<p>Per-mode power decomposition across the broadband sweep.</p>

The vertical grey dotted lines mark the cut-on frequencies <i>f</i>₁ = <i>c</i>/(4<i>a</i>) and <i>f</i>₂ = <i>c</i>/(2<i>a</i>).

Physical interpretation: below <i>f</i>₁ only the plane-wave channel carries energy. The <i>n</i> = 1 curves stay identically zero across the whole sweep because the parity selection rule of <a href="plosone.org/article/info:doi/10.1371/journal.pone.0358579#pone.0358579.e057" target="_blank">Eq (14)</a> ( only when <i>m</i> + <i>n</i> is odd) prevents the <i>y</i>-symmetric structure from coupling the plane-wave incidence into odd transverse modes.