We study the role of the individual ferroelectric domain shape on the second-harmonic emission in strontium barium niobate featuring a random quadratic nonlinearity. The noncollinearly emitted second-harmonic signal is scanned in the far-field at different incident angles for different domain size distributions. This offers the possibility to retrieve the Fourier spectrum, corresponding to the spatial domain distribution and domain shape. Based on images of the domain structures retrieved by Čerenkov-type second-harmonic microscopy, domain patterns are simulated, the second-harmonic intensities are calculated, and finally compared with the measurements.

We study systematically the effect of spatial disorder of ferroelectric domains in nonlinear media on the polarization properties of optical frequency conversion. Experimentally, different statistics of domain sizes are created using electric field poling at room temperature. We analyze the evolution of polarization properties of the second- and third-harmonic signals for each created statistic by determining the corresponding relative strength of non-zero components of the second-order susceptibility tensor, d24, d32 and d33. The relative strengths are labeled by means of the control parameter E on the characteristic P-E loop of the studied ferroelectric medium.

We observe simultaneous type I and II Čerenkov-phase matched second-harmonic generation in a disordered nonlinear photonic crystal. The mean width of the disordered ferroelectric domains and the laser beam width are adjusted to be on the same length scale. We analyze the polarization properties, emission angles and intensities of each process.

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