Guided waves represent a vast class of phenomena in which the propagation of collective excitations in various media is steered in required directions by fixed (or, sometimes, reconfigurable) conduits. Arguably, the most well-known and practically important waveguides are single-mode and multi-mode optical fibers [1,2], including their more sophisticated version in the form of photonic crystal fibers [3] and hollow metallic structures transmitting microwave radiation [4]. Light pipes, in the form of hollow tubes with reflecting inner surfaces, are used in illumination techniques. On the other hand, medical stethoscopes offer a commonly known example of a practically important acoustic waveguide. New directions of studies in photonics are focused on waveguides for plasmonic waves on metallic surfaces [5][6][7] (which provide the possibility of using wavelengths much smaller than those corresponding to the traditional optical range, and thus offer opportunities to build much more compact photonic devices) and on the other hand, on the guided transmission of terahertz waves, which also have a great potential for applications [8].Outside of the realm of photonics (optics and plasmonics) and acoustics, wave propagation plays a profoundly important role in many other areas; accordingly, waveguiding settings have drawn a great deal of interest in those areas as well. In particular, as concerns hydrodynamics, natural waveguides-which may be very long-exist for internal waves propagating in stratified liquids (e.g., in the ocean) [9]. Various settings in the form of waveguides for matter waves are well known in studies of Bose-Einstein condensates in ultracold bosonic gases [10,11]. In solid-state physics, guided propagation regimes for magnon waves in ferromagnetic media are a subject of theoretical and experimental studies [12]. In superconductivity, long Josephson junctions are waveguides for plasma waves [8,13]. The significance of waveguiding in plasma physics is also well-known; e.g., Ref [14][15][16].Below, a very brief overview of basic theoretical models and experimental realizations of various physical implementations of the waveguiding phenomenology is given. The text is structured according to the character of the guided wave propagation: linear or nonlinear and conservative or dissipative, as well as according to the materials used in the underlying settings, natural or artificial.This presentation definitely does not aim to include an exhaustive bibliography on this vast research area. References are given chiefly to review articles and books summarizing the known results, rather than to original papers where the results were first published. However, in some cases original papers are also cited if it is necessary in the context of the presentation.
Linear WaveguidesThe basic waveguiding structure is a single-mode conduit, designed with a sufficiently small transverse size and boundary conditions at the boundary between the guiding core and surrounding cladding, which admits the propagation of a single tr...