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

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 $\hslash m$ of the orbital angular momentum onto the propagation axis, where $m$ is an integer. In this Letter, we show that it is possible to produce high-energy twisted photons by Compton backscattering of twisted laser photons off ultrarelativistic electrons. Such photons may be of interest for experiments related to the excitation and disintegration of atoms and nuclei, and for studying the photoeffect and pair production off nuclei in previously unexplored experimental regimes.

Figure 1

The twisted photon vector potential component ${\mathcal{A}}_{\varkappa m{k}_z\Lambda }^{\mu }(t,x,y,z)$ is shown for $\mu =2$ ($y$ component), $\varkappa =1$, $m=5$, $k_z=\sqrt{24}$, and $\Lambda =1$. The plot displays $g(x,y)=|{\mathcal{A}}_{\varkappa m{k}_z\Lambda }^{\mu }(0,x,y,0){|}^2$ as a function of $x$ and $y$. The complex phase of the vector potential, which is a superposition of terms proportional to $e^{4i{\phi }_r}$ and $e^{6i{\phi }_r}$, is indicated by the variation of the color of the wave function on the rainbow scale.

Figure 2

Initial (above) and final (below) states for the head-on Compton backscattering geometry of a twisted photon. According to Eq. (24), the conical momentum spread $\varkappa$ of the initial twisted photon is preserved (${\varkappa }^{\prime }=\varkappa$) during the scattering, but the propagation energy increases: ${\omega }^{\prime }=\sqrt{k_z^{\prime 2}+{\varkappa }^{\prime 2}}\gg \omega =\sqrt{k_z^2+{\varkappa }^2}$.