Self-focusing Of Gaussian Laser Beam Research Articles

Self-Focusing of Gaussian Laser Beam in an Axially Magnetized Plasma

A well established parabolic equation approach to study the evolution of self-focusing of Gaussian laser beam in underdense, magnetized plasma has been presented. The uniform external magnetic field is assumed to be applied along (forward) as well as opposite (reverse) to the direction of propagation of laser beam. The nonlinear differential equation governing dimensionless beam-width parameter is derived under WKB and paraxial approximations. It is observed that forward (reverse) magnetic field increases (decreases) the self-focusing of Gaussian laser beam as compared to the unmagnetized case of reference.

Relativistic-Ponderomotive Self-Focusing of Gaussian Laser Beam Propagating in Magnetized Cold Quantum Plasma

Relativistic-Ponderomotive Self-Focusing of Gaussian Laser Beam Propagating in Magnetized Cold Quantum Plasma

Resonant second harmonic generation in plasma under exponential density ramp profile

Resonant second harmonic generation of a relativistic self-focused laser beam in plasma under exponential density ramp profile is investigated. It has been found that the self-focusing of Gaussian laser beam becomes stronger in plasma with exponential density ramp profile hence, leads to enhance the resonant second harmonic generation. The periodic variation of the normalized second-harmonic amplitude with normalized distance has been analyzed for different laser and plasma parameters. Therefore, enhanced second harmonic generation on account of relativistic self-focusing of fundamental laser beam in plasma under plasma density transition is observed. One may notice that exponential density ramp plays an important role in making the self-focusing stronger which in turn enhances the second harmonic generation in plasma.

Exponential density transition based self-focusing of Gaussian laser beam in collisional plasma

In this work, nonlinear aspects of a high intensity Gaussian laser beam propagating in plasma having upward density ramp of tangent and exponential profiles are studied. We have employed the nonlinearity in dielectric function of plasma due to nonuniform heating of carriers along the wavefront of the laser beam which is important in collisional plasmas. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel–Kramers–Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing is systematically carried out and compared with tangent density ramp profile. It is found that exponential plasma density ramp causes the laser beam to become more focused than tangent density ramp over several Rayleigh length and gives reasonably interesting results.

Weakly relativistic self-focusing of Gaussian laser beam in magnetized cold quantum plasma

AbstractIn the present paper, we have studied self-focusing of Gaussian laser beam in weakly relativistic magnetized cold quantum plasma. When interparticle distance is comparable to the de Broglie wavelength of charged particles, we cannot neglect the quantum contribution of plasma constituents. Therefore, propagation characteristics are studied by taking in to account quantum contribution in the presence of static magnetic field applied along the beam propagation. Our results show that the magnetic field plays a key role in achieving additional focusing, it modifies the quiver motion of electrons by adding cyclotron frequency to the natural frequency of oscillating electrons during laser beam propagation. The results are compared with those of weakly relativistic quantum plasma and weakly relativistic magnetized plasma. The self-focusing is found to be more pronounced when axial magnetic field is increased in the present model. We have setup the non-linear differential equation for the evolution of beam-width parameter by well-known paraxial ray approximation and solved it with the help of computational technique.

Self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive cold quantum plasma

The paper presents investigation on self-focusing and self-phase modulation of Gaussian laser beam in a weakly relativistic and ponderomotive regime by taking into account the quantum effects. We have reported additional self-focusing for reduced value of beam width parameter on account of nonlinear dielectric contribution of relativistic ponderomotive plasma. Moreover, the significant contribution of the quantum effects to enhance the self-focusing and minimize the longitudinal phase shift has been noticed. A comparison has also been attempted with relativistic and ponderomotive, relativistic cold quantum and classical relativistic regimes. In the present investigation, we have observed that for the case of relativistic ponderomotive cold quantum plasma, the focusing is found to be earlier and strongest. Also, the minimum amount of phase shift is obtained. We have setup the nonlinear differential equations for the beam-width parameter and self-phase modulation by using variational approach and solved them numerically by the Runge-Kutta method.

Sensitiveness of light absorption for self-focusing at laser–plasma interaction with weakly relativistic and ponderomotive regime

AbstractIn the present paper, we have examined the sensitiveness of light absorption for self-focusing of Gaussian laser beam in plasma. By introducing dielectric function of plasma under ponderomotive and weakly relativistic regime, we have established the differential equation for beam-width parameter by using parabolic equation approach under Wentzel-Kramers-Brillouin and paraxial approximations and solved it numerically. In order to incorporate the sensitiveness of light absorption for self-focusing, behavior of normalized beam-width parameter; plasma density distribution with dimensionless distance of propagation is presented graphically and discussed. Numerical analysis shows that light absorption plays a vital role in self-focusing of laser beam in plasma under weakly relativistic and ponderomotive regime and gives reasonably interesting results.

Combined effect of relativistic and ponderomotive nonlinearity on self-focusing of Gaussian laser beam in a cold quantum plasma

AbstractIn the present paper, we have investigated self-focusing of Gaussian laser beam in relativistic ponderomotive (RP) cold quantum plasma. When de Broglie wavelength of charged particles is greater than or equal to the inter particle distance or equivalently the temperature is less than or equal to the Fermi temperature, quantum nature of the plasma constituents cannot be ignored. In this context, we have reported self-focusing on account of nonlinear dielectric contribution of RP plasma by taking into consideration the impact of quantum effects. We have setup the nonlinear differential equation for the beam-width parameter by paraxial ray and Wentzel Kramers Brillouin approximation and solved it numerically by the Runge Kutta Fourth order method. Our results show that additional self-focusing is achieved in case of RP cold quantum plasma than relativistic cold quantum plasma and classical relativistic case. The pinching effect offered by quantum plasma and the combined effect of relativistic and ponderomotive nonlinearity greatly enhances laser propagation up to 20 Rayleigh lengths.

Effect of light absorption on relativistic self-focusing of Gaussian laser beam in plasma

In the present paper, we have studied the effect of light absorption on relativistic self-focusing of Gaussian laser beam propagating through plasma. We have obtained the differential equation for beam width parameter by using parabolic equation approach under the usual WKB and paraxial approximations. The effect of light absorption on the behavior of beam-width parameter, normalized intensity and plasma dielectric function is presented graphically and discussed. It shows that absorption play an important role in weakening the relativistic self-focusing of laser beam during propagation in plasma and gives reasonably interesting results.

Response to “Comment on ‘Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma’” [Phys. Plasmas 21, 064701 (2014)

Habibi and Ghamari have presented a Comment on our paper [Phys. Plasmas 20, 072703 (2013)] by examining quantum dielectric response in thermal quantum plasma. They have modeled the relativistic self-focusing of Gaussian laser beam in cold and warm quantum plasmas and reported that self-focusing length does not change in both situations. In this response, we have reached the following important conclusions about the comment itself.

Ponderomotive self-focusing of Gaussian laser beam in warm collisional plasma

The propagation characteristics of a Gaussian laser beam through warm collisional plasma are investigated by considering the ponderomotive force nonlinearity and the complex eikonal function. By introducing the dielectric permittivity of warm unmagnetized plasma and using the WKB and paraxial ray approximations, the coupled differential equations defining the variations of laser beam parameters are obtained and solved numerically. Effects of laser and plasma parameters such as the collision frequency, the initial laser intensity and its spot size on the beam width parameter and the axis laser intensity distribution are analyzed. It is shown that, self-focusing of the laser beam takes place faster by increasing the collision frequency and initial laser spot size and then after some distance propagation the laser beam abruptly loses its initial diameter and vastly diverges. Furthermore, the modified electron density distribution is obtained and the collision frequency effect on this distribution is studied.

Comment on “Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma” [Phys. Plasmas 20, 072703 (2013)

Patil and Takale in their recent article [Phys. Plasmas 20, 072703 (2013)], by evaluating the quantum dielectric response in thermal quantum plasma, have modeled the relativistic self-focusing of Gaussian laser beam in a plasma. We have found that there are some important shortcomings and fundamental mistakes in Patil and Takale [Phys. Plasmas 20, 072703 (2013)] that we give a brief description about them and refer readers to important misconception about the use of the Fermi temperature in quantum plasmas, appearing in Patil and Takale [Phys. Plasmas 20, 072703 (2013)].

Effect of Self-focusing of Gaussian Laser Beam on Second Harmonic Generation in Relativistic Plasma

In the present paper, effect of self-focusing of gaussian laser beam on second harmonic generation in relativistic plasma is investigated. An expression for density perturbation associated with plasma wave has been derived, which acts as a source for second harmonic generation. Moment theory approach has been used to set up wave equation for the laser beam. Effect of the intensity of the laser beam and plasma density on the harmonic yield is studied in detail. It is predicted from the analysis that harmonic yield increases due to increase in the plasma density and intensity of the laser beam.

Comparison of two theories during self-focusing of Gaussian laser beam in thermal conduction-loss predominant plasmas

In the present paper, self-focusing phenomenon occurring as a result of non-linear interaction of intense laser beam with thermal conduction-loss predominant plasmas is studied by following both approaches viz. paraxial theory approach and moment theory approach. Non-linear differential equations for the beam width parameters of laser beam have been set up and solved numerically in both cases to study the variation of beam width parameters with normalized distance of propagation. Effects of laser intensity as well as plasma density on the beam width parameters have also been analyzed. It is observed from the analysis that in case of moment theory approach, strong self-focusing of laser beam is observed as compared to paraxial theory approach.

Self-focusing of Gaussian laser beam in collisionless plasma and its effect on stimulated Raman scattering process

This paper presents an investigation of self-focusing of Gaussian laser beam in collisionless plasma and its effect on stimulated Raman scattering process. The pump beam interacts with a pre-excited electron plasma wave thereby generating a back-scattered wave. On account of Gaussian intensity distribution of laser beam, the time independent component of the ponderomotive force along a direction perpendicular to the beam propagation becomes finite, which modifies the background plasma density profile in a direction transverse to pump beam axis. This modification in density affects the incident laser beam, electron plasma wave and back-scattered beam. We have set up the non-linear differential equations for the beam width parameters of the main beam, electron plasma wave, back-scattered wave and SRS-reflectivity by taking full non-linear part of the dielectric constant of collisionless plasma with the help of moment theory approach. It is observed from the analysis that focusing of waves greatly enhances the SRS reflectivity.

Self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive regime using upward ramp of plasma density

We have studied the steady state self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive regime for upward increasing plasma ramp density profile. We have obtained the differential equation for beam width parameter by using parabolic equation approach under the usual Wentzel–Kramers–Brillouin and paraxial approximations. The variation of beam width parameter with respect to dimensionless distance of propagation is presented graphically by varying the parameters of density profile, intensity parameter, and electronic temperature. It shows that the above stated parameters play an important role in propagation characteristics and give reasonably interesting results.

Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma

In the present paper, we have employed the quantum dielectric response in thermal quantum plasma to model relativistic self-focusing of Gaussian laser beam in a plasma. We have presented an extensive parametric investigation of the dependence of beam-width parameter on distance of propagation in relativistic thermal quantum plasma. We have studied the role of Fermi temperature in the phenomenon of self-focusing. It is found that the quantum effects cause much higher oscillations of beam-width parameter and better relativistic focusing of laser beam in thermal quantum plasma in comparison with that in the relativistic cold quantum plasma and classical relativistic plasma. Our computations show more reliable results in comparison to the previous works.

Self-focusing of Gaussian Laser Beam Through Collisional Plasmas: Moment Theory Approach

In the present paper, self-focusing of Gaussian laser beam through collisional plasma is studied by moment theory approach. Nonlinear differential equation for beam width parameter of laser beam has been set up and solved numerically to study the variation of beam width parameter with normalized distance of propagation. Effect of absorption coefficient and plasma density on the beam width parameter has been studied. It is observed from the analysis that increasing the value of absorption coefficient brings about reduction in extent of self-focusing on account of decrease in energy of beam, which is equivalent to weakening of nonlinearity effect. On the other hand, increase in plasma density results in a sharp decrease in focusing length due to increase in nonlinear part of dielectric constant.

Self-focusing of Gaussian laser beam in collisionless plasma and its effect on stimulated Brillouin scattering process

This paper presents an investigation of self-focusing of Gaussian laser beam in collisionless plasma and its effect on stimulated Brillouin scattering process. The pump beam interacts with a pre-excited ion-acoustic wave thereby generating a back-scattered wave. On account of Gaussian intensity distribution of laser beam, the time independent component of the ponderomotive force along a direction perpendicular to the beam propagation becomes finite, which modifies the background plasma density profile in a direction transverse to pump beam axis. This modification in density affects the incident laser beam, ion-acoustic wave and back-scattered beam. We have set up non-linear differential equations for the beam width parameters of the main beam, ion-acoustic wave, back-scattered wave and SBS-reflectivity with the help of moment and paraxial theory approach. Results of the moment theory approach have been compared with that of paraxial theory approach. It has been observed from the analysis that reflectivity of the back-scattered wave is less in moment theory approach as compared to paraxial theory approach.

Impact of linear absorption on self-focusing of Gaussian laser beam in collisional plasma

The authors have investigated impact of linear absorption on self-focusing of Gaussian laser beam in collisional plasma. The nonlinearity in dielectric constant considered herein is mainly due to the elastic electron–ion collisions. A second order differential equation of dimensionless beam width parameter has been derived and solved numerically. It is observed that absorption plays a vital role in self-focusing of laser beams and weakens the stationary oscillatory character of beam-width parameter with distance of propagation. We have also considered the effect of intensity, relative density and parameter characterizing nature of collisions on propagation characteristics.