Enhancement of self focusing of laser beams in a degenerate magnetoactive solid state plasma

This paper presents an investigation of the enhancement of self focusing of high frequency EM waves in a compensated degenerate magnetoactive solid state plasma. The nonlinearity in the dielectric constant responsible for self focusing arises due to nonuniform heating and consequent redistribution Of carriers. A rigorous kinetic treatment valid beyond the perturbation limit has been presented assuming the carrier relaxation time to be energy dependent. The results show that the self-focusing of extraordinary waves is enhanced while that of ordinary waves is reduced with $\text{ω}{}_{\mathrm{c}}\text{ω}$ increasing. However the focusing of extraordinary waves is not possible when ω_c > ω. The effect of degeneracy is also found to enhance the self-focusing of the waves while that of the enhanced absorption is to suppress the self-focusing process.     

Nonlinear oscillatory waveguide propagation in a plasma

The presence of an intense Gaussian laser beam gives rise to a ponderomotive force on electrons in a collisionless plasma, leading to a redistribution of electron density along the wave-front and consequently to an intensity dependent dielectric constant which saturates with increasing intensity. The intensity dependent dielectric constant is responsible for beam propagation in an oscillatory waveguide. It is seen that (i) a beam of radiusr ₀ less thanr _0min (?c/ω _p) cannot be focused in the plasma regardless of its power, (ii) minimum dimension of oscillatory waveguide increases with increasing power of the beam. Similar results are also obtained for collisional plasma where nonlinearity arises due to nonuniform heating and consequent redistribution of carriers.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity:Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated.An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field,with linear absorption and due to saturation effects for arbitrary large intensity.The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters.Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode.Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence.The beam is more focussed at lower intensity in both cases viz.extraordinary and ordinary mode.     

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity: Effect of Linear Absorption

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode.     

Self-focusing and defocusing of cosh Gaussian laser beam in the presence of nonlinearity of ponderomotive force and temperature gradient

In this paper, the propagation of Cosh Gaussian laser beam and its interaction with isothermal plasma without temperature gradient as well as the effect of the exponential electron temperature gradient are investigated. Here the ponderomotive nonlinearity force is effective mechanism. This force can modify the electron density distribution. All the investigations are carried out for different initial plasma temperatures. Using Maxwell’s equations we obtained the nonlinear second-order differential equation of the dimensionless beam-width parameter (f) on the distance of propagation for several initial electron temperatures and exponential temperature variations. These equations are solved numerically by taking WKB and paraxial approximation. Under the effect of initial electron temperature, self-focusing and defocusing of hyperbolic cosine (cosh) Gaussian laser beam is distinguished. Furthermore, the exponential temperature gradient cause to stationary propagation mode breaks, and self-focusing or defocusing properties is observable.     

Propagation regimes of intense circularly polarized laser beam in magnetoactive plasma

This paper presents an analytical and numerical investigation of an intense circularly polarized wave propagating along the static magnetic field parallel to oscillating magnetic field in magnetoactive plasma. In the relativistic regime such a magnetic field is created by pulse itself. The authors have studied different regimes of propagation with relativistic electron mass effect for magnetized plasma. An appropriate expression for dielectric tensor in relativistic magnetoactive plasma has been evaluated under paraxial theory. Two modes of propagation as extraordinary and ordinary exist; because of the relativistic effect, ultra-strong magnetic fields are generated which significantly influence the propagation of laser beam in plasma. The nature of propagation is characterized through the critical-divider curves in the normalized beam width with power plane For given values of normalized density (ω_p/ω) and magnetic field (ω_c/ω) the regions are namely steady divergence (SD), oscillatory divergence (OD) and self-focusing (SF). Numerical computations are performed for typical parameters of relativistic laser-plasma interaction: magnetic field B = 10-100 MG; intensity I = 10¹⁶ to 10²⁰ W/cm²; laser frequency ω = 1.1 × 10¹⁵ s⁻¹; cyclotron frequency ω_c = 1.7 × 10¹³ s⁻¹; electron density n_e = 2.18 × 10²⁰ cm⁻³. From the calculations, we confirm that a circularly polarized wave can propagate in different regimes for both the modes, and explicitly indicating enhancement in wave propagation, beam focusing/self-guiding and penetration of E-mode in presence of magnetic field.     

Beat excitation of terahertz radiation in a semiconductor slab in a magnetic field

Two infrared lasers of frequencies ω₁ and ω₂ propagating in the TM/TE mode along $\stackrel{?}{z}$ direction in a rippled density semiconductor waveguide are shown to resonantly excite terahertz radiation at the beat frequency when ripple wave number is suitably chosen to satisfy the phase matching. The wave vector of the density ripple is along the direction of laser propagation while a static magnetic field is applied transverse to it. The lasers exert a ponderomotive force on the electrons at the beat frequency. This force, in the presence of density ripple and transverse magnetic field, produces a nonlinear current at the terahertz frequency. The magnetic field enhances the amplitude of the terahertz wave. However terahertz yield is significantly higher in the TM mode laser beating than in the TE mode laser beating.     

General Schrödinger equation for whistler waves propagating along a magnetic field

The general Schrödinger equation (GSE) for whistler waves with their group velocity directed along an external magnetic field is derived. The “mean” wave vector of the wave beam may be parallel to or have an angle Θ = arccos(2ω/ω_c) with the magnetic field. Applications of GSE to the whistler propagation in density ducts are considered. The results are important for the problem of the self-focusing of whistler waves.     

Coupling surface plasmon waves across gaps in a dielectric/metal interface by transformation optics

Propagation of a Gaussian laser beam in a plasma is analyzed by including the nonlinearity associated with the relativistic mass and the ponderomotive force. We set up the nonlinear differential equation for beam width parameter using parabolic equation approach and solve it numerically. Our results show that the ponderomotive self-focusing contributes in the relativistic self-focusing of the laser beam. An impact of plasma electron temperature, relative density parameter, and intensity parameter on the propagation of the laser beam has been explored.     

Excitation of multiple wakefields by short laser pulses in quantum plasmas

We present a theoretical investigation of the excitation of multiple electrostatic wakefields by the ponderomotive force of a short electromagnetic pulse propagating through a dense plasma. It is found that the inclusion of the quantum statistical pressure and quantum electron tunneling effects can qualitatively change the classical behavior of the wakefield. In addition to the well-known plasma oscillation wakefield, with a wavelength of the order of the electron skin depth (λe=c/ωpe, which in a dense plasma is of the order of several nanometers, where c is the speed of light in vacuum and ωpe is the electron plasma frequency), wakefields in dense plasmas with a shorter wavelength (in comparison with λe) are also excited. The wakefields can trap electrons and accelerate them to extremely high energies over nanoscales.     

Ponderomotive acceleration of electrons by an ultrashort laser pulse

By using the corrected solutions for an ultrashort laser pulse, we study the laser-driven electron violent acceleration in vacuum. Our simulations demonstrate that an ultrashort laser pulse with an intensity a₀≡eE₀/m_eωc=3 can accelerate electrons to an energy more than 0.5 GeV. The scaling laws for the net energy gain in different pulse length and laser radius at focus are also studied. Its acceleration mechanism is found to be ponderomotive acceleration.     

Use of modal energy transfer as a new damping device with controllable bandwidth

This paper presents a new design of nonlinear dynamic absorber (NDA) using the phenomenon of modal energy transfer between the symmetric mode and the anti-symmetric mode of a curved beam. It can reduce the resonance vibration of a primary structure with a controllable operational frequency range. The energy transfer is initiated by an autoparametric vibration and the excitation force required is lowest when the ratio of the resonance frequencies of the first symmetric mode (ω₁) and first anti-symmetric mode (ω₂) is close to 2.The resonance frequency of the first anti-symmetric mode (ω₂) can be altered to control the operational frequency range. The autoparametric vibration response can be used to create an energy-dissipative region with a controllable bandwidth. It is also possible to create a non-dissipative region in between two dissipative regions. This is useful for providing damping for a conventional dynamic absorber without adding high damping material. The damping is due to the dissipation of energy to anti-symmetric mode. Numerical calculations indicate that the resonance vibration of a primary structure can be successfully reduced using this approach. The results are verified with experimental data.     

Characteristics of paraxial propagation of a super Lorentz—Gauss SLG01 mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss（SLG） 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

Sub-millimeter third harmonic generation in n-InSb waveguide

Resonant third harmonic generation of a sub-millimeter wave in n-InSb waveguide embedded with a density ripple is investigated. The non-linearity arises through the modulation of free electron mass while the ripple accounts for the phase mismatch. The efficiency of the third harmonic generation is large. However, as the plasma frequency increases the attenuation rate of the third harmonic increases and the third harmonic efficiency decreases as (ω_pb/c) is raised.     

Scattering of relativistic electrons by a focused laser pulse

The problem of the motion of a classical relativistic electron in a focused high-intensity laser pulse is solved. A new three-dimensional model of the electromagnetic field, which is an exact solution of Maxwell’s equations, is proposed to describe a stationary laser beam. An extension of the model is proposed. This extension describes a laser pulse of finite duration and is an approximate solution of Maxwell’s equations. The equations for the average motion of an electron in the field of a laser pulse, described by our model, are derived assuming weak spatial and temporal nonuniformities of the field. It is shown that, to a first approximation in the parameters of the nonuniformities, the average (ponderomotive) force acting on a particle is described by the gradient of the ponderomotive potential, but it loses its potential character even in second order. It is found that the three-dimensional ponderomotive potential is asymmetric. The trajectories of relativistic electrons moving in a laser field are obtained and the cross sections for scattering of electrons by a stationary laser beam are calculated. It is shown that reflection of electrons from the laser pulse and the surfing effect are present in the model studied. It is found that for certain impact parameters of the incident electrons the asymmetic ponderomotive potential can manifest itself effectively as an attractive potential. It is also shown that even in the case of a symmetric potential the scattering cross section contains singularities, known as rainbow scattering. The results are applicable for fields characterized by large (compared to 1) values of the dimensionless parameter η² = e ²〈E ²〉/m ²ω² and arbitrary electron energies.     

Surface wave second harmonic generation over a n-type semiconductor

The sharp gradient in the intensity of a surface wave over a simiconductor-vacuum interface gives rise to a strong ponderomotive force on electrons and thus generates a second harmonic wave. The power of the second harmonic shows a resonance at $\text{ω =}\text{ω}{}_{\mathrm{p}}\text{2}$ (ω and ω_p being the wave and plasma frequencies) and tends to a saturation value at very high values of ω_p.     

Excitation of upper-hybrid plasma wake wave by a low-frequency extraordinary electromagnetic wave

The excitation of upper-hybrid wake electrostatic wave by interaction of an extraordinary Gaussian wave propagating perpendicular to the external magnetic field in a cold homogeneous plasma is investigated using magnetohydrodynamics theory. The plasma oscillations can be excited due to the charge separation appeared by the ponderomotive force of the electromagnetic wave whose frequency is considered in the lower pass band. By obtaining the equation governing the plasma wake, the dependency of the wake amplitude on the physical parameters is studied. It is observed that larger wake oscillation takes place when the pulse length is approximately close to 3λ_p/π and the X-wave frequency is greater than ω_p, which means that the phase velocity is less than the speed of light in vacuum (v_p < c).     

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.     

Distribution regimes of intense laser beam in a self-consistent plasma channel

In the present work, we investigate the distributed regimes of an intense laser beam in a self-consistent plasma channel. As the intensity of the laser beam increases, the relativistic mass effect as well as the ponderomotive expulsion of electrons modifies the dielectric function of the medium due to which the medium exhibits nonlinearity. Based on Wentzel–Kramers–Brillouin and paraxial ray theory, the steady-state solution of an intense, Gaussian electromagnetic beam is studied. A differential equation of the beamwidth parameter with the distance of propagation is derived, including the effects of relativistic self-focusing (SF) and ponderomotive self-channeling. The nature of propagation and radial dynamics of the beam in plasma depend on the power, width of the beam, and Ω _p, the ratio of plasma to wave frequency. For a given value of Ω _p (<1), the distribution regimes have been obtained in beampower–beamwidth plane, characterizing the regimes of propagation as steady divergence, oscillatory divergence, and SF. The related focusing parameters are optimized introducing plasma density ramp function, and spot size of the laser beam is analyzed for inhomogeneous plasma. This results in overcoming the diffraction and guiding the laser beam over long distance. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction studies.     

Investigation of the diocotron instability of an infinitely wide sheet electron beam by using the macroscopic cold-fluid model theory

This paper investigates the diocotron instability of an infinitely wide relativistic sheet electron beam in conducting walls propagating through a uniform magnetic field by using the macroscopic cold-fluid model theory. Assuming low-frequency perturbations with long axial wavelengths, the eigenvalue equation and the dispersion relation are acquired for a sheet electron beam with sharp boundary profile and uniform density. The results presented in this paper has developed the use of the macroscopic cold-fluid model theory by extending the parameter of the electron cyclotron frequency ω_c to a wider usage range, which is restricted to be much larger than the plasma frequency ω_p in the previous research work. Theoretical analyses and numerical calculations indicate that the transport of the sheet electron beam will be completely stabilized by augmenting the normalized beam thickness to a conductor gap larger than a threshold λ_b, which is greatly dependent on the parameter ω_c/ω_p. The larger ω_c/ω_p is, the smaller λ_b will be needed. Moreover, the system parameters, including the wave number k_x of the perturbations and the relativistic mass factor γ_b, will also influence the growth rate of diocotron instability obviously.