Dense Multi-directional second-harmonic emission via deterministic aperiodic wavefront engineering

We demonstrate real-time control of second-harmonic (SH) emission through deterministic aperiodic phase modulation of a fundamental wave (FW) using a spatial light modulator (SLM). This method generates a quasi-continuous spectrum of reciprocal lattice vectors (RLVs), enabling gap-free and multi-directional SH patterns in homogeneous nonlinear media — overcoming both the fabrication constraints of nonlinear photonic crystals (NPCs) and the spectral discreteness inherent in periodic SLM modulation. Experimentally, one-dimensional modulation produces a high density of SH spots, while two-dimensional orthogonal modulation yields programmable matrix-type SH arrays. Angularly resolved measurements confirm the predicted SH trajectories, and the observed quadratic intensity dependence verifies the nonlinear nature of the emission. This work establishes wavefront engineering as a versatile paradigm for adaptive nonlinear photonics, with promising applications in dynamic optical interconnects and reconfigurable beam routing.