Rigid elastic waveguide mode
= Rigid elastic waveguide mode
In a homogeneous elastic layer $-H<z<H$ with rigid boundaries, in-plane propagating modes mix P- and SV-waves. For phase speed $c>c_P>c_S$, one even-horizontal, odd-vertical family obeys
$$
a\tan(akH)=-\frac{\tan(bkH)}b,
\qquad
a=\sqrt{\frac{c^2}{c_P^2}-1},
\quad
b=\sqrt{\frac{c^2}{c_S^2}-1}.
$$