Experimental demonstration of higher-order Laguerre-Gauss mode interferometry

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 LG 33 mode in optical resonators. We show that the Pound-Drever-Hall error signal for a LG 33 mode in a linear optical resonator is identical to that of the more commonly used LG 00 mode, and demonstrate the feedback control of the resonator with a LG 33 mode. We succeeded to increase the mode purity of a LG 33 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