Model for coherence transfer in a backward optical parametric oscillator

The mirrorless backward optical parametric oscillator (BOPO), where the signal and idler waves are propagating in opposite directions, will establish a distributed feedback mechanism and thus optical parametric oscillation without the need to apply mirrors or external feedback to the cavity. It has been recently demonstrated experimentally by exploiting the periodic poling technique in second-order nonlinear crystals, that the sub-micrometer structured medium achieves an efficient quasi-phase-matching of the three wave interaction in the backward configuration. A remarkable property of such BOPO is the high degree of coherence of the backward wave component, whose spectrum may be several order of magnitudes narrower than that of the pump, due to the convectioninduced phase-locking mechanism. Experimentally and numerically proved the transfer of coherent phase modulations from the pump wave to the parametrically down-converted waves, we show here that this is also possible for a broad bandwidth spectrally incoherent pump. In order to accurately describe the nonlinear counter-propagation dynamics of the three dispersive waves, we have developed for the first time to our knowledge a new numerical scheme which combines the method of the trajectories usually employed to solve the three-wave interaction and the intraband group velocity dispersion effect is performed in the spectral domain with the help of the Fast Fourier Transform (FFT) technique. The model accurately conserves the number of photons and the Manley-Rowe invariants. This allowed us to predict various configurations of MOPOs in which, thanks to the convection-induced phase-locking mechanism, a highly coherent backward wave is spontaneously generated from a highly incoherent pump wave.