In this chapter, we discuss nanophotonic devices based on the

Thue-Morse sequence. This sequence has some peculiar theoretical

properties related to the singular-continuous measure of its Fourier

transforms that improve the optical properties compared with their

periodic counterparts. The distinctive spatial distribution of optical

mode, which are neither extended nor localized, and the complex

bandgap structures of the energy spectrum open new avenues

to design more versatile optical devices. On this basis, optical

multilayers based on the Thue-Morse sequence have been exploited

as omnidirectional mirrors, chemical sensors, and light-emitting

devices. The square tiling based on the Thue-Morse sequence has

also been discussed, and we show how the possibility to modulate

the aperiodicity enhances the lasing effect.