Diffractionless image propagation and frequency conversion via four-wave mixing exploiting the thermal motion of atoms

A setup to frequency-convert an arbitrary image encoded in the spatial profile of a probe field onto a signal field using four-wave mixing in a thermal atom vapor is proposed. The atomic motion is exploited to cancel diffraction of both signal and probe fields simultaneously. We show that an incoherent probe field can be used to enhance the transverse momentum bandwidth which can be propagated without diffraction, such that smaller structures with higher spatial resolution can be transmitted. It furthermore compensate linear absorption with non-linear gain, to improve the four-wave mixing performance since the propagation dynamics of the various field intensities is favorably modified.