Validity of the paraxial approximation for electron acceleration with radially polarized laser beams

Direct acceleration of collimated monoenergetic sub-femtosecond electron bunches driven by a radially polarized laser pulse

High-quality ultrashort electron beams have diverse applications in a variety of areas, such as 4D electron diffraction and microscopy, relativistic electron mirrors and ultrashort radiation sources. Direct laser acceleration (DLA) mechanism can produce electron beams with a large amount of charge (several to hundreds of nC), but the generated electron beams usually have large divergence and wide energy spread. Here, we propose a novel DLA scheme to generate high-quality ultrashort electron beams by irradiating a radially polarized laser pulse on a nanofiber. Since electrons are continuously squeezed transversely by the inward radial electric field force, the divergence angle gradually decreases as electrons transport stably with the laser pulse. The well-collimated electron bunches are effectively accelerated by the circularly-symmetric longitudinal electric field and the relative energy spread also gradually decreases. It is demonstrated by three-dimensional (3D) simulations that collimated monoenergetic electron bunches with 0.75° center divergence angle and 14% energy spread can be generated. An analytical model of electron acceleration is presented which interprets well by the 3D simulation results.

On the importance of frequency-dependent beam parameters for vacuum acceleration with few-cycle radially polarized laser beams

Tightly focused, ultrashort radially polarized laser beams have a large longitudinal field, which provides a strong motivation for direct particle acceleration and manipulation in a vacuum. The broadband nature of these beams means that chromatic properties of propagation and focusing are important to consider. We show via single-particle simulations that using the correct frequency-dependent beam parameters is imperative, especially as the pulse duration decreases to the few-cycle regime. The results with different spatio-spectral amplitude profiles show either a drastic increase or decrease of the final accelerated electron energy depending on the shape, motivating both proper characterization and potentially a route to optimization.

Investigation of the null reconstruction effect of an orthogonal elliptical polarization hologram at a large recording angle

We report on the null reconstruction effect (NRE) of an elliptical polarization volume hologram with orthogonal elliptically, circularly, and linearly polarized waves, respectively. The NRE is a special phenomenon in polarization holography, which means the diffraction efficiency declines to zero when the hologram is reconstructed by an orthogonally polarized reading wave. In our previous work [Opt. Express24, 1641 (2016)OPEXFF1094-408710.1364/OE.24.001641; Opt. Lett.42, 1377 (2017)OPLEDP0146-959210.1364/OL.42.001377; Opt. Express23, 8880 (2015)OPEXFF1094-408710.1364/OE.23.008880], the NRE of polarization holography recorded by linear and circular polarization waves has been investigated. Compared with linear and circular polarization holography, elliptical polarization holography represents a more general and unified recording hologram. However, no work on the NRE of elliptical polarization holography, as far as we know, has been reported until now. In this paper, the NRE of elliptical polarization holography is investigated and demonstrated theoretically and experimentally. First, the conditions of achieving NRE in elliptical polarization holography are studied based on vector holography theory. The results indicate that the NRE is a common phenomenon in polarization holography written by linear, circular, and elliptical polarization waves. Then, a series of experiments of NRE in a polarization hologram written by orthogonal elliptically, circularly, and linearly polarized waves is carried out. The NRE of elliptical polarization holography is experimentally observed, and the results are in nice agreement with the theoretical analysis. The NRE of elliptical polarization holography is expected to be applied in high-density optical data storage and polarization-controlled holographic elements.

Linearly polarized laser beam with generalized boundary condition and non-paraxial corrections

Linearly polarized Gaussian beams, under the slowly varying envelope approximation, tightly focused by a perfect parabola modeled with the integral formalism of Ignatovsky are found to be well approximated with a generalized Lax series expansion beyond the paraxial approximation. This allows obtaining simple analytic formulas of the electromagnetic field in both the direct and momentum spaces. It significantly reduces computing time, especially when dealing with the problem of simulating direct laser acceleration. The series expansion formulation depends on integration constants that are linked to boundary conditions. They are found to depend significantly on the region of space over which the integral formulation is fit. Consequently, the net acceleration of electrons initially at rest is extremely sensitive to the chosen set of initial parameters due to the extreme focusing investigated here. This suggests avoiding too tight focusing schemes in order to obtain reliable predictions when the process of interest is sensitive mainly to the field and not the intensity.

Influence of longitudinal chromatism on vacuum acceleration by intense radially polarized laser beams

We report with single-particle simulations that longitudinal chromatism, a commonly occurring spatio-temporal coupling in ultrashort laser pulses, can have a significant influence in the longitudinal acceleration of electrons via high-power, tightly-focused, and radially polarized laser beams. This effect can be advantageous, and even more so when combined with small values of temporal chirp. However, the effect can also be highly destructive when the magnitude and sign of the longitudinal chromatism is not ideal, even at very small magnitudes. This motivates the characterization and understanding of the driving laser pulses and further study of the influence of similar low-order spatial-temporal couplings on such acceleration.

Mapping complex polarization states of light on a solid

Polarization states of light, represented by different points on a Poincaré sphere, can be readily analyzed for a Gaussian beam by a combination of wave plates and polarizers. However, this method cannot be extended to higher-order Poincaré spheres and complex polarization patterns produced by coherent superpositions of vector vortex (VV) beams. We demonstrate the visualization of complex polarization patterns by imprinting them onto a solid surface in the form of periodic nano-gratings oriented parallel to the local structure of the electric field of light. We design unconventional surface structures by controlling the superposition of VV beams. Our method is of potential interest to the production of sub-wavelength nano-structures.

Laser-Induced Linear-Field Particle Acceleration in Free Space

Linear-field particle acceleration in free space (which is distinct from geometries like the linac that requires components in the vicinity of the particle) has been studied for over 20 years, and its ability to eventually produce high-quality, high energy multi-particle bunches has remained a subject of great interest. Arguments can certainly be made that linear-field particle acceleration in free space is very doubtful given that first-order electron-photon interactions are forbidden in free space. Nevertheless, we chose to develop an accurate and truly predictive theoretical formalism to explore this remote possibility when intense, few-cycle electromagnetic pulses are used in a computational experiment. The formalism includes exact treatment of Maxwell’s equations and exact treatment of the interaction among the multiple individual particles at near and far field. Several surprising results emerge. We find that electrons interacting with intense laser pulses in free space are capable of gaining substantial amounts of energy that scale linearly with the field amplitude. For example, 30 keV electrons (2.5% energy spread) are accelerated to 61 MeV (0.5% spread) and to 205 MeV (0.25% spread) using 250 mJ and 2.5 J lasers respectively. These findings carry important implications for our understanding of ultrafast electron-photon interactions in strong fields.

Relativistic Acceleration of Electrons Injected by a Plasma Mirror into a Radially Polarized Laser Beam

We propose a method to generate femtosecond, relativistic, and high-charge electron bunches using few-cycle and tightly focused radially polarized laser pulses. In this scheme, the incident laser pulse reflects off an overdense plasma that injects electrons into the reflected pulse. Particle-in-cell simulations show that the plasma injects electrons ideally, resulting in a dramatic increase of charge and energy of the accelerated electron bunch in comparison to previous methods. This method can be used to generate femtosecond pC bunches with energies in the 1-10 MeV range using realistic laser parameters corresponding to current kHz laser systems.

Short pulse laser beam beyond paraxial approximation

Nonparaxial perturbative equations are derived from the scalar wave equation by taking into account spatiotemporal couplings. General solutions are obtained in Fourier space and further transformed back in direct space. They depend on parameters that can be used to match various boundary conditions and the perturbative expansion of any nonparaxial exact solutions. This parametrization is used to study the sensitivity of direct electron acceleration off an ultrashort tightly focused laser pulse to nonparaxial corrections of radially polarized electromagnetic fields.

S-shaped non-paraxial corrections to general astigmatic beams

Non-paraxial perturbation wave equations are solved for general astigmatic Gaussian beams for the first time, to the best of our knowledge, in the angular spectrum representation by taking into account generic boundary conditions. Expressions for second-order corrections are derived and exemplified with an optical cavity made of two cylindrical mirrors. Non-paraxial corrections can lead, depending on the choice of boundary conditions, to a transverse S-shaped beam mode, which has been qualitatively been observed in a highly divergent non-planar four-mirror cavity.

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.

Direct electron acceleration with tightly focused TM(0,1) beams: boundary conditions and non-paraxial corrections

Non-paraxial corrections for a scalar optical field that follows the Helmotz equation are extracted for the first time, to the best of our knowledge, in the angular spectrum representation by taking into account generic boundary conditions. Those integration constants are compared with closed-form solutions and approximate series expansions usually obtained by other authors. This method is particularized to the direct electron acceleration with a tightly focused TM(0,1) laser beam to demonstrate that these constants have a strong effect on the final average energy and quality of the electron beam.