Temporal lenses for attosecond and femtosecond electron pulses

Abstract

Here, we describe the ''temporal lens'' concept that can be used for the focus and magnification of ultrashort electron packets in the time domain. The temporal lenses are created by appropriately synthesizing optical pulses that interact with electrons through the ponderomotive force. With such an arrangement, a temporal lens equation with a form identical to that of conventional light optics is derived. The analog of ray diagrams, but for electrons, are constructed to help the visualization of the process of compressing electron packets. It is shown that such temporal lenses not only compensate for electron pulse broadening due to velocity dispersion but also allow compression of the packets to durations much shorter than their initial widths. With these capabilities, ultrafast electron diffraction and microscopy can be extended to new domains,and, just as importantly, electron pulses can be delivered directly on an ultrafast techniques target specimen.attosecond imaging ͉ ultrafast techniques W ith electrons, progress has recently been made in imaging structural dynamics with ultrashort time resolution in both microscopy and diffraction (ref. 1 and references therein). Earlier, nuclear motions in chemical reactions were shown to be resolvable on the femtosecond (fs) time scale using pulses of laser light (ref. 2 and references therein), and the recent achievement of attosecond (as) light pulses (for recent reviews, see refs. 3-6) has opened up this temporal regime for possible mapping of electron dynamics. Electron pulses of femtosecond and attosecond duration, if achievable, are powerful tools in imaging. The ''electron recombination'' techniques used to generate such attosecond electron pulses require the probing electron to be created from the parent ions (to date no attosecond electron pulses have been delivered on an arbitrary target) and for general applications it is essential that the electron pulse be delivered directly to the specimen.In ultrafast electron microscopy (UEM) (7), the electron packet duration is determined by the initiating laser pulse, the dispersion of the electron packet due to an initial energy spread and electron-electron interactions (see, e.g., ref. 8). Because packets with a single electron can be used to image (1, 7), and the initiating laser pulse can in principle be made very short (Ͻ10 fs), the limiting factor for the electron pulse duration is the initial energy spread. In photoelectron sources this spread is primarily due to the excess energy above the work function of the cathode (8), and is inherent to both traditional photocathode sources (9) and optically induced field emission sources (10-13). Energytime uncertainty will also cause a measurable broadening of the electron energy spread, when the initiating laser pulse is decreased below Ϸ10 fs. For ultrafast imaging techniques to be advanced into the attosecond temporal regime, methods for dispersion compensation and new techniques to further compress electron pulses to the attosecond regime need to be developed.A rec...

Detecting Electron Motion in Atoms and Molecules

“…The temporal widths of these electron pulses, however, range from femtosecond to picosecond, which is inadequate for studying electronic motion in atoms and molecules. Recently, methods have been proposed for producing single-electron, attosecond pulses [14][15][16]. The attosecond temporal and subangstrom spatial resolutions of such short keV electron pulses (at the target location) would make the four-dimensional (4D) study of electronic motion feasible.…”

“…The few-femtosecond laser pulse creates a superposition of electronic states which is then probed by a time-delayed, 10 keV single-electron attosecond pulse. The electron pulse may be generated by photoemission [15,17] and then compressed to an attosecond duration by a spatially dependent ponderomotive potential [15,16]. By adjusting the time delay between the pump and the probe pulses, the 4D motion of the oscillating charge distribution is manifested in the time-resolved diffraction images of the scattered electrons.…”

Perspective: 4D ultrafast electron microscopy—Evolutions and revolutions

“…85 A novel "all-optical" method for compression directly to the attosecond domain involves the creation of "temporal lenses" made by ultrashort laser pulses. 86,87 The technique relies on the ponderomotive FIG. 9.…”

Laser Beam Shaping by Interference: Desirable Pattern

“…Doughnut modes correspond to a first order Laguerre-Gaussian laser mode with a profile depicted in Fig.9d. This result is important for application like doughnut mode creation for the temporally focusing of electron pulses (Hilbert et al,2009), (Helseth, 2004).…”