Diffraction of cylindrical reflectors surrounding an in-plane semiconductor micocavity

In-plane microresonators consisting of an ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructure waveguide and deep etched cylindrical trenches give both out-of-plane and lateral-light confinement. The air trenches, acting as a Bragg reflector also allow diffraction into air, so that the far-field pattern reveals interesting information on the resonant cavity modes. By the use of a two-dimensional cylindrical model and a transfer-matrix method based on Hankel functions, the energy and angular dependences of the diffracted field are calculated and successfully compared to measurements.