Systematic Control of Primary and Secondary Structure Periods in Four-Beam Direct Laser Interference Patterning

Four-beam Direct Laser Interference Patterning (DLIP) enables the fabrication of periodic surface micro- or nanostructures with various geometrical features. In practice, even a small deviation in beam alignment can alter the resulting morphology, leading to isotropic circular dot patterns, anisotropic structures, rotated patterns, and secondary periodic modulation superimposed on the primary structure. In this work, five representative four-beam DLIP cases were experimentally fabricated, resulting in clearly distinguishable surface morphologies. To identify the incident beam parameters from the fabricated patterns, a Two-Beam Decomposition Method (TBDM) was used. The complex four-beam DLIP structures were decomposed into their six pairwise two-beam configurations, and the angles of incidence (AoIs) and azimuthal angles were reconstructed from the measured spatial periods and relative fringe orientations. Based on the reconstructed beam parameters, an analytical wavevector framework was used to explain the formation of primary structure periods and the secondary period. The obtained results establish a direct correlation between the beam geometry and fabricated surface morphology in four-beam DLIP. The proposed TBDM approach provides a systematic framework for analyzing multi-beam interference patterns and for intentionally designing the complex DLIP-based surface structures with controlled primary and secondary periods.