Fig. 1: Origin of topological singularity induced by symmetry breaking.
From: Observation of spatiotemporal optical vortices enabled by symmetry-breaking slanted nanograting
a Schematic of STOV generation, showing an ultrafast light pulse transmitting through an optical device that is comprised of a one-dimensional slanted grating. The white arrow indicates the polarization direction of the incident pulse. b, c The band structure and Q factors of the TE-mode along the kx axis at θ = 0° (red) and θ = 15°(blue), respectively, with the insets showing the mode profiles in the two unit-cells at the Γ point (kx = 0). d For a C2 symmetric structure, the complex transmission coefficient s presents only one nodal line in the ω-kx space and does not show a spiral phase in the frequency-momentum space. e By breaking the C2 symmetry and the z-mirror symmetry, an isolated zero-transmission singularity associated with a spiral phase appears at the BZ center near the resonant frequency. Middle panel of (d, e): the amplitude distribution of the transmission coefficient. Lower panel of (d, e): the phase distribution corresponding to the red rectangle region.
