourier method [21], while the electron plasma density is obtained by second-order Runge-Kutta integration of Eq. (4). The spatial distributions in Fig. 1 were calculated for the time corresponding to the maximum electric field intensity in a linear regime at the focal spot (z = 0 and t = 0 correspond to position of this linear focal spot). The space step was chosen equal to 0.065 µm. As we can see, the laser beam is gathered while its intensity reach critical intensity allowing effective multiphoton ionization (in the case of fused silica, it is six-photon ionization). Excited electron plasma leads to reducing the medium refractive index and, as a result, electromagnetic field flows around region with the low optical density. After region with electron plasma, the electromagnetic field is gathered again. With increasing the input laser beam energy, the number of self-steepening (interchanging between flow around and gathering of electromagnetic field) processes is increased, too. Also, we clearly observe multiple cone formation (from Fig. 1 the characteristic cone angles can be determined as 13° for 0.135 J, 16° and 6° for 0.675 J, and 30°, 16° and 10° for 1.35 J) in the electric field intensity at laser power increasing and formation of plasma cone (this cone angle is decreased from 25° down to 20° at input energy increasing) with the vertex of a cone opposite to vertex of a cone for electric field intensity. a) Electric field intensity, 1013 W/cm2 z, m x ,  m -10 0 10 20 -2 0 2 0.5 1 1.5 2 2.5 Plasma density, 1021 cm-3 z, m -10 0 10 20 0 0.2 0.4 b) Electric field intensity, 1013 W/cm2 z, m x ,  m -10 0 10 20 -4 -2 0 2 4 1 2 3 Plasma density, 1021 cm-3 z, m -10 0 10 20 0 0.2 0.4 0.6 0.8 c) Electric field intensity, 1013 W/cm2 z, m x ,  m -10 0 10 20 -5 0 5 1 2 3 Plasma density, 1021 cm-3 z, m -10 0 10 20 0 0.5 1 Fig. 1. Spatial distribution of the electric field intensity and plasma density at propagation of an intense light pulse through non-linear medium (fused silica) for various input light energies: 0.135 (a), 0.675 (b) and 1.35 m (c) and for time corresponding to the electric field intensity maximum in the linear regime at the focal spot (t = 0). Name Value Notatio n Unit point number for x discretization 512 Nx point number for y discretization 512 Ny point number for t discretization 256 Nt first order dispersion parameter 4.894 1 fs/m second order dispersion parameter 0.034 2 fs2/m refractive index 1.4533 n0 non-linear refractive index 3.75·10- 16 n2 (W/cm2)-1 initial electron density 2.1·1022 0 cm-3 multiphoton ionization cross section 9.6·10-70 6 (W/cm2)-6/s ionization energy 9 Ui eV collision time 20 c fs electron recombination time 150 r fs reduced electron mass 0.64  me input energy 0.135 Iinput J z points number 400 Nz z-step 0.25 z m pulse waist (for 40× magnitude) 0.7 w0 m distance from linear focus and simulation start position 15 d m Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 48-54. © 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 52 a) x ,  m time, fs z = 10 m -200 -100 0 100 200 -2 0 2 time, fs -200 -100 0 100 200 x ,  m z = 5 m -2 0 2 x ,  m Electric field intensity, 1013 W/cm2 z = 2.5 m -2 0 2 0 1 2 Plasma density, cm-3 10 14 10 16 10 18 10 20 b) x ,  m time, fs z = 10 m -200 -100 0 100 200 -4 -2 0 2 4 time, fs -200 -100 0 100 200 x ,  m z = 5 m -4 -2 0 2 4 x ,  m z = 0 m -4 -2 0 2 4 x ,  m Electric field intensity, 1013 W/cm2 z = –5 m -4 -2 0 2 4 0.5 1 1.5 2 Plasma density, cm-3 10 14 10 16 10 18 10 20 c) x ,  m time, fs z = 10 m -200 -100 0 100 200 -5 0 5 time, fs -200 -100 0 100 200 x ,  m z = 5 m -5 0 5 x ,  m z = 0 m -5 0 5 x ,  m Electric field intensity, 1013 W/cm2 z = –5 m -5 0 5 0 1 2 3 Plasma density, cm-3 10 14 10 16 10 18 10 20 Fig. 2. Time evolution of light intensity and plasma density at z position depicted in Fig. 1 at fixed position y = 0 for various input light energies: 0.135 (a), 0.675 (b) and 1.35 m (c). The temporal evolution of electric field intensity and plasma density in plane y = 0 for laser beam propagation in fused silica at various positions in propagation beam direction corresponding to white dashed lines in Fig. 1 for various input electromagnetic energies are presented in Fig. 2. For the best contrast, the plasma density is presented in the logarithmic scale. Since Eq. (1) is written in the frame of reference moving at the group velocity of the pulse, the real time axis should be shifted by β1z. This scattering of laser beams in the form of multiple cones is connected with excitation of plasma waves. To proof this, the Fourier discrete transformations (FDT) of the electric field and plasma density over both transverse coordinate and time are presented in Fig. 3. This transformation allowed us to see dispersion relations. Here, we can see formation of a quasi-periodic structure with period about 0.14 µm in the plasma density. Also, Fig. 3 demonstrates formation of plasma waves and such wave could be estimation following to the Bohm–Gross dispersion relation,   2222 2/3 pleppl kv , where eep mne 0 2  is the plasma frequency, eeBe mTkv 2 – thermal speed of electrons, kpl – electron plasma wave vector, kB – Boltzmann constant, and Te – electron temperature. These dispersion curves are presented in Fig. 3 by dashed lines. It was found that the linear plasma response gives us quantitative description of formation of plasma waves in the nonlinear regime. For the case of 0.135 J laser pulse, the electron temperature is changed from 106 K up to 6·106 K with the effective plasma density 1018 cm. For the case of 0.675 J laser pulse, the electron temperature is changed from 6·106 K down to 3·106 K with the effective plasma density 1018 cm. For the case of 1.35 µJ laser pulse, the electron temperature is changed from 4·106 K up to 107 K with the effective plasma density 1019, 1018 and 4·1018 cm. These values agree in their order with the estimations made in [9] and corresponding periodicity in plasma density is about 0.14 µm. For periodic structure the Brillouin zones are shown by dashed-dotted lines in Fig. 3 for FDT of plasma density. The peculiarities in FDT of electric field intensity could be estimated using the dispersion relation for light waves propagating in electron plasma (bulk plasmon polaritons):   222 / plppl knc , where kph is the light wave vector and n – plasma refractive index. These dispersion waves are presented in Fig. 3 by solid lines. For the FDT of electric field intensity in Fig. 3, the value of wave vector could be obtained from kx = kph sinθ, where θ is the angle between kx and kz components of the wave vector. For fitting, we used 15 angle that corresponds to the angle between cone generatrices and laser beam propagation direction. Also, there are some lines with constant wave vectors in FDT of the electric Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 48-54. © 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 53 field intensity with unknown nature. The corresponding lengths for these lines are 0.23, 0.17 and 0.14 m and they still unchangeable in the case of input energy changing (dotted lines in Fig. 3). a)  , 1 /f s k x , 1/m z = 10 m 0 10 20 30 40 0 0.5 k x , 1/m 0 10 20 30 40  , 1 /f s z = 5 m 0 0.5 FDT of electric field intensity, a.u.  , 1 /f s z = 2.5 m 0 0.5 FDT of plasma density, a.u. b)  , 1 /f s k x , 1/m z = 10 m 0 10 20 30 40 0 0.5 k x , 1/m 0 10 20 30 40  , 1 /f s z = 5 m 0 0.5  , 1 /f s z = 0 m 0 0.5 FDT of electric field intensity, a.u.  , 1 /f s z = –5 m 0 0.5 FDT of plasma density, a.u. c)  , 1 /f s k x , 1/m z = 10 m 0 10 20 30 40 0 0.5 k x , 1/m 0 10 20 30 40  , 1 /f s z = 5 m 0 0.5  , 1 /f s z = 0 m 0 0.5 FDT of electric field intensity, a.u.  , 1 /f s z = –5 m 0 0.5 FDT of plasma density, a.u. Fig. 3. Coordinate-time Fourier discrete transformation for electric field and plasma density from Fig. 2. Dashed lines correspond to dispersion dependences for surface waves, solid lines – for bulk plasmon polaritons, and dashed-dotted lines – Brillouin zones. 4. Conclusions In this paper, propagation of an ultra-short laser pulse (150 fs) in transparent medium (fused silica) has been studied in regime of high input powers (0.135, 0.675 and 1.35 J) using the nonlinear Schrödinger equation with taking into account the group velocity dispersion, diffraction, self-focusing (optical Kerr effect) and absorption for multiphoton and avalanche ionization processes as well as continuity equation for the electron plasma density. The dynamic of interaction between the laser pulse and electron plasma that is induced by this pulse demonstrates complicated nature of ultrafast light- matter interaction, where competition between self- focusing and plasma defocusing processes leads to formation of multiple cones for the electric filed intensity and single cone formation for the plasma density. 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