## 1 An Overview of the Topic and Its Ramifications
### Waveguides Built of Artificial Materials  
The experimental and theoretical results outlined above were obtained in naturally existing media (and, accordingly, theoretical models of such media), or in settings produced by straightforward modifications of natural media, such as the aforementioned multi-core bundled guiding structures burnt in bulk silica [63; 64; 26]. Still natural--but more unusual--optical materials are photonic crystals (PhCs) [66] and quasicrystals [67; 68], as well as PhC-based heterostructures and interfaces [69], and PhC fibers [70; 71; 72]; i.e., holey fibers in which inner voids form a PhC structure in the transverse plane. The difference between the traditional monolithic conduits (which guide light by means of the appropriate transverse profile of the refractive index) and PhCs is that PhCs implement the _bandgap-guidance_ principle, steering the transmission of different optical modes according to the spectral bandgap structure, as induced by the underlying crystalline lattice. Related to PhC fibers are waveguides built as large-radius hollow fibers, with a specially designed multi-layer cladding, which--by means of the Bragg-reflection mechanism (acting in the radial direction)--support the _omniguiding_ regime of the transmission of light in such conduits. As a result, the omniguiding fibers (alias _Bragg fibers_) may provide a quasi-single regime of the propagation for selected modes, even if the large-area fiber is a multi-mode one. This is possible because all the modes except for the selected one will be suppressed by strong losses [73]. It is relevant to mention that another guidance mechanism is also possible which makes use of lattice structures similar to those underlying PhCs and PhC fibers; however, differently from them, these are _nonlinear lattices_[74]; i.e., spatially periodic modulations of the local nonlinearity coefficient. Naturally, such nonlinear lattices and their combinations with the usual linear lattices [75] are appropriate for steering nonlinear modes--first of all, solitons [74; 75]. Furthermore, a new mechanism (thus far elaborated theoretically) for guided transmission of one- and two-dimensional spatial optical solitons, as well as their matter-wave counterparts in BEC, makes use of a purely self-defocusing nonlinearity, growing from center to periphery in the \(D\)-dimensional space faster than \(r^{D}\), where \(r\) is the radial coordinate [76]. This scheme was predicted to stabilize a large number of diverse self-trapped (soliton-like) modes, both fundamental ones and complex topologically-organized objects, such as three-dimensional _hopfions_[77] (i.e., vortex rings with internal twist which carry two independent topological numbers: the vorticity and the twist). PhCs and their various modifications may indeed be considered as natural materials because such structures are found in various animals, accounting for their coloration [78]. On the other hand, the recent progress in photonics has produced remarkable results in the form of artificially built media, which exhibit completely novel properties that are not possible in natural media; a very important example is provided by _left-handed metamaterials_, featuring negative values of the refractive index [79; 80]. This property may be used for realization of fascinating applications, such as superlensing (which breaks the diffraction limit of imaging [81]), and optical cloaking (lending partial invisibility to small objects [82]). Other well-known examples of purposely designed artificial optical media with extraordinary properties include hyperbolic metamaterials, whose tensors of the dielectric permittivity and/or magnetic permeability feature principal values of opposite signs [83; 84], planar metasurfaces [85; 86], epsilon-near-zero materials, in which the refractive index nearly vanishes [87], photonic topological insulators [88; 89] (which exemplify the area of _topological photonics_[90]), and others.