Stabilization of laser beam alignment to an optical resonator by heterodyne detection of off-axis modes

We demonstrate a method for real time alignment of a Gaussian beam to an optical resonator. While thefrequency of a source laser is stabilized to a fundamental cavity mode resonance, phase modulation sidebands are applied at the off-axis mode frequencies. Asymmetrical transmission of the sideband at the frequency of each off-axis mode produces amplitude modulated optical signals and indicates the extent of the misalignments. Phase sensitive detection of these optical signals provides the error signals which are minimized by a control system that steers the input beam. In this way, optimum coupling of an injected source beam can be maintained to the fundamental mode of the resonator. This active alignment technique has demonstrated a sensitivity to tilts of 0.1 nrad/ radicalHz and to lateral beam displacements of 0.08 nm/ radicalHz in the ~1-Hz-1-kHz frequency range. These values correspond to 2 parts in 10(7) radicalHz for both the far-field divergence angle and the beam waist size. Such performance is within a factor of 2 of the shot noise limitation of the error signal measurement for a detected power of 160 microW.