New beat length for writing periodic structures using Bessel beams

With the ultimate aim of exploiting the self-focusing behaviour to create periodic structures, we have investigated the behaviour of Bessel-Gauss beams in Kerr-like nonlinear media and have identified that a previously proposed nonlinear beat length is inaccurate with increasing power. By studying the behaviour of the beam we suggest a correction; providing a much better description of the beat length. This correction is tested against results from numerical simulations confirming the improved accuracy. Within the, scalar, nonparaxial limit we show that this modified beat length is valid for beam powers surpassing the paraxial self-focusing threshold. From this modified beat length equation, the appropriate experimental variables may be chosen to create accurate periodic structures by direct laser writing in a single exposure.