= Optical mode matching
<Optical mode matching> makes the spatial field of an incident beam equal to a desired <optical cavity> <normal mode>. For fundamental circular <Gaussian beams>, matching the <complex beam parameter> fixes the <beam waist> size and location; the <optical axis>, <polarization> and <frequency> must also match. A single converging <optical lens> connects waist <Rayleigh ranges> $z_A,z_B$ only when $f^2\geq z_Az_B$. With $s=\sqrt{f^2/(z_Az_B)-1}$, waist-to-lens distances obey $u=f\pm z_As$, $v=f\pm z_Bs$ with correlated signs, followed by physical distance constraints.
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