Steady-state self-focusing of rippled laser beams in plasmas: arbitrary nonlinearity

1992 ◽  
Vol 48 (1) ◽  
pp. 107-118 ◽  
Author(s):  
M. S. Sodha ◽  
S. Konar ◽  
K. P. Maheshwari
Keyword(s):  
Dielectric Constant ◽  
Thermal Conduction ◽  
Critical Power ◽  
Laser Beams ◽  
Main Beam ◽  
Effective Dielectric Constant ◽  
Beam Power ◽  
Nonlinear Part ◽  
Self Focusing ◽  
Paraxial Ray

This paper presents an analysis of the self-focusing of a rippled Gaussian laser beam in a plasma when the nonlinear part of the effective dielectric constant is arbitrarily large. Considering the nonlinearity to arise from ponderomotive, collisional or thermal-conduction phenomena and following the approach of Akhmanov, Sukhorukov and Khokhlov (which is based on the WKB and paraxial-ray approximation) the phenomenon of self-focusing of rippled laser beams is studied for arbitrary magnitude of nonlinearity. For ponderomotive and collisional nonlinearities, the present theory leads to two values of the critical power for self-focusing of the beam, Pcrl and Pcr2, which depend on the amplitudes and phase difference of the main beam and the ripple. When the beam power P lies between the two critical values (i.e. Pcr1 < P < Pcr2), the medium behaves as an oscillatory waveguide; the beam first converges and then diverges, again converges, and so on. For P < Pcr2, the beam first diverges, then converges, then diverges, and so on. When thermal conduction is the dominant mechanism of nonlinearity of the dielectric constant, only one value of the threshold critical power Pcr for self-focusing of the beam exists. When the beam power P < Pcr, the medium behaves as an oscillatory waveguide.

scholarly journals Nonlinear relativistic self-focusing of laser radiation in plasmas: Arbitrary intensity

1994 ◽  
Vol 12 (4) ◽  
pp. 623-632 ◽  
Author(s):  
M. Asthana ◽  
K.P. Maheshwari ◽  
M.S. Sodha
Keyword(s):  
Dielectric Constant ◽  
Critical Power ◽  
Laser Pulses ◽  
Density Fluctuations ◽  
Effective Dielectric Constant ◽  
Gaussian Laser Beam ◽  
Nonlinear Part ◽  
Self Focusing ◽  
Paraxial Ray ◽  
Arbitrary Intensity

A paraxial theory of relativistic self-focusing of a Gaussian laser beam in plasmas, when the nonlinear part of the effective dielectric constant is arbitrarily large, is presented. The plasma is taken to be homogeneous without any density fluctuations being necessary. The approach of Akhmanov et al. based on the WKB and paraxial ray approximations has been followed. It is seen that the saturating nature of nonlinearity leads to two values of critical power of the beam (Pcrl and Pcr2) for self-focusing. When the power of the beam P lies between the two critical values (i.e., Pcr1 < P < Pcr2), the medium behaves as an oscillatory waveguide; the beam first converges and then diverges, converges again, and so on. For P > Pcr2 the beam first diverges, then converges, then diverges, and so on. Because the relativistic mechanism is instantaneous, the theory is applicable to the understanding of selffocusing of laser pulses also.

Relativistic self-focusing of a rippled laser beam in a plasma

1999 ◽  
Vol 62 (4) ◽  
pp. 389-396 ◽  
Author(s):  
M. V. ASTHANA ◽  
A. GIULIETTI ◽  
DINESH VARSHNEY ◽  
M. S. SODHA
Keyword(s):  
Refractive Index ◽  
Laser Beam ◽  
The Self ◽  
Laser Beams ◽  
Radial Dependence ◽  
Main Beam ◽  
Gaussian Laser Beam ◽  
Self Focusing ◽  
Saturation Effects ◽  
Paraxial Ray

This paper presents an analysis of the relativistic self-focusing of a rippled Gaussian laser beam in a plasma. Considering the nonlinearity as arising owing to relativistic variation of mass, and following the WKB and paraxial-ray approximations, the phenomenon of self-focusing of rippled laser beams is studied for arbitrary magnitude of nonlinearity. Pandey et al. [Phys. Fluids82, 1221 (1990)] have shown that a small ripple on the axis of the main beam grows very rapidly with distance of propagation as compared with the self-focusing of the main beam. Based on this analogy, we have analysed relativistic self-focusing of rippled beams in plasmas. The relativistic intensities with saturation effects of nonlinearity allow the nonlinear refractive index in the paraxial regime to have a slower radial dependence, and thus the ripple extracts relatively less energy from its neighbourhood.

scholarly journals Relativistic self-focusing of transmitted laser radiation in plasmas

2000 ◽  
Vol 18 (1) ◽  
pp. 101-107 ◽  
Author(s):  
MEENU V. ASTHANA ◽  
DINESH VARSHNEY ◽  
M.S. SODHA
Keyword(s):  
Dielectric Constant ◽  
Laser Radiation ◽  
Critical Power ◽  
Interaction Process ◽  
Gaussian Laser Beam ◽  
Laser Plasma Interaction ◽  
Paraxial Ray Approximation ◽  
Self Focusing ◽  
Beam Incident ◽  
Paraxial Ray

This paper presents an analysis of relativistic self-focusing of a Gaussian laser beam incident normally on a plane interface of a linear medium and a nonlinear, nonabsorbing plasma with an intensity dependent dielectric constant. Considering the nonlinearity to arise from the relativistic variation of mass and the Lorentz force on electrons. Following Wentzel–Kramers–Brillouin (WKB) and paraxial ray approximation the phenomenon of relativistic self-focusing of the transmitted laser radiation has been analyzed for the arbitrary magnitude of nonlinearity. Change in the intensity distribution along the wavefront of the Gaussian beam, due to refraction at the interface has also been taken into account. The variation of beamwidth parameter with distance of propagation, self trapping condition and critical power has been evaluated. Numerical estimates for typical parameters of laser plasma interaction process indicate the refraction at the interface to have a significant effect on self-focusing.

scholarly journals Relativistic interaction of rippled laser beams with plasmas

2000 ◽  
Vol 18 (3) ◽  
pp. 399-403 ◽  
Author(s):  
M.V. ASTHANA ◽  
A. GIULIETTI ◽  
D. GIULIETTI ◽  
L.A. GIZZI ◽  
M.S. SODHA
Keyword(s):  
Laser Beam ◽  
Critical Power ◽  
Radial Dependence ◽  
Main Beam ◽  
Gaussian Laser Beam ◽  
Self Focusing ◽  
Relativistic Interaction ◽  
Saturation Effects ◽  
Paraxial Ray ◽  
Initial Power

An investigation of the growth of a radially symmetrical ripple, superimposed on a Gaussian laser beam in a plasma is presented. Based on WKB and paraxial ray approximation the phenomenon of relativistic self-focusing (RSF) is analytically investigated. The differential equation for beamwidth parameter of rippled laser beam is evaluated. The ripple gets focused when the initial power of the ripple is greater than the critical power for focusing. The focusing is found to be considerably affected by the power of the main beam and the phase angle between the electric vectors of the main beam and the ripple. At higher intensities the saturation effects of nonlinearity become predominant, making the nonlinear refractive index in the paraxial region have slower radial dependence, and thus the ripple extract relatively less energy from its neighborhood. The case of magnetized plasmas is also preliminarily discussed.

scholarly journals Relativistic Propagation of Linearly/Circularly Polarized Laser Radiation in Plasmas

ISRN Optics ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Sonu Sen ◽  
Meenu Asthana Varshney ◽  
Dinesh Varshney
Keyword(s):  
Dielectric Constant ◽  
Critical Power ◽  
Laser Pulses ◽  
Interaction Process ◽  
Laser Beams ◽  
Laser Beam Propagation ◽  
Circularly Polarized ◽  
Nonlinear Dielectric ◽  
Laser Plasma Interaction ◽  
Self Focusing

Paraxial theory of relativistic self-focusing of Gaussian laser beams in plasmas for arbitrary magnitude of intensity of the beam has been presented in this paper. The nonlinearity in the dielectric constant arises on account of relativistic variation of mass. An appropriate expression for the nonlinear dielectric constant has been used to study laser beam propagation for linearly/circularly polarized wave. The variation of beamwidth parameter with distance of propagation, self-trapping condition, and critical power has been evaluated. The saturating nature of nonlinearity yields two values of critical power of the beam ( and ) for self-focusing. When the beam diverges. When the beam first converges then diverges and so on. When the beam first diverges and then converges and so on. Numerical estimates are made for linearly/circularly polarized wave applicable for typical values of relativistic laser-plasma interaction process in underdense and overdense plasmas. Since the relativistic mechanism is instantaneous, this theory is applicable to understanding of self-focusing of laser pulses.

scholarly journals Dynamics of Gaussian spikes on Gaussian laser beam in relativistic plasma

2009 ◽  
Vol 27 (4) ◽  
pp. 587-593 ◽  
Author(s):  
A. Singh ◽  
M. Aggarwal ◽  
T.S. Gill
Keyword(s):  
Differential Equations ◽  
Laser Beam ◽  
Nonlinear Differential Equations ◽  
Beam Width ◽  
Main Beam ◽  
Gaussian Laser Beam ◽  
Runge Kutta Method ◽  
Self Focusing ◽  
Gaussian Perturbation ◽  
Paraxial Ray

AbstractIn the present paper, we have investigated the growth of a Gaussian perturbation superimposed on a Gaussian laser beam. The nonlinearity we have considered is of relativistic type. We have setup the nonlinear differential equations for beam width parameter of the main beam, growth and width of the laser spike by using the WKB and paraxial ray approximation. These are coupled ordinary differential equations and therefore these are simultaneously solved numerically using the Runge Kutta method. It has been observed from the analysis that self-focusing/defocusing of the main beam and the spike determine the growth dynamic of the spike.

scholarly journals On the exploration of graphical and analytical investigation of effect of critical beam power on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma

2018 ◽  
Vol 36 (2) ◽  
pp. 254-260 ◽  
Author(s):  
T. U. Urunkar ◽  
S. D. Patil ◽  
A. T. Valkunde ◽  
B. D. Vhanmore ◽  
K. M. Gavade ◽  
...  
Keyword(s):  
Differential Equation ◽  
Turning Points ◽  
Beam Width ◽  
Analytical Investigation ◽  
Graphical Analysis ◽  
Magnetized Plasma ◽  
Laser Beams ◽  
Beam Power ◽  
Equation Approach ◽  
Self Focusing

AbstractThe paper gives graphical and analytical investigation of the effect of critical beam power on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive non-linearity. The standard Akhmanov's parabolic equation approach under Wentzel–Kramers–Brillouin (WKB) and paraxial approximations is employed to investigate the propagation of cosh-Gaussian laser beams in collisionless magnetized plasma. Especially, the concept of numerical intervals and turning points of critical beam power has evolved through graphical analysis of beam-width parameter differential equation of cosh-Gaussian laser beams. The results are discussed in the light of numerical intervals and turning points.

INTERACTION OF INTENSE SHORT LASER PULSES WITH AIR AND DIELECTRIC MATERIALS

2007 ◽  
Vol 21 (03n04) ◽  
pp. 615-625 ◽  
Author(s):  
S. EISENMANN ◽  
Y. KATZIR ◽  
A. ZIGLER ◽  
G. FIBICH ◽  
E. LOUZON ◽  
...  
Keyword(s):  
Critical Power ◽  
Laser Pulses ◽  
Dielectric Materials ◽  
Laser Beams ◽  
Threshold Fluence ◽  
Short Pulses ◽  
Self Focusing ◽  
Chirped Pulses ◽  
Short Laser Pulses ◽  
Wide Gap

A study of the propagation of intense short laser pulses in air and the interaction of these pulses with distant targets is described. It is shown that the beam filamentation pattern can be controlled by introducing beam astigmatism. In addition, it is demonstrated that the collapse distance of intense femtosecond laser beams scales as P -1/2 for input powers that are moderately above the critical power for self focusing, and that at higher powers the collapse distance scales as P -1. Related to the interaction of intense short pulses with distant targets, it is measured that the threshold fluence for optical damage in wide gap materials is lower by up to 20% for negatively chirped pulses than for positively chirped, at pulse durations ranging from 60 fs to 1 ps.

scholarly journals Domains of modulation parameter in the interaction of finite Airy–Gaussian laser beams with plasma

2020 ◽  
Vol 38 (3) ◽  
pp. 204-210
Author(s):  
V. S. Pawar ◽  
S. R. Kokare ◽  
S. D. Patil ◽  
M. V. Takale
Keyword(s):  
Absorption Coefficient ◽  
Collisionless Plasma ◽  
Beam Width ◽  
The Self ◽  
Laser Beams ◽  
Linear Absorption Coefficient ◽  
Linear Absorption ◽  
Self Focusing ◽  
Modulation Parameter ◽  
Paraxial Ray

AbstractIn this paper, self-focusing of finite Airy–Gaussian (AiG) laser beams in collisionless plasma has been investigated. The source of nonlinearity considered herein is relativistic. Based on the Wentzel–Kramers–Brillouin (WKB) and paraxial-ray approximations, the nonlinear coupled differential equations for beam-width parameters in transverse dimensions of AiG beams have been established. The effect of beam's modulation parameter and linear absorption coefficient on the self-focusing/defocusing of the beams is specifically considered. It is found that self-focusing/defocusing of finite AiG beams depends on the range of modulation parameter. The extent of self-focusing is found to decrease with increase in absorption.

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