Dark solitons in a paraxial superfluid of light

The occurrence of dark solitons is predicted in a light superfluid, following the model proposed by Rodrigues et al, (Phys. Rev. A 101:043810, 2020). The nonlinear Schrödinger equation modelling light beam propagation in the paraxial approximation is adopted as a basis to investigate the nonlinear dynamics of the associated electric field, by means of the Madelung fluid formalism. Our investigation narrows down to the defocusing optical regime (i.e. when the coupling strength is positive, g> 0 i.e. when the Kerr nonlinearity coefficient is negative χ⁽³⁾< 0), where linear analysis predicts a stable (wave envelope) mode. In the opposite case (g< 0 , χ⁽³⁾> 0), the angular frequency for long wavelengths becomes imaginary, thus describing an unstable (purely growing or decaying) mode. Nonlinear analysis, based on a multiscale perturbative scheme, leads to Korteweg-de Vries (KdV)-type equation coupled to a linear inhomogenous partial differential equation, for the first- and second-order perturbations, respectively. Localized (solitonic) solutions of these equations (possessing a dressed profile) are shown to model dark-type solitons in the light envelope equation, leading to the conclusion that “photon-acoustic” wavepackets form and propagate in a light superfluid (for negative values of the Kerr nonlinearity). A parametric study showing the impact of the value of χ⁽³⁾ on the structural characteristics of dark solitons is also carried out.