Cavity-enhanced optical bottle beam as a mechanical amplifier

We analyze the resonant cavity enhancement of a hollow "optical bottle beam" for the dipole-force trapping of dark-field-seeking species. We first improve upon the basic bottle beam by adding further Laguerre-Gaussian components to deepen the confining potential. Each of these components itself corresponds to a superposition of transverse cavity modes, which are then enhanced simultaneously in a confocal cavity to produce a deep optical trap needing only a modest incident power. The response of the trapping field to displacement of the cavity mirrors offers an unusual form of mechanical amplifier in which the Gouy phase shift produces an optical Vernier scale between the Laguerre-Gaussian beam components.