This paper presents an investigation on the self-focusing of a cosh-Gaussian laser beam in the thermal quantum plasma (TQP) by taking into account the effects of relativistic nonlinearity. An appropriate nonlinear Schrödinger equation has been solved analytically by applying the variational approach. The self-focusing and the self-phase modulation are examined under a variety of parameters. The self-trapping of a cosh-Gaussian laser beam is further studied at various values of the decentered parameter, b with different absorption levels, ${k}^{\prime}_i$. Numerical analysis shows that these parameters play a vital role in propagation characteristics. The significant contribution of the quantum effects to enhance the self-focusing and minimize the longitudinal phase has been observed. Further, a comparison has been made with the classical relativistic (CR), the relativistic cold quantum (RCQ), and the thermal quantum (TQ) regimes. The self-focusing is found to occur earlier and is strongest for the case of TQP in the present analysis.

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.

We propose a scheme for terahertz (THz) radiation generation by non-linear mixing of two cosh-Gaussian laser beams in axially magnetized plasma with spatially periodic density ripple where electron-neutral collisions have been taken into account. The laser beams exert a non-linear ponderomotive force due to spatial non-uniformity in the intensity. The plasma electrons acquire non-linear oscillatory velocity under the influence of ponderomotive force. This oscillatory velocity couples with preformed density ripples (n′ = n0αeiαz) to generate a strong transient non-linear current that resonantly derives THz radiation of frequency ~ωh (upper hybrid frequency). Laser frequencies (ω1 and ω2) are chosen such that the beat frequency (ω) lies in the THz region. The periodicity of density ripple provides phase-matching conditions (ω = ω1 − ω2 and $\vec k = \vec k_1 - \vec k_2 + {\rm \vec \alpha} $) to transfer maximum momentum from laser to THz radiation. The axially applied external magnetic field can be utilized to enhance the non-linear coupling and control various parameters of generated THz wave. The effects of decentered parameters (b), collisional frequency (νen), and magnetic field strength (B0 = ωcm/e) are analyzed for strong THz radiation generation. Analytical results show that the amplitude of THz wave enhances with decentered parameters as well as with the magnitude of axially applied magnetic field. The THz amplitude is found to be highly sensitive to collision frequency.

This 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.

This paper presents analytical calculations for terahertz (THz) radiation by beating of two cosh-Gaussian laser beams in a density rippled collisional magnetized plasma. Lasers beams exert a ponderomotive force on the electrons of plasma in beating frequency which generates THz waves. The magnetic field was considered parallel to the direction of lasers which leads to propagate right-hand circularly polarized or left-hand circularly polarized waves in the plasma depending on the phase matching conditions. Effects of collision frequency, decentered parameter of lasers and the magnetic field strength are analyzed for THz radiation generation. By the optimization of laser and plasma parameters, the efficiency of order 27% can be achieved.

In this paper, we have investigated the propagation characteristics of cosh-Gaussian laser beam in magnetoplasma using relativistic nonlinearity. The field distribution in the medium is expressed in terms of beam width parameter an and decentred parameter b. An appropriate nonlinear Schräodinger equation has been solved analytically using variational approach. The behaviour of beam width parameter with dimensionless distance of propagation ξ for various b values is examined. Self-phase modulation and self-trapping is also studied under variety of parameters. Further, the effect of magnetic field on self-focusing of the beam have been explored.