Diffraction manipulation of arbitrary images by Four-Wave-Mixing

In recent years, the resonant interaction of light with atoms to reduce or eliminate the diffraction spreading of beamlike fields by manipulating the
susceptibility in real space and inducing a gradient of the index of refraction.

Recently, a new technique based on a Raman transition was suggested and experimentally demonstrated to manipulate (eliminate, double or reverse) the diffraction of an arbitrary image imprinted on a light beam for any distance along the propagation direction. Unlike other methods, the technique operates in the wave vector  space, and prescribe nonuniformity in k-space that completely counterbalances the optical diffraction, which is also k-depended. For many applications (imaging, microscopy, lithography, switching and more) high resolution and low absorption is needed. In the aforementioned scheme strong absorption is unavoidable due to non-zero raman detuning.

In this work, we suggest a new scheme, also operating in k-space, which utilizes the k-dependency of four-wave-mixing (FWM). The inherent gain of the FWM process allows us to avoid the absorption and achieve high resolution. We introduce a microscopic model based on Liouville-Maxwell equations and compare it with FWM in recent hot vapor experiments. We use this model to show that with specific choice of frequencies, the  k-dependency of the FWM process can be used to eliminate the diffraction of a propagating light beam. We also show demonstration of negative diffraction, implementing negative index lens with accompanying gain. We analyze the resolution limitations of our scheme and look for ways to enhance it. We find that for cold atoms at high density (10^13), a resolution of 1 micron can be achieved.