Self-bound droplets of light with orbital angular momentum

Systems with competing attractive and repulsive interactions have a tendency to condense into droplets. This is the case for water in a sink, liquid helium, and dipolar atomic gases. Here we consider a photon fluid which is formed in the transverse plane of a monochromatic laser beam propagating in an attractive (focusing) nonlocal nonlinear medium. In this setting we demonstrate the formation of the optical analog of matter-wave droplets and study their properties. The system we consider admits droplets that carry orbital angular momentum. We find bound states possessing liquidlike properties, such as bulk pressure and compressibility. Interestingly, these droplets of light, as opposed to optical vortices, form due to the competition between long-range $s$-wave (monopole) and $d$-wave (quadrupole) interactions as well as diffraction.