Generation of High-Energy Photons with Large Orbital Angular Momentum by Compton Backscattering

Abstract

Usually, photons are described by plane waves with a definite 4-momentum. In addition to plane-wave photons, "twisted photons" have recently entered the field of modern laser optics; these are coherent superpositions of plane waves with a defined projection m of the orbital angular momentum onto the propagation axis, where m is integer. In this paper, we show that it is possible to produce high-energy twisted photons by Compton backscattering of twisted laser photons off ultra-relativistic electrons. Such photons may be of interest for experiments related to the excitation and disintegration of atoms and nuclei, and for studying the photo-effect and pair production off nuclei in previously unexplored experimental regimes.PACS numbers: 13.60. Fz, 42.65.Ky, 27.70.Jj, 12.20.Ds Introduction.-An interesting research direction in modern optics is related to experiments with so-called "twisted photons." These are states of the laser beam whose photons have a defined value m of the angular momentum projection on the beam propagation axis where m is a (large) integer [1]. An experimental realization [2] exists for states with projections as large as m = 200. Such photons can be created from usual laser beams by means of numerically computed holograms. The wavefront of such states rotates around the propagation axis, and their Poynting vector looks like a corkscrew (see Fig. 1 in Ref. [1]). It was demonstrated that micron-sized teflon and calcite "particles" start to rotate after absorbing twisted photons [3].In this Letter, we show that it is possible to convert twisted photons from an energy range of about 1 eV to a higher energies of up to a hundred GeV using Compton backscattering off ultra-relativistic electrons. In principle, Compton backscattering is an established method for the creation of high-energy photons and is used successfully in various application areas from the study of photonuclear reactions [4,5] to colliding photon beams of high energy [6]. However, the central question is how to treat Compton backscattering of twisted photons, whose field configuration is manifestly different from plane waves. Below, we use relativistic Gaussian units with c = 1, = 1, α ≈ 1/137. We denote the electron mass by m e and write the scalar product of 4-vectors k = (ω, k) andTwisted photon.-We wish to construct a twisted photon state with definite longitudinal momentum k z , absolute value of transverse momentum κ and projection m of the orbital angular momentum onto the z axis (propagation axis). We start from a plane-wave photon state with 4-momentum k = (ω, k) and helicity Λ = ±1,

Scattering of wave packets with phases

“…Vortex electrons with the kinetic energy of 200 − 300 keV can be focused to a spot of anÅngström size [21], their OAM can be as high as = 200 [22], their magnetic moment increases proportionally to [13], and this brings about new effects in the electromagnetic radiation [23,24]. Such photons and electrons were also proved useful for optical manipulation [14], for probing phase of a transition amplitude, for creating pairs entangled in their OAM [25][26][27][28][29][30], etc.…”

“…In this case the measure dn f may also include discrete variables such as the OAM. A need for spatial-and temporal localization of the detected states appears, for instance, in the theory of neutrino oscillations [4][5][6] or in QED calculations with the twisted photons [25,26].…”

Quantum Čerenkov Radiation: Spectral Cutoffs and the Role of Spin and Orbital Angular Momentum

“…This issue is of great interest today because it recently became possible to shape the quantum wave packet of a single electron [32][33][34][35], imprinting it with OAM [32][33][34][36][37][38] or with other intriguing shapes [35,39].…”

Coherent optical vortices from relativistic electron beams

“…Traditionally, these "optical vortices" are created by shaping of the phase front of a laser as it passes through different optical media [11][12][13], such as spiral phase plates [14] or computer generated holograms [15]. Analogous techniques have also been used to transform x-rays into vortices at synchrotron light sources [16,17], and alternate methods suggest vortex beams can be created through Compton back-scattering [18] or harmonic emission in undulators [19]. Here, we report on a completely different technique in which a simple Gaussian laser pulse is used to generate fully coherent l = 1 OAM light purely through its interaction with a relativistic electron beam (e-beam).…”