 Passive cavity input-output transfer function

For $\dot{a}=-\gamma a/2-\sqrt{\gamma }{b}_0$ and $b_1=\sqrt{\gamma }a+b_0$, zero-initial-data Laplace transforms give the displayed transfer function. For $\gamma >0$ its pole is in the open left half-plane, while $|G(i\omega )|=1$ and its zero lies in the right half-plane. Passing through $-1$ in this plant's frequency plot is not evidence of an unstable open cavity: a Nyquist stability criterion needs an explicitly specified feedback return ratio.