= Symmetric concave-mirror resonator
{title2=$0<L<2R$}
Two identical concave mirrors of curvature radius R separated by L have half-round-trip ray matrix $A=\begin{pmatrix}1&L\\-2/R&1-2L/R\end{pmatrix}$. Its <determinant> is one and its trace is $2(1-L/R)$. The <eigenvalues> are a conjugate unit-modulus pair for the displayed interval. At the confocal point $L=R$, $A^2=-I$, so it is bounded despite the full-round-trip trace reaching minus two. Matching a <Gaussian beam>'s mirror wavefront gives $z_R^2=(L/2)(R-L/2)$ and $\pi w_0^2=\lambda z_R$. The endpoints are degenerate limiting geometries, not finite confined Gaussian modes.
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