The present paper is concerned with the physical properties of the phenomenon of spatial spin resonance (SSR) of polarized neutrons and its applications. The SU(2) group provides a mathematical tool for the theoretical discussion of SSR. The experimental work made use of the WWR-M reactor at the Leningrad Nuclear Physics Institute of the USSR Academy of Sciences. The theoretical analysis of SSR is based, in physical terms, on the concept of two distortion scales of the alternating magnetic field in the frame of reference of a moving neutron, playing the principal role in SSR. A period of the alternating magnetic field is adopted as a unit of scale. Large- scale distortions correspond to a region of the resonance spectrum in the vicinity of the principal resonance maximum, whereas small-scale distortions are mapped in zones away from this maximum. An analysis has enabled us to calculate and design resonators with which it is possible to act on specified parts of the resonance spectrum. These modified resonators are provided by the so-called “shaped meander” and “double meander” configuration, which permit the suppression of the subsidiary maxima and the high-order resonance spectrum. Some applications of these resonators are presented as devices for monochromatization of a polarized thermal neutron beam.