Extended Data Fig. 7: Details on self-collimation effect.
From: Directive giant upconversion by supercritical bound states in the continuum
a, Isofrequency far-field intensity map in momentum space showing nontrivial vanishing strips. b, Cut lines of the Z-transform revealing a narrow divergence independent of the incident/outgoing wavevector along the orthogonal direction (cross of zeros). c, Phase map in the near field showing a phase vortex singularity. d, Corresponding near-field intensity map showing self-collimation. e, Experimental proof realized with a rescaled geometry supporting the same band structure at 532 nm: a 20× objective lens focuses the laser (SC, NKT Photonics, filtered at 532 nm) onto the patterned PCNS (red rectangle). The peculiar energy–momentum dispersion induces a resonant field that propagates in plane without spreading along the principal directions (±1, 0) and (0, ±1), in agreement with the simulation in b.