Spin-orbit-coupled fluids of light in bulk nonlinear media

Spontaneous breaking of time translation symmetry in a spin-orbit-coupled fluid of light

“…Breaking of translation invariance along z is observed in the input-output correlation δI(r ⊥ , 0)δI(r ⊥ , z) . tem [30], based on the fundamental coupling between the polarization and the trajectory of optical fields subjected to a refractive-index gradient [31][32][33][34][35][36]. In the presence of an optical nonlinearity, such a coupling is achieved by letting an inhomogeneous optical field propagate in the nonlinear medium and make it deviate from its regime of paraxial propagation.…”

“…In the presence of an optical nonlinearity, such a coupling is achieved by letting an inhomogeneous optical field propagate in the nonlinear medium and make it deviate from its regime of paraxial propagation. The inhomogeneous spatial profile gives rise to a nonlinear refractive-index gradient, which couples to the optical spin via the SOC terms emerging beyond paraxiality [30].…”

“…In the same spirit as in Ref. [30], we define an Hamiltonian H(2) = Π T Ẋ + Ẋ † Π * − L(2) depending on X and the conjugate momenta vector Π = ∂ L(2) /∂ ẊT . The effectivetime evolution of X and Π is governed by the Hamilton equations Ẋ = ∂ H(2) /∂Π T and Π = −∂ H(2) /∂X T , yielding the eight coupled equations…”

“…In [30], Eq. ( 5) was solved in the ∆k = 0 case (linearly polarized background field), where the matrix of coefficients is constant.…”

“…y, z) is a tensor featuring two independent Kerr indices n 2,d and n 2,s . Equation (1) corresponds to the Euler-Lagrange equation for the action functional S = d 3 r L, where[30] …”