Guided modes of a periodic waveguide usually exist below the light line, if the minimum period of the waveguide is used in the definition, but for some periodic waveguides, there are standing waves with the same period as the waveguide. These non-propagating waves localized around the waveguide core are special guided modes above the light line with a zero wavenumber, and they are related to tr...

Spectrally constrained sequences (SCSs) play an important role in modern communication and radar systems operating over non-contiguous spectrum. Despite numerous research attempts the past years, very few works are known on constructions of optimal SCSs with low cross-correlations. In this paper, we address such a major problem by introducing unifying framework to construct unimodular SCS famil...

The conjugacy relation defines a partition of words into equivalence classes. We call these classes circular words. Periodic properties of circular words are investigated in this article. The Periodicity Theorem of Fine and Wilf does not hold for weak periods of circular words; instead we give a strict upper bound on the length of a non-unary circular word that has two given relatively prime we...