Abstract
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 µm. Good agreement
between numerical and experimental results was found, thus validating the
3-D FEM full-wave investigation.
© 2008 IEEE
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