  Coherent control has enabled various novel phenomena in wave scattering. We
introduce an effect called coherent orthogonal scattering, where the output
wave becomes orthogonal to the reference output state without scatterers. This
effect leads to a unity extinction coefficient and complete mode conversion. We
examine the conditions for this effect and reveal its topological nature by
relating it to the indivisibility between the dimension and the winding number
of scattering submatrices. These findings deepen our understanding of
topological scattering phenomena.
