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 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.