to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The rise time of intense radiation determines the maximum field strength atoms can be exposed to before their polarizability dramatically drops due to the detachment of an outer electron. Recent progress in ultrafast optics has allowed the generation of ultraintense light pulses comprising merely a few field oscillation cycles. The arising intensity gradient allows electrons to survive in their bound atomic state up to external field strengths many times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency, resulting in a significant extension of the frontiers of nonlinear optics and (nonrelativistic) high-field physics. Implications include the generation of coherent harmonic radiation up to kiloelectronvolt photon energies and control of the atomic dipole moment on a subfemtosecond $(1{\mathrm{f}\mathrm{s}=10}^{\mathrm{\ensuremath{-}}15}\mathrm{}\mathrm{s})$ time scale. This review presents the landmarks of the 30-odd-year evolution of ultrashort-pulse laser physics and technology culminating in the generation of intense few-cycle light pulses and discusses the impact of these pulses on high-field physics. Particular emphasis is placed on high-order harmonic emission and single subfemtosecond extreme ultraviolet/x-ray pulse generation. These as well as other strong-field processes are governed directly by the electric-field evolution, and hence their full control requires access to the (absolute) phase of the light carrier. We shall discuss routes to its determination and control, which will, for the first time, allow access to the electromagnetic fields in light waves and control of high-field interactions with never-before-achieved precision.

Intense few-cycle laser fields: Frontiers of nonlinear optics

Femtosecond filamentation in transparent media

Particle accelerators are used in a wide variety of fields, ranging from medicine and biology to high-energy physics. The accelerating fields in conventional accelerators are limited to a few tens of MeV m(-1), owing to material breakdown at the walls of the structure. Thus, the production of energetic particle beams currently requires large-scale accelerators and expensive infrastructures. Laser-plasma accelerators have been proposed as a next generation of compact accelerators because of the huge electric fields they can sustain (>100 GeV m(-1)). However, it has been difficult to use them efficiently for applications because they have produced poor-quality particle beams with large energy spreads, owing to a randomization of electrons in phase space. Here we demonstrate that this randomization can be suppressed and that the quality of the electron beams can be dramatically enhanced. Within a length of 3 mm, the laser drives a plasma bubble that traps and accelerates plasma electrons. The resulting electron beam is extremely collimated and quasi-monoenergetic, with a high charge of 0.5 nC at 170 MeV.

A laser-plasma accelerator producing monoenergetic electron beams

Laser-driven accelerators, in which particles are accelerated by the electric field of a plasma wave (the wakefield) driven by an intense laser, have demonstrated accelerating electric fields of hundreds of GV m-1 (refs 1–3) These fields are thousands of times greater than those achievable in conventional radio-frequency accelerators, spurring interest in laser accelerators4,5 as compact next-generation sources of energetic electrons and radiation To date, however, acceleration distances have been severely limited by the lack of a controllable method for extending the propagation distance of the focused laser pulse The ensuing short acceleration distance results in low-energy beams with 100 per cent electron energy spread1,2,3, which limits potential applications Here we demonstrate a laser accelerator that produces electron beams with an energy spread of a few per cent, low emittance and increased energy (more than 109 electrons above 80 MeV) Our technique involves the use of a preformed plasma density channel to guide a relativistically intense laser, resulting in a longer propagation distance The results open the way for compact and tunable high-brightness sources of electrons and radiation

https://escholarship.org/content/qt9c55r46s/qt9c55r46s.pdf?t=lnras5

High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding

Stimulated backscattered harmonic radiation generated by the interaction of an intense pump-laser field with an electron beam or plasma is analyzed using a fully nonlinear, relativistic, fluid theory valid to all orders in the pump-laser amplitude. The backscattered radiation occurs at odd harmonics of the Doppler-shifted incident laser frequency. The growth rates, saturation levels (efficiencies), and thermal limitations are calculated for the backscattered harmonic radiation. This mechanism may provide a practical method for producing coherent radiation in the XUV regime.

Stimulated backscattered harmonic generation from intense laser interactions with beams and plasmas

The interaction of intense, femtosecond laser pulses with a dielectric medium is examined using a numerical simulation. The simulation uses the one-dimensional electromagnetic wave equation to model laser pulse propagation. In addition, it includes multiphoton ionization, electron attachment, Ohmic heating of free electrons, and temperature-dependent collisional ionization. Laser pulses considered in this study are characterized by peak intensities approximately 10(12) -10(14) W/cm(2) and pulse durations approximately 10-100 fsec . These laser pulses interacting with fused silica are shown to produce above-critical plasma densities and electron energy densities sufficient to attain experimentally measured damage thresholds. Significant transmission of laser energy is observed even in cases where the peak plasma density is above the critical density for reflection. A damage fluence based on absorbed laser energy is calculated for various pulse durations. The calculated damage fluence threshold is found to be consistent with recent experimental results.

Transmission of intense femtosecond laser pulses into dielectrics.

A laser pulse from an ultrashort pulse laser (USPL) is fired into the atmosphere. The USPL pulse is configured to generate a plasma filament at a predefined target in the atmosphere, in which free, or “seed,” electrons are generated by multi-photon or tunneling ionization of the air molecules in the filament. A second pulse is fired into the atmosphere to form a heater beam that impinges on the plasma filament and thermalizes the seed electrons within the plasma filament, leading to the collisional excitation of the electrons in the filament. The excited electrons collisionally excite various electronic and vibrational states of the air molecules in the filament, causing population inversions and lasing, e.g., exciting the C 3 Π u →B 3 Π g (v=0→0) transition of the N 2 in the atmosphere to cause lasing at 337 nm.

Remotely Induced Atmospheric Lasing

A method for up-shifting the frequency of a subpicosecond laser pulse that utilizes the interaction of the pulse with a co-propagating relativistic ionization front is examined. The induced frequency shift is found to initially scale linearly with the propagation time \ensuremath{\tau}. Asymptotically, the frequency scales as ${\mathrm{\ensuremath{\tau}}}^{1/2}$. Phase-slippage limitations may be overcome by appropriately increasing the plasma density as a function of \ensuremath{\tau}, thus allowing for substantially higher-frequency shifts.

Frequency up-shifting of laser pulses by copropagating ionization fronts.

: In this work, a promising new electron cyclotron wear oscillator is proposed and analyzed. The configuration utilizes an open resonator cavity containing a gyrating electron beam which translates along an external magnetic field. The magnetic field is directed perpendicular to the axis of symmetry of the open resonator. Because the wave-particle interaction volume is extremely large, the total input electron beam power can be high and the power density low.

Phillip Sprangle

Papers

Stimulated backscattered harmonic generation from intense laser interactions with beams and plasmas

Transmission of intense femtosecond laser pulses into dielectrics.

Remotely Induced Atmospheric Lasing

Frequency up-shifting of laser pulses by copropagating ionization fronts.

Theory of the Quasi-Optical Electron Cyclotron Maser.