  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.
