Naturally grown ferroelectric crystals such as Strontium Barium Niobate (SBN) often exhibit an irregular multidomain structure with rod-like domains [1]. These disordered nonlinear quadratic crystals have attracted a considerable attention in recent years due to their potential benefits for nonlinear parametric processes [2]. Despite being usually considered as disadvantageous in typical nonlinear optical phenomena due to the low efficiency of the NL process, the randomness of the nonlinear media offers potential applications in broadband frequency generation [3] and ultra-short pulse monitoring [4]. These applications utilize the fact that the crystal with disordered anti-parallel domains forms, in fact, a two-dimensional photonic nonlinear structure with an infinite number of ¿2 reciprocal vectors corresponding to various local nonlinear gratings. Consequently, such structure enables phase matching of various parametric processes at the same time, over an ultra-broad spectral range and in different spatial directions [5]. Fig. 1 represents a schematic illustration of such type of random crystal placed in a typical experimental set-up where the fundamental beam shines the crystal and the SH spatial distribution is recorded. In Fig. 1b a numerically generated random distribution of up and down ferroelectric domains is represented by bright and dark colors, respectively. However, recent experiments with random domain SBN crystals also demonstrated that the emission pattern of the generated waves may differ drastically from sample to sample, going from a spatially homogeneous pattern to exhibiting distinct intensity peaks [3][4][5][6][7][8]. This behavior points towards the existence of significant differences in the actual distributions of ferroelectric domains in different samples. In fact, observations of random domains ranging from tens of nanometers to few microns have been reported in the literature [1].
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