Interaction of Relativistic Electron-Vortex Beams with Few-Cycle Laser Pulses

Abstract

We study the interaction of relativistic electron-vortex beams (EVBs) with laser light. Exact analytical solutions for this problem are obtained by employing the Dirac-Volkov wave functions to describe the (monoenergetic) distribution of the electrons in vortex beams with well-defined orbital angular momentum. Our new solutions explicitly show that the orbital angular momentum components of the laser field couple to the total angular momentum of the electrons. When the field is switched off, it is shown that the laser-driven EVB coincides with the field-free EVB as reported by Bliokh et al. [Phys. Rev. Lett. 107, 174802 (2011)]. Moreover, we calculate the probability density for finding an electron in the beam profile and demonstrate that the center of the beam is shifted with respect to the center of the field-free EVB.

Electron vortices: Beams with orbital angular momentum

“…The study of an electron vortex beam with strong laser fields has also opened up the possibility of accelerating non-relativistic twisted electrons using focused electromagnetic fields (Karlovets, 2012) or beam steering using the high electric fields due to an ultrashort pulsed beam Hayrapetyan et al, 2014). Research into laser-electron beam interaction also allows coherent optical vortex beams to be produced (Hemsing et al, 2013).…”

Position, spin, and orbital angular momentum of a relativistic electron

“…In fact, q = R, and its expectation value for a single-electron state corresponds to the center of the probability density (center of charge), while the center of energy is defined as r E = N / H = q . The difference is important, e.g., for the "relativistic Hall effect" (11), where the center of energy r E undergoes the transverse shift twice as large as the center of the probability density [54,55,57]. Second, the projected position operator R and the spin-Hall effect corresponding to it appeared in 1959 in the work of Adams and Blount [33] (up to some arithmetic inaccuracies therein).…”

“…However, SOI effects appear in nonparaxial corrections to the paraxial regime [9] and their accurate analysis requires full nonparaxial solutions, just as for solutions of Maxwell's equations [24,25]. In this manner, a typical nonparaxial vortex solution of the Dirac equation with vortex charge in the main component (surviving in the paraxial limit) acquires extra components with vortices of charge + 2s z , where s z = ±1/2 corresponds to the two states of the longitudinal projection of the rest-frame spin of the electron [8][9][10][11][12]26,27]. However, only one of these components is present in [18] and, furthermore, calculations of the expectation value of the operator (r × α) z (where α is the usual matrix operator characterizing the Dirac probability current) yielded /E (where E is the electron energy).…”

“…Using a covariant position operator for the Dirac electron, we also introduced the corresponding separately conserved spin and orbital AM of a relativistic electron and described observable spin-orbit interaction (SOI) effects. Later, Dirac-Bessel electron beams were employed in the contexts of high-energy physics, scattering, and radiation problems [8,[10][11][12][13][14][15].…”

A New Twist on Relativistic Electron Vortices

“…We introduce analytic solutions of the Dirac equation in the form of exponential wave packets and we argue that they properly describe relativistic electron beams carrying angular momentum. Introduction.-Recent advances in experiments with relativistic (100-300 keV) electron beams [1][2][3][4][5][6][7][8][9] carrying orbital angular momentum call for a mathematical description based on the Dirac equation. The generally used Schrödinger equation gives an inadequate description because the differences between the nonrelativistic and relativistic wave functions are essential.…”