Spatial tailoring of four-wave mixing via optically induced nonlinear and linear gratings in atomic vapors

Spatial discrete control of the light field has long been regarded as a fascinating and prominent area in optics. Here, we propose two distinct approaches to spatially manipulate the four-wave mixing (FWM) signal by introducing a one-dimensional standing wave into its nonlinear generation and linear propagation dynamics. The FWM is generated by two pump fields and one reference field in an atomic vapor. First, we encode the standing-wave pattern into one pump field and successfully transfer its periodic distribution to the FWM signal. The spatially distributed pump field can modulate the third-order nonlinearity in a discrete manner and induce an equivalent nonlinear amplitude grating, which discretely diffracts the generated FWM signal within a rather wide frequency tuning range. In addition, we also established a linear refractive index grating with the assistance of electromagnetically induced transparency (EIT) by employing the same standing wave to modulate the Gaussian FWM signal in a cascaded atomic configuration. Owing to the instantaneously adjustable EIT condition, we have both theoretically and experimentally demonstrated the sensitive inversion on the bright and dark fringes of the discretized FWM signal by inverting the sign of the two-photon detuning. This work opens opportunities for engineering nonlinear optical effects through optically induced reconfigurable gratings.