SU(2)-Hidden symmetry of two-level media: Propagation of higher-order ultimately short-wave excitations with nonzero angular momenta

Following the SU(2)-symmetry analysis, we perform a more detailed investigation of interaction of ultimately short-wave optical solitons with the two-level media within the viewpoint of propagation of higher-order waveguide excitations with nonzero angular momenta. As a result, we derive a new partial differential evolution model system expressed within the Hilbert space while describing the propagation of circularly polarized optical waveguide excitations. Accordingly, we solve the previous Hamiltonian system and address the expression of the one-soliton solution. We hence depict its spectrum which shows the distribution of the wave-frequency for circular polarization with a pulse-profile. Besides, investigating the variations of the electric field of the medium with respect to the population inversion integral, we discuss some typical features which profiles strongly depend upon the wave-frequency of the carrier. Accordingly, we pay particular interests to the ultimately short waveguide excitations while studying their interactions through the two-wave and three-wave depictions, and their shifts characterizing their nonlinear and rotating scattering features. As a result, we find that such features actually represent the elastic interactions between individual wave structures with the soliton properties arising from the interplay between the nonlinearity and the dispersion. We address some physical implications of the results obtained previously.