= Flying focus
A <flying focus> is an <optical pulse> whose position of maximum focusing varies with time because different <frequencies> focus at different axial locations and arrive at different times. For a broad incident <Gaussian beam>, $f(\omega)=f_0+\beta(\omega-\omega_0)$ and <spectral phase> $\psi=\eta(\omega-\omega_0)^2$ give $z=f(\omega)$ and $t=\psi'(\omega)+z/c$, hence $v_f/c=[1+2\eta c/\beta]^{-1}$. This is the velocity of a focusing pattern, which can exceed $c$ or be negative without individual portions of the field propagating faster than <light>.
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