Universal behavior of the scattering matrix near thresholds in photonics

Scattering thresholds and their associated spectral square root branch points are ubiquitous in photonics. In this Letter, we show that the scattering matrix has a simple universal behavior near scattering thresholds. We use unitarity, reciprocity, and time-reversal symmetry to construct a two-parameter model for a two-port scattering matrix near a threshold. We demonstrate this universal behavior in three different optical systems, namely a photonic crystal slab, a planar dielectric interface, and a junction between metallic waveguides of different widths.