Ising- and Bloch fronts in 2D parametric wave mixing

In optical systems, in which light is generated by a degenerate, phase-matched wave mixing process, a field can be described by a real-valued function of space and time. Due to the real-valued nature of the field (a consequence of the phase matching between pump and generated wave) one would expect the phase domains to be separated by "black" domain walls, across which the amplitude of the field crosses zero. However, we have experimentally observed that besides Ising fronts (real field) there are also Bloch fronts (complex field) in the field generated by degenerate four wave mixing in a BaTiO₃-resonator. We have applied the 2D Fourier transform technique and a fitting procedure for reconstructing the complex field and the phase and amplitude structure of the fronts. We find that the Fourier transform technique is more generally applicable and the experiment shows that it works well. Numerical solutions of the model are in a good agreement with the experiment concerning the presence of Ising and Bloch type fronts and changing in phase by π across the front (Bloch as well of Ising type). To allow further tests of this model, an improved version of the four wave mixing experiment has to be set.