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.

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• Linear acoustics
• Photonics
• Polarization of light
• Wave scattering
• Abstract algebra
• Electromagnetic wave theory
• Light scattering
• S-matrix method in transport