Nonlinear $X$-wave formation in the backward wave optical parametric oscillator pumped by subnanosecond laser pulses is studied. The wavelengths of 1064 nm and its second harmonic are used for pumping. $3\mathrm{D}+1\mathrm{D}$ (three dimensional space and time) numerical model is implemented to simulate the formation of the generated forward and backward waves. Contrary to the conventional $1\mathrm{D}+1\mathrm{D}$ model, the $3\mathrm{D}+1\mathrm{D}$ model allows the formation of conical beam structures. The nonlinear $X$-wave propagation in the backward direction with respect to the phase velocity direction is demonstrated in the case of negative $X$-wave velocity.

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• Nonlinear optics
• Optical parametric oscillators & amplifiers