  Photonic crystals are characterized by a spatial modulation of the dielectric
constant on the length scale of the wavelength of light giving rise to energy
ranges where light cannot propagate through the crystal - the photonic band
gap. While mostly photonic crystals are referred to as periodic arrangements,
in this review we aim to highlight as well how aperiodicity and disorder
affects light modulation. In this review article, we introduce the concepts of
periodicity, quasi-periodicity, and disorder in photonic crystals, focussing on
the one-dimensional case. We discuss in detail the physical peculiarities, the
fabrication techniques, and the applications of periodic, quasi-periodic, and
disorder photonic structures, highlighting how the degree of crystallinity
matters in the manipulation of light. We report different types of disorder in
1D photonic structures and we discuss their properties in terms of light
transmission. We discuss the relationship between the average total
transmission, in a range of wavelengths around the photonic band gap of the
corresponding photonic crystal, and the homogeneity of the photonic structures,
quantified by the Shannon index. Then we discuss the light transmission in
structures in which the high refractive index layers are aggregated in clusters
following a power law distribution. Finally, in the case of structures in which
the high refractive index layers are aggregated in clusters with a truncated
uniform distribution, we discuss: i) how different refractive index contrast
tailors the total light transmission; ii) how the total light transmission is
affected by the introduction of defects made with a third material.
