  We propose a method to selectively populate a large angular momentum state of
ultracold atoms (each with an orbital angular momentum $l \approx 2 \hbar$) in
the Mott regime of a two-dimensional optical lattice. This is done by
periodically modulating the lattice amplitude and implementing an additional
rectangular lattice of shorter wavelength at an angle of $\pi/4$. The specific
pulse sequences are designed using a four-level model for each well and are
implemented sequentially. The results are confirmed with numerical simulations
of the full Schroedinger equation. The methods of this paper are another step
in constructing a modular toolbox of operations for creating higher orbital
states in optical lattices.
