Initial Beam Radius Research Articles

Quality and spatial intensity distribution characteristics of short-exposure spot images of a supercontinuum laser in a turbulent atmosphere.

In this study, considering the combined effects of atmospheric attenuation and turbulence, we examine the spot quality and spatial intensity distribution characteristics of a supercontinuum (SC) laser propagating in a turbulent atmosphere using the multi-layer phase-screen method. An increase in turbulence strength or a decrease in the initial beam radius resulted in a greater impact of the atmospheric turbulence on the SC laser. A decrease in source coherence results in the deterioration of the image quality of the far-field spot. Under moderate to strong turbulence, the scintillation index decreased as the source coherence decreased; however, the opposite trend was observed under weak turbulence. These results are significant for the advancement and optimization of SC laser systems.

Radially Phased-Locked Hermite–Gaussian Correlated Beam Array and Its Properties in Oceanic Turbulence

The descriptions of a radially phased-locked Hermite–Gaussian correlated beam array are introduced, the equation of this beam array in oceanic turbulence is derived, and the intensity profiles of this beam array are shown and analyzed. The results imply that the evolutions of the sub-beam of this beam array in free space are the same as the Hermite–Gaussian correlated beam, while the intensity of this beam array can be adjusted by controlling the initial beam radius R and the coherence length. The intensity profiles of this beam array in free space have multiple spots during propagation, while the same beam array in oceanic turbulence can become a beam spot due to the influences of R and oceanic turbulence. The beam array with smaller coherence length in oceanic turbulence retains the splitting properties better during propagation.

Displacements of a spatially limited light beam in the slant path of oceanic turbulence.

The new oceanic power spectrum of refractive-index of optical turbulent fluctuations in slant path is developed by oceanic temperature structure parameters with depth under weak wind and strong wind conditions. Based on the proposed oceanic power spectrum in slant channel, the analytical expression of the displacement variance of Gaussian beam propagation in slant oceanic turbulent channel is derived. Then the influence of oceanic turbulent parameters in slant path on the beam displacement is investigated. It's shown that oceanic turbulence in slant path with small inner scale, low ratio of temperature and salinity contributions, large tidal velocity and wind speed leads to small beam displacement. For a sufficiently large receiver radius, Gaussian beam with large initial beam radius propagating at large zenith angle can cause small beam displacement in slant path of oceanic turbulence.

Physical properties of relativistic electron beam during long-range propagation in space plasma environment* *Project supported by the Joint Funds of the National Natural Science Foundation of China (Grant Nos. 61372050 and U1730247).

It is known that ion channel can effectively limit the radial expansion of an artificial electron beam during its long-range propagation in the space plasma environment. Most prior studies discussed the focusing characteristics of the beam in the ion channel, but the establishment process and transient properties of the ion channel itself, which also plays a crucial role during the propagation of the relativistic electron beam in the plasma environment, were commonly neglected. In this study, a series of two-dimensional (2D) particle-in-cell simulations is performed and an analytical model of ion channel oscillation is constructed according to the single-particle motion. The results showed that when the beam density is higher than the density of plasma environment, ion channel can be established and always continues to oscillate periodically over the entire propagation. Multiple factors, including the beam electron density, initial beam radius, and the plasma density can affect the oscillation properties of ion channel. Axial velocity of the beam oscillates synchronously with the ion channel and this phenomenon will finally develop into a two-stream instability which can seriously affect the effective transport for relativistic electron beam. Choosing appropriate beam parameters based on various plasma environments may contribute to the improvement of the stability of ion channel. Additionally, radial expansion of the beam can be limited by ion channel and a stable long-range propagation in terrestrial atmosphere may be achieved.

Optimal power of laser beams propagating from the ground through the atmosphere to space orbits

It is shown that, when a high-power laser beam propagates from the ground through the atmosphere to space orbits, there is an optimal beam power that maximizes the target intensity due to self-focusing effect in the atmosphere, even if the atmospheric extinction exists. The B integral is an important parameter to describe self-focusing effect quantitatively. It is found that the value of B integral corresponding to optimal beam power is a constant. Based on this characteristic of the optimal B integral and the concept of the equivalent atmospheric extinction coefficient proposed in this paper, we derive the analytical formula of the optimal beam power, which presents an effective design rule to optimize the target intensity. In addition, it is shown that the optimal beam power increases as the initial beam radius, the wavelength, the atmospheric extinction coefficient, and the aerosol scale height increase.

The Evolution of Beam Spot in the Geomagnetic Field During Long-Range Propagation of Relativistic Electron Beam

Research on the location and shape of a beam spot at a target altitude can lay the foundation for understanding and diagnosing the long-range propagation of relativistic electron beams. Only a few studies have focused on this approach. In this study, a terrestrial atmosphere with a 3-D geomagnetic field was constructed in accordance with the International Geomagnetic Reference Field model and a relevant atmosphere model. Monte Carlo simulations were applied to the long-range propagation of relativistic (1–10 MeV) electron beams in the altitude range of 200–300 km. The results showed that when beams with various parameters were emitted in one location, the centers of the beam spots were distributed in concentric circles with different radii. The direction of the geomagnetic field determined the locations of the circle centers, whereas the beam energy and pitch angle determined the radii. When the initial gyrophase changed, the center of the beam spot rotated through the same angle. The beam spot was distributed as a partial ring with a width mainly related to the initial beam radius when the energy spread was relatively small. If the energy spread exceeded the limit, the beam spot was ring-shaped; the ring width was determined by both the initial beam radius and the energy spread.

Diffraction-Ray Optics of Femtosecond Laser Pulses Propagating in Air Under the Influence of the Normal Group Velocity Dispersion

Results of theoretical study of the femtosecond Ti:Sa laser pulse propagation in air under the influence of the normal group velocity dispersion are presented. The use of the diffraction-ray tube method for an analysis of numerical solutions of the nonlinear Schrodinger equation in chromatic dispersion medium with the Kerr and plasma nonlinearity makes it possible to determine the main regularities of the femtosecond laser pulse selffocusing and filamentation in air for various pulse durations, initial beam radii, and peak powers. It is shown that under the influence of the group velocity dispersion, the filamentation terminates with an increase in the initial radius of the laser beam even at high values of supercritical powers. With an increase in the dispersion distortions of the pulse, the radius of the energetically replenishing diffraction-ray tube, the angular divergence of the post-filamentation light channel, and the nonlinear focus coordinate normalized to the Rayleigh length increase in the central time slices of the laser pulse and its integral pattern.

Speckle characteristics of vortex beams scattered from rough targets in turbulent atmosphere

In this study, the echo speckle characteristics of the Laguerre-Gauss (LG) vortex beams scattered from random rough surface targets were examined based on the Rytov Approximation Theory. In addition, the expressions of the intensity correlation and coherence functions, along with the normalized intensity variances of the speckle fields, were derived. The coherent lengths and scintillation indexes of the speckle fields were then numerically simulated, and the speckle characteristics of the Laguerre-Gauss vortex beam were compared with those of the Gaussian beams. The effects of the topological charges, rough target radii, initial beam radii, turbulence intensities, and roughness degrees of the targets on the speckle characteristics of the LG vortex beams were analyzed. This study's results showed that in the weak turbulence regions, the target characteristics were the main influencing factors of the speckle fields. Meanwhile, in the strong turbulence regions, the turbulence effects were the main influencing factors of the speckle fields. The influence effects of turbulent atmosphere and target characteristics on the coherent lengths and scintillation effects of the vortex beam echoes were observed to be less than those of the Gaussian beams. In addition, the influence effects of the turbulent atmosphere on coherent lengths and scintillation effects of the vortex beams echoes with small topology were found to be minimal. Therefore, this study's results can potentially provide theoretical and technical guidance for the future applications of laser target detection, target recognition, and speckle measurement processes in space.

Estimation of the Characteristics of the Domain of Multiple Filamentation of Femtosecond Laser Pulses in Air Based on the Single Filamentation Model

Characteristics of the domain of multiple filamentation in air are estimated based on the numerical solution of a nonlinear Schrodinger equation in the single filamentation statement. The method of diffraction-ray tubes was used to describe the single filamentation of laser pulses. The efficiency of this method for interpreting experimental results and predicting effects is shown, which is important when planning experiments. The characteristic size of small-scale intensity inhomogeneities in the laser centimeter-radius beam profile, which induce a multiple filamentation of femtosecond pulses, is shown to be several millimeters. An increase in the initial laser beam radius during telescoping increases the sizes of the initial small-scale intensity inhomogeneities, and reduces their power. This leads to an increase in the distance to the start of filamentation. An increase in the initial beam power promotes the elongation of the filaments and increases their number.

Дифракционно-лучевая оптика распространения фемтосекундных лазерных импульсов в условиях нормальной дисперсии в воздухе

The results of a theoretical study of the propagation of femtosecond pulses of a Ti:Sa laser under normal dispersion conditions in air are presented. The use of the diffraction-beam tube method for the analysis of numerical solutions of the nonlinear Schrödinger equation in a dispersion medium with Kerr-plasma nonlinearity made it possible to determine the basic regularities of femtosecond laser pulses self-focusing and filamentation in air at various pulse lengths, initial beam radius, and peak powers. It is shown that in the case of the group velocity dispersion influence with an increase in the initial laser beam radius, the filamentation breaks down even at large supercritical powers. It is shown that with an increase in the dispersion distortions of the pulse the radius of the energetically replenishing diffraction beam tube, the angular divergence of the post-filamentation light channel, and the nonlinear focus coordinate normalized to the Rayleigh length for the central time layers of the laser pulse and the integral picture are increasing.

Control of Multiple Filamentation of Femtosecond Laser Pulses in Air

The results are presented of experiments on controlling the characteristics of the multiple filamentation domain of femtosecond laser pulses along atmospheric paths via variations in the initial spatial focusing, beam radius, and pulse energy, as well as the optical field structure at the initial beam aperture.

Diffraction-ray tube analysis of ultrashort high-intensity laser pulse filamentation in air

The results of theoretical simulation of femtosecond Ti:Sapphire laser pulse propagation in air in the self-focusing and filamentation regimes are presented. The self-focusing of pulsed radiation was analyzed based on the diffraction-ray tracing method, within which the beam power propagates within specific light structures, known as the diffraction-ray tubes. These tubes do not intersect in space and do not exchange their energy, but the changes in their shape and cross-section reflect the physical effects occurring with the radiation during its propagation through the medium. This allows discovering the formation of specific light structures in a laser beam during its self-focusing. One of these structures is the energy-replenishing diffraction-ray tube (ERT), which provides the filamentation domain with the necessary light energy and exists also in the form of a high-intensity light channel during the post-filamentation propagation of a pulse. The dependences of the radius and power of this energy-replenishing tube on the initial beam radius and peak radiation power at a fixed pulse length are derived. It is revealed that the radiation energy expenditure for filamentation decreases as the beam radius increases. The peak power in ERT does not exceed the critical self-focusing power for a Gaussian beam during the post-filamentation propagation of a pulse and weakly depends on the initial pulse parameters.

Simulation of Self-focusing of Femtosecond Laser Pulses with Normal Dispersion in Air Using the Diffraction-Beam Tube Approach

Based on numerical simulation and qualitative analysis, the effect of the group velocity dispersion on the formation of light structures during self-focusing and filamentation of femtosecond Ti:sapphire laser pulses in air is studied. The main features of the filamentation have been determined at various pulse duration, initial beam radii, and peak radiation powers based on the results of numerical solutions of the nonlinear Schrodinger equation in a Kerr-plasma dissipative dispersion medium and using the diffraction-beam tube approach. Dispersion is detected in the cases where the dispersion length is not a minimum at the scale of the process. It is shown that the relative (normalized to Rayleigh length) coordinate of the beginning of filamentation increases as the dispersion distortions of the pulse increase, and the filamentation channel length is reduced. For shorter laser pulses (tens of femtoseconds), the filamentation ceases as the laser beam radius increases. The size of the energy-replenishing diffraction-beam tube and the angular divergence of postfilamentation light channels increase for this class of pulses.

Enhancement of terahertz field in the relativistic coupling of high power laser with magnetized plasma

In this article, the relativistic nonlinear self-focusing of a right circular polarized laser beam propagated through magnetized plasma was investigated. The high power of laser beam which resulted from the self-focusing effect was exploited to excite an electromagnetic wave to the terahertz frequency range. By controlling the external longitudinal magnetic field, a high stabilized terahertz field was observed. At terahertz frequency (1THz) where the initial laser beam radius (x0=20μm) and initial laser beam intensity (I0=1017W/cm2), the highest terahertz radiation power attained was about tens of gigawatts that associated with best stabilization seen.

Simulation of Self-Focusing of Femtosecond Laser Pulses in Air by the Method of Diffraction-Beam Tubes

Results of the theoretical study of the propagation of femtosecond pulses of a Ti:Sapphire laser in air under self-focusing and filamentation are presented. The self-focusing of laser pulses is analyzed on the basis of the method of diffraction-beam tubes. The analysis established that specific light structures were formed in a laser beam during self-focusing. One of such structures is an energy-replenishing diffraction-beam tube, which provides the necessary energy for filamentation and has the form of a high-intensity light channel during postfilamentation pulse propagation. The dependences of the radius and power of the energy-replenishing tube on the initial beam radius and peak power at a fixed pulse length are derived. It is revealed that the energy consumption of radiation for the filamentation decreases with an increase in the beam radius. The peak power contained in the energy-replenishing light tube during the postfilamentation laser pulse propagation does not exceed the critical self-focusing power of a Gaussian beam and weakly depends on the initial pulse parameters.

Transport of moderately relativistic electron beam in dense plasma

Transport of moderate relativistic micro electron beam in overdense plasma is investigated using numerical simulation and analytical modeling. It is found that if the product of the initial beam current density jb and radius R0 is above a lower limit, which scales like , where ne is the plasma density, the beam will periodically self pinch and relax as it propagates. Otherwise the beam diverges. But if is too large, the pinching behavior becomes quite different. Such micro-beam transport behavior can be attributed to the nonlinear dynamics of the beam electrons in overdense plasma.

Significant enhancement in the propagation of cosh-Gaussian laser beam in a relativistic–ponderomotive plasma using ramp density profile

AbstractThe 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.

Effects of finite inner and outer scales on the scintillation index of turbulent slant path

In this paper, the effects of nonzero inner scales and finite outer scales are investigated, in the context of Gaussian beam propagation along a slant path under general turbulence conditions. Theoretical expressions for the cut-off spatial frequencies are derived with an approach method, and thereby a modified scintillation model is developed to incorporate inner scale and outer scale parameters in the analysis. Then, inner and outer scale effects on the downlink are analysed with respect to the zenith angle, the altitude of the transmitter, the initial beam radius, as well as the turbulence strength. Numerical results indicate that the effects of a finite outer scale mainly influence transmission that occurs at large zenith angles or high altitudes, while the inner scale effects are more prevalent. This study may be helpful to improve the accuracy of calculation of slant-path scintillation index, and thus benefit the characterization and optimization of space/air-ground laser communication systems.

Changes in orbital-angular-momentum modes of a propagated vortex Gaussian beam through weak-to-strong atmospheric turbulence.

The radial average-power distribution and normalized average power of orbital-angular-momentum (OAM) modes in a vortex Gaussian beam after passing through weak-to-strong atmospheric turbulence are theoretically formulated. Based on numerical calculations, the role of the intrinsic mode index, initial beam radius and turbulence strength in OAM-mode variations of a propagated vortex Gaussian beam is explored, and the validity of the pure-phase-perturbation approximation employed in existing theoretical studies is examined. Comparison between turbulence-induced OAM-mode scrambling of vortex Gaussian beams and that of either Laguerre-Gaussian (LG) beams or pure vortex beams has been made. Analysis shows that the normalized average power of OAM modes changes with increasing receiver-aperture size until it approaches a nearly stable value. For a receiver-aperture size of practical interest, OAM-mode scrambling is severer with a larger mode index or smaller initial beam radius besides stronger turbulence. Under moderate-to-strong turbulence condition, for two symmetrically-neighboring extrinsic OAM modes, the normalized average power of the one with an index closer to zero may be greater than that of the other one. The validity of the pure-phase-perturbation approximation is determined by the intrinsic mode index, initial beam radius and turbulence strength. It makes sense to jointly control the amplitude and phase of a fundamental Gaussian beam for producing an OAM-carrying beam.

Nonlinear laser pulse response in a crystalline lens.

The propagation characteristics of a spatial Gaussian laser pulse have been studied inside a gradient-index structured crystalline lens with constant-density plasma generated by the laser-tissue interaction. The propagation of the laser pulse is affected by the nonlinearities introduced by the generated plasma inside the crystalline lens. Owing to the movement of plasma species from a higher- to a lower-temperature region, an increase in the refractive index occurs that causes the focusing of the laser pulse. In this study, extended paraxial approximation has been applied to take into account the evolution of the radial profile of the Gaussian laser pulse. To examine the propagation characteristics, variation of the beam width parameter has been observed as a function of the laser power and initial beam radius. The cavitation bubble formation, which plays an important role in the restoration of the elasticity of the crystalline lens, has been investigated.