  We theoretically investigate a driven-dissipative model of strongly
interacting photons in a nonlinear optical cavity in the presence of a
synthetic magnetic field. We show the possibility of using a
frequency-dependent incoherent pump to create a strongly-correlated $\nu = 1/2$
bosonic Laughlin state of light: thanks to the incompressibility of the
Laughlin state, fluctuations in the total particle number and excitation of
edge modes can be tamed by imposing a suitable external potential profile for
photons. We further propose angular momentum-selective spectroscopy of the
emitted light as a tool to obtain unambiguous signatures of the microscopic
physics of the quantum Hall liquid of light.
