Angular Momentum of Twisted Radiation from an Electron in Spiral Motion

Abstract

We theoretically demonstrate for the first time that a single free electron in circular/spiral motion emits twisted photons carrying well defined orbital angular momentum along the axis of the electron circulation, in adding to spin angular momentum. We show that, when the electron velocity is relativistic, the radiation field contains harmonic components and the photons of l-th harmonic carry  l total angular momentum for each. This work indicates that twisted photons are naturally emitted by free electrons and more ubiquitous in laboratories and in nature than ever been thought.

Helical Phase Structure of Radiation from an Electron in Circular Motion

“…It has been argued that the radiation field of such a case possesses angular momentum, even though the spin and orbital angular momentum are difficult to separate 15 . Recently we have successfully derived an expression for the ratio of the angular momentum density to the energy density for the radiation emitted by an electron in circular motion in a separate paper, taking a different mathematical approach 16 . The expression shows that a photon of the l -th harmonic carries the total angular momentum whose z-component is equal to l .…”

Generation of GeV positron and γ-photon beams with controllable angular momentum by intense lasers

“…The instantaneous radiation power emitted by the electron scales as h h ( ) g 2 and the photon angular momentum can be then approximately written as h h 1 with a high angular momentum conversion efficiency of~0.15%. Since the γ-photons are emitted by electrons in helical motion and via the NCS of a CP pulse, the resulting high angular momentum γ-rays may carry away well-defined orbital angular momentum along the propagation direction, which has been verified theoretically in recent several studies [28,29]. By manipulating the electron motion in plasmas, it is a potential way for generating γ-ray beams with coherent angular momentum.…”

“…High-energy particle beams with angular momentum have an additional degree of freedom and unique characteristics, which offer exciting and promising new tools for potential applications [3,[27][28][29] in test of the fundamental physical mechanics, probe of the particle property, generation of vortex beam, etc. For long time ago, it was realized that the circularly-polarized (CP) light beam might behavior like an optical torque [30], the spin angular momentum (SAM) of photons of such light can be transferred to the BAM of particles [31,32].…”

Free-Electron Laser Does the Twist

“…It was shown that harmonic components of radiation produced by a relativistic electron moving on a circular or spiral trajectory, such as the one in a helical undulator, carry a total (spin and orbital) angular momentum of nℏ per photon, where n is the harmonic number [27]. In the paraxial regime, this translates into an OAM content corresponding to l ¼ n − 1; see Ref.…”

“…In the first one, we take advantage of the vortex nature of harmonics emitted in a helical undulator [26,27]; however, unlike the previous experiment [28], where XUV vortices were produced by incoherent undulator emission, we exploit high-harmonic [29] and nonlinear harmonic generation [30][31][32][33] to obtain intense, femtosecond, coherent XUV vortices from a chain of six undulators at the FERMI FEL [34]. The method can be easily implemented at existing FEL facilities.…”