  The compatibility of higher-order Laguerre-Gauss (LG) modes with
interferometric technologies commonly used in gravitational wave detectors is
investigated. In this paper we present the first experimental results
concerning the performance of the LG33 mode in optical resonators. We show that
the Pound-Drever-Hall error signal for a LG33 mode in a linear optical
resonator is identical to that of the more commonly used LG00 mode, and
demonstrate the feedback control of the resonator with a LG33 mode. We
succeeded to increase the mode purity of a LG33 mode generated using a
spatial-light modulator from 51% to 99% upon transmission through a linear
optical resonator. We further report the experimental verification that a
triangular optical resonator does not transmit helical LG modes.
