Synthetic magnetism for photon fluids

We develop a theory of artificial gauge fields in photon fluids for the cases of both second-order and third-order optical nonlinearities. This applies to weak excitations in the presence of pump fields carrying orbital angular momentum and is thus a type of Bogoliubov theory. The resulting artificial gauge fields experienced by the weak excitations are an interesting generalization of previous cases and reflect the PT-symmetry properties of the underlying non-Hermitian Hamiltonian. We illustrate the observable consequences of the resulting synthetic magnetic fields for examples involving both second-order and third-order nonlinearities.

Figure 1

Snapshots of the transverse intensity profile of the light beam as a function of $z$. The input beam at $z=0$ is an elliptic Gaussian with the widths ${\sigma }_X=40k_1^{-1},{\sigma }_Y=20k_1^{-1}$, which will rotate due to the nearly uniform artificial magnetic field in the center of the beam. The dynamics is described by a ${\chi }^{\left(2\right)}$ nonlinearity where the pump beam is a Laguerre-Gaussian beam with winding number $\ell =1$ and amplitude $\mathrm{\Psi }\left(r\right)=\sqrt{5}(r/\sigma )exp[-{(r/\sigma )}^2]$ where $\sigma =50k_1^{-1}$. The resulting intensity shown in the figure is a superposition of the signal and idler components, which forms the dressed state.

Figure 2

Snapshots of the transverse intensity profile of the light beam as a function of $z$. The dynamics is governed by a single component nonlinear Schrödinger equation with a ${\chi }^{\left(3\right)}$ nonlinearity. The input beam at $z=0$ is an elliptic Laguerre-Gaussian beam with winding number of $\ell =1,{\sigma }_X=30k_0^{-1},{\sigma }_Y=20k_0^{-1}$, and peak intensity-dependent refractive index of $\delta n\simeq 0.0087$. The underlying optical vortex causes a rotation of the excitation axis. In other words, the excitation exhibits cyclotron motion. This can be interpreted as having an artificial magnetic field acting on the photon fluid.