Here we report on a simple-to-implement and cost-effective approach for laser pulse contrast enhancement, based on the ${\chi}^{(3)}$ nonlinear self-focusing effect. An intentionally induced and gently controlled self-focusing in a thin glass transforms the time-dependent intensity into variation in beam divergence. Followed by a spatial discriminating filter, only the strongly focused fraction traverses the setup, at the expense of efficiency. A numerical model, accounting for the pulse and material parameters via a Gaussian ABCD matrix, provides an estimate for the instantaneous beam waist and transmission efficiency, which enables us to evaluate the resulting contrast enhancement. The estimated contrast enhancement spans between 0.5 and 2.5 orders of magnitude, in conjunction with approximately 25%–90% estimated efficiency, depending on the pulse parameters. In a preliminary experiment we demonstrated the effect with 10s-μJ sub GW regime with approximately 40$\%$ efficiency and a contrast improvement of more than or equal to 20 dB.

In the paper, relativistic self-focusing in the interaction of laser beam and plasma with periodical density ripple has been studied by the applied WKB approximation and higher-order paraxial theory. The result shows that under the influence of relativistic nonlinear effect, the dielectric function shows the fierce oscillational variation with similar periodicity, which then leads to the intense relativistic beam self-focusing along the propagation distance, such self-focusing also presents similar periodic variation. Besides, in the plasma with periodical density ripple, the initial density and the density ripple amplitude have obvious influence on self-focusing. When the two factors increase, then there will be more strength self-focusing. Choosing the appropriate initial density and the periodic density parameter is benefit to the formation of the more stable self-focusing.

In 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.

In the paper, we applied the paraxial region theory and Wentzel–-Kramers–-Brillouin approximation to study laser beam self-focusing in the interaction of laser and collisional plasma with periodical density ripple. The results have shown that, under the influence of collision nonlinear effect, laser presents stable self-focusing, self-defocusing, and oscillational self-focusing in the plasma. Besides, the parameters of plasma with periodical density ripple have a greater impact on the effect of self-defocusing and oscillational self-focusing than stable self-focusing. In certain conditions, beam self-defocusing and oscillational self-focusing would decline and even disappear, and stable self-focusing would further be strengthened. Hence, selecting a suitable periodic plasma system is advantageous for separating self-defocusing and oscillational self-focusing, and for the formation of a more stable collisional self-focusing.

Self-focusing of Gaussian laser beam has been investigated in quantum plasma under the effect of applied axial magnetic field. The nonlinear differential equation has been derived for studying the variations in the beam-width parameter. The effect of initial plasma electron temperature and the axial magnetic field on self-focusing and normalized intensity are studied. Our investigation reveals that normalized intensity increases to tenfolds where quantum effects are dominant. The normalized intensity further increases to twelvefolds on increasing the magnetic field.

A band-stop angular filter (BSF) based on hump volume Bragg gratings (HVBGs) is proposed. Band-stop filtering in a two-stage amplifier laser system is discussed and simulated. Simulation results show that small-scale self-focusing effects in the laser system can be effectively suppressed with the BSF due to the control of fast nonlinear growth in a specific range of spatial frequencies in the laser beam. Near-field modulation of the output beam from the laser system was decreased from 2.69 to 1.37 by controlling the fast nonlinear growth of spatial frequencies ranging from $0.6~\text{mm}^{-1}$ to $1.2~\text{mm}^{-1}$ with the BSF. In addition, the BSF can be used in a plug-and-play scheme and has potential applications in high-power laser systems.

This paper presents a scheme for second harmonic generation (SHG) of q-Gaussian laser beam in plasma channel created by ignitor heater technique. The ignitor beam creates plasma by tunnel ionization of air. The heater beam heats the plasma electrons and establishes a parabolic density profile. The third beam (q-Gaussian beam) is guided in this plasma channel under the combined effects of density nonuniformity of the plasma channel and relativistic mass nonlinearity of the plasma electrons. The propagation of q-Gaussian laser beam through the plasma channel excites an electron plasma wave at pump frequency that interacts with the incident laser beam to produce its second harmonics. The formulation is based on finding the numerical solution of the nonlinear Schrodinger wave equation for the fields of the incident laser beams with the help of moment theory approach. Particular emphasis is put on dynamical variations of the spot size of the laser beams and conversion efficiency of the second harmonics with distance of propagation.

In this paper, the scheme of generation of second harmonics of incident electromagnetic wave having a Hermite–Gaussian intensity profile in an under dense relativistic plasma has been presented. The relativistic mass variation of electrons by the intense electric field of incident beam generates the density gradients in background plasma which further excites the electron plasma wave (EPW) at resonant frequency and coupling of the EPW with the incident beam results in the generation of second harmonics of incident beam. Propagation dynamics of the Hermite–Gaussian laser beam in plasma has been studied by the formulation of differential equation for the spot size of the laser beam with the help of method of moments. Numerical simulations have been carried out to solve the differential equation for the dimensionless beam width parameters. Solution of the nonlinear wave equation for the electric field vector of second harmonics of incident beam gives the expression for second-harmonic yield. It has been observed that second-harmonic yield is affected by the different modes of Hermite–Gaussian laser beam in relativistic plasma.

In the present paper, we have investigated self-focusing of the quadruple Gaussian laser beam in underdense cold quantum plasma. The non-linearity chosen is associated with the relativistic mass effect that arises due to quiver motion of electron and electron density perturbation caused by ponderomotive force. The non-linearity modifies the plasma frequency in the dielectric function and hence the refractive index of the medium. The focusing/defocusing of the quadruple laser depends on the refractive index of the medium. We have set up non-linear differential equation that controls the beam width parameter by using well-known paraxial ray approximation and Wentzel–Krammers–Brillouin approximation. The effect of intensity parameter and electron temperature is observed on laser beam self-focusing in the presence of cold quantum plasma. From the results, it is revealed that electron temperature and the initial intensity of the laser beam control the profile dynamics of the laser beam.

The 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.

A nonparaxial investigation for propagation characteristics of q-Gaussian laser beam in rippled density plasma is studied by considering the relativistic nonlinearity. The field distribution in the medium is expressed in terms of q parameter and beam width parameter f. Nonlinear parabolic partial differential equation governing the evolution of complex envelope in slowly varying approximation is solved in a modulated density profile. Analytical theory of self-focusing including higher order terms in the expansion of dielectric function up to fourth order is developed and the variation of beam width parameter f with the distance of propagation for different parameters is studied. One may note that increased value of density ripple, laser intensity and depth of modulation, increases self-focusing whereas a lower value of q shows strong self-focusing. A comparative study between paraxial and nonparaxial study has also conducted. This study is useful for research in high energy density physics.

The paper presents an investigation on self-focusing of cosh-Gaussian (ChG) laser beam in a relativistic–ponderomotive non-uniform plasma. It is observed numerically that the selection of decentered parameter and initial beam radius determines the focusing/defocusing of ChG laser beam. For given value of these parameters, the plasma density ramp of suitable length can avoid defocusing and enhance focusing effect significantly. Focusing length and extent of focusing may also be controlled by varying slope of the ramp density. A comparison with Gaussian beam has also been attempted for optimized set of parameters. The results establish that ChG beam focuses earlier and sharper relative to Gaussian beam. We have setup the non-linear differential equation for the beam width parameter using Wentzel–Kramers–Brillouin and paraxial ray approximation and solved it numerically using Runge–Kutta method.

In 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.

In this paper, self-focusing of asymmetric cosh-Gaussian laser beams in collisionless magnetized plasma has been studied. The non-linearity in dielectric constant considered herein is mainly due to the ponderomotive force. The non-linear coupled differential equations for the beam width parameters in transverse dimensions of the beam have been obtained by using WKB and paraxial approximations under parabolic equation approach. The numerical computation is completed by using fourth-order Runge–Kutta method. The effect of unlike decentered parameters in both transverse dimensions of the beam on self-focusing of cosh-Gaussian beams has been presented. Further, the effect of the static magnetic field and polarization modes of the laser has been explored.

The 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 (r 0) or having minimum pulse duration (t 0) depending on the normalized distance.

A 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.

Stimulated 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.

Ponderomotive non-linearities arising by propagation of a linearly polarized laser beam through high-density quantum plasma are studied. The intense laser beam sets the plasma electrons in quiver motion and consequently ponderomotive non-linearity sets in leading to electron density perturbation inside the plasma. The interaction formalism has been built using the quantum hydrodynamic model. Laser beam traversing through high-density quantum plasma acquires an additional focusing tendency due to the perturbation induced by ponderomotive force in the plasma density. The ponderomotive force causes the beam to focus and the quantum effects contribute in focusing. The transverse magnetization of quantum plasma enhances the self-focusing and increase in magnetic field limits the spot size.