Modal analysis of the scattering coefficients of an open cavity in a waveguide

The characteristics of an acoustic scatterer are often described by scattering coefficients. The understanding of the mechanisms involved in the frequency dependent features of the coefficients has been a challenge task, owing to the complicated coupling between the waves in open space and the modes inside the finite scatterer. In this paper, a frequency-dependent modal description of the scattering coefficient is utilized to study the modal properties of the scatterer. The important role that eigenmodes play in defining the features of the scattering coefficients is revealed via an expansion of the coefficients by the eigenmodes. The results show the local extrema of the scattering coefficients can be attributed to the constructive/destructive interference of resonant and non-resonant modes. In particular, an approximated equation, which is equivalent to the standard Fano formula, is obtained to describe the sharp anti-symmetric Fano characteristics of the scattering coefficients. The special cases where scattering is dominated by a single resonance eigenmode, corresponding to the “resonance transmission”, are also illustrated.