  Based on the rigorous generalized Mie theory solution of Maxwell's equations
for dielectric cylinders we theoretically investigate the optical properties of
two-dimensional deterministic structures based on the Fibonacci, Thue-Morse and
Rudin-Shapiro aperiodic sequences. In particular, we investigate band-gap
formation and mode localization properties in aperiodic photonic structures
based on the accurate calculation of their Local Density of States (LDOS). In
addition, we explore the potential of photonic structures based on aperiodic
order for the engineering of radiative rates and emission patterns in
Erbium-doped silicon-rich nitride photonic structures.
