  In the photonic spin Hall effect (SHE), also known as transverse shift,
incident light photons with opposite spins are spatially separated in the
transverse direction due to the spin-orbit interaction of light. Here, we
propose a gain-assisted model to control the SHE in the reflected probe light.
In this model, a probe light is incident on a cavity containing a three-level
dilute gaseous atomic medium, where the interaction between the atom and the
control field follows two-photon Raman transitions. We show that the direction
of photonic spin accumulations can be switched between positive and negative
values across the Brewster angle in both the anomalous and normal dispersion
regimes. For the same magnitude of control fields, the peak value of the
photonic SHE is higher in the anomalous dispersion region compared to the
normal dispersion regime. Additionally, the angular range around the Brewster
angle is wider in the normal dispersion regime than in the anomalous dispersion
region. Furthermore, the peak value of the photonic SHE and the angular range
is controllable by changing the Rabi frequencies of the control fields and the
probe field detuning. The measurement of photonic SHE based on gain assistance
may enable spin-related applications such as optical sensing.
