可实现飞行焦点的方案

X-ray source based on the Thomson scattering of laser interacting with energetic electron beams features high photon energy, small spot size, and good collimation. However, the photon number is insufficient for practical application because of the small cross section of the Thomson scattering. To solve this problem, here, we replace a traditional Gaussian laser pulse with a flying focus laser pulse to extend interaction length and restrain nonlinear effects. Simulation results show that the scattered photon number can be increased by about 25 and 2 times for high and low energy lasers, respectively. In particular, a 1010 photon number can be generated with a 10 J flying focus laser pulse, and the energy spread can also be greatly reduced for high energy laser, from a broad spectrum to a monoenergetic peak. Combining these two advantages, the peak spectrum brightness of x ray is 3 × 108 photons/keV at 240 keV, which is about three orders of magnitude more than the traditional case.

By using a high-intensity flying focus laser, the dephasingless [ Phys. Rev. Lett. 124 134802 (2020)] or phase-locked [ Nat. Photon. 14 475 (2020)] laser wakefield acceleration (LWFA) can be realized, which may overcome issues of laser diffraction, pump depletion, and electron dephasing which are always suffered in usual LWFA. The scheme thus has the potentiality to accelerate electrons to TeV energy in a single acceleration stage. However, the controlled electron injection has not been self-consistently included in such schemes. Only external injection was suggested in previous theoretical studies, which requires other accelerators and is relatively difficulty to operate. Here, we numerically study the actively controlled density transition injection in phase-locked LWFA to get appropriate density profiles for amount of electron injection. The study shows that compared with LWFA driven by lasers with fixed focus, a larger plasma density gradient is necessary. Electrons experience both transverse and longitudinal loss during acceleration due to the superluminal group velocity of the driver and the variation of the wakefield structure. Furthermore, the periodic deformation and fracture of the flying focus laser in the high-density plasma plateau make the final injected charge also depend on the beginning position of the density downramp. Our studies show a possible way for amount of electron injection in LWFA driven by flying focus lasers.

An advanced focusing scheme, called a “flying focus,” uses a chromatic focusing system combined with a broadband laser pulse with its colors arranged in time to propagate a high intensity focus over a distance that can be much greater than its Rayleigh length while decoupling the speed at which the peak intensity propagates from its group velocity. The flying focus generates a short effective pulse duration with a small diameter focal spot that co- or counter-propagates along the optical axis at any velocity. Experiments validating the concept measured subluminal (−0.09c) to superluminal (39c) focal spot velocities with a nearly constant peak intensity over 4.5 mm. Experiments that increased the peak intensity above the ionization threshold for gas demonstrated ionization waves propagating at the velocity of the flying focus. These ionization waves of any velocity overcome several laser-plasma propagation issues, including ionization-induced refraction. The flying focus presents opportunities to overcome current fundamental limitations in laser-plasma amplifiers, laser wakefield accelerators, photon accelerators, and high-order frequency conversion.

Abstract Combining a chirped laser pulse with a chromatic lens yields a flying focus—a laser focus that moves dynamically in time. This provides control over the propagation of the peak laser intensity within an extended focal region that can be many times larger than the system’s Rayleigh length. Any velocity is achievable, including backward relative to the laser propagation direction. Previous simulation results have shown that a laser beam with a flying focus can create a counter-propagating ionization wave and subsequently pump a frequency-downshifted laser via the stimulated Raman scattering instability. Compared to a conventional Raman amplification scheme, several advantages were highlighted, including improved temperature control, plasma uniformity, and precursor growth mitigation. Here, we extend those results to demonstrate additional benefits: (1) the flying focus makes it possible for an unseeded Raman amplifier to produce a short, high-intensity beam; and (2) the flying focus minimizes collisional absorption of the pump, facilitating amplifier operation at higher plasma densities. Preliminary experiments have laid the groundwork for a high-performance plasma-based laser amplifier. The focal spot dynamics were initially confirmed at low intensity. It was subsequently demonstrated that ionization waves of arbitrary velocity can be produced at higher intensity. Here, we show a counter-propagating ionization front moving at approximately the speed of light—the optimal result for a Raman amplifier.

The extreme electric fields created in high-intensity laser-plasma interactions could generate energetic ions far more compactly than traditional accelerators. Despite this promise, laser-plasma accelerator experiments have been limited to maximum ion energies of ∼100 MeV/nucleon. The central challenge is the low charge-to-mass ratio of ions, which has precluded one of the most successful approaches used for electrons: laser wakefield acceleration. Here, we show that a laser pulse with a focal spot that moves transverse to the laser propagation direction enables wakefield acceleration of ions to GeV energies in underdense plasma. Three-dimensional particle-in-cell simulations demonstrate that this relativistic-intensity "transverse flying focus" can trap ions in a comoving electrostatic pocket, producing a monoenergetic collimated ion beam. With a peak intensity of 10^{20} W/cm^{2} and an acceleration distance of 0.44 cm, we observe a proton beam with 23.1 pC charge, 1.6 GeV peak energy, and 3.7% relative energy spread. This approach allows for compact high-repetition-rate production of high-energy ions, highlighting the capability of more generalized spatiotemporal pulse shaping to address open problems in plasma physics.

Vacuum birefringence is one of the most fascinating properties of quantum electrodynamics. In laser-induced vacuum polarization signatures, the interaction length is usually limited by the pump laser's Rayleigh length and temporal length. Here, we show that a flying focus pump with focus velocity $--c$ can overcome the short interaction length of the tightly focused pump laser, providing high intensity and long interaction length at the same time, which may lead to the experimental detection of vacuum birefringence.

A method to generate ultrahigh intense electromagnetic fields is suggested, based on the laser pulse compression, carrier frequency upshift, and focusing by a counterpropagating breaking plasma wave, relativistic flying parabolic mirror. This method allows us to achieve the quantum electrodynamics critical field (Schwinger limit) with present-day laser systems.

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The process of emission of electromagnetic radiation does not occur instantaneously, but is ``formed'' over a finite time known as the radiation formation time. In the ultrarelativistic regime, the corresponding (longitudinal) formation length is given by the formation time times the speed of light and controls several features of radiation. Here, we elucidate the importance of the transverse formation length (TFL) by investigating nonlinear Compton scattering by an electron initially counterpropagating with respect to a flying focus laser beam. The TFL is related to the transverse size of the radiation formation ``volume'' and, unlike the longitudinal formation length, has a quantum origin. Since the TFL is typically of the order of the Compton wavelength, where any laser field can be assumed to be approximately uniform, related quantum interference effects have been ignored. However, we show analytically that if the focus in a flying focus beam with ${n}_{L}\ensuremath{\gg}1$ cycles moves at the speed of light and backwards with respect to the beam propagation direction, the effects of the TFL undergo a large enhancement proportional to ${n}_{L}$ and may substantially alter the differential emission probability for feasible flying focus pulses.

An exact solution of the Dirac equation in the presence of an arbitrary electromagnetic plane wave is found, which corresponds to a focused electron wave packet, with the focus of the wave packet moving at the speed of light in the opposite direction of the average momentum of the electron wave packet (unless the plane wave is so intense to reflect the electron). The photon spectrum emitted by such an electron wave packet in the presence of a linearly polarized plane wave is studied both analytically and numerically. The spectrum is also compared with the one emitted by a single-momentum, plane-wave electron in the case of the electron being initially counterpropagating (on average for the flying-focus case) with the plane wave and within the locally constant field approximation. It is found that if the electron flying-focus wave packet is focused beyond a Compton wavelength, the angular distribution of the emitted radiation along the magnetic field of the electromagnetic plane wave is broader than for an electron with definite momentum. Corresponding the maximum value of the photon yield on the transverse plane is smaller in the flying-focus electron case. This could represent an experimental signature of a laser-driven flying-focus electron wave packet. Published by the American Physical Society 2024

A chirped laser pulse focused by a chromatic lens exhibits a dynamic, or flying, focus in which the trajectory of the peak intensity decouples from the group velocity. In a medium, the flying focus can trigger an ionization front that follows this trajectory. By adjusting the chirp, the ionization front can be made to travel at an arbitrary velocity along the optical axis. We present analytical calculations and simulations describing the propagation of the flying focus pulse, the self-similar form of its intensity profile, and ionization wave formation. The ability to control the speed of the ionization wave and, in conjunction, mitigate plasma refraction has the potential to advance several laser-based applications, including Raman amplification, photon acceleration, high-order-harmonic generation, and THz generation.

Dephasingless laser wakefield acceleration (DLWFA), a novel laser wakefield acceleration concept based on the recently demonstrated “flying focus” technology, offers a new paradigm in laser-plasma acceleration that could advance the progress toward a TeV linear accelerator using a single-stage system without guiding structures. The recently proposed NSF OPAL laser facility could be the transformative technology that enables this grand challenge in laser-plasma acceleration. We review the viable parameter space for DLWFA based on the scaling of its performance with laser and plasma parameters, and we compare that performance to traditional laser wakefield acceleration. These scalings indicate the necessity for ultrashort, high-energy laser architectures such as NSF OPAL to achieve groundbreaking electron energies using DLWFA. Initial results from MTW-OPAL, the platform for the 6-J DLWFA demonstration experiment, show a tight, round focal spot over a distance of 3.7 mm. New particle-in-cell simulations of that platform indicate that using hydrogen for DLWFA reduces the amount of laser light that is distorted due to refraction at ionization fronts. An experimental path, and the computational and technical design work along that path, from the current status of the field to a single-stage, 100-GeV electron beam via DLWFA on NSF OPAL is outlined. Progress along that path is presented.

A high-intensity laser pulse propagating through a medium triggers an ionization front that can accelerate and frequency upshift the photons of a second pulse. The maximum upshift is ultimately limited by the accelerated photons outpacing the ionization front or the ionizing pulse refracting from the plasma. Here, we apply the flying focus-a moving focal point resulting from a chirped laser pulse focused by a chromatic lens-to overcome these limitations. Theory and simulations demonstrate that the ionization front produced by a flying focus can frequency upshift an ultrashort optical pulse to the extreme ultraviolet over a centimeter of propagation. An analytic model of the upshift predicts that this scheme could be scaled to a novel tabletop source of spatially coherent x rays.

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This work demonstrates that a space-time-structured laser pulse, such as a flying focus, can enhance observable signatures of strong-field quantum electrodynamics for currently available experimental parameters. Specifically, the energy radiated and photon yield can be significantly increased by colliding an ultrarelativistic electron with a flying-focus pulse instead of a typical stationary-focus pulse with the same energy.

Laser plasma wakefields can provide extremely high fields both in transverse and longitudinal directions, which are very suitable for short-lived charged particle acceleration, such as muons. To get efficient capture and acceleration, we have numerically investigated the acceleration of externally injected muons in laser wakefields driven by usual Gaussian or flying focus lasers. The muons are produced from high-energy electrons interacting with high-Z solid targets, which typically have a broad energy spectrum ranging from hundreds of MeV to several GeV. We classify these muons into three categories according to their initial energies and suggest different drivers for the wakefield acceleration. For low-energy muons (such as E0∼ 600 MeV), as their velocity is much smaller than the phase velocity of a typical wakefield, the optimal driver laser is the combination of a Gaussian laser with a flying focus laser. For moderate-energy muons (such as E0∼ 1.5 GeV), using a Gaussian laser as the driver is the best choice due to its ability to achieve phase-locked acceleration. For high-energy muons (such as E0∼ 5 GeV), in order to avoid dephasing, which usually happens in LWFA, the flying focus laser is suggested to realize phase-locked acceleration. The final muon energies obtained in three cases are 1.2, 2.6, and 6.0 GeV, respectively, with trapping efficiencies of 88%, 92%, and 86%, and the relative energy spread of 2%, 13%, and 10%. Our study demonstrates the possibility for efficient muon acceleration by all optical acceleration with hundred terawatt-class lasers.

An axiparabola-based flying focus laser possesses a long focal depth, a small focal spot, and a controllable group velocity. It has been proposed for wide applications, such as phase-locked laser wakefield acceleration and photon acceleration. We numerically study the propagation of axiparabola-focused laser pulses in plasmas and find that such lasers can propagate stably over long distances in plasmas at low intensity. When the laser intensity increases to the relativistic intensity, they no longer propagate stably. Pulse front deformation and fracture appear due to the formation of plasma density modulations. We propose three schemes to mitigate the unstable propagation of axiparabola-focused lasers: (i) adding a radially dependent pulse front delay, (ii) placing the plasma away from the beginning of the focal line, and (iii) using an axiparabola mirror with a negative focal line. All these methods are relatively easy to implement. Our studies can provide guidance for applications of axiparabola-focused lasers.

A laser beam's peak intensity may be programmed to move at an arbitrary velocity by adjusting the focal time and location of its frequencies, temporal slices, or annuli. Such ``flying focus'' beams show promise in enabling new laser-matter applications. To assess these possibilities, the authors analytically describe the electromagnetic fields of flying-focus pulses with arbitrary polarization and orbital angular momentum.

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Flying focus is a technique that uses a chirped laser beam focused by a highly chromatic lens to produce an extended focal region within which the peak laser intensity can propagate at any velocity. When that intensity is high enough to ionize a background gas, an ionization wave will track the intensity isosurface corresponding to the ionization threshold. We report on the demonstration of such ionization waves of arbitrary velocity. Subluminal and superluminal ionization fronts were produced that propagated both forward and backward relative to the ionizing laser. All backward and all superluminal cases mitigated the issue of ionization-induced refraction that typically inhibits the formation of long, contiguous plasma channels.

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.

We propose a new laser amplifier scheme utilizing stimulated Raman scattering in plasma in conjunction with a "flying focus"-a chromatic focusing system combined with a chirped pump beam that provides spatiotemporal control over the pump's focal spot. Pump intensity isosurfaces are made to propagate at v=-c so as to be in sync with the injected counterpropagating seed pulse. By setting the pump intensity in the interaction region to be just above the ionization threshold of the background gas, an ionization wave is produced that travels at a fixed distance ahead of the seed. Simulations show that this will make it possible to optimize the plasma temperature and mitigate many of the issues that are known to have impacted previous Raman amplification experiments, in particular, the growth of precursors.

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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.

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Flying-focus pulses promise to revolutionize laser-driven secondary sources by decoupling the trajectory of the peak intensity from the native group velocity of the medium over distances much longer than a Rayleigh range. Previous demonstrations of the flying focus have either produced an uncontrolled trajectory or a trajectory that is engineered using chromatic methods that limit the duration of the peak intensity to picosecond scales. Here we demonstrate a controllable ultrabroadband flying focus using a nearly achromatic axiparabola-echelon pair. Spectral interferometry using an ultrabroadband superluminescent diode was used to measure designed super- and subluminal flying-focus trajectories and the effective temporal pulse duration as inferred from the measured spectral phase. The measurements demonstrate that a nearly transform- and diffraction-limited moving focus can be created over a centimeter-scale—an extended focal region more than 50 Rayleigh ranges in length. This ultrabroadband flying-focus and the novel axiparabola-echelon configuration used to produce it are ideally suited for applications and scalable to >100 TW peak powers.

"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.

We introduce a new class of (2+1) dimensional circle Pearcey beams (CPBs) with the abruptly autofocusing (AAF) characteristics. Compared with circular Airy beams, CPBs can increase the peak intensity contrast, shorten the focus distance and, especially, eliminate the oscillation after the focal point. Furthermore, we discuss the influence of the optical vortices (including on-axis, off-axis, and vortex pairs) on the light intensity distribution of the CPBs during propagating.

By introducing spatiotemporal pulse shaping techniques to multiphoton microscopy it is possible to obtain video-rate images with depth resolution similar to point-by-point scanning multiphoton microscopy while mechanically scanning in only one dimension. This is achieved by temporal focusing of the illumination pulse: The pulsed excitation field is compressed as it propagates through the sample, reaching its shortest duration (and highest peak intensity) at the focal plane before stretching again beyond it. This method is applied to produce, in a simple and scalable setup, video-rate two-photon excitation fluorescence images of Drosophila egg chambers with nearly 100,000 effective pixels and 1.5 microm depth resolution.

In this Letter, we introduce a new class of abruptly autofocued and rotated circular chirp Pearcey Gaussian vortex beams (AARCCPGVBs) which tend to abruptly autofocused circular chirp Pearcey vortex beams or chirp Gaussian vortex beams by adjusting the spatial distribution factors. Different from other rotated beams [Opt. Lett.31, 694 (2006) OPLEDP0146-959210.1364/OL.31.000694 and Opt. Lett.31, 2199 (2006)OPLEDP0146-959210.1364/OL.31.002199], the AARCCPGVBs are autofocused abruptly, maintain a low rotating speed before the focal point, and rotate abruptly and quickly in the focal point. Further, the position of the focal point in the propagating direction can also be controlled by adjusting the chirp factor.

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The propagation dynamics of intense femtosecond laser pulses in argon have been investigated theoretically and the results are compared with experimental data. It was found that in the initial stage the pulse propagates with the focal point moving ahead of the original one. The central beam of the trailing part experiences defocusing owing to ionization by the leading part and then regains self-focusing provided by power from the outer part. On propagating further, a quasistable balance is established between self-focusing and defocusing due to ionization-induced nonlinearity and diffraction, causing the beam to propagate in a self-guided mode. Furthermore, it was shown that the front of the split pulse decays faster, while the trailing edge experiences self-focusing and self-defocusing until a self-guided propagation mode is achieved. Multiple pulse splitting and shortening as a result of the dynamics near the focal point were also observed.

We have generated and detected a longitudinally polarized (Z-polarized) terahertz (THz) wave by focusing a conically propagating THz beam generated from a plasma filament induced by a femtosecond laser pulse. In the experiment, we observed a radially polarized field in a collimated region and Z-polarized field at focus in the time domain. The maximum value of the Z-polarized THz electric field reached 1.0 kV/cm. It was also quantitatively discussed about the Z-polarized field and the radial field at the focal point. We expect this technique to find application in THz time domain spectroscopy.

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Optical manipulation of disclinations and defects in liquid crystal films was demonstrated and discussed in terms of mass transfer induced by radiation pressure and of molecular rotation under the optical electric field. Orientation of liquid crystal molecules was controlled by changing the polarization direction of a focused cw laser beam. A disclination line could be deformed by moving the focal spot, just like drawing a bow. A point defect followed the laser beam so that it could be freely transported in the film. When two disclination points were optically manipulated to become fused, the defects disappeared immediately and did not return after switching off the laser.

To solve the underestimation of closed-crack depth, we have developed an imaging method, subharmonic phased array for crack evaluation (SPACE). However, a single-array SPACE can image only the vicinity of a transmission focal point (TFP) when the TFP is fixed. In this study, we have developed a confocal SPACE that defines multiple TFPs for imaging closed cracks over a wide area. We demonstrated its usefulness by measuring a stress corrosion crack (SCC). Moreover, we proposed a radarlike display that shows single-focus images with a line indicating the incident direction. By applying it to the SCC specimen, a moving crack response (MCR) was observed with varying incident angles. To analyze this behavior, we performed a simulation using a finite-difference time-domain (FDTD) method with a damped double node (DDN) model. Furthermore, we examined the ratio of the subharmonic to fundamental responses depending on the stress ratio between input wave stress and crack closure stress (σc).

Optical waveguides have been inscribed in fused silica by focusing femtosecond laser pulses with an axicon. The axicon is a conical lens that allows obtaining an optical beam with a transverse intensity profile that follows a zero-order Bessel function. This profile is invariant along a certain distance (>1 cm). The advantage of using axicon is that the beam is focused along a narrow focal line of a few micron width. Therefore the inscription of waveguides can be done without moving the glass sample. The waveguides so fabricated exhibit low losses and no detectable birefringence due their excellent circular symmetry. By translating the glass sample during the inscription process, we have induced a refractive index change along a thin plane in order to fabricate planar waveguides.

Intense ultrashort light pulses comprising merely a few wave cycles became routinely available by the turn of the millennium. The technologies underlying their production and measurement as well as relevant theoretical modeling have been reviewed in the pages of Reviews of Modern Physics (Brabec and Krausz, 2000). Since then, measurement and control of the subcycle field evolution of few-cycle light have opened the door to a radically new approach to exploring and controlling processes of the microcosm. The hyperfast-varying electric field of visible light permitted manipulation and tracking of the atomic-scale motion of electrons. Striking implications include controlled generation and measurement of single attosecond pulses of extreme ultraviolet light as well as trains of them, and real-time observation of atomic-scale electron dynamics. The tools and techniques for steering and tracing electronic motion in atoms, molecules, and nanostructures are now becoming available, marking the birth of attosecond physics. In this article these advances are reviewed and some of the expected implications are addressed.

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We report on the generation of ultrashort tunable pulses with a cavityless traveling-wave scheme consisting of a parametric superfluorescence seed source and a parametric amplifier. We show that the traveling-wave approach, with its advantages of simplicity and direct generation of tunable energetic single pulses, can be used in the femtosecond regime, and to this end we discuss the performances that were obtained with pump pulses of ≈1-ps and 200-fs duration at wavelengths of 0.53 and 0.6 μm, respectively. Of particular interest is the β-barium borate-based traveling-wave parametric generator (type-II phase matching), since it offers the possibility of generating nearly transform-limited pulses that are continuously tunable within a wide spectral range to as high as 3 μm in the IR. With a diffraction-limited pump at 0.53 μm. we obtained tunable pulses in a 1.2× diffraction-limited beam, which could be focused, with an f/20 optics lens, to an intensity of 1013 GW/cm2. A temperature-tuned lithium triborate-based femtosecond parametric generator, with its smaller group-velocity dispersion and absence of walk-off, can operate at a pump energy of as low as 30 μJ in a 200-fs pulse.

We demonstrate terahertz-induced lensing (TIL), the focusing and defocusing of an ultrashort “probe” laser pulse induced by a collinearly traveling terahertz pulse in an electro-optic crystal. The intensity change on the axis of the probe beam after the crystal is shown to be linear with the terahertz (THz) electric field and can thus be used to measure the THz wave form. We show that the sensitivity of TIL is comparable to conventional electro-optic sampling, with the advantage of being applicable to all classes of electro-optic crystals, including strongly birefringent ones. The better sensitivity of TIL is demonstrated using the highly birefringent organic salt DAST (4-N,N-dimethylamino-4′-N′-methyl stilbazolium tosylate).

<a href="http://oe.osa.org/virtual_issue.cfm?vid=36">Focus Serial: Frontiers of Nonlinear Optics</a> We investigate ultrashort laser pulse filamentation within the framework of spontaneous X Wave formation. After a brief overview of the filamentation process we study the case of an intense filament co-propagating with a weaker seed pulse. The filament is shown to induce strong Cross-Phase-Modulation (XPM) effects on the weak seed pulse: driven by the pump, the seed pulse undergoes pulse splitting with the daughter pulses slaved to their pump counterparts. They undergo strong spatio-temporal reshaping and are transformed into XWaves traveling at the same group velocities as the pump split-off pulses. In the presence of a gain mechanism such as Four-Wave-Mixing or Stimulated Raman Scattering, energy is then transferred from the pump filament leading to amplification of the seed X Wave and formation of a temporally compressed intensity peak.

The energy and power of ultrashort pulses amplified in neodymium glass lasers are restricted by the nonlinear interaction between the laser radiation and the optical medium of the laser itself. In the case of nearly parallel light beams traveling across an amplifier the restrictions are due to the damage resulting from self-focusing, whereas in the case of diverging beams the restrictions are imposed by the broadening of the spectrum and the scattering of the radiation.

A new mechanism of laser acceleration of charged particles is investigated in detail. Upon irradiation by tightly focused high-intensity ultrashort laser pulses, the acceleration of electrons travelling along the laser beam axis is determined by the longitudinal ponderomotive force and the longitudinal component of the electric field of the laser wave. It is found that the action of the longitudinal field on an electron may be unidirectional during many optical cycles, i.e., the phase slip effect is overcome. Lasers with currently highest possible parameters are shown to enable electron acceleration up to energies ε ∼ 1 GeV, which is comparable to the energies attainable on `large' accelerators of the SLAC type (ε ∼ 30 — 50 GeV). Unlike the schemes considered in the literature, the acceleration in this case is insensitive to the initial field phase (the effect of electron bunching is absent), it is possible to accelerate slow (nonrelativistic) electrons, and the problem of accelerated electron extraction from the field does not exist.

The extraordinary ability of space-charge waves in plasmas to accelerate charged particles at gradients that are orders of magnitude greater than in current accelerators has been well documented. We develop a phenomenological framework for laser wakefield acceleration (LWFA) in the 3D nonlinear regime, in which the plasma electrons are expelled by the radiation pressure of a short pulse laser, leading to nearly complete blowout. Our theory provides a recipe for designing a LWFA for given laser and plasma parameters and estimates the number and the energy of the accelerated electrons whether self-injected or externally injected. These formulas apply for self-guided as well as externally guided pulses (e.g. by plasma channels). We demonstrate our results by presenting a sample particle-in-cell (PIC) simulation of a $30\text{ }\mathrm{fs}$, 200 TW laser interacting with a 0.75 cm long plasma with density $1.5\ifmmode\times\else\texttimes\fi{}{10}^{18}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ to produce an ultrashort (10 fs) monoenergetic bunch of self-injected electrons at 1.5 GeV with 0.3 nC of charge. For future higher-energy accelerator applications, we propose a parameter space, which is distinct from that described by Gordienko and Pukhov [Phys. Plasmas 12, 043109 (2005)] in that it involves lower plasma densities and wider spot sizes while keeping the intensity relatively constant. We find that this helps increase the output electron beam energy while keeping the efficiency high.

Phase-matched harmonic conversion of visible laser light into soft x-rays was demonstrated. The recently developed technique of guided-wave frequency conversion was used to upshift light from 800 nanometers to the range from 17 to 32 nanometers. This process increased the coherent x-ray output by factors of 10(2) to 10(3) compared to the non-phase-matched case. This source uses a small-scale (sub-millijoule) high repetition-rate laser and will enable a wide variety of new experimental investigations in linear and nonlinear x-ray science.

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A system of equations is proposed that describes the dynamics of a laser pulse containing a few optical cycles (ultrashort pulse) in the transparency region of a medium with induced birefringence. In this case, the approximation of slowly varying envelopes, which is standard in the case of monochromatic signals, is inapplicable. An approximate solution is found for the case when the dispersion spreading length is much smaller than the length of the polarisation ellipse beating. It has the form of a travelling soliton-like bound state of ordinary and extraordinary components. The conditions for the stability of this pulse with respect to self-focusing are determined.

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Restricted by pulse dispersion, dephasing, and bunch deflection, it has been a challenging task to realize high-gain particle acceleration and bunch focusing by using an ultrashort-pulse laser to drive an integrable acceleration structure, which is necessary to develop an on-chip particle accelerator for practical applications. Here we propose a laser-driven traveling-wave linac (linear accelerator), which uses the cascade reflection and refraction of an ultrashort laser pulse on a microscale dielectric structure to achieve long-range laser-particle interaction, avoiding waveguide dispersion, and enhancing sustainable acceleration gradient. It is scalable and extensible, and can realize full-course particle acceleration by using a single laser source via the inverse Cherenkov effect. With this accelerator scheme, we further propose a dynamic synchronization and focusing method, which not only counteracts dephasing but also restrains the bunch spread and deflection caused by space-charge and emittance effects, realizing stable bunch transport and acceleration in a tiny-size bunch channel without resorting to the need for external focusing equipment. This accelerator scheme paves the way toward a high-efficiency laser-driven all-dielectric on-chip particle accelerator for practical applications.

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We investigate the phase matching of a high-harmonic generation by intense, 20 fs laser pulses in a gas-filled capillary waveguide. We identify several regimes in which the harmonic field can build up coherently: a balance of atomic and waveguide dispersions, noncollinear Cerenkov phase matching, and a balance of atomic and plasma dispersions. The role of atomic dispersion is examined by measuring and calculating the harmonic signal for several gases. We also predict and provide preliminary evidence for a regime where phase matching occurs only at specific fractional ionization levels, where the harmonic signal is sensitive to the absolute phase of the carrier wave.

Attosecond pulses in the extreme ultraviolet (XUV) spectral range are today routinely generated via high-order harmonic generation (HHG), when intense ultrashort laser pulses are focused into a gaseous generation medium. The effect is most easily understood in a semi-classical picture [1]. An electron can tunnel ionize from the distorted atomic potential, pick up kinetic energy in the laser field, potentially return to its parent ion and recombine. The excess energy is emitted as XUV photon. The process repeats for every half-cycle of the driving field, resulting in a train of attosecond pulses and in the frequency domain in the well-known, odd-order comb of harmonics. Two main families of electron trajectories leading to the same photon energy can be distinguished into "short" and "long", according to their time of travel in the continuum. Due to the complicated nature of the HHG process, attosecond pulses usually cannot be separated into their temporal and spatial profiles, but instead have strong chromatic aberration and are spatio-temporally coupled [2-4].

In this paper, we study the traveling wave solutions for a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrödinger (NLS) equation in the ultrashort-pulse regime. The corresponding traveling wave systems of the equivalent complex short-pulse equations are two singular planar dynamical systems with four singular straight lines. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.

We propose a new method for self-injection of high-quality electron bunches in the plasma wakefield structure in the blowout regime utilizing a "flying focus" produced by a drive beam with an energy chirp. In a flying focus the speed of the density centroid of the drive bunch can be superluminal or subluminal by utilizing the chromatic dependence of the focusing optics. We first derive the focal velocity and the characteristic length of the focal spot in terms of the focal length and an energy chirp. We then demonstrate using multidimensional particle-in-cell simulations that a wake driven by a superluminally propagating flying focus of an electron beam can generate GeV-level electron bunches with ultralow normalized slice emittance (∼30 nm rad), high current (∼17 kA), low slice energy spread (∼0.1%), and therefore high normalized brightness (>10^{19} A/m^{2}/rad^{2}) in a plasma of density ∼10^{19} cm^{-3}. The injection process is highly controllable and tunable by changing the focal velocity and shaping the drive beam current. Near-term experiments at FACET II where the capabilities to generate tens of kA, <10 fs drivers are planned, could potentially produce beams with brightness near 10^{20} A/m^{2}/rad^{2}.

A laser system producing controllable and stable pulses with high power and ultrashort duration at high repetition rate is a key component of a high energy laser-plasma accelerator (LPA). Precise characterization and control of laser properties are essential to understanding laser-plasma interactions required to build a 10-GeV class LPA. This paper discusses the diagnostics, control and performance parameters of a 1 Hz, 1 petawatt (PW) class laser at the Berkeley Lab Laser Accelerator (BELLA) facility. The BELLA PW laser provided up to 46 J on target with a 1% level energy fluctuation and 1.3-μrad pointing stability. The spatial profile was measured and optimized by using a camera, wavefront sensor, and deformable mirror (ILAO system). The focus waist was measured to be r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 53 μm and the fraction of energy within the circular area defined by the first minimum of the diffraction pattern (r = 67 μm) was 0.75. The temporal profile was controlled via the angle of incidence on a stretcher and a compressor, as well as an acousto-optic programmable dispersive. The temporal pulse shape was measured to be about 33 fs in full width at half maximum (WIZZLER and GRENOUILLE diagnostics). In order to accurately evaluate peak intensity, the energy-normalized peak fluence, and energy-normalized peak power were analyzed for the measured spatial and temporal mode profiles, and were found to be 15 kJ/(cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> J) with 6% fluctuation (standard deviation) and 25 TW/J with 5% fluctuation for 46-J on-target energy, respectively. This yielded a peak power of 1.2 PW and a peak intensity of 17×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> W/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with 8% fluctuation. A method to model the pulse shape for arbitrary compressor grating distance with high accuracy was developed. The pulse contrast above the amplified spontaneous emission pedestal was measured by SEQUOIA and found to be better than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup> . The first order spatiotemporal couplings (STCs) were measured with GRENOUILLE, and a simulation of the pulse's evolution at the vicinity of the target was presented. A maximum pulse front tilt angle of less than 7 mrad was achieved. The reduction of the peak power caused by the first order STCs was estimated to be less than 1%. The capabilities described in this paper are essential for generation of high quality electron beams.

Abstract The fundamental idea of Laser Wakefield Acceleration (LWFA) is reviewed. An ultrafast intense laser pulse drives coherent wakefields of relativistic amplitude with the high phase velocity robustly supported by the plasma. The structures of wakes and sheaths in plasma are contrasted. While the large amplitude of wakefields involves collective resonant oscillations of the eigenmode of the entire plasma electrons, the wake phase velocity ~ c and ultrafastness of the laser pulse introduce the wake stability and rigidity. When the phase velocity gets smaller, wakefields turn into sheaths. When we deploy laser ion acceleration or high density LWFA in which the phase velocity of plasma excitation is low, we encounter the sheath dynamics. A large number of world-wide experiments show a rapid progress of this concept realization toward both the high energy accelerator prospect and broad applications. The strong interest in this has driven novel laser technologies, including the Chirped Pulse Amplification, the Thin Film Compression (TFC), the Coherent Amplification Network, and the Relativistic Compression (RC). These in turn have created a conglomerate of novel science and technology with LWFA to form a new genre of high field science with many parameters of merit in this field increasing exponentially lately. Applications such as ion acceleration, X-ray free electron laser, electron and ion cancer therapy are discussed. A new avenue of LWFA using nanomaterials is also emerging, adopting X-ray laser using the above TFC and RC. Meanwhile, we find evidence that the Mother Nature spontaneously created wakefields that accelerate electrons and ions to very high energies.

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Enhancement of the quality of laser wake-field accelerated (LWFA) electron beams implies the improvement and controllability of the properties of the wake waves generated by ultra-short pulse lasers in underdense plasmas. In this work we present a compendium of useful formulas giving relations between the laser and plasma target parameters allowing one to obtain basic dependences, e.g. the energy scaling of the electrons accelerated by the wake field excited in inhomogeneous media including multi-stage LWFA accelerators. Consideration of the effects of using the chirped laser pulse driver allows us to find the regimes where the chirp enhances the wake field amplitude. We present an analysis of the three-dimensional effects on the electron beam loading and on the unlimited LWFA acceleration in inhomogeneous plasmas. Using the conditions of electron trapping to the wake-field acceleration phase we analyse the multi-equal stage and multiuneven stage LWFA configurations. In the first configuration the energy of fast electrons is a linear function of the number of stages, and in the second case, the accelerated electron energy grows exponentially with the number of stages. The results of the two-dimensional particle-in-cell simulations presented here show the high quality electron acceleration in the triple stage injection–acceleration configuration.

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Spatiotemporal control refers to a class of optical techniques for structuring a laser pulse with coupled spacetime-dependent properties, including moving focal points, dynamic spot sizes, and evolving orbital angular momenta. Here we introduce the concept of arbitrarily structured laser (ASTRL) pulses, which generalizes these techniques. The ASTRL formalism employs a superposition of prescribed pulses to create a desired electromagnetic field structure. Several examples illustrate the versatility of ASTRL pulses to address a broad range of laser-based applications, including laser wakefield acceleration, inertial confinement fusion, nanophotonics, and attosecond physics.

Coherent short-wavelength radiation from laser-plasma interactions is of increasing interest in disciplines including ultrafast biomolecular imaging and attosecond physics. Using solid targets instead of atomic gases could enable the generation of coherent extreme ultraviolet radiation with higher energy and more energetic photons. Here we present the generation of extreme ultraviolet radiation through coherent high-harmonic generation from self-induced oscillatory flying mirrors--a new-generation mechanism established in a long underdense plasma on a solid target. Using a 30-fs, 100-TW Ti:sapphire laser, we obtain wavelengths as short as 4.9 nm for an optimized level of amplified spontaneous emission. Particle-in-cell simulations show that oscillatory flying electron nanosheets form in a long underdense plasma, and suggest that the high-harmonic generation is caused by reflection of the laser pulse from electron nanosheets. We expect this extreme ultraviolet radiation to be valuable in realizing a compact X-ray instrument for research in biomolecular imaging and attosecond physics.

It has been proposed that laser-induced relativistic plasma mirror can accelerate if the plasma has a properly tailored density profile. Such accelerating plasma mirrors can serve as analog black holes to investigate Hawking evaporation and the associated information loss paradox. Here we reexamine the underlying dynamics of mirror motion in a graded-density plasma to provide an explicit trajectory as a function of the plasma density and its gradient. Specifically, a decreasing plasma density profile (down-ramp) along the direction of laser propagation would in general accelerate the mirror. In particular, a constant-plus-exponential density profile would generate the Davies–Fulling trajectory with a well-defined analog Hawking temperature, which is sensitive to the plasma density gradient but not to the density itself. We show that without invoking nano-fabricated thin-films, a much lower density gas target at, for example, ∼1×1017cm−3, would be able to induce an analog Hawking temperature, kBTH∼3.1×10−2eV, in the far-infrared region. We hope that this would help to better realize the experiment proposed by Chen and Mourou.

The acceleration of polarized electrons and protons in strong laser and plasma fields is a very attractive option to obtain polarized beams in the GeV range. We investigate the feasibility of particle acceleration in strong fields without destroying an initial polarization, taking into account all relevant mechanisms that could cause polarization losses, i.e. the spin precession described by the T-BMT equation, the Sokolov-Ternov effect and the Stern-Gerlach force. Scaling laws for the (de-)polarization time caused by these effects reveal that the dominant polarization limiting effect is the rotation of the single particle spins around the local electromagnetic fields. We compare our findings to test-particle simulations for high energetic electrons moving in a homogeneous electric field. For high particle energies the observed depolarization times are in good agreement with the analytically estimated ones.

The irradiation of few-nm-thick targets by a finite-contrast high-intensity short-pulse laser results in a strong pre-expansion of these targets at the arrival time of the main pulse. The targets decompress to near and lower than critical densities with plasmas extending over few micrometers, i.e. multiple wavelengths. The interaction of the main pulse with such a highly localized but inhomogeneous target leads to the generation of a short channel and further self-focusing of the laser beam. Experiments at the Glass Hybrid OPCPA Scaled Test-bed (GHOST) laser system at University of Texas, Austin using such targets measured non-Maxwellian, peaked electron distribution with large bunch charge and high electron density in the laser propagation direction. These results are reproduced in 2D PIC simulations using the EPOCH code, identifying direct laser acceleration (DLA) [1] as the responsible mechanism. This is the first time that DLA has been observed to produce peaked spectra as opposed to broad, Maxwellian spectra observed in earlier experiments [2]. This high-density electrons have potential applications as injector beams for a further wakefield acceleration stage as well as for pump-probe applications.

We investigate dense relativistic electron mirror generation from a micro-droplet driven by circularly polarized Laguerre-Gaussian lasers. The surface electrons are expelled from the droplet by the laser's radial electric field and evolve into dense sheets after leaving the droplet. These electrons are trapped in the potential well of the laser's transverse ponderomotive force and are steadily accelerated to about 100 MeV by the longitudinal electric field. Particle-in-cell simulations indicate that the relativistic electron mirrors are characterized by high beam charge, narrow energy spread, and large angular momentum, which can be utilized for bright X/γ-ray emission and photon vortex formation.

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A laser pulse composed of a fundamental and properly phased second harmonic exhibits an asymmetric electric field that can drive a time-dependent current of photoionized electrons. The current produces an ultrashort burst of terahertz (THz) radiation. When driven by a conventional laser pulse, the THz radiation is emitted into a cone with an angle determined by the dispersion of the medium. Here we demonstrate that the programmable-velocity intensity peak of a spatiotemporally structured, two-color laser pulse can be used to control the emission angle, focal spot, and spectrum of the THz radiation. Of particular interest for applications, a structured pulse with a subluminal intensity peak can drive highly focusable, on-axis THz radiation. Published by the American Physical Society 2024

Laser wakefield accelerators rely on the extremely high electric fields of nonlinear plasma waves to trap and accelerate electrons to relativistic energies over short distances. When driven strongly enough, plasma waves break, trapping a large population of the background electrons that support their motion. Aside from limiting the maximum electric field, this trapping can lead to accelerated electron bunches with large energy spreads. Here, we introduce a novel regime of plasma wave excitation and wakefield acceleration that allows for arbitrarily high electric fields while avoiding the deleterious effects of unwanted trapping. The regime, enabled by spatiotemporal shaping of laser pulses, exploits the property that nonlinear plasma waves with superluminal phase velocities cannot trap charged particles and are therefore immune to wave breaking.

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Radiation reaction (RR) is the oldest still-unsolved problem in electrodynamics. In addition to conceptual difficulties in its theoretical formulation, the requirement of exceedingly large charge accelerations has thus far prevented its unambiguous experimental identification. Here, we show how measurable RR effects in a laser-electron interaction can be achieved through the use of flying focus pulses (FFPs). By allowing the focus to counterpropagate with respect to the pulse phase velocity, a FFP overcomes the intrinsic limitation of a conventional laser Gaussian pulse (GP) that limits its focus to a Rayleigh range. For an electron initially also counterpropagating with respect to the pulse phase velocity, an extended interaction length with the laser peak intensity is achieved in a FFP. As a result, the same RR deceleration factors are obtained, but at FFP laser powers orders of magnitude lower than for ultrashort GPs with the same energy. This renders the proposed setup much more stable than those using GPs and allows for more accurate in situ diagnostics. Using the Landau-Lifshitz equation of motion, we show numerically and analytically that the capability of emerging laser systems to deliver focused FFPs will allow for a clear experimental identification of RR.

Photon accelerators can spectrally broaden laser pulses with high efficiency in moving electron density gradients driven in a rapidly ionizing plasma. When driven by a conventional laser pulse, the group velocity walk-off experienced by the accelerated photons and deterioration of the gradient from diffraction and plasma refraction limit the extent of spectral broadening. Here we show that a laser pulse with a shaped space-time and transverse intensity profile overcomes these limitations by creating a guiding density profile at a tunable velocity. Self-photon acceleration in this profile leads to dramatic spectral broadening and intensity steepening, forming an optical shock that further enhances the rate of spectral broadening. In this new regime, multi-octave spectra extending from 400 to 60 nm wavelengths, which support near-transform-limited $&lt;400$ as pulses, are generated over $&lt;100 \ensuremath{\mu}\mathrm{m}$ of interaction length.

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.

Spatiotemporal control encompasses a variety of techniques for producing laser pulses with dynamic intensity peaks that move independently of the group velocity. This controlled motion of the intensity peak offers a new approach to optimizing laser-based applications and enhancing signatures of fundamental phenomena. Here, we demonstrate spatiotemporal control with a plasma optic. A chirped laser pulse focused by a plasma lens exhibits a moving focal point, or “flying focus,” that can travel at an arbitrary, predetermined velocity. Unlike currently used conventional or adaptive optics, a plasma lens can be located close to the interaction region and can operate at an orders of magnitude higher, near-relativistic intensity. Published by the American Physical Society 2024

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We propose to use tightly focused lasers to generate high quality electron beams in laser wakefield accelerators. In this scheme, the expansion of the laser beam after the focal position enlarges the size of wakefield bubble, which reduces the effective phase velocity of the wake and triggers injection of plasma electrons. This scheme injects a relatively long beam with high charge. The energy spread of the injected beam can be minimized if an optimal acceleration distance is chosen so that the beam chirp is suppressed. Particle-in-cell simulations indicate that electron beams with the charge on the order of nanocoulomb, the energy spread of $\ensuremath{\sim}1%$, and the normalized emittance of $\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{mm}\text{ }\mathrm{mrad}$ can be generated in uniform plasma using $\ensuremath{\sim}100\text{ }\text{ }\mathrm{TW}$ laser pulses. An empirical formula is also given for predicting the beam charge. This injection scheme, with a very simple setup, paves the way toward practical high-quality laser wakefield accelerators for table-top electron and radiation sources.

The mechanism of ablation of solids by intense femtosecond laser pulses is described in an explicit analytical form. It is shown that at high intensities when the ionization of the target material is complete before the end of the pulse, the ablation mechanism is the same for both metals and dielectrics. The physics of this new ablation regime involves ion acceleration in the electrostatic field caused by charge separation created by energetic electrons escaping from the target. The formulas for ablation thresholds and ablation rates for metals and dielectrics, combining the laser and target parameters, are derived and compared to experimental data. The calculated dependence of the ablation thresholds on the pulse duration is in agreement with the experimental data in a femtosecond range, and it is linked to the dependence for nanosecond pulses.

High harmonic generation by relativistically intense laser pulses from overdense plasma layers is surveyed. High harmonics are generated in form of (sub-)attosecond pulses when the plasma surface rebounds towards the observer with relativistic velocity. Different cases are considered. The "relativistically oscillating mirror" (ROM) model, describing the most typical case, is analyzed in detail. The resulting harmonic spectrum is usually a power law with the exponent -8/3 [baeva2006relativistic], but possible exceptions due to "higher order γ-spikes" are considered. It is shown that under certain conditions, ultra-dense electron nanobunches can be formed at plasma surface that emit coherent synchrotron radiation. The resulting spectrum is much flatter and leads to the formation of a giant attosecond pulse in the reflected radiation. The harmonics radiation is also considered in time domain, where they form a train of attosecond pulses. It is characterized and a possibility to select a single attosecond pulse via polarization gating is described. Further, the line structure in relativistic harmonic spectra is analyzed. It is shown that the harmonics have an intrinsic chirp and it can be responsible for experimentally observed spectral modulations. Finally, high harmonic generation is considered in realistic three-dimensional geometry. It is shown that free space diffraction can act as a high pass filter, altering the spectrum and the reflected field structure. The high harmonics tend to be self-focused by the reflecting surface. This leads to a natural angular divergence as well as to field boost at the focal position. Coherently focusing the harmonics using an optimized geometry may result in a significantly higher field than the field of the driving laser.

Our experiment shows that external focusing strongly influences the plasma density and the diameter of femtosecond Ti-sapphire laser filaments generated in air. The control of plasma filament parameters is suitable for many applications such as remote spectroscopy, laser induced electrical discharge, and femtosecond laser material interactions. The measurements of the filament showed the plasma density increases from 10(15)cm(-3) to 2 x 10(18)cm(-3) when the focal length decreases from 380 cm to 10 cm while the diameter of the plasma column varies from 30 microm to 90 microm. The experimental results are in good qualitative agreement with the results of numerical simulations.

Abstract Grating eliminated no-nonsense observation of ultrafast incident laser light e-fields is an experimental technique for the full characterization of ultrashort laser pulses. It requires the nonlinear conversion of broadband ultrashort optical pulses into their second harmonic generation (SHG) that is relatively tightly focused on a thick SHG crystal. In this paper, the laser focusing problem is experimentally presented and demonstrated in the measurements of 780 nm chirped pulses emitted from a Ti:sapphire oscillator. In this experimental study, it has been shown how the focusing effect can cause distortions in the trace of the chirped pulses. It is demonstrated that the measurement of broadband pulses requires that the beam have a wide angular divergence. Therefore, a tight focusing is essential. A long focal length leads to a smaller range of angles incident on the crystal causing an insufficient divergence angle. Finally, the ability of this device in the characterization of double and complicated chirped pulses is described. The broadening of complex chirped pulses after passing through a thick BK7 glass is measured and the group velocity dispersion of the BK7 glass is calculated as about 47.3 fs 2 mm −1 . Also the train of double chirped pulses created using a Michelson interferometer is measured and the spectral fringes marked by phase jumps are observed. The experimental results of the retrieved phases and intensities are in good agreement with independently measured data.

A study of the properties of multi-MeV proton emission from thin foils following ultraintense laser irradiation has been carried out. It has been shown that the protons are emitted, in a quasilaminar fashion, from a region of transverse size of the order of 100-200 microm. The imaging properties of the proton source are equivalent to those of a much smaller source located several hundred microm in front of the foil. This finding has been obtained by analyzing proton radiographs of periodically structured test objects, and is corroborated by observations of proton emission from laser-heated thick targets.

By focusing petawatt peak power laser light to intensities up to 10 21 W cm -2 , highly relativistic plasmas can now be studied. The force exerted by light pulses with this extreme intensity has been used to accelerate beams of electrons and protons to energies of a million volts in distances of only microns. This acceleration gradient is a thousand times greater than in radio-frequency-based accelerators. Such novel compact laser-based radiation sources have been demonstrated to have parameters that are useful for research in medicine, physics and engineering. They might also someday be used to ignite controlled thermonuclear fusion. Ultrashort pulse duration particles and x-rays that are produced can resolve chemical, biological or physical reactions on ultrafast (femtosecond) timescales and on atomic spatial scales. These energetic beams have produced an array of nuclear reactions, resulting in neutrons, positrons and radioactive isotopes. As laser intensities increase further and laser-accelerated protons become relativistic, exotic plasmas, such as dense electron-positron plasmas, which are of astrophysical interest, can be created in the laboratory. This paper reviews many of the recent advances in relativistic laser-plasma interactions.

4f pulse shapers have been widely used to temporally manipulate femtosecond optical pulses by spectral filtering. When the temporal waveform is manipulated with a spatial light modulator consisting of segmented pixels, the spatial profile of the output beam also varies because of diffraction at the pixel array, which is known as a spatiotemporal coupling effect. This effect produces a complicated spatio-temporal profile near the focus of the ultrashort pulses, which may affect the interpretation of experimental results obtained with shaped ultrashort pulses. We investigate the spatial intensity distribution at the focus of temporally shaped pulses through ablation experiments. The three-dimensional space-time beam profile is also numerically calculated.

We describe a setup consisting of a 4f pulse shaper and a microscope with a high-NA objective lens and discuss the aspects most relevant for an undistorted spatiotemporal profile of the focused beam. We demonstrate shaper-assisted pulse compression in focus to a sub-10-fs duration using phase-resolved interferometric spectral modulation (PRISM). We introduce a nanostructure-based method for sub-diffraction spatiotemporal characterization of strongly focused pulses. The distortions caused by optical aberrations and space-time coupling from the shaper can be reduced by careful setup design and alignment to about 10 nm in space and 1 fs in time.

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The ability to perform optical sectioning is one of the great advantages of laser-scanning microscopy. This introduces, however, a number of difficulties due to the scanning process, such as lower frame rates due to the serial acquisition process. Here we show that by introducing spatiotemporal pulse shaping techniques to multiphoton microscopy it is possible to obtain full-frame depth resolved imaging completely without scanning. Our method relies on temporal focusing of the illumination pulse. The pulsed excitation field is compressed as it propagates through the sample, reaching its shortest duration at the focal plane, before stretching again beyond it. This method is applied to obtain depth-resolved twophoton excitation fluorescence (TPEF) images of drosophila egg-chambers with nearly 105 effective pixels using a standard Ti:Sapphire laser oscillator.

We achieved automated optical control over coherent lattice responses that were both time- and position-dependent across macroscopic length scales. In our experiments, spatiotemporal femtosecond pulse shaping was used to generate excitation light fields that were directed toward distinct regions of crystalline samples, producing terahertz-frequency lattice vibrational waves that emanated outward from their multiple origins at lightlike speeds. Interferences among the waves resulted in fully specified far-field responses, including tilted, focusing, or amplified wavefronts. Generation and coherent amplification of terahertz traveling waves and terahertz phased-array generation also were demonstrated.

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We report the broadband characterization of the propagation of light through a multiple scattering medium by means of its multispectral transmission matrix. Using a single spatial light modulator, our approach enables the full control of both the spatial and spectral properties of an ultrashort pulse transmitted through the medium. We demonstrate spatiotemporal focusing of the pulse at any arbitrary position and time with any desired spectral shape. Our approach opens new perspectives for fundamental studies of light-matter interaction in disordered media, and has potential applications in sensing, coherent control, and imaging.

While the concept of focusing usually applies to the spatial domain, it is equally applicable to the time domain. Real-time imaging of temporal focusing of single ultrashort laser pulses is of great significance in exploring the physics of the space-time duality and finding diverse applications. The drastic changes in the width and intensity of an ultrashort laser pulse during temporal focusing impose a requirement for femtosecond-level exposure to capture the instantaneous light patterns generated in this exquisite phenomenon. Thus far, established ultrafast imaging techniques either struggle to reach the desired exposure time or require repeatable measurements. We have developed single-shot 10-trillion-frame-per-second compressed ultrafast photography (T-CUP), which passively captures dynamic events with 100-fs frame intervals in a single camera exposure. The synergy between compressed sensing and the Radon transformation empowers T-CUP to significantly reduce the number of projections needed for reconstructing a high-quality three-dimensional spatiotemporal datacube. As the only currently available real-time, passive imaging modality with a femtosecond exposure time, T-CUP was used to record the first-ever movie of non-repeatable temporal focusing of a single ultrashort laser pulse in a dynamic scattering medium. T-CUP's unprecedented ability to clearly reveal the complex evolution in the shape, intensity, and width of a temporally focused pulse in a single measurement paves the way for single-shot characterization of ultrashort pulses, experimental investigation of nonlinear light-matter interactions, and real-time wavefront engineering for deep-tissue light focusing.

Pulse shaping has become a powerful tool in generating complicated ultrafast optical waveforms to meet specific application needs. Traditionally, pulse shaping focuses on the temporal waveform synthesis. Recent interests in structuring light in the spatiotemporal domain rely on Fourier analysis. A space-to-time mapping technique allows us to directly imprint complex spatiotemporal modulation through taking advantage of the relationship between frequency and time of chirped pulses. The concept is experimentally verified through the generation of spatiotemporal optical vortex (STOV) and STOV lattice. The power of this method is further demonstrated by STOV polarity reversal, vortex collision, and vortex annihilation. Such a direct mapping technique opens tremendous potential opportunities for sculpturing complex spatiotemporal waveforms.

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We report on the generation of coherent phonon polaritons in ZnTe, GaP, and ${\mathrm{LiTaO}}_{3}$ using ultrafast optical pulses. These polaritons are coupled modes consisting of mostly far-infrared radiation and a small phonon component, which are excited through nonlinear optical processes involving the Raman and the second-order susceptibilities (respectively, impulsive stimulated Raman scattering and difference frequency generation). We probe their associated hybrid vibrational-electric field, in the THz range, by electro-optic sampling methods. The measured field patterns agree very well with calculations for the field due to a distribution of dipoles that follows the shape and moves with the group velocity of the optical pulses. For a tightly focused pulse, the pattern is identical to that of classical Cherenkov radiation by a moving dipole. Results for other shapes and, in particular, for the planar and transient-grating geometries are accounted for by a convolution of the Cherenkov field due to a point dipole with the function describing the slowly varying intensity of the pulse. Hence, polariton fields resulting from pulses of arbitrary shape can be described quantitatively in terms of expressions for the Cherenkov radiation emitted by an extended source. Using the Cherenkov approach, we recover the phase-matching conditions that lead to the selection of specific polariton wave vectors in the planar and transient grating geometry as well as the Cherenkov angle itself. The formalism can be easily extended to media exhibiting dispersion in the THz range. Calculations and experimental data for pointlike and planar sources reveal significant differences between the so-called superluminal and subluminal cases where the group velocity of the optical pulses is, respectively, above and below the highest phase velocity in the infrared. Using the Cherenkov radiation formalism, the fields generated by a spatiotemporally shaped pulse in a thick dispersive medium can be calculated analytically.

We experimentally demonstrate spatiotemporal focusing of light on single nanocrystals embedded inside a strongly scattering medium. Our approach is based on spatial wave front shaping of short pulses, using second harmonic generation inside the target nanocrystals as the feedback signal. We successfully develop a model both for the achieved pulse duration as well as the observed enhancement of the feedback signal. The approach enables exciting opportunities for studies of light propagation in the presence of strong scattering as well as for applications in imaging, micro- and nanomanipulation, coherent control and spectroscopy in complex media.

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.

Complex media have emerged as a powerful and robust framework to control light-matter interactions designed for task-specific optical functionalities. Studies on wavefront shaping through disordered systems have demonstrated optical wave manipulation capabilities beyond conventional optics, including aberration-free and subwavelength focusing. However, achieving arbitrary and simultaneous control over the spatial and temporal features of light remains challenging. In particular, no practical solution exists for field-level arbitrary spatiotemporal control of wave packets. A new paradigm shift has emerged in the terahertz frequency domain, offering methods for absolute time-domain measurements of the scattered electric field, enabling direct field-based wave synthesis. In this work, we report the experimental demonstration of field-level control of single-cycle terahertz pulses on arbitrary spatial points through complex disordered media.

We analyze the spatiotemporal distortions of an ultrashort pulse focused through a thin scattering surface. We show and experimentally verify that in such a scenario temporal distortions are proportional to the distance from the optical axis and are present only outside the focal point, as result of geometrical path length differences. We use wavefront shaping to correct for the spatiotemporal distortions and to temporally compress chirped input pulses through the scattering medium.

Abstract We demonstrate, for the first time, a single-shot, complete spatiotemporal measurement of pulses from a terawatt-scale, multi-stage-amplified, low repetition-rate laser source. The ultrashort pulse electric field, E ( x,y,z,t ), is spatiotemporally complex due to distortions that accrue from multiple chirped-pulse amplifiers, which requires a complete characterization. Meanwhile, the instability of the laser source introduces field profiles that vary significantly from pulse to pulse, which, together with the low repetition-rate (15 shots/hour), requires the use of a single-shot measurement technique. To accomplish the measurements, we used a wavelength-multiplexed, digital-holographic technique called Spatially and Temporally Resolved Intensity and Phase Evaluation Device: Full Information from a Single Hologram, specially tailored to measure picosecond pulses at a wavelength of about 1 μ m. Specifically, individual pulses from the compact multipulse terawatt laser were measured, with up to 0.3 J per shot of energy and ∼2 ps pulse durations, at 1052 nm. With these measurements, we characterized several major spatiotemporal distortions that affect the peak intensity at the laser focus, as well as the pulse-shape instability on a shot-to-shot basis. Our technique allows detailed diagnosis of laser pulses (especially high-order spatiotemporal distortions) and provides straightforward four-dimensional animations of pulse propagation to a focus.

Spatiotemporal optical vortices (STOVs), arise naturally during nonlinear self-focusing collapse arrest. Here, we use a 4-f pulse shaper to impose STOVs linearly on a Gaussian pulse and directly measure the vortex in spatiotemporal domains.

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Here we investigate the propagation properties of spatiotemporal sharply autofocused single-Airy-ring Airy Gaussian vortex (AiRAiGV) and dual-Airy-ring Airy Gaussian vortex (dAiRAiGV) wave packets by solving the (3+1) D Schrödinger equation in free space. We can change the spatial part of the wave packets into Airy or Gaussian distribution by choosing the different spatial distribution factors b_s. In particular, only when the shape of the pulses is set well with appropriate temporal distribution factor b_t and initial velocity v in the temporal domain, dAiRAiGV wave packets can simultaneously autofocus in the spatial and temporal domains and the peak intensity is increased dozens of times at the focus more than that at the initial plane. Furthermore, properties of dAiRAiGV wave packets with a vortex in the center and off-axis vortex pairs are also discussed.

Simple analytical approaches for implementing strong field coherent control schemes are often elusive due to the complexity of the interaction between the intense excitation field and the system of interest. Here, we demonstrate control over multiphoton excitation in a three-level resonant system using simple, analytically derived ultrafast pulse shapes. We utilize a two-dimensional spatiotemporal control technique, in which temporal focusing produces a spatially dependent quadratic spectral phase, while a second, arbitrary phase parameter is scanned using a pulse shaper. In the current work, we demonstrate weak-to-strong field excitation of $^{85}\mathrm{Rb}$, with a $\ensuremath{\pi}$ phase step and the quadratic phase as the chosen control parameters. The intricate dependence of the multilevel dynamics on these parameters is exhibited by mapping the data onto a two-dimensional control landscape. Further insight is gained by simulating the complete landscape using a dressed-state, time-domain model, in which the influence of individual shaping parameters can be extracted using both exact and asymptotic time-domain representations of the dressed-state energies.

A simple scalar model for describing spatiotemporal dispersion of pulses, beyond the classic ``slowly varying envelopes $+$ Galilean boost'' approach, is studied. The governing equation has a cubic nonlinearity, and we focus here mainly on contexts with normal group-velocity dispersion. A complete analysis of continuous waves is reported, including their dispersion relations and modulational instability characteristics. We also present a detailed derivation of exact analytical dark solitons, obtained by combining direct-integration methods with geometrical transformations. Classic results from conventional pulse theory are recovered asymptotically from the spatiotemporal formulation. Numerical simulations test theoretical predictions for modulational instability and examine the robustness of spatiotemporal dark solitons against perturbations to their local pulse shapes.

Surface plasmon polariton (SPP) provides an important platform for the design of various nanophotonic devices. However, it is still a big challenge to achieve spatiotemporal manipulation of SPP under both spatially nanoscale and temporally ultrafast conditions. Here, we propose a method of spatiotemporal manipulation of SPP pulse in a plasmonic focusing structure illuminated by a dispersed femtosecond light. Based on dispersion effect of SPP pulse, we achieve the functions of dynamically controlled wavefront rotation in SPP focusing and redirection in SPP propagation within femtosecond range. The influences of structural parameters on the spatiotemporal properties of SPP pulse are numerically studied, and an analytical model is built to explain the results. The spatiotemporal coupling of modulated SPP pulses to dielectric waveguides is also investigated, demonstrating an ultrafast turning of propagation direction. This work has great potential in applications such as on-chip ultrafast photonic information processing, ultrafast beam shaping and attosecond pulse generation.

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