Confocal optical resonator

A symmetric confocal optical resonator has two concave mirrors of equal curvature $R$, separated by $R$. Its symmetric fundamental Gaussian beam has a central beam waist and Rayleigh range $R/2$. Its ideal transverse spectrum has degeneracies, so transmission at one resonance need not certify exclusive excitation of the fundamental normal mode.

For two equal mirrors of radius $L$ separated by $L$, a Gaussian waist at the centre is reflected to another waist at the same plane. Putting $a=L/2$, the mirror maps $q=a+i{z}_R$ to $-a+i{a}^2/z_R$, so the reflected Rayleigh range is $a^2/z_R$. Both beams have equal spots on the mirrors although their waist radii differ. Equal waist sizes select $z_R=L/2$.