We develop theoretical background for the new nonlinear optical phenomenon of narrowly directed monochromatic IR conical emission which has been recently observed when 248-nm UV filaments propagate in xenon (V. D. Zvorykin, et al., Laser Phys. Lett. 13, 125404 (2016)). We treat it as coherent stimulated four-wave mixing process in which two pump KrF laser photons are converted into the coupled pair of resonance IR(828 nm) and VUV (147 nm) photons through 5p5(2P3/2)6p[1/2]0→5p5(2P3/2)6s[3/2]1o and 5p5(2P3/2)6s[3/2]1o→1S0 transitions. We explore the coherent interaction regime which proceeds at a time scale shorter than transverse relaxation time T2. The momentum and energy conservation laws determine the characteristic angle of conical emission. We find that the threshold of this coherent process is determined by the KrF laser pump pulse area.
Dressed intensity noise correlation and intensity-difference squeezing of spontaneous parametric four-wave mixing process in a Pr^3+:YSO crystal