  We use a 1030 nm laser with 7 ps pulse duration and average power up to 100 W
to ablate pyramid-shape subwavelength structures (SWS) on alumina and sapphire.
The SWS give an effective and cryogenically robust anti-reflection coating in
the millimeter-wave band. We demonstrate average ablation rate of up to 34
mm$^3$/min and 20 mm$^3$/min for structure heights of 900 $\mu$m and 750 $\mu$m
on alumina and sapphire, respectively. These rates are a factor of 34 and 9
higher than reported previously on similar structures. We propose a model that
relates structure height to cumulative laser fluence. The model depends on the
absorption length $\delta$, which is assumed to depend on peak fluence, and on
the threshold fluence $\phi_{th}$. Using a best-fit procedure we find an
average $\delta = 630$ nm and 650 nm, and $\phi_{th} = 2.0^{+0.5}_{-0.5}$
J/cm$^2$ and $2.3^{+0.1}_{-0.1}$ J/cm$^2$ for alumina and sapphire,
respectively, for peak fluence values between 30 and 70 J/cm$^{2}$. With the
best fit values, the model and data values for cumulative fluence agree to
within 10%. Given inputs for $\delta$ and $\phi_{th}$ the model is used to
predict average ablation rates as a function of SWS height and average laser
power.
