Theory Of Self-focusing Research Articles

Theory of small-scale self-focusing of spatially partially coherent beams and its implications for high-power laser system

Theory of small-scale self-focusing of spatially partially coherent beams and its implications for high-power laser system

Theoretical analysis on small-scale self-focusing of multi-wavelength beams in an isotropic medium

An analytic model for nonlinear propagation theory is developed for multi-wavelength laser beams propagating in an isotropic media. The small-scale self-focusing theoretical solution of multi-wavelength beams is obtained and is superposed by eigenfunctions with multiple local fastest-growth frequency, so the traditional B-integral obtained from a single-wavelength beam cannot be used to describe the small-scale self-focusing of multi-wavelength beams. Some laws for multi-wavelength beams propagating in an isotropy medium are also found, such as the self-focusing distance decreasing, the large angle scattering increasing and the spatial distributions of each wavelength trending to be consistent. The theoretical laws are confirmed by integrated numerical simulations and provide an explanation for the final optics phenomenon in high power lasers. The results promote the understanding of self-focusing theory and provide a very promising tool for beam control, which can transfer information from one beam to another through isotropic media.

Generation of high-charge electron beam in a subcritical-density plasma through laser pulse self-trapping

To maximize the charge of a high-energy electron beam accelerated by an ultra-intense laser pulse propagating in a subcritical plasma, the pulse length should be longer than both the plasma wavelength and the laser pulse width, which is quite different from the standard bubble regime. In addition, the laser-plasma parameters should be chosen to produce the self-trapping regime of relativistic channeling, where the diffraction divergence is balanced by the relativistic nonlinearity such that the laser beam radius is unchanged during pulse propagation in a plasma over many Rayleigh lengths. The condition for such a self-trapping regime is the same as what was empirically found in several previous simulation studies in the form of the pulse width matching condition. Here, we prove these findings for a subcritical plasma, where the total charge of high-energy electrons reaches the multi-nC level, by optimization in a 3D PIC simulation study and compare the results with an analytic theory of relativistic self-focusing. A very efficient explicitly demonstrated generation of high-charge electron beams opens a way to a high-yield production of gammas, positrons, and photonuclear particles.

Study on impact of spatial filter on a hot image through medium with gain

The evolution of hot image formation through medium with gain in consideration of the effect of spatial filter is theoretically and numerically investigated. Based on the linear diffraction theory and small-scale self-focusing theory of Bespalov and Talanov, intensity distribution of hot image in conjugate plane is derived analytically. Then, the peak intensity of hot image for different medium gain and different pinhole sizes are discussed in detail, the results show theoretical analysis is mostly approximate to the numerical simulations, furthermore, it is found that suppressing effect on peak intensity ratio with small gain coefficient is larger than that with bigger ones for determined pinhole size.

Relativistic Propagation of Linearly/Circularly Polarized Laser Radiation in Plasmas

Paraxial theory of relativistic self-focusing of Gaussian laser beams in plasmas for arbitrary magnitude of intensity of the beam has been presented in this paper. The nonlinearity in the dielectric constant arises on account of relativistic variation of mass. An appropriate expression for the nonlinear dielectric constant has been used to study laser beam propagation for linearly/circularly polarized wave. The variation of beamwidth parameter with distance of propagation, self-trapping condition, and critical power has been evaluated. The saturating nature of nonlinearity yields two values of critical power of the beam ( and ) for self-focusing. When the beam diverges. When the beam first converges then diverges and so on. When the beam first diverges and then converges and so on. Numerical estimates are made for linearly/circularly polarized wave applicable for typical values of relativistic laser-plasma interaction process in underdense and overdense plasmas. Since the relativistic mechanism is instantaneous, this theory is applicable to understanding of self-focusing of laser pulses.

Effect of nonlinear absorption on self focusing of short laser pulse in a plasma

Paraxial theory of self focusing of short pulse laser in a plasma under transient and saturating effects of nonlinearity and nonlinear absorption is developed. The absorption is averaged over the cross-section of the beam and is different for different time segments of the pulse. The electron temperature includes cumulative effect of previous history of temporal profile of pulse intensity, however, the ambipolar diffusion is taken to be faster than the heating time. The relaxation effect causes self-distortion of the pulse temporal profile where as the nonlinear absorption weakens self focusing. For the pulses of duration comparable to the electron ion collision time, the front part of the pulse gets defocused where as the latter part undergoes periodic self focusing.

Filamentation of a sharply focused ultrashort laser pulse at wavelengths of 800 and 400 nm: Measurements of the nonlinear index of air refraction

We present the results of experimental investigations of the filamentation dynamics of high-power ultrashort Ti:Sapphire-laser pulses with wavelengths of 800 and 400 nm with their sharp focusing in air. The dependences of position and dimensions of a plasma channel generated in the nonlinear beam focus zone on the laser pulse power are obtained. The effective value of the nonlinear index of air refraction related to the optical Kerr effect is determined for two laser wavelengths from processing of the dependences when using laser radiation self-focusing theory.

非线性介质中会聚高功率激光的焦点位置控制

In order to control the propagation of high power laser beam and make the laser beam focus at any position without quality degradation,the change of high-power laser focal positions was investigated.The proposed research was based on the theory of lens-focusing and laser self-focusing in nonlinear media.Influences of different kinds of factors on the focal position were analyzed.Through numerical solution of the nonlinear Schrdinger equation,the relationships of the focal position with input power,initial waist and focal length of lens were obtained,and thus the method to control the beam focal position was found.The numerical simulations coincide with the theoretical analysis.

包覆非线性克尔介质的纳米金属孔结构实现光束的分裂与聚焦现象

We demonstrate that a finite number of nano-slits can realize beam splitting and focusing of light by coating the metallic film surfaces with nonlinear Kerr medium. The numerical simulation shows that the beam splitting and focusing can be controlled by the incident light intensity. The splitting angle is quasi-periodically modulated by the incident light intensity, and the focusing length of forward propagating transmitted light decreases as the incident light intensity increases. These effects are explained by the surface plasmon polariton Bloch modes and self-focusing theory.

Skin depth plasma front interaction mechanism with prepulse suppression to avoid relativistic self-focusing for high-gain laser fusion

Measurements of the ion emission from targets irradiated with neodymium glass and iodine lasers were analyzed and a very significant anomaly observed. The fastest ions with high charge number Z, which usually are of megaelectron volt energy following the relativistic self-focusing and nonlinear-force acceleration theory, were reduced to less than 50 times lower energies when 1.2 ps laser pulses of about 1 J were incident. We clarify this discrepancy by the model of skin depth plasma front interaction in contrast to the relativistic self-focusing with filament generation. This was indicated also from the unique fact that the ion number was independent of the laser intensity. The skin layer theory prescribes prepulse control and lower (near relativistic threshold) laser intensities for nonlinear-force-driven plasma blocks for high-gain ignition similar to light ion beam fusion.

Paraxial lens approximation and self-focusing theory

When a lens is not prepared with an exact quadratic profile but is approximated by such a profile, there is considerable arbitrariness in the choice of the quadratic profile. Only one of these choices is optimal and gives the correct description of the physical optics involved. Laser beam self-focusing is chosen as the example in case, and it is shown that the optimal energy-conserving solution is equivalent to the variational and moments theories of self-focusing while at the same time it is paraxial in nature. Hankel-transformation techniques are used to prove this.

Paraxial theory of slow self-focusing.

We present a theory of slow self-focusing that is paraxial in nature, gives the field including the phase and eikonal explicitly, while it also agrees with the results of variational and moments theories. After presenting the features of the theory, particularly its similarity to the central force problem, we go on to reformulate the theory for an absorbing medium. We find that the laser beam focuses to a constant beamwidth with a small phase-front curvature depending on the extent of absorption. The theory is applicable to a whole range of saturating nonlinearities although it specializes to two plasma cases, the ponderomotive force based and the relativistic electron quiver based nonlinearities, for definitive results.

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.

Exactly integrable nonlinear Schrodinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion

We show that the methodology based on the generalized inverse scattering transform (IST) concept provides a systematic way to discover the novel exactly integrable nonlinear Schrodinger equation models with varying dispersion, nonlinearity and gain or absorption. The fundamental innovation of the present approach is to notice that it is possible both to allow for a variable spectral parameter with new dependent variables and to apply of the famous moving in time focuses concept of the self-focusing theory to the IST formalism. We show that for nonlinear optics this algorithm is a useful tool to design novel dispersion managed fiber transmission lines and soliton lasers. Fundamental soliton management regimes are predicted.

Nonlinear Propagation of Intense Short Pulses Through Underdense Plasmas

Currently there is much interest in the interaction of high-intensity ultra-short laser pulses with plasmas. Applications include the recently proposed Fast Ignitor Concept for Inertial Confinement Fusion. In the present work we make an analytical investigation of nonlinear propagation of intense short pulses through underdense plasmas. When a laser beam is focused into a plasma, self-focusing and self-channeling can occur as a result of relativistic modification of electron mass in the laser field and the reduction of electron density on the focal region due to the expulsion of electrons by laser ponderomotive force. The paper presents a paraxial theory of self-focusing of intense laser pulses due to expulsion of plasma electrons produced by the extreme ponderomotive force of a focused laser pulse. The nonlinear dielectric constant, self-focusing equation relating the variation of beamwidth parameter with distance of propagation, self-trapping condition and critical power are evaluated. The results suggest a self-focusing of the laser pulse in the plasma.

Paraxial theory of self-focusing of cylindrical laser beams. I. ABCD laws

A paraxial formulation of steady-state self-focusing is presented, taking due care of the correct paraxial approximation of the plasma frequency and the resultant nonlinear refractive index of the plasma in the presence of the electromagnetic field of a high-powered laser beam. For the laser beam and plasma refractive index description, the correct momentum space of the photons in circular cylindrical geometry of the laser beam is the transformation in terms of the Laguerre-Gauss modes that lead to the correct non-Taylor series paraxial approximation of the beam and its propagation equation. For self-trapping, the same conditions as the moments and variational approaches result. The natural way to express the results for self-focusing in this approximation is in terms of the so-called ABCD laws for the beam parameters, presented here for the self-similar beam propagation of a centrally humped (Gaussian) beam. These laws define a one-complex-parameter group of transformations [the SU(2) group for the absorptionless case and the restricted Lorentz group in general] that describe the evolution of the self-focusing beam; they naturally lead to the application of the concept of geometric phase to the self-focusing beam presented in the paper.

Nonlinear wave collapse and strong turbulence

The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions.

Theory of Incoherent Self-Focusing in Biased Photorefractive Media

A theory describing propagation and self-focusing of partially spatially incoherent light beams in nonlinear media is developed. It is shown that this process is effectively governed by an infinite set of coupled nonlinear Schr\odinger-like equations, provided they are initially appropriately weighted with respect to the incoherent angular power spectrum of the source. The particular case of spatially incoherent beam propagation in biased photorefractive media is considered in detail. Numerical simulations indicate that spatial compression as well as self-trapped states are possible under appropriate conditions. Our results are in good agreement with recent experimental observations.

Vector theory of self-focusing of an optical beam in Kerr media

The scalar theory of the self-focusing of an optical beam is not valid for a very narrow beam, and a correct description of the beam behavior requires a vector analysis in this case. A vector nonparaxial theory is developed from the vector Maxwell equations by application of an order-of-magnitude analysis method. For the same input beam, the numerical results of self-focusing from both scalar and vector theories are compared. It is found by the vector theory that a linearly polarized circular input beam becomes elliptical in the selffocusing process.

Nonlinear relativistic self-focusing of laser radiation in plasmas: Arbitrary intensity

A paraxial theory of relativistic self-focusing of a Gaussian laser beam in plasmas, when the nonlinear part of the effective dielectric constant is arbitrarily large, is presented. The plasma is taken to be homogeneous without any density fluctuations being necessary. The approach of Akhmanov et al. based on the WKB and paraxial ray approximations has been followed. It is seen that the saturating nature of nonlinearity leads to two values of critical power of the beam (Pcrl and Pcr2) for self-focusing. When the power of the beam P lies between the two critical values (i.e., Pcr1 < P < Pcr2), the medium behaves as an oscillatory waveguide; the beam first converges and then diverges, converges again, and so on. For P > Pcr2 the beam first diverges, then converges, then diverges, and so on. Because the relativistic mechanism is instantaneous, the theory is applicable to the understanding of selffocusing of laser pulses also.