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In this paper the coupled Maxwell-Bloch equations which describe thepropagation of two optical pulses in an optical medium with coherentthree-level atoms are studied by Darboux transformation. The general nth-orderrogue wave solution involving two different choices of multiple roots for thespectral characteristic equation and the multiparametric nth-order semirationalsolution are both obtained in terms of Schur polynomials. The explicit roguewave solutions and semirational solutions from first to second order areprovided. In contrast to the known Peregrine soliton, dark and four-petaledstructures, some unusual patterns such as triple-hole, twisted-pair, compositefour-petaled and composite dark rogue waves are put forward. Moreover, theinteraction between dark-bright soliton and dark rogue wave and interactionbetween breather and dark rogue wave are shown. Further, the higher-ordernonlinear superposition modes which feature triple and quadrupletemporal-spatial distributions are presented. Finally, the state transitionbetween rogue wave and W-shaped soliton is found where the modulationinstability growth rate tends to zero under the low perturbation frequency.Particularly, the dark and double-peak W-shaped solitons are examined.

The three-level coupled Maxwell-Bloch equations: rogue waves, semirational rogue waves and W-shaped solitons