  Particle beam scattering is a conventional technique for detecting the nature
of matter. We studied the scattering problem of a cluster connected to multiple
leads. We established the connection between the eigenstate of the topological
scattering center and the transmission and reflection amplitudes for the
resonant scattering process. We discovered that as an application, this
approach enables the detection of the edge state in the band gap for both
Hermitian and non-Hermitian systems and the identification of the topology of a
system. We investigated two types of Su-Schrieffer-Heeger chains as examples.
In addition, we proposed a dynamic scheme through an evanescently
coupled-waveguide array to detect the edge state on the basis of measured
transmission intensity. Numerical simulation revealed that pattern visibility
can be the signature of the edge states.
