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.     

Non-paraxial theory of self-defocusing/focusing of a laser pulse in a multiple-ionizing gas

The self-focusing of a laser pulse through a tunnel ionizing gas (helium) has been studied in both non-relativistic and relativistic regimes, relaxing the near-axis approximation. In the non-relativistic regime, the laser pulse produces multiple ionization of the gas and faces strong defocusing due to the steep radial density gradient caused by the same. The uneven defocusing of paraxial and marginal rays leads to a beam acquiring a ring shaped intensity distribution. In the relativistic regime, the laser pulse produces fully ionized plasma within a few wave periods, subsequently the relativistic mass effect and the ponderomotive force induced electron cavitation cause periodic self-focusing. PACS 52.38.Hb; 42.65.Jx     

Impact of light absorption and temperature on self-focusing of zeroth-order Bessel–Gauss beams in a plasma with relativistic–ponderomotive regime

The influence of light absorption and temperature on self-focusing of zeroth-order Bessel–Gauss beams through plasma, with relativistic–ponderomotive regime, is investigated in this paper. The nonlinear differential equation for beam-width is established by using parabolic equation approach under Wentzel–Kramers–Brillouin (WKB) paraxial approximation and solved numerically. The numerical results show the effects of beam parameter, relative density plasma, intensity parameter, absorption coefficient and plasma electron temperature on self-focusing of zeroth-order Bessel–Gauss beams in plasma. The self-focusing of Gaussian beams in the considered plasma is also deduced as a particular case in the present work.     

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.     

Quadruple Gaussian Laser Beam Profile Dynamics in Collisionless Magnetized Plasma

This paper presents an investigation of self-focusing of a quadruple Gaussian laser beam in collisionless magnetized plasma. The nonlinearity due to ponderomotive force which arises on account of nonuniform intensity distribution of the laser beam is considered. The nonlinear partial differential equation governing the evaluation of complex envelope in the slowly varying envelope approximation is solved using a paraxial formalism. The self-focusing mechanism in magnetized plasma, in the presence of self-compression mechanism will be analyzed in contrast to the case in which it is absent. It can be observed that, in case of ponderomotive nonlinearity, the self-compression mechanism obstructs the pulse self-focusing above a certain intensity value. The effect of an external magnetic field is to generate pulses with smaller spot size and shorter compression length. The lateral separation parameter and the initial intensity of the laser beam play a crucial role on focusing and compression parameters. Also, the three-dimensional analysis of pulse propagation is presented by coupling the self-focusing equation with the self-compression one.     

在稀薄等离子体中激光传播的相对论自聚焦

讨论超强、超短脉冲激光在稀薄等离子体中传播过程的某些性质;用二维快速傅立叶变换求解波动方程.相对论自聚焦的基本方程包括非线性源项和衍射的影响.由于有质动力和相对论的影响,使等离子体的频率降低,从而使折射指数发生改变,影响激光在等离子体中的传播.在入射激光功率(p)超过临界功率(p_c)时,激光在传播过程中产生自聚焦;反之,激光在传播过程中逐渐衰减,不产生自聚焦.     

Nonlinear propagation of an intense Laguerre–Gaussian laser pulse in a plasma channel

The nonlinear propagation of an intense Laguerre–Gaussian(LG) laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method. The evolution equation of the spot size is derived including the effects of relativistic self-focusing, preformed channel focusing, and ponderomotive self-channeling. The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size, periodically focusing and defocusing oscillation,catastrophic focusing, and solitary waves are obtained. Compared with the laser pulse with fundamental Gaussian(FG)mode, it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse, while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse. Thus, the matched condition for the intense LG laser pulse with constant spot size is released obviously, while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.     

Effect of light absorption and temperature on self-focusing of finite Airy–Gaussian beams in a plasma with relativistic and ponderomotive regime

In the present paper, we have studied the influence of light absorption and temperature on self-focusing of finite Airy–Gaussian beams in plasma by considering the combined effects of relativistic and the ponderomotive regime. The nonlinear differential equations of dimensionless beam-width parameter are derived using the paraxial ray and Wentzel–Kramers–Brillouin approximation, and they are solved numerically. The effect of absorption coefficient, plasma electron temperature, relative plasma density, intensity parameter and modulation parameter beam on the self-focusing of finite Airy–Gaussian beams in plasma is presented numerically and discussed.     

Experimental study of relativistic self-focusing andself-channeling of an intense laser pulse in an underdense plasma

This paper reports on experimental investigations on relativistic self-focusing and self-channeling of a terawatt laser pulse (0.7 TW⩽P⩽15 TW) in an underdense plasma. We present results obtained with picosecond (τ=1 ps) and subpicosecond (τ=0.4 ps) pulses. In the “long pulse” regime, modifications in the laser propagation are observed for Pc, the critical power for self-focusing. By contrast, self-guiding of subpicosecond pulses is observed for P≈P_c. Using a paraxial envelope model describing the laser propagation and taking into account the plasma response to the ponderomotive force, it is shown that a maximum laser intensity of 5-15 times that reached in vacuum may be achieved when P is in the (1.25-4)×P_c range. It is also demonstrated that ion motion may significantly reduce the effective P_c     

超强短脉冲激光在不同密度分布等离子体中的自聚焦

讨论高斯型强激光束在具有初始柱对称密度分布的低密度冷等离子体中传播时，等离子体密度分布的不同对激光自聚焦的影响.推导出可以判断更有利于自聚焦发生的评价函数，这样通过比较不同密度分布的评价函数值就可以判断哪种密度分布更有利于自聚焦的发生.为了说明这种方法的有效性，对评价函数进行分析得出：在相同的激光场中等离子体柱的轴心密度给定时(以激光的光轴为轴)，离轴越远的地方密度越大及密度变化越陡，自聚焦越容易发生；相对论效应与有质动力共同作用比相对论的单独作用，自聚焦更容易发生.数值模拟证实了评价函数能准确的预测在不 关键词： 自聚焦 相对论效应 有质动力 评价函数     

Approximated Vector Potential of Intense Laser Pulses in a Pair Plasma

A （3＋1 ）-dimensional Kadomtse-Petviashvili （KP） equation for nonlinearly interacting intense laser pulses with an electron-positron （e-p） plasma is derived. Taking into account the combined action of the relativistic particle mass increase and the relativistic light ponderomotive force, using the perturbation method, and allowing different types solution, we discuss the analytical solution of （3＋1）-dimensional KP-I equation, and give the approximate solutions of vector potential of the intense laser pulse in e-p plasma. Our results may be significantly useful in understanding the nonlinear wave propagation and interaction of intense laser beams in an e-p plasma.     

Self-focusing in a plasma due to ponderomotive forces and relativistic effects

The propagation of intense laser pulses in a plasma is discussed in terms of a constant shape, paraxial ray approximation. Self-focusing due to ponderomotive forces and relativistic effects is investigated. It is found that the stationary self-focusing behaviour of each mechanism treated separately is similar, with several orders of magnitude difference in critical power. In stationary self-focusing due to the combined mechanisms, complete saturation of ponderomotive self-focusing prevents the occurrence of relativistic effects. Self-focusing lengths and minimum radii are given for a large range of beam powers. A characteristic focal spot radius is found which depends only on the plasma density.     

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.     

Pulse chirping effect on controlling the transverse cavity oscillations in nonlinear bubble regime

The propagation of an intense laser pulse in an under-dense plasma induces a plasma wake that is suitable for the acceleration of electrons to relativistic energies. For an ultra-intense laser pulse which has a longitudinal size shorter than the plasma wavelength, λp, instead of a periodic plasma wave, a cavity free from cold plasma electrons, called a bubble, is formed behind the laser pulse. An intense charge separation electric field inside the moving bubble can capture the electrons at the base of the bubble and accelerate them with a narrow energy spread. In the nonlinear bubble regime, due to localized depletion at the front of the pulse during its propagation through the plasma, the phase shift between carrier waves and pulse envelope plays an important role in plasma response. The carrier–envelope phase(CEP) breaks down the symmetric transverse ponderomotive force of the laser pulse that makes the bubble structure unstable. Our studies using a series of two-dimensional(2D) particle-in-cell(PIC) simulations show that the frequency-chirped laser pulses are more effective in controlling the pulse depletion rate and consequently the effect of the CEP in the bubble regime. The results indicate that the utilization of a positively chirped laser pulse leads to an increase in rate of erosion of the leading edge of the pulse that rapidly results in the formation of a steep intensity gradient at the front of the pulse. A more unstable bubble structure, the self-injections in different positions, and high dark current are the results of using a positively chirped laser pulse. For a negatively chirped laser pulse, the pulse depletion process is compensated during the propagation of the pulse in plasma in such a way that results in a more stable bubble shape and therefore, a localized electron bunch is produced during the acceleration process. As a result, by the proper choice of chirping, one can tune the number of self-injected electrons, the size of accelerated bunch and its energy spectrum to the values required for practical applications.     

Relativistic channel-coupling focusing enhanced nonlinear guiding of an intense laser beam in a plasma channel

We employ the variational method to study the optical guiding of an intense laser beam in a preformed plasma channel without using the weakly relativistic approximation. Apart from the dependence on the laser power and the nonlinear channel strength parameter, the beam focusing properties is shown also to be governed by the laser intensity. Relativistic channel-coupling focusing, arising from the coupling between relativistic self-focusing and linear channel focusing, can enhance relativistic self-focusing but its strength is weaker than that of linear channel focusing.     

超强线极化激光在e-p等离子体中传播的成丝不稳定性

基于超强线极化激光在正负电子对(e-p)等离子体中的传播方程,讨论了相互作用过程中的成丝不稳定性。得到了电磁波的非线性色散关系和不稳定性增长率,并讨论了传播过程中激光强度和等离子体温度对成丝不稳定性的影响。结果表明,成丝不稳定性的强弱主要由相互作用的非线性效应与受有质动力作用后等离子体密度的减小之间的竞争所决定。     

Effects of relativistic and ponderomotive nonlinearities on the interaction of high-power laser beam with an inhomogeneous warm plasma

The influence of relativistic-ponderomotive nonlinearities and the plasma inhomogeneity on the nonlinear interaction between a high-power laser beam and a warm underdense plasma are studied. It is clear that the relativistic ponderomotive force and the electron temperature modify the electron density distribution and consequently change the dielectric permittivity of the plasma. Therefore, by presenting the modified electron density and the nonlinear dielectric permittivity of the warm plasma, the electromagnetic wave equation for the propagation of intense laser beam through the plasma is derived. This nonlinear equation is numerically solved and the distributions of electromagnetic fields in the plasma, the variations of electron density, and plasma refractive index are investigated for two different background electron density profiles. The results show that the amplitude of the electric field and electron density oscillations gradually increase and decrease, during propagation in the inhomogeneous warm plasma with linear and exponential density profiles, respectively, and the distribution of electron density becomes extremely sharp in the presence of intense laser beam. It is also indicated that the electron temperature and initial electron density have an impact on the propagation of the laser beam in the plasma and change the plasma refractive index and the oscillations' amplitude and frequency. The obtained results indicate the importance of a proper choice of laser and plasma parameters on the electromagnetic field distributions, density steepening, and plasma refractive index variations in the interaction of an intense laser beam with an inhomogeneous warm plasma.     

强激光脉冲在部分离化等离子体中的传播特性

采用变分法给出了强激光脉冲在部分离化等离子体中传播的参数演化方程,其中考虑了相对论自聚焦、有质动力激发尾波场以及部分离化非线性极化强度的影响。通过非线性动力学分析的方法,得到了强激光脉冲以恒定焦斑半径传播时的激光、等离子体参数匹配条件。研究表明:在部分离化等离子体中,激光自聚焦随着电离程度的增大而增强;有质动力激发的尾波场进一步增强激光脉冲的自聚焦;相对于等离子体密度而言,激光强度对激光脉冲的自聚焦更有影响。     

Skin-Depth Theory Explaining Anomalous Picosecond-Terawatt Laser Plasma Interaction II

The anomaly of ion emission at laser irradiation of targets measured by Badziak et al. was analyzed on the background of the extensive research in the past. In contrast to the irradiation with lasers of longer than 100 ps pulse duration, a drastic decrease of the maximum ion energies was measured with ps pulses. Very strange was the observation that the number of emitted fast ions was intensity independent. The usual ponderomotive or relativistic self-focusing theory and related processes could not explain the results. Instead a direct interaction within the skin depth of the irradiated target was concluded. This model confirms the plane geometry nonlinear force interaction in the ps range producing fast plasma blocks moving perpendicular off or into the target. The block moving into the target opens a new scheme of laser fusion by modifying the experiments of Norreys et al. The use of relatively low subrelativistic laser intensities for the new scheme of laser fusion is evaluated on the background of the long years studies of nonlinear force driven plasma blocks and earlier interpenetration fusion reactions for providing the parameters for expected fusion gains much higher than the experiment of Norreys et al. for a fusion power scheme.     

Self-Focusing and de-Focusing of Intense Left- and Right-Hand Polarized Laser Pulse in Hot Magnetized Plasma in the Presence of an External Non-Uniform Magnetized Field

In this paper, self-focusing of an intense circularly polarized laser beam in the presence of a non-uniform positive guide magnetic field with slope constant parameter δ in hot magnetized plasma, using Maxwell’s equations and relativistic fluid momentum equation is investigated. An envelope equation governing the spot-size of laser beam for both of left- and right-hand polarizations has been derived, and the effects of the plasma temperature and magnetic field on the electron density distribution of hot plasma with respect to variation of normalized laser spot-size has been studied. Numerical results show that self-focusing is better increased in the presence of an external non-uniform magnetic field. Moreover, in plasma density profile, self-focusing of the laser pulse improves in comparison with no non-uniform magnetic field. Also, with increasing slope of constant parameter of the non-uniform magnetic field, the self-focusing increases, and subsequently, the spot-size of laser pulse propagated through the hot magnetized plasma decreases.