Spatially inhomogeneous fields of electromagnetic guided modes exhibit a complex of extraordinary dynamical properties such as the polarization-dependent transverse momentum, helicity-independent transverse spin, spin-associated non-reciprocity and unidirectional propagation, etc. Recently, the remarkable relationship has been established between the spin and propagation features of such fields, expressed through the spin-momentum equations [Proc. Natl. Acad. Sci. 118 (2021) e2018816118] connecting the wave spin with the curl of momentum. Here, the meaning, limitations and specific forms of this correspondence are further investigated, involving the physically transparent and consistent examples of paraxial light fields, plane-wave superpositions and evanescent waves. The conclusion is inferred that the spin-momentum equation is an attribute of guided waves with well defined direction of propagation, and it unites the helicity-independent extraordinary transverse spin with the spatially-inhomogeneous longitudinal field momentum (energy flow) density. Physical analogies with the layered hydrodynamic flows and possible generalizations for other wave fields are discussed. The results can be useful in optical trapping, manipulation and the data processing techniques.
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