  Optical cavities in the near-concentric regime have near-degenerate
transverse modes; the tight focusing transverse modes in this regime enable
strong coupling with atoms. These features provide an interesting platform to
explore multi-mode interaction between atoms and light. Here, we use a spatial
light modulator (SLM) to shape the phase of an incoming light beam to match
several Laguerre-Gaussian (LG) modes of a near-concentric optical cavity. We
demonstrate coupling efficiency close to the theoretical prediction for single
LG modes and well-defined combinations of them, limited mainly by imperfections
in the cavity alignment.
