3-D FEM modeling and fabrication of circular photonic crystal microcavity

In this paper, we study an unconventional kind of quasi-three-dimensional (3-D) photonic crystal (PhC) with circular lattice pattern: it consists of air holes in a GaAs material (n = 3.408) along circular concentric lines. This particular PhC geometry has peculiar behavior if compared with the traditional square and triangular lattices, but it is difficult to model by using conventional numerical approaches such as wave expansion method. The resonance and the radiation aspects are analyzed by the 3-D finite-element method (FEM). The model, based on a scattering matrix approach, considers the cavity resonance frequency and evaluates the input-output relationship by enclosing the photonic crystal slab (PhCS) in a black box in order to define the responses at different input-output ports. The scattering matrix method gives important information about the frequency responses of the passive 3-D crystal in the 3-D spatial domain. A high sensitivity of the scattering parameters to the variation of the geometrical imperfection is also observed. The model is completed by the quality factor (Q-factor) estimation. We fabricated the designed circular photonic crystal over a slab membrane waveguide embedding InAs/GaAs quantum dots emitting around 1.28 μ. Good agreement between numerical and experimental results was found, thus validating the 3-D FEM full-wave investigation.