Photon Acceleration in a Flying Focus

Space-Time Structured Plasma Waves

Electrostatic waves play a critical role in nearly every branch of plasma physics from fusion to advanced accelerators, to astro, solar, and ionospheric physics. The properties of planar electrostatic waves are fully determined by the plasma conditions, such as density, temperature, ionization state, or details of the distribution functions. Here we demonstrate that electrostatic wave packets structured with space-time correlations can have properties that are independent of the plasma conditions. For instance, an appropriately structured electrostatic wave packet can travel at any group velocity, even backward with respect to its phase fronts, while maintaining a localized energy density. These linear, propagation-invariant wave packets can be constructed with or without orbital angular momentum by superposing natural modes of the plasma and can be ponderomotively excited by space-time structured laser pulses like the flying focus.

Dephasingless plasma wakefield photon acceleration

Sandberg and Thomas [Phys. Rev. Lett. 130, 085001 (2023)0031-900710.1103/PhysRevLett.130.085001] proposed a scheme to generate ultrashort, high-energy pulses of XUV photons though dephasingless photon acceleration in a beam-driven plasma wakefield. An ultrashort laser pulse is placed in the plasma wake behind a relativistic electron bunch such that it experiences a comoving negative density gradient and therefore shifts up in frequency. Using a tapered density profile provides phase-matching between driver and witness pulses. In this paper, we give the details of the wakefield solutions and phase-matching conditions used to generate the phase-matching density profile. The short, high-density, and weak driver limits are considered. We show, explicitly, the numerical algorithm used to calculate the density profiles.

(3+1)-dimensional Pearcey-Gaussian wave packet with arbitrary velocity driven by flying focus

The group velocity (GV) modulation of space-time wave packets (STWPs) along the transverse and longitudinal directions in free space is constrained by various factors. To surmount this limitation, a technique called "flying focus" has been developed, which enables the generation of laser pulses with dynamic focal points that can propagate at arbitrary velocities independent of GV. In this Letter, we propose a (3+1)-dimensional Pearcey-Gauss wave packet based on the "flying focus" technique, which exhibits superluminal propagation, transverse focus oscillation, and longitudinal periodic autofocusing. By selecting appropriate parameters, we can flexibly manipulate the position, the size, and the number of focal points- or make the wave packet follow a desired trajectory. This work may pave the way for the advancement of space-time structured light fields.

Programmable-trajectory ultrafast flying focus pulses

"Flying focus" techniques produce laser pulses with dynamic focal points that travel distances much greater than a Rayleigh length. The implementation of these techniques in laser-based applications requires the design of optical configurations that can both extend the focal range and structure the radial group delay. This article describes a method for designing optical configurations that produce ultrashort flying focus pulses with programmable-trajectory focal points. The method is illustrated by several examples that employ an axiparabola for extending the focal range and either a reflective echelon or a deformable mirror-spatial light modulator pair for structuring the radial group delay. The latter configuration enables rapid exploration and optimization of flying foci, which could be ideal for experiments.

Charged particle beam transport in a flying focus pulse with orbital angular momentum

We demonstrate the capability of flying focus (FF) laser pulses with ℓ=1 orbital angular momentum (OAM) to transversely confine ultrarelativistic charged particle bunches over macroscopic distances while maintaining a tight bunch radius. A FF pulse with ℓ=1 OAM creates a radial ponderomotive barrier that constrains the transverse motion of particles and travels with the bunch over extended distances. As compared with freely propagating bunches, which quickly diverge due to their initial momentum spread, the particles cotraveling with the ponderomotive barrier slowly oscillate around the laser pulse axis within the spot size of the pulse. This can be achieved at FF pulse energies that are orders of magnitude lower than required by Gaussian or Bessel pulses with OAM. The ponderomotive trapping is further enhanced by radiative cooling of the bunch resulting from rapid oscillations of the charged particles in the laser field. This cooling decreases the mean-square radius and emittance of the bunch during propagation.

Photon Acceleration from Optical to XUV

The propagating density gradients of a plasma wakefield may frequency upshift a trailing witness laser pulse, a process known as "photon acceleration." In uniform plasma, the witness laser will eventually dephase because of group delay. We find phase-matching conditions for the pulse using a tailored density profile. An analytic solution for a 1D nonlinear plasma wake with an electron beam driver indicates that, even though the plasma density decreases, the frequency shift reaches no asymptotic limit, i.e., is unlimited provided the wake can be sustained. In fully self-consistent 1D particle-in-cell (PIC) simulations, more than 40 times frequency shifts were demonstrated. In quasi-3D PIC simulations, frequency shifts up to 10 times were observed, limited only by simulation resolution and nonoptimized driver evolution. The pulse energy increases in this process, by a factor of 5, and the pulse is guided and temporally compressed by group velocity dispersion, resulting in the resulting extreme ultraviolet laser pulse having near-relativistic (a_{0}∼0.4) intensity.

Spatiotemporal control of laser intensity through cross-phase modulation

Spatiotemporal pulse shaping provides control over the trajectory and range of an intensity peak. While this control can enhance laser-based applications, the optical configurations required for shaping the pulse can constrain the transverse or temporal profile, duration, or orbital angular momentum (OAM). Here we present a novel technique for spatiotemporal control that mitigates these constraints by using a "stencil" pulse to spatiotemporally structure a second, primary pulse through cross-phase modulation (XPM) in a Kerr lens. The temporally shaped stencil pulse induces a time-dependent focusing phase within the primary pulse. This technique, the "flying focus X," allows the primary pulse to have any profile or OAM, expanding the flexibility of spatiotemporal pulse shaping for laser-based applications. As an example, simulations show that the flying focus X can deliver an arbitrary-velocity, variable-duration intensity peak with OAM over distances much longer than a Rayleigh range.

Advanced laser development and plasma-physics studies on the multiterawatt laser

The multiterawatt (MTW) laser, built initially as the prototype front end for a petawatt laser system, is a 1053 nm hybrid system with gain from optical parametric chirped-pulse amplification (OPCPA) and Nd:glass. Compressors and target chambers were added, making MTW a complete laser facility (output energy up to 120 J, pulse duration from 20 fs to 2.8 ns) for studying high-energy-density physics and developing short-pulse laser technologies and target diagnostics. Further extensions of the laser support ultrahigh-intensity laser development of an all-OPCPA system and a Raman plasma amplifier. A short summary of the variety of scientific experiments conducted on MTW is also presented.

Spectrally resolved wedged reversal shearing interferometer

In this Letter, we introduce a technique to fully determine the spatio-temporal electric field E(x,y,t) of an arbitrary ultrashort pulse. By passing the beam through a wedged reversal shearing interferometer followed by a scanning Michelson interferometer, the field autocorrelation of the shearing interferograms is measured. The spectrum of the shearing interferograms is obtained after a Fourier transform by the Whittaker-Shannon sampling theorem, yielding the amplitude and wavefront information at every wavelength. With the addition of the phase information of a single point, we are able to directly reconstruct the spatio-temporal electric field E(x,y,t) of an arbitrary ultrashort pulse.

Nonlinear spatiotemporal control of laser intensity

Spatiotemporal control over the intensity of a laser pulse has the potential to enable or revolutionize a wide range of laser-based applications that currently suffer from the poor flexibility offered by conventional optics. Specifically, these optics limit the region of high intensity to the Rayleigh range and provide little to no control over the trajectory of the peak intensity. Here, we introduce a nonlinear technique for spatiotemporal control, the "self-flying focus," that produces an arbitrary trajectory intensity peak that can be sustained for distances comparable to the focal length. The technique combines temporal pulse shaping and the inherent nonlinearity of a medium to customize the time and location at which each temporal slice within the pulse comes to its focus. As an example of its utility, simulations show that the self-flying focus can form a highly uniform, meter-scale plasma suitable for advanced plasma-based accelerators.

Accelerating and Decelerating Space-Time Optical Wave Packets in Free Space

Although a plethora of techniques are now available for controlling the group velocity of an optical wave packet, there are very few options for creating accelerating or decelerating wave packets whose group velocity varies controllably along the propagation axis. Here we show that "space-time" wave packets in which each wavelength is associated with a prescribed spatial bandwidth enable the realization of optical acceleration and deceleration in free space. Endowing the field with precise spatiotemporal structure leads to group-velocity changes as high as ∼c observed over a distance of ∼20  mm in free space, which represents a boost of at least ∼4 orders of magnitude over X waves and Airy pulses. The acceleration implemented is, in principle, independent of the initial group velocity, and we have verified this effect in both the subluminal and superluminal regimes.

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.

Dephasingless Laser Wakefield Acceleration

Laser wakefield accelerators (LWFAs) produce extremely high gradients enabling compact accelerators and radiation sources but face design limitations, such as dephasing, occurring when trapped electrons outrun the accelerating phase of the wakefield. Here we combine spherical aberration with a novel cylindrically symmetric echelon optic to spatiotemporally structure an ultrashort, high-intensity laser pulse that can overcome dephasing by propagating at any velocity over any distance. The ponderomotive force of the spatiotemporally shaped pulse can drive a wakefield with a phase velocity equal to the speed of light in vacuum, preventing trapped electrons from outrunning the wake. Simulations in the linear regime and scaling laws in the bubble regime illustrate that this dephasingless LWFA can accelerate electrons to high energies in much shorter distances than a traditional LWFA-a single 4.5 m stage can accelerate electrons to TeV energies without the need for guiding structures.

Controlling the velocity of a femtosecond laser pulse using refractive lenses

The combination of temporal chirp with a simple chromatic aberration known as longitudinal chromatism leads to extensive control over the velocity of laser intensity in the focal region of an ultrashort laser beam. We present the first implementation of this effect on a femtosecond laser. We demonstrate that by using a specially designed and characterized lens doublet to induce longitudinal chromatism, this velocity control can be implemented independent of the parameters of the focusing optic, thus allowing for great flexibility in experimental applications. Finally, we explain and demonstrate how this spatiotemporal phenomenon evolves when imaging the ultrashort pulse focus with a magnification different from unity.

Measurement and control of large diameter ionization waves of arbitrary velocity

Large diameter, flying focus driven ionization waves of arbitrary velocity (IWAV's) were produced by a defocused laser beam in a hydrogen gas jet, and their spatial and temporal electron density characteristics were measured using a novel, spectrally resolved interferometry diagnostic. A simple analytic model predicts the effects of power spectrum non-uniformity on the IWAV trajectory and transverse profile. This model compares well with the measured data and suggests that spectral shaping can be used to customize IWAV behavior and increase controlled propagation of ionization fronts for plasma-photonics applications.