  We study the coherence properties of a laser beam after propagation along a
one-dimensional lossless nonlinear optical waveguide. Within the paraxial,
slowly-varying-envelope, and single-transverse-mode approximations, the quantum
propagation of the light field in the nonlinear medium is mapped onto a quantum
Gross-Pitaevskii-type evolution of a closed one-dimensional system of many
interacting photons. Upon crossing the entrance and the back faces of the
waveguide, the photon-photon interaction parameter undergoes two sudden jumps,
resulting in a pair of quantum quenches of the system's Hamiltonian. In the
weak-interaction regime, we use the modulus-phase Bogoliubov theory of dilute
Bose gases to describe the quantum fluctuations of the fluid of light and
predict that correlations typical of a prethermalized state emerge locally in
their final form and propagate in a light-cone way at the Bogoliubov speed of
sound in the photon fluid. This peculiar relaxation dynamics, visible in the
light exiting the waveguide, results in a loss of long-lived coherence in the
beam of light.
