Extreme ultraviolet attosecond light beams with fractional angular momentum

Light beams, just like massive objects, can carry angular momentum.The spin angular
momentum of light (SAM) is linked to the polarization of the field: each photon in a circularly
polarized beam carries a well-defined SAM S=1 (in units of the Planck’s constant). In the
90’s, a second form of optical angular momentum, the orbital angular momentum (OAM),
was rediscovered, and associated with “vortex beams”. Photons in a vortex beam carry a
quantum L=l of OAM, where l can be any integer number. Thus, the eigenvalues of the total
angular momentum of ligh, J=L+S, are also integers. During the past decades, different
ways of manipulating the SAM and OAM via nonlinear optical processes have been
reported. Extending these capabilities to the extreme ultraviolet (EUV) spectral domain,
using free electron laser (FEL), synchrotrons, or high harmonic generation (HHG) sources,
gives access to time-resolved applications at femtosecond and attosecond time scales.
In this presentation, we will see that things get more complicated when both the SAM and
the OAM are simultaneously present in a light beam, as is the case for exotic light fields
whose polarization and phase vary in space. Such beams obey certain types of rotational
symmetry, and are eigenstates of a “generalized angular momentum” (GAM). Remarkably,
this new angular momentum can take half-integer values, i.e. the photons in such modes
can carry a quantum of angular momentum equal to half the Planck’s constant, a value
normally associated with fermionic particles. The polarization of GAM modes generally
exhibits a Möbius strip topology. Here, we prepare an intense infrared GAM beam and use it
to drive HHG in a jet of gas (see Figure). By implementing novel angular momentum
measurement techniques in the EUV, we find experimentally that the harmonic of order q
carries a GAM equal to q times that of the driver, while its SAM and OAM are ill-defined. We
conclude that, in some situations, the GAM is the “good” quantum number, efficiently
describing the nonlinear interaction. Such ultrafast EUV beams with fractional angular
momentum could provide original tools to explore new kinds of dichroism in molecules or
magnetic systems.