The concept of quasi-phase-matching (QPM) was introduced at the very beginning of the era of lasers and nonlinear optics as a generic method to increase the efficiency of second order nonlinear interactions. However, it was not until the early 90’s, with the introduction of periodically poled ferroelectrics obtained by electric field poling that the technique began to blossom as an engineering tool to tailor nonlinear interactions. In the QPM approach an artificial wave vector (i.e, artificial modulation of the nonlinear coefficient in the material) is introduced into the phase matching condition in order to compensate for the phase mismatch between the interacting waves induced by material dispersion.

QPM structures are commonly implemented by periodic inversion of domains in ferroelectric crystals. Such periodic structures can be created in the crystal by lithographic patterning with subsequent electric field poling. Several errors can be introduced during the fabrication of QPM gratings such as deviation from the designed duty-cycle or missing reversals that will directly influence the performance of the nonlinear device reducing its efficiency. On the other hand, local errors randomly distributed in the positions of the domain boundaries, so-called random duty cycle (RDC) errors, usually have a small impact on the conversion efficiency of the process for which the grating is designed. RDC errors can arise from local defects in the photolithographic process or from local inhomogeneities in the domain inversion, and are difficult to control. Nevertheless, as the Stanford group had previously shown, RDC errors lead to a pedestal in the spatial frequency spectrum, which in turn can translate into an increase in the conversion efficiency of parasitic, nominally phase mismatched processes, and their effect needs to be taken into account.

In this comprehensive paper, the authors present a thorough analysis of RDC errors and show case studies of several QPM applications where RDC errors play a significant role, both for high- and low- intensity systems. The model presented here should be taken into account for anyone designing a QPM- based system for which it is important to control parasitic processes.

In the last two decades, considerable efforts have been put into improving the material quality and developing domain-engineering techniques in variety of materials such as LiNbO3, LiTaO3, and KTiOPO4, leading to commercialization of QPM devices. Nevertheless, this paper shows that we still have not reached the end of the road, and that a qualitative leap in structuring technology and material development is required in order to achieve QPM devices free of parasitic effects.

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