Channel-Differentiated Topological Charge Flips and Formation of Janus Bound States in the Continuum in Single-Layer Photonic Lattices

The topological charge of a bound state in the continuum (BIC) can flip when the BIC merges with other polarization singularities or, as recently shown, at band flips. Here, using a coupled-mode analysis, we derive an analytical expression for the topological charge of symmetry-protected BICs in one-dimensional single-layer photonic lattices. The expression captures both merging-induced and band-flip-induced charge flips. We find that, during a band flip, the topological charge of the BIC reverses with the formation of lines of circular polarization that cross at the $Γ$ point. In vertically symmetric lattices, each charge flip occurs simultaneously in the upward and downward radiation channels. Breaking vertical symmetry makes both kinds of charge flips channel-differentiated, creating a parameter interval in which the BIC carries opposite topological charges in the two channels and forms a Janus BIC. We show that Janus BICs also emerge in experimentally accessible one- and two-dimensional silicon-based photonic lattices. Our results link the topological charge of a BIC directly to the band structure and the channel-resolved radiation amplitudes and establish a basis for channel-selective control of polarization singularities.