Manipulation of high-order scattering processes in ultrasmall optical resonators to control far-field emission

By imposing a set of harmonic perturbations to a microcavity boundary, we induce conversion and mixing of orbital angular momentum of light via surface scattering. Multiple scattering paths are available due to high-order scattering, which can be greatly enhanced by quasidegenerate resonances. By manipulating the relative strengths of these scattering processes, we theoretically synthesize the angular momentum spectra of individual modes so as to control their far-field patterns. We demonstrate experimentally that in wavelength-scale cavities of a fixed shape, the neighboring modes can have dramatically different emission directionality. This phenomenon is robust against slight shape deviation and surface roughness, and provides a general mechanism to control the emission direction of ultrasmall resonators.