  Quasiperiodic Fibonacci-like and fractal Cantor-like single- and multiple-row
nanopillar waveguides are investigated theoretically employing the finite
difference time domain (FDTD) method. It is shown that resonant modes of the
Fibonacci and Cantor waveguides can have a Q-factor comparable with that of a
point-defect resonator embedded in a periodic nanopillar waveguide, while the
radiation is preferably emitted into the waveguide direction, thus improving
coupling to an unstructured dielectric waveguide located along the structure
axis. This is especially so when the dielectric waveguide introduces a small
perturbation in the aperiodic structure, breaking the structure symmetry while
staying well apart from the main localization area of the resonant mode. The
high Q-factor and increased coupling with external dielectric waveguide suggest
using the proposed deterministically aperiodic nanopillar waveguides in
photonic integrated circuits.
