Beam Width Parameter Research Articles

Self-focusing of Hermite-cosh-Gaussian laser beam in semiconductor quantum plasma

Self-focusing of Hermite-cosh-Gaussian (HchG) laser beam in semiconductor quantum plasma (ScQP) has been presented by considering the decentred parameter and quantum effect. We drive the equation of beam width parameter by using parabolic wave equation and solved it numerically by using WKB approximation. Our simulation results show that HchG beam gives freedom to source parameters that influence the self-focusing significantly. Additional self-focusing has been observed in ScQP than that of classical case of reference. The quantum plasma also adds pinching effect to laser propagation in semiconductor like germanium which further enhances the self-focusing more and more in ScQP.

Relativistic self-focusing of finite Airy-Gaussian beams in collisionless plasma using the Wentzel‐Kramers‐Brillouin approximation

In this paper, we present a preliminary study of relativistic self-focusing of finite Airy-Gaussian beams in collisionless plasma taking into consideration the relativistic nonlinearity in the dielectric constant. The differential equation for the beam width parameter of the finite Airy-Gaussian beam is derived by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations through parabolic wave equation approach. The behavior of beam width parameter with distance of propagation is investigated at different parameters of plasma and those of the considered beams family. Our results detect that the beam is more focused at higher values aperture coefficient and higher intensity parameter. Furthermore, a strong oscillatory behavior of the beam width parameter and better focusing during laser propagation in plasma is apparent.

Investigation of Weakly Relativistic Ponderomotive Effects on Self-Focusing During Interaction of High Power Elliptical Laser Beam with Plasma

This paper presents an investigation of weakly relativistic ponderomotive effects on self-focusing during interaction of high power elliptical laser beam with plasma. The nonlinear differential equations for the beam width parameters of elliptical laser beam have set up by using Wentzal–Krammers–Brillouin (WKB) and paraxial approximations. These equations have been solved numerically by using fourth order Runge–Kutta method to study the variation of these beam width parameters against normalized distance of propagation. Effects of variation in laser beam intensity, plasma density and electron temperature on the beam width parameters are also analyzed.

Generation of terahertz radiation by intense hollow Gaussian laser beam in magnetised plasma under relativistic-ponderomotive regime

This paper explores the self-focusing of hollow Gaussian laser beam (HGLB) in collisionless magnetized plasma and its effect on the generation of THz radiation in the presence of relativistic-ponderomotive nonlinearity. The relativistic change of electron mass and electron density perturbation due to the ponderomotive force leads to self-focusing of the laser beam in plasma. Nonlinear coupling between the intense HGLB and electron plasma wave leads to generation of THz radiation in plasma. Resonant excitation of THz radiation at different frequencies of laser and electron plasma wave satisfies proper phase matching conditions. Appropriate expressions for the beam width parameter of the laser beam and the electric vector of the THz wave have been evaluated under the paraxial-ray and Wentzel-Kramers Brillouin approximations. It is found that the yield of THz amplitude depends on the focusing behaviour of laser beam, magnetic field, and background electron density. Numerical simulations have been carried out to investigate the effect of laser and plasma parameters on self-focusing of the laser beam and further its effect on the efficiency of the generated THz radiation.

Pulse-compression and self-focusing of Gaussian laser pulses in plasma having relativistic–ponderomotive nonlinearity

AbstractThe mathematical model for the propagation of intense laser pulse in a plasma having Gaussian profile is investigated. The model has been formulated considering that the relativistic–ponderomotive nonlinearity dominates over other nonlinearities in the plasma. Model equation for self-compression and self-focusing properties of the laser pulse has been set up and solved by both semi-analytical and numerical methods. The result indicates that due to the effect of group velocity dispersion, diffraction of the laser pulse and the nonlinearity of medium, the pulse width parameter as well as beam width parameter of pulse gets focused at a different normalized distance, and hence the normalized intensity is also deferred at those points. Numerical simulation shows an oscillatory behavior of intensity during propagation in the plasma either having minimum beam radius (r0) or having minimum pulse duration (t0) depending on the normalized distance.

Propagation characters of multi-Gaussian beam with large eccentric displacement in collisionless plasma: Higher order paraxial theory

The multiple coherent identical Gaussian beams with symmetry distribution are abbreviated as multi-Gaussian beam, of which the propagation characters in collisionless plasma are studied with the WKB method and higher order paraxial theory. The initial beam profile presents the flat top like or hollow like distribution when the eccentric displacement is large enough. Based on the derived nonlinear propagation equations, the initial condition analyses are performed, and the impact of eccentric displacement on the free propagation effect and ponderomotive nonlinearity is thoroughly discussed. The propagation characters of dimensionless beam width parameter, spot intensity, and spatial distribution of plasma electron density are presented. Results show that the initial spot intensity is expanding outwards along the propagation and the ring structure of electron evacuation in plasmas is generated.

Average intensity and spreading of an astigmatic sinh-Gaussian beam with small beam width propagating in atmospheric turbulence

Propagation properties of astigmatic sinh-Gaussian beams (ShGBs) with small beam width in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel integral, analytical formulae for the average intensity and the effective beam size of an astigmatic ShGB are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of an astigmatic ShGB propagating in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of atmospheric turbulence on the propagation properties of astigmatic ShGBs are also discussed in detail. In particular, for sufficiently small beam width and sinh-part parameter as well as suitable astigmatism, we show that the average intensity pattern converts into a perfect dark-hollow profile from initial two-petal pattern when ShGBs with astigmatic aberration propagate through atmospheric turbulence.

Relativistic effects on evolution of a q-Gaussian laser beam in magnetoplasma: Application of higher order corrections

In this research work, the authors have investigated the propagation characteristics of a q-Gaussian laser beam in a magnetoplasma by considering the relativistic nonlinearity. The field distribution in the medium is expressed in terms of beam width parameter f and q parameter. Higher order terms in the expansion of the dielectric function and the eikonal have been taken into account. The behavior of the beam width parameter with a dimensionless distance of propagation ξ for various values of q is examined. The phenomenon of self-trapping is also studied under variety of parameters. Further, the effect of the magnetic field on the self-focusing of the laser beam has also been explored.

High intensity laser beam propagation through a relativistic warm magnetoplasma

In this work, nonlinear aspects of a circularly polarized high intensity Gaussian laser beam propagating in a relativistic warm magnetized plasma are studied, taking into account the relativistic ponderomotive force. The differential equation governing the dimensionless beam width parameter is achieved and numerically solved by introducing the dielectric permittivity of such plasma and using the paraxial ray approximation. The effects of entrance laser intensity and its polarization state, external magnetic field, and electron temperature on the laser spot size evolution are studied. It is found that for both right and left-handed polarization states increasing initial laser intensity deteriorates the self-focusing mechanism while rising electron temperature improves it. It is also observed that enhancing magnetic field leads to faster and stronger self-focusing in the case of right-handed polarization and an attenuation in the self-focusing process in the case of left-handed one. In addition, the spatial distribution of normalized modified electron density as well as laser intensity profiles as a function of plasma length and beam radius is plotted and discussed for three self-focusing, self-trapping, and defocusing regimes.

Tunable terahertz radiation generation by nonlinear photomixing of cosh-Gaussian laser pulses in corrugated magnetized plasma

AbstractThis paper presents a scheme of THz generation by nonlinear photomixing of two cosh-Gaussian lasers pulses having different frequencies (ω1, ω2) and wave numbers $(\vec k_1, \vec k_2 )$ and same electrical field amplitude in a corrugated plasma embedded with transverse static magnetic field. Cosh-Gaussian laser pulses have steep gradient in intensity profile along with wider cross-section, which exerts a stronger nonlinear ponderomotive force at ω1 − ω2 and $\vec k_1 - \vec k_2 $ on plasma electrons imparting a nonlinear oscillatory velocity to plasma electrons. Oscillatory plasma electrons couple with the density ripple n′ = nα0eiαx to produce a nonlinear current, which is responsible for resonant THz radiation at frequency $\sim\left( {{\rm \omega} _{\rm c}^2 + {\rm \omega} _{\rm p}^2} \right)^{1/2} $. The amplitude, efficiency and beam quality of THz radiation can be optimized by choosing proper corrugation factor (α of the plasma), applied magnetic field (ωc), decentered parameter (b), and beam width parameter a0 of cosh-Gaussian lasers. An efficiency of $\sim\!10^{ - 2} - 10^{ - 1} $ is achieved for laser electric field E = 3.2 × 109 V/cm.

Excitation of nonlinear ion acoustic wave and stimulated Brillouin scattering of hollow Gaussian beam in relativistic plasma

AbstractIn the present work, excitation of nonlinear ion acoustic wave (IAW) in collisionless plasma by laser beam having null intensity at the center is examined considering relativistic nonlinearity. The differential equation for beam-width parameter is determined considering relativistic nonlinearity using the paraxial and Wentzel–Kramers–Brillouin approximations by the parabolic equation method. The propagation features of the IAW are found to be modified due to the nonlinearity present in the system. The hollow Gaussian beam (HGB) gets nonlinearly coupled with the seed IAW, results in excitation of nonlinear IAW. The interaction of nonlinear IAW with pump beam demonstrated stimulated Brillouin scattering (SBS) of HGB. It is found that the power of IAW and power of SBS is affected with the order of HGB. The power of IAW and backscattered power of SBS is determined analytically and numerically for various orders of HGB. It is found that the power of IAW and the backscattering is diminished for higher order of HGB.

Growth of spike in relativistic Gaussian laser beam in a plasma and its effect on third-harmonic generation

AbstractA paraxial ray formalism is developed to study the evolution of an on axis intensity spike on a Gaussian laser beam in a plasma dominated by relativistic and ponderomotive non-linearities. Ion motion is taken to be frozen. A single beam width parameter characterizes the evolution of the spike. The spike introduces two competing influences: diffraction divergence and self-convergence. The former grows with the reduction in spot size of the spike, while the latter depends on the gradient in non-linear permittivity. Parameter δ = (ωpr00/c) a00/(3.5 r00/r01) characterizes the relative importance of the two, where r01 and r00 are the spike and main beam radii, ωp is the plasma frequency, and a00 is the normalized laser amplitude. For δ > 1, the intensity ripple causes faster self-focusing of the beam; higher the ripple amplitude stronger the focusing. In the opposite limit, diffraction divergence increases more rapidly, slowing down the self-focusing of the beam. As the beam intensity rises due to self-focusing, it causes stronger generation of the third harmonic.

Propagation characteristics of Hermite-cosh-Gaussian laser beam in a rippled density plasmas

AbstractIn the present research work, the authors have investigated the self-focusing and defocusing of Hermite-cosh-Gaussian laser (HChG) beam in an inhomogeneous rippled density plasmas. By taking the relativistic non-linearity into account, an equation for envelope is set up and solved using Wentzel–Kramers–Brillouin and the paraxial ray approximation. An ordinary non-linear differential equation governing the beam width parameter as a function of propagation distance is set up for different mode structures of the beam. Further, a numerical study of this differential equation is carried for suitable set of plasma and laser parameters. The beam undergoes periodic self-focusing/defocusing due to relativistic non-linearity. We also report the comparison between self-focusing/defocusing of HChG beam in the absence and presence of density ripple. Presence of ripple does not only leads to substantial increase in self-focusing length, but also results in oscillatory character with decreasing f. In a relativistic case, strong oscillatory self-focusing and defocusing is observed. Further, self-focusing is enhanced with increased value of decentered parameter.

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.

Stimulated Brillouin backscattering of hollow Gaussian laser beam in collisionless plasma under relativistic–ponderomotive regime

AbstractStimulated Brillouin backscattering of an intense hollow Gaussian laser beam (HGLB) from collisionless plasma has been investigated under relativistic–ponderomotive regime. The main feature of considered hollow Gaussian laser beam is having the same power at different beam orders with null intensity at the center. Backscattered radiation is generated due to nonlinear interaction between main beam (pump beam) with pre-excited ion acoustic wave (IAW). Modified coupled equations has been set up for the beam width parameters of the main beam, ion-acoustic wave, back-scattered wave, and back reflectivity of stimulated Brillouin scattering (SBS) with the help of the Wentzel–Kramers–Brillouin approximation, fluid equations and paraxial theory approach. These coupled equations are solved analytically and numerically to study the laser intensity in the plasma, the variation of amplitude of the excited IAW and back reflectivity of SBS. The back reflectivity of SBS is found to be highly sensitive to the order of the HGLB, intensity of main laser beam, and plasma density for typical laser and plasma parameters. The focusing of main laser beam (hollow Gaussian) and IAW significantly affected the back reflectivity of SBS. The results show that the self-focusing and back reflectivity is enhanced for higher order modes of HGLB.

Effect of the transverse magnetic field on spatiotemporal dynamics of quadruple Gaussian laser beam in plasma in weakly relativistic and ponderomotive regime

The spatiotemporal dynamics of a quadruple Gaussian laser beam in plasma is studied in the presence of an external magnetic field by taking into account the relativistic and ponderomotive nonlinearities. Using the paraxial approximation approach, two coupled equations for longitudinal (in time) and transverse (in space) beam width parameters are derived. Their evolution determines the pulse dynamics in time and space. The effects of the initial laser parameters, such as the lateral separation and laser intensity on self-focusing and self-compression mechanisms, are discussed. The results illustrate that the laser beam is focussed and compressed in an enhanced manner in the presence of an external magnetic field. The three dimensional spatiotemporal profile of the normalized intensity of the pulse is studied at different positions where the beam is either focussed or compressed. A three dimensional portrait of the normalized intensity as a function of distance and time is also shown.

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.

Self-focusing of a laser beam in the rippled density magnetoplasma

In the present paper, we have investigated the self-focusing of intense laser beam in rippled density magnetoplasma. The differential equation for the beam width parameter is obtained by following WKB and paraxial approximations and solved it numerically. The behaviour of beam width parameter with dimensionless distance of propagation is extensively investigated for different values of laser and plasma parameters and is strongly influenced by the magnetic field. The results are discussed and presented graphically. It is seen that the density ripple of suitable wave number increases the self-focusing property of laser beam in magnetoplasma. Meanwhile, an increase in the values of magnetic field increases the strength of the self-focusing, especially in shorter distance of propagation. Furthermore, increase in plasma frequency (plasma density) causes more reduction in the spot size of laser beam and consequently increases the rate of self-focusing of laser beam in magnetoplasma.

GeV electron acceleration by a Gaussian field laser with effect of beam width parameter in magnetized plasma

Electron acceleration due to a circularly polarized (CP) Gaussian laser field has been investigated theoretically in magnetized plasma. A Gaussian laser beam possesses trapping forces on electrons during its propagation through plasma. A single particle simulation indicates a resonant enhancement of electron acceleration with a Gaussian laser beam. The plasma is magnetized with an axial magnetic field in same direction as that of laser beam propagation. The dependence of laser beam width parameter on electron energy gain with propagation distance has been presented graphically for different values of laser intensity. Electron energy gain is relatively high where the laser beam parameter is at its minimum value. Enhanced energy gain of the order of GeV is reported with magnetic field under 20MG in plasma. It is also seen that the axial magnetic field maintains the electron acceleration for large propagation distance even with an increasing beam width parameter.

Self-Focusing/Defocusing of Chirped Gaussian Laser Beam in Collisional Plasma with Linear Absorption**Supported by a financial grant from CSIR, New Delhi, India, under Project No. 03(1277)/13/EMR-II

This paper presents an investigation on the self-focusing/defocusing of chirped Gaussian laser beam in collisional plasma with linear absorption. We have derived the differential equation for the beam width parameter by using WKB and paraxial approximations and solved it numerically. The effect of chirp and other laser plasma parameters is seen on the behavior of beam width parameter with dimensionless distance of propagation. The results are discussed and presented graphically. Our simulation results show that the amplitude of oscillations decreases with the distance of propagation. Due to collisional frequency, the laser beam shows fast divergence which can be minimized by the introduction of chirp parameter. The chirp decreases the effect of defocusing and increases the ability of self-focusing of laser beam in collisional plasma.