Creating High-Harmonic Beams with Controlled Orbital Angular Momentum

A beam of light with an angle-dependent phase $\Phi = \ell \phi$, where $\phi$ is the azimuthal coordinate, about the beam axis carries an orbital angular momentum (OAM) of $\ell \hbar$ per photon. Such beams have been exploited to provide superresolution in visible-light microscopy. The ability to create extreme ultraviolet or soft-x-ray beams with controllable OAM would be a critical step towards extending superresolution methods to extremely small feature size. Here we show that OAM is conserved during the process of high-harmonic generation (HHG). Experimentally, we use a fundamental beam with $\ell = 1$ and interferometrically determine that the {\it q}-th harmonic has an OAM quantum number $\ell$ equal to its harmonic order {\it q}. We also show theoretically how to couple an arbitrary low value of the OAM quantum number $\ell$ to any harmonic order {\it q} in a controlled manner. Our results open a route to microscopy on the molecular, or even submolecular, scale. \\ Reference: G. Gariepy, J. Leach, K.T. Kim, T. J. Hammond, E. Frumker, R.W. Boyd, and P. B. Corkum, Phys. Rev. Lett. 113, 153901 (2014).