Electron acceleration by a tightly focused laser beam

Effects of Colliding Laser Pulses Polarization on e^{-}e^{+} Cascade Development in Extreme Focusing

The onset and development of electron-positron cascade in a standing wave formed by multiple colliding laser pulses requires tight focusing in order to achieve the maximum laser intensity. There, steep spatiotemporal gradients in the laser intensity expel seed particles from the high-intensity region and thus can prevent the onset of a cascade. We show that radially polarized laser pulses ensure that the seed electrons are present at the focal plane at the moment of the highest amplitude even in the case of extreme focusing. This feature reduces the required laser power for the onset of a cascade 100 times (80 times) compared to circularly (linearly) polarized laser pulses having the same focal spot radius and duration.

Highly collimated intense radiation from electron collisions with a tightly focused linearly polarized laser pulse

The use of high-energy radiation generated by electron collisions with a laser pulse is an effective method to treat cancer. In this paper, the spatial properties of radiation produced by electron collisions with a tightly focused linearly polarized laser pulse are investigated. Theoretical derivations and numerical simulations within the framework of classical electrodynamics show that the stronger the laser intensity, the higher the initial electron energy, and the longer the laser pulse, which can produce greater radiation power. An increase in the laser intensity expands the range of electron radiation and therefore reduces the collimation of the radiation. The collimation in the radiation is better when colliding with an electron of higher initial energy. The phenomenon that the radiated power of the electron varies periodically with the initial phase of the laser is also found. The results of this paper have important implications to produce strongly radiating and highly collimated rays.

High-flux neutron generation by laser-accelerated ions from single- and double-layer targets

Contemporary ultraintense, short-pulse laser systems provide extremely compact setups for the production of high-flux neutron beams, such as those required for nondestructive probing of dense matter, research on neutron-induced damage in fusion devices or laboratory astrophysics studies. Here, by coupling particle-in-cell and Monte Carlo numerical simulations, we examine possible strategies to optimise neutron sources from ion-induced nuclear reactions using 1-PW, 20-fs-class laser systems. To improve the ion acceleration, the laser-irradiated targets are chosen to be ultrathin solid foils, either standing alone or preceded by a plasma layer of near-critical density to enhance the laser focusing. We compare the performance of these single- and double-layer targets, and determine their optimum parameters in terms of energy and angular spectra of the accelerated ions. These are then sent into a converter to generate neutrons via nuclear reactions on beryllium and lead nuclei. Overall, we identify configurations that result in neutron yields as high as $$\sim 10^{10}\,{\mathrm{n}}\,{\mathrm{sr}}^{-1}$$ ∼ 10 10 n sr - 1 in $$\sim 1$$ ∼ 1 -cm-thick converters or instantaneous neutron fluxes above $$10^{23}\,{\mathrm{n}}\,{\mathrm{cm}}^{-2}\,{\mathrm{s}}^{-1}$$ 10 23 n cm - 2 s - 1 at the backside of $$\lesssim 100$$ ≲ 100 -$$\upmu$$ μ m-thick converters. Considering a realistic repetition rate of one laser shot per minute, the corresponding time-averaged neutron yields are predicted to reach values ($$\gtrsim 10^7\,{\mathrm{n}} \,{\mathrm{sr}}^{-1}\,{\mathrm{s}}^{-1}$$ ≳ 10 7 n sr - 1 s - 1 ) well above the current experimental record, and this even with a mere thin foil as a primary target. A further increase in the time-averaged yield up to above $$10^8\,{\mathrm{sr}}^{-1}\,{\mathrm{s}}^{-1}$$ 10 8 sr - 1 s - 1 is foreseen using double-layer targets.

Vacuum laser acceleration of super-ponderomotive electrons using relativistic transparency injection

Intense lasers can accelerate electrons to very high energy over a short distance. Such compact accelerators have several potential applications including fast ignition, high energy physics, and radiography. Among the various schemes of laser-based electron acceleration, vacuum laser acceleration has the merits of super-high acceleration gradient and great simplicity. Yet its realization has been difficult because injecting free electrons into the fast-oscillating laser field is not trivial. Here we demonstrate free-electron injection and subsequent vacuum laser acceleration of electrons up to 20 MeV using the relativistic transparency effect. When a high-contrast intense laser drives a thin solid foil, electrons from the dense opaque plasma are first accelerated to near-light speed by the standing laser wave in front of the solid foil and subsequently injected into the transmitted laser field as the opaque plasma becomes relativistically transparent. It is possible to further optimize the electron injection/acceleration by manipulating the laser polarization, incident angle, and temporal pulse shaping. Our result also sheds light on the fundamental relativistic transparency process, crucial for producing secondary particle and light sources.

Compact electron accelerators based on laser-plasma acceleration scheme may be useful for future light sources, radiation therapy etc. Here the authors demonstrate electron acceleration in laser plasma interaction via vacuum laser acceleration and relativistic transparency injection.

Vacuum acceleration of electrons in a dynamic laser pulse

A planar laser pulse propagating in vacuum can exhibit an extremely large ponderomotive force. This force, however, cannot impart net energy to an electron: As the pulse overtakes the electron, the initial impulse from its rising edge is completely undone by an equal and opposite impulse from its trailing edge. Here we show that planarlike "flying focus" pulses can break this symmetry, imparting relativistic energies to electrons. The intensity peak of a flying focus-a moving focal point resulting from a chirped laser pulse focused by a chromatic lens-can travel at any subluminal velocity, forward or backward. As a result, an electron can gain enough momentum in the rising edge of the intensity peak to outrun and avoid the trailing edge. Accelerating the intensity peak can further boost the momentum gain. Theory and simulations demonstrate that these dynamic intensity peaks can backwards accelerate electrons to the MeV energies required for radiation and electron diffraction probes of high energy density materials.

Polarized Ultrashort Brilliant Multi-GeV γ Rays via Single-Shot Laser-Electron Interaction

Generation of circularly polarized (CP) and linearly polarized (LP) γ rays via the single-shot interaction of an ultraintense laser pulse with a spin-polarized counterpropagating ultrarelativistic electron beam has been investigated in nonlinear Compton scattering in the quantum radiation-dominated regime. For the process simulation, a Monte Carlo method is developed which employs the electron-spin-resolved probabilities for polarized photon emissions. We show efficient ways for the transfer of the electron polarization to the high-energy photon polarization. In particular, multi-GeV CP (LP) γ rays with polarization of up to about 95% can be generated by a longitudinally (transversely) spin-polarized electron beam, with a photon flux meeting the requirements of recent proposals for the vacuum birefringence measurement in ultrastrong laser fields. Such high-energy, high-brilliance, high-polarization γ rays are also beneficial for other applications in high-energy physics, and laboratory astrophysics.

Quantum Mechanisms of Electron and Positron Acceleration through Nonlinear Compton Scatterings and Nonlinear Breit-Wheeler Processes in Coherent Photon Dominated Regime

Electric force is presently the only means in laboratory to accelerate charged particles to high energies, corresponding acceleration processes are classical and continuous. Here we report on how to accelerate electrons and positrons to high energies using ultra intense lasers (UIL) through two quantum processes, nonlinear Compton scattering and nonlinear Breit-Wheeler process. In the coherent photon dominated regime of these two processes, the former can effectively boost electrons/positrons and the latter can produce high energy electrons and positrons with low energy γ photons. The energy needed for such quantum acceleration (QA) is transferred from large numbers of coherent laser photons through the two quantum processes. QA also collimate the generated high energy electrons and positrons along the laser axis and the effective acceleration distance is of microscopic dimensions. Proof of principle QA experiment can be performed on 100 petawatt (PW) scale lasers which are in building or planning.

Ultrarelativistic Electron-Beam Polarization in Single-Shot Interaction with an Ultraintense Laser Pulse

Spin polarization of an ultrarelativistic electron beam head-on colliding with an ultraintense laser pulse is investigated in the quantum radiation-dominated regime. We develop a Monte Carlo method to model electron radiative spin effects in arbitrary electromagnetic fields by employing spin-resolved radiation probabilities in the local constant field approximation. Because of spin-dependent radiation reaction, the applied elliptically polarized laser pulse polarizes the initially unpolarized electron beam and splits it along the propagation direction into two oppositely transversely polarized parts with a splitting angle of about tens of milliradians. Thus, a dense electron beam with above 70% polarization can be generated in tensof femtoseconds with realistic laser pulses. The proposed method demonstrates a way for relativistic electron beam polarization with currently achievable laser facilities.

Analysis on the longitudinal field strength formed by tightly-focused radially-polarized femtosecond petawatt laser pulse

Tight focusing of radially- or azimuthally-polarized electromagnetic waves becomes attractive because of the strong field generation in the longitudinal direction. In this paper, we investigate the strength of longitudinal electric field when a radially-polarized femtosecond PW laser pulse is tightly focused by a parabolic surface. From the calculation using the vector diffraction approach, it has been shown that the highest strength of 2.2 × 10¹³ V/cm can be reached for the longitudinal field with a radially-polarized 11.2-fs, 11.2-J uniform-beam-profile laser pulse. The difference in the strength of longitudinal field with different beam profile and the spectrum of a laser pulse has been also carefully examined. The propagation of a laser spot has been simulated under an extremely-tight-focusing condition (0.25 in terms of f-number) and an achievable field strength for a standing longitudinal field has been examined by colliding two radially-polarized fs PW-level laser pulses.

Single-Shot Carrier-Envelope Phase Determination of Long Superintense Laser Pulses

The impact of the carrier-envelope phase (CEP) of an intense multicycle laser pulse on the radiation of an electron beam during nonlinear Compton scattering is investigated. We have identified a CEP effect specific to the ultrarelativistic regime. When the electron beam counterpropagates with the laser pulse, pronounced high-energy x-ray double peaks emerge near the backward direction relative to the initial electron motion. This is achieved in the relativistic interaction domain, where both the electron energy is required to be lower than for the electron reflection condition at the laser peak and the stochasticity effects in the photon emission need to be weak. The asymmetry parameter of the double peaks in the angular radiation distribution is shown to serve as a sensitive measure for the CEP of up to 10-cycle long laser pulses and can be applied for the characterization of extremely strong laser pulses in present and near future laser facilities.

Multi-GeV electron-positron beam generation from laser-electron scattering

The new generation of laser facilities is expected to deliver short (10 fs–100 fs) laser pulses with 10–100 PW of peak power. This opens an opportunity to study matter at extreme intensities in the laboratory and provides access to new physics. Here we propose to scatter GeV-class electron beams from laser-plasma accelerators with a multi-PW laser at normal incidence. In this configuration, one can both create and accelerate electron-positron pairs. The new particles are generated in the laser focus and gain relativistic momentum in the direction of laser propagation. Short focal length is an advantage, as it allows the particles to be ejected from the focal region with a net energy gain in vacuum. Electron-positron beams obtained in this setup have a low divergence, are quasi-neutral and spatially separated from the initial electron beam. The pairs attain multi-GeV energies which are not limited by the maximum energy of the initial electron beam. We present an analytical model for the expected energy cutoff, supported by 2D and 3D particle-in-cell simulations. The experimental implications, such as the sensitivity to temporal synchronisation and laser duration is assessed to provide guidance for the future experiments.

Generation of arbitrary axisymmetrically polarized pulses by using the combination of 4-f spatial light modulator and common-path optical system

We proposed and constructed a system to realize broadband generation of arbitrary axisymmetrically polarized (AP) pulses with spatial complex amplitude modulation. This system employs the combination of a spatial light modulator in the 4-f configuration (4-f SLM), and a space variant wave plate as a common path interferometer. The 4-f SLM and the common path interferometer offer compensation for spatial dispersion with respect to wavelength and stability to perturbation, respectively. We experimentally demonstrated the various AP pulses generation by applying modulations of fundamental and higher-order Laguerre-Gauss modes, whose radial indices were, respectively, p = 0 and 1, with high purity, which showed that we were able to generate arbitral AP pulses with spatial complex amplitude modulation. This technique is expected to be applied in both classical and quantum communications with higher-order modes.

Angle-resolved stochastic photon emission in the quantum radiation-dominated regime

Signatures of stochastic effects in the radiation of a relativistic electron beam interacting with a counterpropagating superstrong short focused laser pulse are investigated in a quantum regime when the electron’s radiation dominates its dynamics. We consider the electron-laser interaction at near-reflection conditions when pronounced high-energy gamma-ray bursts arise in the backward-emission direction with respect to the initial motion of the electrons. The quantum stochastic nature of the gamma-photon emission is exhibited in the angular distributions of the radiation and explained in an intuitive picture. Although, the visibility of the stochasticity signatures depends on the laser and electron beam parameters, the signatures are of a qualitative nature and robust. The stochasticity, a fundamental quantum property of photon emission, should thus be measurable rather straightforwardly with laser technology available in near future.

Laser-pulse-shape control of seeded QED cascades

QED cascades are complex avalanche processes of hard photon emission and electron-positron pair creation driven by ultrastrong electromagnetic fields. They play a fundamental role in astrophysical environments such as a pulsars’ magnetosphere, rendering an earth-based implementation with intense lasers attractive. In the literature, QED cascades were also predicted to limit the attainable intensity in a set-up of colliding laser beams in a tenuous gas such as the residual gas of a vacuum chamber, therefore severely hindering experiments at extreme field intensities. Here, we demonstrate that the onset of QED cascades may be either prevented even at intensities around 10²⁶ W/cm² with tightly focused laser pulses and low-Z gases, or facilitated at intensities below 10²⁴ W/cm² with enlarged laser focal areas or high-Z gases. These findings pave the way for the control of novel experiments such as the generation of pure electron-positron-photon plasmas from laser energy, and for probing QED in the extreme-intensity regime where the quantum vacuum becomes unstable.

Vector fields in a tight laser focus: comparison of models

We assess several widely used vector models of a Gaussian laser beam in the context of more accurate vector diffraction integration. For the analysis, we present a streamlined derivation of the vector fields of a uniformly polarized beam reflected from an ideal parabolic mirror, both inside and outside of the resulting focus. This exact solution to Maxwell's equations, first developed in 1920 by V. S. Ignatovsky, is highly relevant to high-intensity laser experiments since the boundary conditions at a focusing optic dictate the form of the focus in a manner analogous to a physical experiment. In contrast, many models simply assume a field profile near the focus and develop the surrounding vector fields consistent with Maxwell's equations. In comparing the Ignatovsky result with popular closed-form analytic vector models of a Gaussian beam, we find that the relatively simple model developed by Erikson and Singh in 1994 provides good agreement in the paraxial limit. Models involving a Lax expansion introduce a divergences outside of the focus while providing little if any improvement in the focal region. Extremely tight focusing produces a somewhat complicated structure in the focus, and requires the Ignatovsky model for accurate representation.

Seeded QED cascades in counterpropagating laser pulses

The growth rates of seeded QED cascades in counterpropagating lasers are calculated with first-principles two- and three-dimensional QED-PIC (particle-in-cell) simulations. The dependence of the growth rate on the laser polarization and intensity is compared with analytical models that support the findings of the simulations. The models provide insight regarding the qualitative trend of the cascade growth when the intensity of the laser field is varied. A discussion about the cascade's threshold is included, based on the analytical and numerical results. These results show that relativistic pair plasmas and efficient conversion from laser photons to γ rays can be observed with the typical intensities planned to operate on future ultraintense laser facilities such as ELI or Vulcan.

Weakly diverging to tightly focused Gaussian beams: a single set of analytic expressions

Analytic expressions describing all vector components of Gaussian beams, linearly polarized as well as radially polarized, are presented. These simple expressions, to high powers in divergence angle, were derived from a single-component vector potential. The vector potential itself, as in the 1979 work of Davis [Phys. Rev. A19, 1177 (1979)PLRAAN1050-294710.1103/PhysRevA.22.1159], was approximated by the first two terms of an infinite series solution of the Helmholtz equation. The expressions presented here were formulated to emphasize the dependence of the amplitude of the various field components on the beam's divergence angle. We show that the amplitude of the axial component of a linearly polarized Gaussian beam scales as the divergence angle squared, whereas the amplitude of the cross-polarized component of a linearly polarized Gaussian beam scales as the divergence angle to the fourth power. Weakly diverging Gaussian beams as well as strongly focused Gaussian beams can be described by exactly the same set of mathematical expressions, up to normalization constant. For a strongly focused linearly polarized Gaussian beam, the ellipticity of the dominant electric field component, typically calculated by the Debye-Wolf integral, is reproduced. For yet higher accuracy, terms with higher powers in divergence angle are presented, but the inclusion of these terms is limited to low divergence angles and short axial distances.

Identifying the Stern-Gerlach force of classical electron dynamics

Different classical theories are commonly applied in various branches of physics to describe the relativistic dynamics of electrons by coupled equations for the orbital motion and spin precession. Exemplarily, we benchmark the Frenkel model and the classical Foldy-Wouthuysen model with spin-dependent forces (Stern-Gerlach forces) to the quantum dynamics as predicted by the Dirac equation. Both classical theories can lead to different or even contradicting predictions how the Stern-Gerlach forces modify the electron’s orbital motion, when the electron moves in strong electromagnetic field configurations of emerging high-intensity laser facilities. In this way, one may evaluate the validity and identify the limits of these classical theories via a comparison with possible experiments to provide a proper description of spin-induced dynamics. Our results indicate that the Foldy-Wouthuysen model is qualitatively in better agreement with the Dirac theory than the widely used Frenkel model.

Spatio-temporal modification of femtosecond focal spot under tight focusing condition

The focusing property of a focal spot of a femtosecond laser pulse is presented under tight focusing conditions (below f-number of 1). The spatial and temporal intensity distributions of a focused electric field are calculated by vector diffraction integrals and coherent superposition method. The validity of the calculation method is examined by comparing the intensity distribution obtained under a high f-number condition to that obtained with the fast Fourier transform method that assumes the scalar paraxial approximation. The spatial and temporal modifications under tight focusing conditions are described for a focused femtosecond laser pulse. The calculation results show that a peak intensity of about 2.5x10(24) W/cm2 can be achievable by tightly focusing a 12-fs, 10 PW laser pulse with a f/0.5 parabolic optic. The precise information on intensity distributions of a femtosecond focal spot obtained under a tight focusing condition will be crucial in assessing a focused intensity and in describing the motion of charged particles under an extremely strong electric field in ultra-relativistic and/or relativistic laser matter-interaction studies.

Electron dynamics controlled via self-interaction

The dynamics of an electron in a strong laser field can be significantly altered by radiation reaction. This usually results in a strongly damped motion, with the electron losing a large fraction of its initial energy. Here we show that the electron dynamics in a bichromatic laser pulse can be indirectly controlled by a comparatively small radiation reaction force through its interplay with the Lorentz force. By changing the relative phase between the two frequency components of the bichromatic laser field, an ultrarelativistic electron bunch colliding head-on with the laser pulse can be deflected in a controlled way, with the deflection angle being independent of the initial electron energy. The effect is predicted to be observable with laser powers and intensities close to those of current state-of-the-art petawatt laser systems.

Robust signatures of quantum radiation reaction in focused ultrashort laser pulses

Radiation-reaction effects in the interaction of an electron bunch with a superstrong focused ultrashort laser pulse are investigated in the quantum radiation-dominated regime. The angle-resolved Compton scattering spectra are calculated in laser pulses of variable duration using a semiclassical description for the radiation-dominated dynamics and a full quantum treatment for the emitted radiation. In dependence of the laser-pulse duration we find signatures of quantum radiation reaction in the radiation spectra, which are characteristic for the focused laser beam and visible in the qualitative behavior of both the angular spread and the spectral bandwidth of the radiation spectra. The signatures are robust with respect to the variation of the electron and laser-beam parameters in a large range. Qualitatively, they differ fully from those in the classical radiation-reaction regime and are measurable with presently available laser technology.

Nonlinear coupling between axisymmetrically-polarized ultrashort optical pulses in a uniaxial crystal

Nonlinear propagation of focused axisymmetrically-polarized ultrashort optical pulses along the optic axis in a uniaxial crystal is investigated experimentally and theoretically. The energy transfer between an azimuthally-polarized pulse and a radially-polarized pulse is observed. To analyze the nonlinear propagation, a general paraxial equation with a third-order nonlinearity for axisymmetrically-polarized pulses in a uniaxial crystal is derived and the extended Stokes parameters (ESPs) based on cylindrical coordinates are newly-introduced. The simulation results by using this equation, providing the calculated ESPs, well explain our experimental observations: 1) the energy transfer is attributed to the four-wave-mixing effect, reflecting the overlapping between the axisymmetrically polarized modes, 2) the variations of the polarization defined from the ESPs are clarified to be affected by the self- and the cross-phase modulations, which make the effective propagation length long or short.

Improved beam waist formula for ultrashort, tightly focused linearly, radially, and azimuthally polarized laser pulses in free space

We derive an asymptotically accurate formula for the beam waist of ultrashort, tightly focused fundamental linearly polarized, radially polarized, and azimuthally polarized modes in free space. We compute the exact beam waist via numerical cubature to ascertain the accuracy with which our formula approximates the exact beam waist over a broad range of parameters of practical interest. Based on this, we describe a method of choosing parameters in the model given the beam waist and pulse duration of a laser pulse.

Fabrication of nitrogen vacancy color centers by femtosecond pulse laser illumination

We report on a novel method to fabricate single, multiple and large-area high-density ensembles of nitrogen vacancy (NV) color centers in synthetic type Ib bulk diamond by femtosecond laser illumination. Electron beams generated in propagation of intense infrared laser pulses in air sputtered on a diamond sample under high temperature aroused by the laser illumination, creating NV color centers. Typical photoluminescence (PL) spectra of NV centers could be observed on the illuminated spots. Photon streams from individual photoluminescent points exhibited anti-bunching effect by the second-order correlation measurement, evidencing single and multiple photon-emitters around the laser illuminated spots.

Vacuum electron acceleration driven by a tightly focused radially polarized Gaussian beam

Electron acceleration in vacuum driven by a tightly focused radially polarized Gaussian beam has been studied in detail. Weniger transformation method is used to eliminate the divergence of the radially polarized electromagnetic field derived from the Lax series approach. And, electron dynamics in an intense radially polarized Gaussian beam is analyzed by using the Weniger transformation field. The roles of the initial phase of the electromagnetic field and the injection angle, position and energy of electron in energy gain of electron have been studied in detail.

Vacuum electron acceleration driven by two crossed Airy beams

Using numerical simulation, we have studied in detail vacuum electron acceleration driven by two crossed Airy beams with identical characteristics except for opposite accelerating directions. An electron injected along the longitudinal central axis is only affected by the combined longitudinal electric field. In addition, a suitable crossed Airy beams scheme is more beneficial to the energy gain of an electron than the single Airy beam acceleration scheme [Opt. Lett. 35, 3258 (2010)]. Meanwhile, the cross angle, the injection energy of the electron, and the initial phase of the Airy beams play significant roles in the energy gain of the electron.

Direct acceleration of an electron in infinite vacuum by a pulsed radially-polarized laser beam

We study the direct acceleration of a free electron in infinite vacuum along the axis of a pulsed radially-polarized laser beam. We find that net energy transfer from laser pulse to electron is maximized with the tightest focusing. We show that the net energy gain of an electron initially moving at a relativistic velocity may exceed more than half the theoretical limit of energy transfer, which is not possible with an initially stationary electron in the parameter space studied. We determine and analyze the power scaling of maximum energy gain, extending our study to include a relatively unexplored regime of low powers and revealing that substantial acceleration is already possible without the use of petawatt peak-power laser technology.

Analysis of electron capture acceleration channel in an Airy beam

Using numerical simulation, we have studied in detail vacuum electron acceleration induced by an Airy beam. The phase of the field varies slowly, and the intensity of the field is independent of the decaying parameter of the beam in the asymmetric field channel [(AFC) Opt. Express 18, 7300 (2010)] formed by the Airy beam. Results show that an electron entering into the AFC may be captured and gain high energy. Meanwhile, the decaying parameter, injection energy, and injection angle of the electron play important roles in the electron energy gain.

Determining the carrier-envelope phase of intense few-cycle laser pulses

The electromagnetic radiation emitted by an ultrarelativistic accelerated electron is extremely sensitive to the precise shape of the field driving the electron. We show that the angular distribution of the photons emitted by an electron via multiphoton Compton scattering off an intense (I>10(20)  W/cm(2)), few-cycle laser pulse provides a direct way of determining the carrier-envelope phase of the driving laser field. Our calculations take into account exactly the laser field, include relativistic and quantum effects and are in principle applicable to presently available and future foreseen ultrastrong laser facilities.

Simulations of vacuum laser acceleration: hidden errors from particle's initial positions

Simulation of vacuum laser acceleration, because of its scheme's simplicity, attracts many people involved in. However, how to put the particle in the initial positions in the field has not been considered seriously in some such schemes. An inattentive choice of electron's initial conditions may lead to misleading results. Here we show that arbitrarily placing the particle within the laser field leads to an overestimation of its energy gain, and offer suggestions for selecting appropriate initial conditions.

Nonparaxial analyses of radially polarized beams diffracted at a circular aperture

On the basis of the vectorial Rayleigh diffraction integral, the analytical expressions for the electromagnetic fields of the radially polarized beams diffracted at a circular aperture are derived, which helps us investigate the propagation properties of the apertured radially polarized beams in the nonparaxial and paraxial regimes. The unapertured and paraxial cases can be viewed as the special cases of the general result obtained in this paper. The analyses indicate that the nonparaxiality of the apertured radially polarized beams depends on the ratio of the waist width to the wavelength and the truncation parameter. In addition, the truncation parameter and the beam order have a great impact on the beam diffraction effect and the beam evolution behavior.

Vacuum laser-driven acceleration by Airy beams

The possibility of enhancing the energy gain in vacuum electron acceleration by Airy beams is examined. The characteristics of transverse acceleration and non-diffraction of Airy beam can lead to the formation of a long "asymmetric field channel" along the propagation axis, where the intense asymmetric field can accelerate the injected electron to higher energy. Meanwhile, the injection energy of electron plays an important role in determining the final energy gain.

Power carried by a nonparaxial TM beam

In paraxial optics, the power carried by an optical beam can be accurately calculated by means of the integral of the squared modulus of its electric field over a plane transverse to the propagation axis. However, for nonparaxial electromagnetic beams, it is more appropriate to define the power carried by the beam by the integral of the longitudinal component of its time-averaged Poynting vector over a plane transverse to the propagation axis. In this paper, the expression of the power carried by a high-aperture transverse magnetic (TM) beam of any order is determined. The general expression of the power carried by a TM beam, which also applies for a transverse electric (TE) beam, is given in terms of a modified Struve function of order equal to an integer plus one-half.

Nonparaxial polarizers

We develop a theoretical description for polarizers that goes beyond the paraxial approximation. By combining existing theories for fields with nonplanar wavefronts, we are able to derive a simple power series expansion expressing the electric field of a light beam after a polarizer as a linear function of the field and its spatial derivatives evaluated before the polarizer. The first few terms of such expansion are explicitly given, and their physical meaning is discussed.

Acceleration of electrons by a tightly focused intense laser beam

The recent proposal to use Weinger transformation field (WTF) [Opt. Express 17, 4959-4969 (2009)] for describing tightly focused laser beams is investigated here in detail. In order to validate the accuracy of WTF, we derive the numerical field (NF) from the plane wave spectrum method. WTF is compared with NF and Lax series field (LSF). Results show that LSF is accurate close to the beam axis and divergent far from the beam axis, and WTF is always accurate. Moreover, electron dynamics in a tightly focused intense laser beam are simulated by LSF, WTF and NF, respectively. The results obtained by WTF are shown to be accurate.

Strong signatures of radiation reaction below the radiation-dominated regime

The influence of radiation reaction (RR) on multiphoton Thomson scattering by an electron colliding head-on with a strong laser beam is investigated in a new regime, in which the momentum transferred on average to the electron by the laser pulse approximately compensates the one initially prepared. This equilibrium is shown to be far more sensitive to the influence of RR than previously studied scenarios. As a consequence, RR can be experimentally investigated with currently available laser systems and the underlying widely discussed theoretical equations become testable for the first time.

Simulation of Gaussian laser beams and electron dynamics by Weniger transformation method

For an electron accelerated by a tightly focused Gaussian laser beam, its dynamics are usually simulated through the field obtained by Lax approach [Phys. Rev. A 11, 1365 (1975)]. However, as Lax series field (LSF) is not always convergent, the obtained results are usually inaccurate and even illogical. Here we report that the divergence of LSF can be eliminated by using Weniger transformation, and the electron dynamics simulated by this new field are logical and accurate.

Fields of a focused linearly polarized Gaussian beam: truncated series versus the complex-source-point spherical-wave representation

Fields of a linearly polarized fundamental Gaussian beam are derived exactly using the propagation characteristics of a complex-source-point spherical wave diverging from the origin. Intensity distributions are calculated and compared with their counterparts in a truncated series. It is found that utility of the exact fields is limited by a discontinuity inherent in the vector potential from which they have been obtained.

Ultrashort focused electromagnetic pulses

In this paper we present a closed analytical description for few-cycle, focused electromagnetic pulses of arbitrary duration and carrier-envelope phase. Because of the vectorial character of light, not all thinkable one-dimensional shapes for the transverse electric field or vector potential can be realized as finite energy three-dimensional (3D) structures. We cope with this problem by using a second potential, which is defined as a primitive to the vector potential. This allows one to construct fully consistent 3D wave-packet solutions for the Maxwell equations, given a solution of the scalar wave equation. The wave equation is solved for ultrashort, Gaussian, and related pulses in paraxial approximation. The solution is given in a closed and numerically convenient form, based on the complex error function. All results undergo thorough numerical testing, validating their correctness and accuracy. A reliable and accurate representation of few-cycle pulses is, e.g., crucial for analytical and numerical theory of vacuum particle acceleration.

Relativistic MeV photoelectrons from the single atom response of argon to a 10 19 W/cm2 laser field

We present photoelectron measurements from argon ionization at 10(19) W/cm(2). Photoelectrons with energies above 400 keV, including a 1.2 MeV cutoff, are in quantitative agreement with a semiclassical, relativistic 3D ionization model that includes a nonparaxial laser field. L-shell photoelectrons have energies and momentum dominated by the field, including the acceleration out of the focus. Yields and angular distributions at 60 keV come from valence shell ionization by strong fields where rescattering and atomic processes determine photoelectron final states.

Accelerating protons to therapeutic energies with ultraintense, ultraclean, and ultrashort laser pulses

Proton acceleration by high-intensity laser pulses from ultrathin foils for hadron therapy is discussed. With the improvement of the laser intensity contrast ratio to 10(-1) achieved on the Hercules laser at the University of Michigan, it became possible to attain laser-solid interactions at intensities up to 10(22) W/cm2 that allows an efficient regime of laser-driven ion acceleration from submicron foils. Particle-in-cell (PIC) computer simulations of proton acceleration in the directed Coulomb explosion regime from ultrathin double-layer (heavy ions/light ions) foils of different thicknesses were performed under the anticipated experimental conditions for the Hercules laser with pulse energies from 3 to 15 J, pulse duration of 30 fs at full width half maximum (FWHM), focused to a spot size of 0.8 microm (FWHM). In this regime heavy ions expand predominantly in the direction of laser pulse propagation enhancing the longitudinal charge separation electric field that accelerates light ions. The dependence of the maximum proton energy on the foil thickness has been found and the laser pulse characteristics have been matched with the thickness of the target to ensure the most efficient acceleration. Moreover, the proton spectrum demonstrates a peaked structure at high energies, which is required for radiation therapy. Two-dimensional PIC simulations show that a 150-500 TW laser pulse is able to accelerate protons up to 100-220 MeV energies.

Exact description of a cylindrically symmetrical complex-argument Laguerre-Gauss beam

Based on the perturbative series representation of a complex-source-point spherical wave an expression for cylindrically symmetrical complex-argument Laguerre-Gauss beams of radial order n is derived. This description acquires the accuracy up to any order of diffraction angle, and its first three corrected terms are in accordance with those given by Seshadri [Opt. Lett.27, 1872 (2002)] based on the virtual source method. Numerical results show that on the beam axis the number of orders of nonvanishing nonparaxial corrections is equal to n. Meanwhile a higher radial mode number n leads to a smaller convergent domain of radius.

Direct high-power laser acceleration of ions for medical applications

Theoretical investigations show that linearly and radially polarized multiterawatt and petawatt laser beams, focused to subwavelength waist radii, can directly accelerate protons and carbon nuclei, over micron-size distances, to the energies required for hadron cancer therapy. Ions accelerated by radially polarized lasers have generally a more favorable energy spread than those accelerated by linearly polarized lasers of the same intensity.

Vacuum electron acceleration and bunch compression by a flat-top laser beam

The field intensity distribution and phase velocity characteristics of a flat-top laser beam are analyzed and discussed. The dynamics of electron acceleration in this kind of beam are investigated using three-dimensional test particle simulations. Compared with the standard (i.e., TEM(00) mode) Gaussian beam, a flat-top laser beam has a stronger longitudinal electric field and a larger diffraction angle. These characteristics make it easier for electrons to be trapped and accelerated by the beam. With a flat-top shape, the laser beam is also applicable to the acceleration of low energy electron and bunch compression.

Comment on "Electron acceleration by an intense short pulse laser in a static magnetic field in vacuum"

K. P. Singh [Phys. Rev. E 69, 056410 (2004)] put forward a scheme of vacuum laser acceleration in a static magnetic field. We point out that one of the assumptions used in their model does not stand on a solid physical ground and that it seriously influences electrons to obtain net energy gains from the laser field.

Fields of a radially polarized Gaussian laser beam beyond the paraxial approximation

Analytic expressions for the fields of a tightly focused radially polarized Gaussian laser beam are derived, accurate to epsilon5, where epsilon is the associated diffraction angle. The fields satisfy Maxwell's equations, and the calculated beam power based on them is significantly different from that of the paraxial-approximation fields.

Light diffraction by a strong standing electromagnetic wave

The nonlinear quantum interaction of a linearly polarized x-ray probe beam with a focused intense standing laser wave is studied theoretically. Because of the tight focusing of the standing laser pulse, diffraction effects arise for the probe beam as opposed to the corresponding plane wave scenario. A quantitative estimate for realistic experimental conditions of the ellipticity and the rotation of the main polarization plane acquired by the x-ray probe after the interaction shows that the implementation of such vacuum effects is feasible with future X-ray Free Electron Laser light.

Laser acceleration of electrons to giga-electron-volt energies using highly charged ions

The recent proposal to use highly charged ions as sources of electrons for laser acceleration [S. X. Hu and A. F. Starace, Phys. Rev. Lett. 88, 245003 (2002)] is investigated here in detail by means of three-dimensional, relativistic Monte Carlo simulations for a variety of system parameters, such as laser pulse duration, ionic charge state, and laser focusing spot size. Realistic laser focusing effects--e.g., the existence of longitudinal laser field components-are taken into account. Results of spatial averaging over the laser focus are also presented. These numerical simulations show that the proposed scheme for laser acceleration of electrons from highly charged ions is feasible with current or near-future experimental conditions and that electrons with GeV energies can be obtained in such experiments.